• Khan Academy
  • Math
    • K-8th grades
    • Eureka Math/EngageNY support
    • Remediation support for Eureka Math/EngageNY
    • On-grade support for Eureka Math/EngageNY
    • High school math
    • Early math
      • Counting
        • Counting
        • Numbers 0 to 120
        • Counting objects
        • Comparing small numbers
      • Addition and subtraction intro
        • What is addition? What is subtraction?
        • Making small numbers
        • Making 10
        • Put together, take apart
        • Relate addition and subtraction
        • Addition and subtraction word problems
      • Place value (tens and hundreds)
        • Teens
        • Tens
        • Comparing 2-digit numbers
        • Hundreds
        • Comparing three-digit numbers
      • Addition and subtraction within 20
        • Addition within 20
        • Subtraction within 20
        • Equal sign
        • Missing number within 20
        • Word problems within 20
        • Word problems with "more" and "fewer"
        • Repeated addition
      • Addition and subtraction within 100
        • Adding 1s and 10s
        • Subtracting 1s and 10s
        • Intro to addition with 2-digit numbers
        • Intro to subtraction with 2-digit numbers
        • Strategies for adding and subtracting within 100
        • Addition within 100
        • Subtraction within 100
        • Word problems within 100
        • Word problems with "more" and "fewer" (within 100)
        • Skip-counting
        • Addition and subtraction missing value problems
      • Addition and subtraction within 1000
        • Adding 1s, 10s, and 100s
        • Subtracting 1s, 10s, and 100s
        • Strategies for adding 2- and 3-digit numbers
      • Measurement and data
        • Length and size
        • Measuring length
        • Comparing and estimating length
        • Length word problems
        • Picture graphs
        • Bar graphs
        • Line plots
        • Time
        • Money
      • Geometry
        • Basic shapes
        • Properties of shapes
        • Composing shapes
        • Fractions of shapes
    • Kindergarten
      • Counting and place value
        • Counting small numbers
        • Numbers 0 to 100
        • Counting objects
        • Comparing small numbers
        • Teens
      • Addition and subtraction
        • What is addition? What is subtraction?
        • Making 10
        • Making small numbers
        • Put together, take apart
        • Addition and subtraction word problems
      • Measurement and geometry
        • Comparing size
        • Basic shapes
        • Comparing shapes
        • Composing shapes
    • 1st grade
      • Place value
        • Numbers 0 to 120
        • Ones and tens
        • Comparing 2-digit numbers
      • Addition and subtraction
        • Relate addition and subtraction
        • Addition within 20
        • Subtraction within 20
        • Equal sign
        • Missing number within 20
        • Word problems within 20
        • Word problems with "more" and "fewer"
        • Adding 1s and 10s
        • Intro to addition with 2-digit numbers
      • Measurement and data
        • Length and size
        • Bar graphs
        • Time
      • Geometry
        • Shapes
        • Fractions of shapes
    • 2nd grade
      • Place value
        • Hundreds
        • Comparing 3-digit numbers
      • Addition and subtraction within 100
        • Repeated addition
        • Adding 1s and 10s
        • Subtracting 1s and 10s
        • Intro to addition with 2-digit numbers
        • Intro to subtraction with 2-digit numbers
        • Strategies for adding and subtracting within 100
        • Addition within 100
        • Subtraction within 100
        • Word problems within 100
        • Word problems with "more" and "fewer" (within 100)
        • Skip-counting
        • Addition and subtraction missing value problems
      • Addition and subtraction within 1000
        • Adding 1s, 10s, and 100s
        • Subtracting 1s, 10s, and 100s
        • Strategies for adding 2- and 3-digit numbers
      • Measurement and data
        • Measuring length
        • Comparing and estimating length
        • Length word problems
        • Picture graphs
        • Bar graphs
        • Line plots
        • Time
        • Money
      • Geometry
        • Shapes
        • Fractions of shapes
    • 3rd grade
      • Addition and subtraction
        • Strategies for adding two and three-digit numbers
        • Adding with regrouping within 1000
        • Subtracting with regrouping within 1000
        • Addition and subtraction missing value problems
      • Multiplication and division
        • Multiplication intro
        • Multiplication facts
        • Relating multiplication and division
        • Division intro
        • Division facts
        • More with 1-digit multiplication and division
        • Properties of multiplication
        • One and two-step word problems
        • Multiplying by tens
        • Patterns in arithmetic
      • Fractions
        • Fractions intro
        • What fractions mean
        • Fractions on the number line
        • Fractions and whole numbers
        • Equivalent fractions
        • Equivalent fractions on the number line
        • Comparing fractions
        • Comparing fractions of different wholes
      • Measurement and data
        • Time
        • Mass
        • Volume
        • Bar graphs
        • Picture graphs
        • Line plots
      • Geometry
        • Area introduction
        • Count unit squares to find area
        • Area formula intuition
        • Multiply to find area
        • Area and the distributive property
        • Decompose figures to find area
        • Perimeter
        • Comparing area and perimeter
        • Perimeter word problems
        • Quadrilaterals
      • Place value and rounding
        • Rounding
    • 4th grade
      • Addition and subtraction
        • Adding multi-digit numbers
        • Subtracting multi-digit numbers
      • Multiplication and division
        • Multiplication by 10s, 100s, and 1000s
        • Multi-digit multiplication: place value and area models
        • Multi-digit multiplication: standard algorithm
        • Comparing with multiplication
        • Division problems that work out nicely
        • Division: place value and area
        • Multi-digit division
        • Remainders
        • Multiplication, division word problems
      • Fractions
        • Equivalent fractions
        • Common denominators
        • Comparing fractions with unlike denominators visually
        • Comparing fractions with unlike denominators
        • Decomposing fractions
        • Adding and subtracting fractions with like denominators
        • Adding and subtracting fractions: word problems
        • Mixed numbers
        • Adding and subtracting mixed numbers
        • Multiplying unit fractions and whole numbers
        • Multiplying whole numbers and fractions
        • Multiplying whole numbers and fractions word problems
        • Fractions with denominators of 10 and 100
      • Decimals
        • Intro to decimals
        • Decimals on the number line
        • Decimals vs. fractions
        • Decimals greater than one
        • Converting decimals to fractions
        • Common fractions and decimals
        • Comparing decimals visually
        • Comparing decimals
      • Measurement and data
        • Estimating mass
        • Estimating volume
        • Estimating length
        • Time
        • Converting units of mass
        • Converting units of volume
        • Converting units of length
        • Converting units of time
        • Money word problems
        • Conversion word problems
        • Area and perimeter
        • Line plots with fractions
      • Geometry
        • Lines, line segments, and rays
        • Parallel and perpendicular
        • Angle introduction
        • Measuring angles
        • Constructing angles
        • Angles in circles
        • Angle types
        • Decomposing angles
        • Line of symmetry
        • Classifying triangles
        • Classifying geometric shapes
      • Factors, multiples and patterns
        • Factors and multiples
        • Prime and composite numbers
        • Math patterns
      • Place value and rounding
        • Intro to place value
        • How 10 relates to place value
        • Ways to write whole numbers (expanded form and written form)
        • Regrouping whole numbers
        • Comparing multi-digit numbers
        • Rounding whole numbers
    • 5th grade
      • Addition and subtraction
        • Common fractions and decimals
        • Adding decimals
        • Subtracting decimals
      • Multiplication and division
        • Multi-digit multiplication
        • Multiplying decimals
        • Multi-digit division
        • Dividing decimals
      • Fractions
        • Visually adding and subtracting fractions with unlike denominators
        • Common denominators
        • Adding and subtracting fractions with unlike denominators
        • Adding and subtracting mixed number with unlike denominators
        • Adding and subtracting fractions with unlike denominators word problems
        • Multiplication as scaling
        • Multiplying fractions and whole numbers
        • Multiplying fractions and whole numbers word problems
        • Multiplying fractions
        • Multiplying mixed numbers
        • Multiplying fractions word problems
        • Fractions as division
        • Dividing unit fractions by whole numbers
        • Dividing whole numbers by unit fractions
        • Dividing fractions and whole numbers word problems
        • Rewriting fractions as decimals
      • Place value and decimals
        • Decimal place value intro
        • Decimals in expanded form
        • Decimals in written form
        • Comparing decimals
        • Rounding decimals
        • Multiplying and dividing whole numbers by 10, 100, and 1000
        • Multiplying and dividing decimals by 10, 100, and 1000
        • Powers of 10
        • Multiplying and dividing with powers of 10
        • Comparing decimal place values
        • Regrouping decimal numbers
      • Measurement and data
        • Volume intro
        • Finding volume
        • Unit conversion
        • Unit measurement word problems
        • Data
      • Geometry
        • Intro to the coordinate plane
        • Coordinate plane word problems
        • Quadrilaterals
      • Algebraic thinking
        • Writing expressions
        • Number patterns
    • 6th grade
      • Ratios, rates, & percentages
        • Intro to ratios
        • Visualize ratios
        • Ratio application
        • Intro to rates
        • Intro to percents
        • Percent, decimal, fraction conversions
        • Percent problems
        • Percent word problems
      • Arithmetic operations
        • Adding decimals
        • Subtracting decimals
        • Adding and subtracting decimals word problems
        • Multiplying decimals
        • Dividing whole numbers
        • Dividing decimals
        • Dividing fractions by fractions
        • Exponents
        • Order of operations
      • Negative numbers
        • Intro to negative numbers
        • Negative decimals & fractions on the number line
        • Number opposites
        • Comparing negative numbers
        • Absolute value
        • Coordinate plane
      • Properties of numbers
        • Properties of numbers
        • Whole numbers & integers
        • Least common multiple
        • Greatest common factor
      • Variables & expressions
        • Parts of algebraic expressions
        • Substitution & evaluating expressions
        • Expression value intuition
        • Evaluating expressions word problems
        • Writing algebraic expressions introduction
        • Writing basic algebraic expressions word problems
        • Combining like terms
        • Distributive property with variables
        • Equivalent expressions
      • Equations & inequalities introduction
        • Algebraic equations basics
        • One-step equations intuition
        • One-step addition & subtraction equations
        • One-step multiplication and division equations
        • Finding mistakes in one-step equations
        • One-step equation word problems
        • Intro to inequalities with variables
        • Dependent and independent variables
      • Geometry
        • Areas of parallelograms
        • Areas of triangles
        • Area of trapezoids & composite figures
        • Geometric solids (3D shapes)
        • Volume with fractions
        • Surface area
        • Polygons on the coordinate plane
      • Data and statistics
        • Dot plots & frequency tables
        • Statistical questions
        • Histograms
        • Mean and median
        • Mean and median challenge problems
        • Interquartile range (IQR)
        • Box plots
        • Mean absolute deviation (MAD)
        • Comparing data displays
        • Shape of data distributions
    • 7th grade
      • Negative numbers: addition and subtraction
        • Intro to adding negative numbers
        • Intro to subtracting negative numbers
        • Adding & subtracting with negatives on the number line
        • Adding & subtracting integers
        • Adding & subtracting negative fractions
        • Addition & subtraction word problems with negatives
        • Absolute value
        • Properties of addition & subtraction
        • Adding & subtracting negative numbers: variables
      • Negative numbers: multiplication and division
        • Multiply & divide negative numbers
        • Multiplication & division word problems with negatives
        • Understanding multiplying and dividing fractions
        • Multiply & divide negative fractions
        • Exponents with negative bases
        • Dividing by zero
        • Order of operations
        • Properties of multiplication & division
      • Fractions, decimals, & percentages
        • Converting fractions to decimals
        • Adding & subtracting rational numbers
        • Percent word problems
        • Rational number word problems
      • Rates & proportional relationships
        • Rate problems with fractions
        • Constant of proportionality
        • Identifying proportional relationships
        • Graphs of proportional relationships
        • Writing & solving proportions
        • Equations of proportional relationships
      • Expressions, equations, & inequalities
        • Combining like terms
        • The distributive property & equivalent expressions
        • Interpreting linear expressions
        • Two-step equations intro
        • Two-step equations with decimals and fractions
        • Two-step equation word problems
        • One-step inequalities
        • Two-step inequalities
      • Geometry
        • Area and circumference of circles
        • Area and circumference challenge problems
        • Vertical, complementary, and supplementary angles
        • Missing angle problems
        • Constructing triangles
        • Slicing geometric shapes
        • Scale drawings
        • Volume and surface area word problems
      • Statistics and probability
        • Basic probability
        • Probability models
        • Compound events and sample spaces
        • Comparing and sampling populations
    • 8th grade
      • Numbers and operations
        • Repeating decimals
        • Square roots & cube roots
        • Irrational numbers
        • Approximating irrational numbers
        • Exponent properties intro
        • Negative exponents
        • Exponent properties (integer exponents)
        • Working with powers of 10
        • Scientific notation intro
        • Arithmetic with numbers in scientific notation
        • Scientific notation word problems
      • Solving equations with one unknown
        • Equations with variables on both sides
        • Equations with parentheses
        • Number of solutions to equations
        • Equations word problems
        • Equations & geometry
      • Linear equations and functions
        • Graphing proportional relationships
        • Solutions to linear equations
        • Intercepts
        • Slope
        • Intro to slope-intercept form
        • Graphing slope-intercept form
        • Writing slope-intercept equations
        • Functions & function notation
        • Linear models
        • Comparing linear functions
        • Constructing linear models for real-world relationships
        • Recognizing functions
        • Linear and nonlinear functions
      • Systems of equations
        • Systems of equations overview
        • Intro to systems of equations
        • Systems of equations with graphing
        • Solving systems with elimination
        • Solving systems with substitution
        • Number of solutions to systems of equations
        • Systems of equations word problems
      • Geometry
        • Angles between intersecting lines
        • Triangle angles
        • Pythagorean theorem
        • Pythagorean theorem application
        • Pythagorean theorem and distance between points
        • Pythagorean theorem proofs
        • Volume
      • Geometric transformations
        • Transformations intro
        • Translations
        • Rotations
        • Reflections
        • Properties & definitions of transformations
        • Dilations
        • Congruence and similarity
      • Data and modeling
        • Introduction to scatter plots
        • Interpreting scatter plots
        • Estimating lines of best fit
        • Two-way tables
    • Class 5 (India)
      • Review of shapes, operations and large numbers
        • Revision of shapes, estimation, simple operations, large numbers
      • Shapes and angles
        • Angles and unit of measurement for angles
      • Area and perimeter - Part 1
        • Areas and patterns
      • Parts and wholes
        • Fraction comparisons and equivalent fractions
      • Symmetry
        • Line of symmetry
        • Rotational symmetry
      • Factors and multiples
        • Factors and multiples
      • Patterns
        • Patterns
      • Visualizing 3-D objects
        • Representing 3-D objects on paper in the form of nets
      • Decimals
        • Decimals
      • Area and perimeter - Part 2
        • Area and perimeter
      • Ways to multiply and divide
        • Strategies for multiplication and division
      • Volume and weight
        • Volume
        • Weight
    • Class 6 (India)
      • Knowing our numbers
        • Comparing 3-digit numbers
        • Comparing multi-digit numbers
        • Lakhs, crores, millions, and billions
        • Word problems involving lakhs and crores
        • System of measurement
        • Rounding
        • Rounding whole numbers
        • Roman numerals
      • Whole numbers
        • Number line of whole numbers
        • Arithmetic properties of whole numbers
        • Distributive property
      • Playing with numbers
        • Factors and multiples
        • Prime and composite numbers
        • Divisibility tests
        • Prime factorisation
        • Common factors and multiples
        • Lowest common multiple
        • Highest common factor
      • Basic geometrical ideas
        • Lines, line segments, and rays
        • Angle introduction
        • Introduction to polygons
        • Curves and polygons
      • Understanding elementary shapes
        • Angle types
        • Measuring angles
        • Constructing angles
        • Parallel and perpendicular
        • Classifying triangles
        • Quadrilaterals
        • Geometric solids (3D shapes)
      • Integers
        • Intro to negative numbers
        • Number opposites
        • Absolute value
        • Order integers
        • Introduction to adding integers
        • Introduction to subtracting integers
        • Adding & subtracting integers
        • Adding & subtracting with negatives on the number line
      • Fractions
        • Fractions intro
        • Fractions on the number line
        • Fractions and whole numbers
        • Equivalent fractions
        • Equivalent fractions on the number line
        • Common denominators
        • Comparing fractions
        • Mixed numbers
        • Decomposing fractions
        • Adding and subtracting fractions with like denominators
        • Visually adding and subtracting fractions with unlike denominators
        • Adding and subtracting fractions with unlike denominators
        • Adding and subtracting mixed numbers
        • Adding and subtracting mixed number with unlike denominators
        • Adding and subtracting fractions with unlike denominators word problems
      • Decimals
        • Intro to decimals
        • Decimal place value intro
        • Decimals in expanded form
        • Decimals in written form
        • Comparing decimal place values
        • Comparing decimals
        • Decimals on the number line
        • Rewriting decimals as fractions
        • Common fractions and decimals
        • Adding decimals
        • Adding decimals: standard algorithm
        • Subtracting decimals
        • Subtracting decimals: standard algorithm
        • Adding and subtracting decimals word problems
      • Data Handling
        • Pictographs (Picture graphs)
        • Bar graphs
      • Mensuration
        • Count unit squares to find area
        • Multiply to find area
        • Area and the distributive property
        • Decompose figures to find area
        • Perimeter
        • Comparing area and perimeter
        • Area word problems
        • Perimeter word problems
      • Algebra
        • Overview and history of algebra
        • Intro to variables
        • Substitution & evaluating expressions
        • Writing algebraic expressions introduction
        • Writing basic algebraic expressions word problems
        • Algebraic equations basics
      • Ratio and Proportion
        • Introduction to ratios
        • Ratio word problems
        • Intro to rates
        • Identifying proportional relationships
        • Writing & solving proportions
      • Symmetry
        • Line of symmetry
      • Practical geometry
        • Constructing angles
        • Constructing perpendiculars
    • Class 7 (India)
      • Integers
        • Integer addition and subtraction review
        • Arithmetic properties
        • Multiplying & dividing negative numbers
      • Fractions and decimals
        • Multiplying unit fractions and whole numbers
        • Multiplying whole numbers and fractions
        • Multiplication as scaling
        • Multiplying fractions
        • Multiplying mixed numbers
        • Multiplying fractions word problems
        • Fractions as division
        • Dividing unit fractions by whole numbers
        • Dividing whole numbers by unit fractions
        • Dividing fractions by fractions
        • Dividing fractions word problems
        • Multiplying decimals
        • Multiplying decimals: standard algorithm
        • Dividing decimals
        • Dividing decimals: standard algorithm
      • Data Handling
        • Mean and median: The basics
        • Interpreting data from bar graphs
        • Basic theoretical probability
      • Simple equations
        • Algebraic equations basics
        • One-step equations intuition
        • One-step addition & subtraction equations
        • One-step multiplication and division equations
        • One-step equation word problems
      • Lines and angles
        • Vertical, complementary, and supplementary angles
        • Angles between intersecting lines
      • The triangle and its properties
        • Triangle angles
        • Equilateral and isosceles triangles
        • Triangle inequality theorem
        • Pythagoras theorem
      • Congruence of triangles
        • Transformations and congruence
        • Triangle congruence
      • Comparing quantities
        • Intro to percents
        • Percent, fraction, decimal conversions
        • Percent problems
        • Percent word problems
      • Rational numbers
        • Intro to rational numbers
        • Comparing rational numbers
        • Adding & subtracting rational numbers
        • Multiplication and division of rational numbers
        • Rational number word problems
      • Practical geometry
        • Construction of triangles when the lengths of its three sides are known (SSS Criterion)
      • Perimeter and area
        • Area and perimeter
        • Area of triangles
        • Area of shapes on grids
        • Area and circumference of circles
        • Area of composite figures
      • Algebraic Expressions
        • The constituents of an expression
        • Combining like terms- part 1/1
        • Combining like terms- part 2/1
        • Adding & subtracting algebraic expressions
        • Adding and subtracting algebraic expressions : two variables
        • Finding the value of an expression
        • Number patterns
      • Powers and exponents
        • Exponents
        • Exponent properties- part 1/1
        • Exponent properties- part 2/1
        • Scientific notation
        • Orders of magnitude
      • Symmetry
        • Lines of symmetry for regular polygons
        • Rotational symmetry
      • Visualising solid shapes
        • Nets for building 3D shapes
        • Viewing different sections of a solid
    • Class 8 (India)
      • Linear equations in one variable
        • Two-steps equations intro
        • Old school equations with Sal
        • Linear equations with variables on both sides
        • Linear equations with parentheses
        • Analyzing the number of solutions to linear equations
        • Linear equations word problems
        • Two-step equation word problems
      • Understanding Quadrilaterals
        • Angles with polygons
        • Quadrilateral types
        • Quadrilateral proofs and angles
      • Data Handling
        • Categorical data displays
        • Histograms
        • Pie Charts
        • Basic theoretical probability
        • Probability using sample spaces
      • Square and square roots
        • Square roots
        • Simplifying square roots
      • Cubes and cube roots
        • Cube roots
      • Algebraic expressions and Identities
        • Adding & subtracting polynomials (Part1/2)
        • Adding and subtracting polynomials (Part2/2)
        • Multiplying monomials
        • Multiplying monomials by polynomials
        • Multiplying binomials
        • Special products of binomials
        • Multiplying binomials by polynomials
        • Polynomials word problems
      • Visualising solid shapes
        • Geometric solids (3D shapes)
        • 2D vs. 3D objects
        • Scale drawing
      • Mensuration
        • Area of trapezoids & composite figures
        • Surface area
        • Volume of rectangular prisms
        • Volume and surface area of cylinder
      • Exponents and powers
        • Negative exponents
        • Scientific notation
        • Orders of magnitude
        • Arithmetic with numbers in scientific notation
        • Scientific notation word problems
      • Direct and inverse proportion
        • Direct and inverse proportion
      • Factorization
        • Introduction to factorization
        • Factoring monomials
        • Factoring polynomials by taking common factors
        • Evaluating expressions with unknown variables
        • Factoring quadratics intro
        • Factoring quadratics by grouping
        • Factoring polynomials with quadratic forms
        • Factoring quadratics: Difference of squares
        • Factoring quadratics: Perfect squares
        • Strategy in factoring quadratics
        • Factoring polynomials with special product forms
      • Introduction to graphs
        • Intro to the coordinate plane
        • Coordinate plane word problems
      • Playing with numbers
        • Divisibility tests
    • Class 9 (India)
      • Number systems
        • Irrational numbers
        • Rational numbers and repeating decimals
        • Sums and products of rational and irrational numbers
        • Exponent properties review
        • Radicals
        • Rational exponents intro
        • Properties of exponents (rational exponents)
        • Advanced: exponent & radical evaluation
        • Simplifying square roots
        • Simplifying radicals (higher-index roots)
        • Radicals (miscellaneous videos)
      • Polynomials
        • Introduction to polynomials
        • Zeroes of a polynomial
        • Long division of polynomials
        • Polynomial Remainder Theorem
        • Advanced polynomial factorization methods
      • Coordinate geometry
        • Intro to the coordinate plane
        • Coordinate plane: quadrant 1
        • Quadrants on the coordinate plane
        • Coordinate plane: 4 quadrants
        • Coordinate plane word problems
      • Linear equations in two variables
        • Introduction to linear equations in 2 variables
        • Graph of a Linear Equation in Two Variables
        • Linear models word problems
      • Introduction to Euclid's geometry
        • Introduction to Euclidean geometry
      • Lines and angles
        • Geometric definitions
        • Angle types
        • Vertical, complementary, and supplementary angles
        • Angles between intersecting lines
        • Triangle angles
      • Triangles
        • Congruence of triangles and the criteria for congruence
        • Proofs of general theorems that use triangle congruence
        • Theorems concerning triangle properties
        • Inequalities in a Triangle
      • Quadrilaterals
        • Quadrilaterals
        • Quadrilateral proof and angles
      • Areas of parallelograms and triangles
        • Area of Parallelogram
        • Area of a triangle
      • Circles
        • Circle basics
        • Chord and Circles
        • Points and Circles
        • Inscribed angles
        • Inscribed shapes problem solving
      • Constructions
        • Basic constructions
      • Heron's Formula
        • Finding the area of a triangle using Heron's formula
      • Surface areas and volumes
        • Surface area
        • Volume of cubes and cuboids
        • Volume of cones, cylinders, and spheres
      • Statistics
        • Presentation of Data
        • Graphical Representation of Data using bar graphs
        • Graphical representation of data using histograms
        • Measures of Central Tendency
      • Probability
        • Probability basics
    • Class 10 (India)
      • Real numbers
        • The Fundamental Theorem of Arithmetic
        • GCF and LCM
        • Proofs related to irrational numbers
        • Converting fractions to repeating decimals
      • Polynomials
        • Finding zeros of polynomials
        • Long division of polynomials
      • Pair of linear equations in two variables
        • Geometrical interpretation of pair of linear equations in two variables:
        • Algebraic methods to solve pair of linear equations in two variables
        • System of equations : word problems
      • Quadratic equations
        • Solving quadratics by using factorisation
        • Solution of a Quadratic Equation by Completing the Square
        • Solving quadratics using the quadratic formula
      • Arithmetic progressions
        • Arithmetic Progression
        • nth term of an AP
        • Sum of First n Terms of an AP
      • Triangles
        • Introduction to triangle similarity
        • Solving similar triangles
        • Pythagoras Theorem
      • Coordinate geometry
        • Distance Formula
        • Section Formula
        • Area of Triangle
      • Introduction to trigonometry
        • Introduction to trigonometry
        • Trigonometric Ratios of Complementary Angles
        • Trigonometric Identities
      • Some applications of trigonometry
        • Word problems: Applications of trigonometry
      • Circles
        • Tangent to a Circle
      • Constructions
        • Construction of Tangents to a Circle
      • Area Related to Circles
        • Areas of parts of a circle
        • Areas of Combinations of Plane Figures
      • Surface Areas and Volumes
        • Conversion of Solid from One Shape to Another
      • Probability
        • Probability basics
    • Class 11 (India)
      • Sets
        • Intersection and union of sets
        • Types of sets
        • Operations on sets
      • Relations and functions
        • Evaluating functions
        • Inputs and outputs of a function
        • Interpreting function notation
        • Functions and equations
        • Introduction to the domain and range of a function
        • Determining the domain of a function
        • Recognizing functions
        • Maximum and minimum points
        • Intervals where a function is positive, negative, increasing, or decreasing
        • Interpreting features of graphs
        • Combining functions
        • Piecewise functions
        • Determining the domain of advanced functions
        • Determining the range of advanced functions
      • Exponential and Logarithmic functions
        • Introduction to logarithms
        • The constant e and the natural logarithm
        • Properties of logarithms
        • Change of base formula for logarithms
        • Exponential equations: logarithms
        • Solving exponential models
        • Logarithmic scale (optional)
      • Advanced: Playing with graphs
        • Shifting functions
        • Stretching functions
        • Symmetry of functions
        • Symmetry of polynomial functions
        • Graphs of absolute value functions
        • Graphs of radical functions
        • Graphs of exponential functions
        • Graphs of logarithmic functions
        • Graphs of polynomials using their zeroes
        • End behavior of polynomial functions
        • Graphs of polynomials
      • Trigonometric functions
        • Intro to radians
        • Trigonometric values of special angles
        • Trigonometric functions
        • The graphs of sine, cosine, and tangent
        • Trigonometric identities
        • Trigonometric equations
      • Principle of mathematical induction
        • Deductive and inductive reasoning
        • Principle of mathematical induction
      • Complex numbers
        • What are the imaginary numbers?
        • What are the complex numbers?
        • The complex plane
        • Adding & subtracting complex numbers
        • Multiplying complex numbers
        • Complex conjugates & dividing complex numbers
        • Absolute value & angle of complex numbers
        • Distance & midpoint of complex numbers
        • Polar form of complex numbers
        • Multiplying & dividing complex numbers in polar form
      • Linear inequalities
        • Introduction to inequalities with variables
        • One-step inequalities
        • Two-step inequalities
        • Multi-step inequalities
        • Compound inequalities
        • Checking solutions of two-variable inequalities
        • Constraining solutions of two-variable inequalities
        • Graphing two-variable inequalities
      • Permutations and combinations
        • Fundamental Principle of Counting
        • Permutations
        • Combinations
      • Binomial theorem
        • Binomial Theorem for Positive Integral Indices
      • Sequence and series
        • Sequences
        • Basic sigma notation
        • Finite arithmetic series
        • Finite geometric series
        • Finite geometric series applications
        • Sum to n terms of special series
      • Straight lines
        • x-intercepts and y-intercepts
        • Slope
        • Horizontal & vertical lines
        • Intro to slope-intercept form
        • Graphing slope-intercept equations
        • Parallel and perpendicular lines on the coordinate plane
        • Equations of parallel and perpendicular lines
        • Writing slope-intercept equations
        • Point-slope form
        • Standard form
        • Summary: Forms of two-variable linear equations
        • Distance between a point and a line
      • Conic sections
        • Introduction to conic sections
        • Features of a circle
        • Standard equation of a circle
        • Expanded equation of a circle
        • Features of an ellipse
        • Equation of an ellipse
        • Foci of an ellipse
        • Features of a parabola
        • Features of a hyperbola
        • Foci of a hyperbola
        • Identifying conic sections from their expanded equations
      • Limits
        • Limits introduction
        • Limits from tables
        • Limits from graphs
        • One-sided limits
        • One-sided vs. Two-sided limits
        • Formal definition of limits (optional)
        • Review: Limits basics
        • Limits from equations (direct substitution)
        • Limits from equations (factoring & rationalizing)
        • Squeeze theorem
        • Limits of trigonometric functions
        • Limits of piecewise functions
        • Review: Limits from equations
      • Derivatives
        • Introduction to differential calculus
        • Derivative as slope of tangent line
        • Derivative as instantaneous rate of change
        • Secant lines
        • Derivative as a limit
        • Formal definition of derivative
        • Using the formal definition of derivative
        • Derivative as a function
        • Review: Derivative basics
      • Differentiation
        • Basic differentiation rules
        • Power rule
        • Polynomial functions differentiation
        • Rational functions differentiation (intro)
        • Radical functions differentiation (intro)
        • Sine & cosine, eˣ and ln(x) derivatives
        • Review: Basic differentiation
        • Product rule
      • Statistics
        • Measures of dispersion
        • Range
        • Mean absolute deviation (grouped data)
        • Variance and standard deviation (ungrouped data):
        • Comparing distributions
      • Probability
        • Basic probability
        • Addition rule for probability
        • Compound probability of independent events using diagrams
        • Compound probability of independent events using the multiplication rule
        • Probability using combinatorics
    • Class 12 (India)
      • Relations and functions
        • Introduction to inverses of functions
        • Finding inverse functions
        • Verifying that functions are inverses
        • Determining whether a function is invertible
        • Formal definition of inverse functions (optional)
        • Binary operations
      • Inverse trigonometric functions
        • Basic concepts of inverse trigonometry
        • Domain and range of inverse trigonometric functions
      • Matrices
        • Introduction to matrices
        • Adding & subtracting matrices
        • Multiplying matrices by scalars
        • Properties of matrix addition & scalar multiplication
        • Multiplying matrices by matrices
        • Properties of matrix multiplication
        • Transpose of a matrix
        • Elementary matrix row operations
        • Invertible matrices
        • Inverse of a matrix by elementary operations
      • Determinants
        • Determinants
        • Properties of determinants
        • Adjoint and inverse of a matrix using minors and cofactors
        • Solving equations with inverse matrices
        • Determinants in more depth (Optional)
      • Continuity & differentiability
        • Continuity at a point
        • Review: Limits of combined & composite functions
        • Continuous functions
        • Review: Intermediate value theorem
        • Differentiability
        • Review: Differentiation basics
        • Product rule
        • Quotient rule
        • Chain rule
        • Review: Product, quotient, & chain rule
        • Rational functions differentiation
        • Radical functions differentiation
        • Trigonometric functions differentiation
        • Exponential functions differentiation
        • Logarithmic functions differentiation
        • Derivatives capstone
      • Advanced differentiation
        • Implicit differentiation introduction
        • Implicit differentiation (advanced examples)
        • Inverse trig functions differentiation
        • Derivatives of inverse functions
        • Disguised derivatives
        • Proofs for the derivatives of eˣ and ln(x)
        • Logarithmic differentiation
        • Review: Advanced differentiation
        • Higher-order derivatives
        • Mean value theorem
      • Playing with graphs (using differentiation)
        • Critical points
        • Increasing & decreasing intervals
        • Relative minima & maxima
        • Absolute minima & maxima
        • Review: Increasing/decreasing intervals & extrema
        • Concavity
        • Points of inflection
        • Sketching graphs using calculus
        • Review: Concavity & points of inflection
      • Applications of derivatives
        • Approximations
        • Rectilinear motion (optional)
        • Related rates
        • Tangents & Normals
        • Optimization
        • Applied rates of change
        • L'Hôpital's rule
        • Review: Derivative applications
      • Indefinite Integrals
        • Antiderivatives
        • Indefinite integrals intro
        • Indefinite integrals of common functions
        • Review: Indefinite integrals & antiderivatives
        • Integration by parts
        • u-substitution
        • Reverse chain rule
        • Partial fraction expansion
        • Integration using trigonometric identities
        • Trigonometric substitution
      • Definite Integrals
        • Functions defined by integrals
        • Fundamental theorem of calculus
        • Fundamental theorem of calculus: chain rule
        • Definite integral as area
        • Definite integral properties
        • Review: Definite integral basics
        • Definite integral evaluation
        • Definite integrals of piecewise functions
        • Challenging definite integrals
        • Improper integrals
        • Riemann sums
        • Riemann sums with sigma notation
        • Trapezoidal rule
        • Definite integral as the limit of a Riemann sum
        • Review: Riemann sums
      • Application of integrals
        • Area under simple curves
        • Area between two curves
        • Area defined by polar graphs
        • Arc length (optional)
      • Differential equations
        • Intro to differential equations
        • Slope fields (optional)
        • Separable equations
        • Homogeneous equations
        • Exact equations and integrating factors
      • Vector algebra
        • Vector basics
        • Scalar multiplication
        • Magnitude of vectors
        • Vector addition & subtraction
        • Combined vector operations
        • Unit vectors
        • Magnitude & direction form of vectors
        • Adding vectors in magnitude & direction form
        • Component form of vectors
        • Applications of vectors
        • Multiplication of a vector by a scalar
        • Dot product: Scaler product of two vectors
        • Cross product: Vector product of two vectors
      • Linear Programming
        • Modeling with linear inequalities
      • Probability of events
        • Review: Multiplication rule for independent events
        • Review: Combinatorics and probability
        • Multiplication rule for dependent events
        • Conditional probability and independence
        • Baye's Theorem
        • Discrete and continuous random variables and probability models
        • Expected value
        • Variance of random variables
        • Binomial random variables
        • Poisson distribution (optional)
    • Arithmetic
      • Addition and subtraction
        • Basic addition and subtraction
        • Addition and subtraction within 20
        • Strategies for adding and subtracting within 100
        • Addition within 100
        • Subtraction within 100
        • Word problems within 100
        • Multi-digit addition with regrouping
        • Multi-digit subtraction with regrouping
      • Multiplication and division
        • Multiplication intro
        • Multiplication by 10s, 100s, and 1000s
        • Multiplication: place value and area models
        • Multi-digit multiplication
        • Division intro
        • Division: place value and area
        • Multi-digit division (no remainders)
        • Remainders
        • Multi-digit division (remainders)
        • Multiplication and division word problems
      • Negative numbers
        • Intro to negative numbers
        • Order negative numbers
        • Number opposites
        • Absolute value
        • Intro to adding negative numbers
        • Intro to subtracting negative numbers
        • Adding & subtracting negative numbers
        • Multiplying & dividing negative numbers
      • Fractions
        • Fractions intro
        • Fractions on the number line
        • Equivalent fractions
        • Comparing fractions
        • Common denominators
        • Decomposing fractions
        • Adding and subtracting fractions with like denominators
        • Mixed numbers
        • Adding and subtracting fractions with unlike denominators
        • Adding and subtracting mixed number with unlike denominators
        • Adding and subtracting fractions word problems
        • Multiplying whole numbers and fractions
        • Multiplication as scaling
        • Multiplying fractions
        • Multiplying mixed numbers
        • Multiplying fractions word problems
        • Fractions as division
        • Dividing unit fractions and whole numbers
        • Dividing fractions by fractions
        • Dividing fractions word problems
      • Decimals
        • Intro to decimals
        • Decimals on the number line
        • Rounding decimals
        • Comparing decimals
        • Rewriting decimals as fractions
        • Adding decimals
        • Subtracting decimals
        • Adding and subtracting decimals word problems
        • Multiplying decimals
        • Dividing decimals
    • Pre-algebra
      • Arithmetic properties
        • Place value
        • Rounding whole numbers
        • Regrouping whole numbers
        • Order of operations
        • Arithmetic properties
        • Distributive property
        • Rational and irrational numbers
      • Factors and multiples
        • Divisibility tests
        • Factors and multiples
        • Prime numbers
        • Prime factorization
        • Least common multiple
        • Greatest common factor
      • Reading and interpreting data
        • Representing data
        • Stem and leaf plots
        • Picture graphs, bar graphs, and histograms
        • Frequency tables and dot plots
        • Number patterns
      • Measurement
        • Area of rectangles
        • Perimeter
        • Volume of a rectangular prism
      • Fractions
        • Fractions intro
        • Fractions on the number line
        • Equivalent fractions
        • Comparing fractions
        • Common denominators
        • Decomposing fractions
        • Adding and subtracting fractions with like denominators
        • Mixed numbers
        • Adding and subtracting fractions with unlike denominators
        • Adding and subtracting mixed number with unlike denominators
        • Adding and subtracting fractions word problems
        • Multiplying whole numbers and fractions
        • Multiplication as scaling
        • Multiplying fractions
        • Multiplying mixed numbers
        • Multiplying fractions word problems
        • Fractions as division
        • Dividing unit fractions and whole numbers
        • Dividing fractions by fractions
        • Dividing fractions word problems
      • Decimals
        • Intro to decimals
        • Decimals on the number line
        • Rounding decimals
        • Comparing decimals
        • Rewriting decimals as fractions
        • Adding decimals
        • Subtracting decimal
        • Adding and subtracting decimals word problems
        • Multiplying decimals
        • Dividing decimals
      • Negative numbers and coordinate plane
        • Intro to negative numbers
        • Order negative numbers
        • Number opposites
        • Absolute value
        • Intro to adding negative numbers
        • Intro to subtracting negative numbers
        • Adding & subtracting negative numbers
        • Multiplying & dividing negative numbers
        • Coordinate plane
      • Ratios, rates, proportions
        • Intro to ratios
        • Visualize ratios
        • Ratio application
        • Intro to rates
        • Intro to percents
        • Percent, fraction, decimal conversions
        • Percent problems
        • Percent word problems
        • Identifying proportional relationships
        • Writing & solving proportions
      • Equations, expressions, and inequalities
        • Intro to variables
        • Substitution & evaluating expressions
        • Expression value intuition
        • Constructing numeric expressions
        • Evaluating expressions word problems
        • Writing algebraic expressions introduction
        • Writing basic algebraic expressions word problems
        • Algebraic equations basics
        • One-step equations intuition
        • One-step addition & subtraction equations
        • One-step multiplication and division equations
        • One-step equation word problems
        • Inequalities: Greater than and less than basics
        • Two-step equations intro
        • Dependent and independent variables
      • Exponents, radicals, and scientific notation
        • Exponents
        • Square roots
        • Cube roots
        • Exponent properties
        • Negative exponents
        • Scientific notation
        • Orders of magnitude
        • Computing with scientific notation
    • Algebra basics
      • Foundations
        • Negative numbers
        • Absolute value
        • Exponents
        • Square roots
        • Order of operations
        • Fractions
        • Decimals, fractions and percentages
        • Operations with decimals
        • Area of triangles
        • Circumference and area of circles
      • Algebraic expressions
        • Introduction to variables
        • Substitution & evaluating expressions
        • Writing algebraic expressions
        • Combining like terms
        • Distributive property
        • Equivalent algebraic expressions
        • Nested fractions
      • Linear equations and inequalities
        • One-step equations
        • Two-steps equations
        • Multi-step equations
        • One-step inequalities
        • Two-step inequalities
        • Multi-step inequalities
        • Writing & solving proportions
      • Graphing lines and slope
        • Coordinate plane
        • Solutions to two-variable linear equations
        • x-intercepts and y-intercepts
        • Slope
        • Horizontal & vertical lines
        • Slope-intercept form intro
        • Writing slope-intercept equations
        • Graphing two-variable inequalities
      • Systems of equations
        • Systems of equations overview
        • Systems of equations intro
        • Elimination method for systems of equations
        • Substitution method for systems of equations
        • Number of solutions to systems of equations
        • Solving any system of linear equations
      • Expressions with exponents
        • Exponent properties intro
        • Negative exponents
        • Exponent properties (integer exponents)
        • Scientific notation intro
        • Scientific notation word problems
      • Quadratics and polynomials
        • Adding & subtracting polynomials
        • Multiplying binomials
        • Special products of binomials
        • Factoring polynomials by taking common factors
        • Factoring quadratics 1
        • Factoring quadratics 2
        • Factoring quadratics: Difference of squares
        • Factoring quadratics: Perfect squares
        • Solving quadratic equations by factoring
      • Equations and geometry
        • Triangle angles
        • Pythagorean theorem
        • Triangle similarity intro
        • Solving similar triangles
    • Algebra I
      • Algebra foundations
        • Overview and history of algebra
        • Introduction to variables
        • Substitution and evaluating expressions
        • Evaluating expressions word problems
        • Writing algebraic expressions introduction
        • Dependent & independent variables
        • Combining like terms
        • Introduction to equivalent algebraic expressions
        • Interpreting linear expressions
        • Division by zero
      • Solving equations
        • Algebraic equations basics
        • Why we do the same thing to both sides of an equation
        • One-step addition & subtraction equations
        • One-step multiplication & division equations
        • Two-steps equations intro
        • Two-step equation word problems
        • Linear equations with variables on both sides
        • Linear equations with parentheses
        • Analyzing the number of solutions to linear equations
        • Linear equations word problems
        • Linear equations with unknown coefficients
      • Solving inequalities
        • Introduction to inequalities with variables
        • One-step inequalities
        • Two-step inequalities
        • Multi-step inequalities
        • Compound inequalities
      • Working with units
        • Rate conversion
        • Appropriate units
        • Word problems with multiple units
      • Linear equations & graphs
        • Two-variable linear equations intro
        • x-intercepts and y-intercepts
        • Slope
        • Horizontal & vertical lines
        • Intro to slope-intercept form
        • Graphing slope-intercept equations
        • Writing slope-intercept equations
        • Point-slope form
        • Standard form
        • Summary: Forms of two-variable linear equations
      • Functions
        • Evaluating functions
        • Inputs and outputs of a function
        • Functions and equations
        • Interpreting function notation
        • Introduction to the domain and range of a function
        • Determining the domain of a function
        • Recognizing functions
        • Maximum and minimum points
        • Intervals where a function is positive, negative, increasing, or decreasing
        • Interpreting features of graphs
        • Average rate of change
        • Average rate of change word problems
        • Unit review
      • Linear word problems
        • Interpreting linear functions and equations
        • Comparing linear functions
        • Constructing linear models for real-world relationships
        • Linear models word problems
      • Sequences
        • Introduction to arithmetic sequences
        • Constructing arithmetic sequences
        • Introduction to geometric sequences
        • Constructing geometric sequences
        • Modeling with sequences
        • General sequences
      • Systems of equations
        • Systems of equations overview
        • Introduction to systems of equations
        • Equivalent systems of equations and the elimination method
        • Solving systems of equations with substitution
        • Manipulating expressions with unknown variables
        • Number of solutions to systems of equations
        • Solving any system of linear equations
        • Systems of equations word problems
      • Inequalities (systems & graphs)
        • Checking solutions of two-variable inequalities
        • Graphing two-variable inequalities
        • Modeling with linear inequalities
      • Absolute value & piecewise functions
        • Graphs of absolute value functions
        • Piecewise functions
      • Rational exponents & radicals
        • Exponent properties review
        • Radicals
        • Rational exponents intro
        • Properties of exponents (rational exponents)
        • Advanced exponent & radical evaluation
        • Simplifying square roots
        • Simplifying radicals (higher-index roots)
      • Exponential growth & decay
        • Exponential vs. linear growth
        • Exponential expressions
        • Graphs of exponential growth
        • Exponential vs. linear growth over time
        • Exponential decay
        • Exponential functions from tables & graphs
      • Polynomials
        • Intro to polynomials
        • Adding & subtracting polynomials
        • Adding and subtracting polynomials: two variables
        • Multiplying monomials
        • Multiplying monomials by polynomials
        • Multiplying binomials
        • Multiplying binomials by polynomials
        • Special products of binomials
        • Polynomials word problems
      • Factorization
        • Introduction to factorization
        • Factoring monomials
        • Factoring polynomials by taking common factors
        • Evaluating expressions with unknown variables
        • Factoring quadratics intro
        • Factoring quadratics by grouping
        • Factoring polynomials with quadratic forms
        • Factoring quadratics: Difference of squares
        • Factoring quadratics: Perfect squares
        • Strategy in factoring quadratics
        • Factoring polynomials with special product forms
      • Quadratics
        • Parabolas intro
        • Quadratic factored form
        • Solving quadratics by taking square roots
        • Quadratic vertex form
        • Solving quadratics by factoring
        • Completing the square
        • The quadratic formula
        • Quadratic standard form
        • Features & forms of quadratic functions
        • Transforming parabolas
        • Unit review
      • Irrational numbers
        • Irrational numbers
        • Sums and products of rational and irrational numbers
        • Proofs concerning irrational numbers
    • Algebra II
      • Functions
        • Combining functions
        • Composing functions
        • Modeling situations by combining and composing functions
        • Shifting functions
        • Stretching functions
        • Introduction to inverses of functions
        • Finding inverse functions
        • Verifying that functions are inverses
        • Determining whether a function is invertible
      • Complex numbers
        • What are the imaginary numbers?
        • What are the complex numbers?
        • The complex plane
        • Adding and subtracting complex numbers
        • Multiplying complex numbers
      • Arithmetic with polynomials
        • Adding and subtracting polynomials
        • Multiplying polynomials
        • Long division of polynomials
        • Synthetic division of polynomials
        • Practice dividing polynomials with remainders
        • Polynomial Remainder Theorem
      • Polynomials
        • The binomial theorem
        • Understanding the binomial theorem
        • Factoring polynomials - Quadratic forms
        • Factoring polynomials - Special product forms
        • Advanced polynomial factorization methods
        • Proving polynomial identities
        • Polynomial identities with complex numbers
        • Quadratic equations with complex numbers
        • The Fundamental Theorem of Algebra
        • Finding zeros of polynomials
        • Zeros of polynomials and their graphs
        • End behavior of polynomial functions
        • Graphs of polynomials
        • Introduction to symmetry of functions
        • Symmetry of polynomial functions
      • Radical relationships
        • Solving square-root equations
        • Extraneous solutions of radical equations
        • Solving cube-root equations
        • Domain of radical functions
        • Graphs of radical functions
      • Rational relationships
        • Simplifying rational expressions
        • Multiplying & dividing rational expressions
        • Adding & subtracting rational expressions
        • Nested fractions
        • Solving rational equations
        • Direct and inverse variation
        • End behavior of rational functions
        • Discontinuities of rational functions
        • Graphs of rational functions
        • Modeling with rational functions
      • Exponential growth & decay
        • Equivalent forms of exponential expressions
        • Solving exponential equations using properties of exponents
        • Interpreting the rate of change of exponential models
        • Constructing exponential models according to rate of change
        • Advanced interpretation of exponential models
        • Distinguishing between linear and exponential growth
      • Exponentials & logarithms
        • Introduction to logarithms
        • The constant e and the natural logarithm
        • Properties of logarithms
        • The change of base formula for logarithms
        • Solving exponential equations with logarithms
        • Solving exponential models
        • Graphs of exponential functions
        • Graphs of logarithmic functions
        • Logarithmic scale (optional)
      • Trigonometry
        • Introduction to radians
        • The unit circle definition of sine, cosine, and tangent
        • The graphs of sine, cosine, and tangent
        • Basic trigonometric identities
        • Trigonometric values of special angles
        • The Pythagorean identity
        • Introduction to amplitude, midline, and extrema of sinusoidal functions
        • Finding amplitude and midline of sinusoidal functions from their formulas
        • Period of sinusoidal functions
        • Graphing sinusoidal functions
        • Constructing sinusoidal functions
      • Advanced equations & functions
        • Solving equations by graphing
        • Systems of quadratic equations
        • Interpreting the symmetry of algebraic models
        • Interpreting the end behavior of algebraic models
        • Interpreting the periodicity of algebraic models
        • Comparing features of functions
      • Series
        • Arithmetic sequences
        • Basic sigma notation
        • Finite arithmetic series
        • Geometric sequences
        • Finite geometric series
        • Finite geometric series applications
      • Modeling
        • Modeling with one-variable equations and inequalities
        • Manipulating formulas
      • Conic sections
        • Introduction to conic sections
        • The features of a circle
        • Standard equation of a circle
        • Expanded equation of a circle
        • Focus and directrix of a parabola
    • Basic geometry
      • Lines
        • Lines, line segments, and rays
        • Parallel and perpendicular
      • Angles
        • Angle introduction
        • Measuring and drawing angles
        • Angles in circles
        • Angle types
        • Vertical, complementary, and supplementary angles
        • Angles between intersecting lines
      • Shapes
        • Properties of shapes
        • Quadrilaterals
        • Triangles
        • Classifying geometric shapes
        • Triangle angles
        • Geometric solids (3D shapes)
      • Coordinate plane
        • Coordinate plane: quadrant 1
        • Coordinate plane: 4 quadrants
        • Quadrants on the coordinate plane
        • Reflecting points on coordinate plane
        • Quadrilaterals on the coordinate plane
        • Drawing polygons in the coordinate plane
      • Area and perimeter
        • Count unit squares to find area
        • Area of rectangles
        • Perimeter
        • Area of parallelograms
        • Area of triangles
        • Area of trapezoids & composite figures
        • Area and circumference of circles
      • Volume and surface area
        • Volume of rectangular prisms
        • Volume with fractions
        • Surface area
        • Volume of cones, cylinders, and spheres
      • Pythagorean theorem
        • Pythagorean theorem
        • Pythagorean theorem application
        • Pythagorean theorem and distance between points
        • Pythagorean theorem proofs
      • Transformations, congruence, and similarity
        • Line of symmetry
        • Transformations intro
        • Translations
        • Rotations
        • Reflections
        • Properties & definitions of transformations
        • Dilations
        • Congruence and similarity
    • High school geometry
      • Geometry foundations
        • Intro to Euclidean geometry
        • Angles
        • Polygons
        • Area
      • Transformations
        • Introduction to rigid transformations
        • Translations
        • Rotations
        • Reflections
        • Rigid transformations overview
        • Dilations
        • Properties & definitions of transformations
        • Symmetry
      • Congruence
        • Transformations & congruence
        • Triangle congruence
        • Theorems concerning triangle properties
        • Working with triangles
        • Theorems concerning quadrilateral properties
        • Proofs of general theorems that use triangle congruence
        • Constructing bisectors of lines & angles
      • Similarity
        • Definitions of similarity
        • Introduction to triangle similarity
        • Solving similar triangles
        • Angle bisector theorem
        • Solving problems with similar & congruent triangles
        • Solving modeling problems with similar & congruent triangles
      • Right triangles & trigonometry
        • Pythagorean theorem
        • Pythagorean theorem proofs
        • Special right triangles
        • Introduction to the trigonometric ratios
        • Solving for a side in a right triangle using the trigonometric ratios
        • Solving for an angle in a right triangle using the trigonometric ratios
        • Modeling with right triangles
        • Trigonometric ratios & similarity
        • Sine & cosine of complementary angles
        • Law of sines
        • Law of cosines
        • Solving general triangles
      • Solid geometry
        • Solid geometry intro
        • Density
        • 2D vs. 3D objects
      • Analytic geometry
        • Distance and midpoints
        • Dividing line segments
        • Problem solving with distance on the coordinate plane
        • Parallel & perpendicular lines on the coordinate plane
        • Equations of parallel & perpendicular lines
      • Circles
        • Circle basics
        • Arc measure
        • Arc length (degrees)
        • Introduction to radians
        • Arc length (radians)
        • Sectors
        • Inscribed angles
        • Inscribed shapes problem solving
        • Properties of tangents
        • Standard equation of a circle
        • Expanded equation of a circle
        • Constructing regular polygons inscribed in circles
        • Constructing circumcircles & incircles
        • Constructing a line tangent to a circle
    • Trigonometry
      • Trigonometry with right triangles
        • Introduction to the trigonometric ratios
        • Solving for a side in a right triangle using the trigonometric ratios
        • Solving for an angle in a right triangle using the trigonometric ratios
        • Modeling with right triangles
        • Trigonometric ratios and similarity
        • Sine and cosine of complementary angles
        • Trigonometric ratios of special triangles
        • Introduction to the Pythagorean trigonometric identity
        • The reciprocal trigonometric ratios
      • Trigonometry with general triangles
        • The law of sines
        • The law of cosines
        • Solving general triangles
      • The unit circle definition of sine, cosine, and tangent
        • Introduction to radians
        • The unit circle definition of sine, cosine, and tangent
        • The graphs of sine, cosine, and tangent
        • Basic trigonometric identities
        • Trigonometric values of special angles
        • The Pythagorean identity
        • Long live Tau
      • Graphs of trigonometric functions
        • The graphs of sine, cosine, and tangent
        • Introduction to amplitude, midline, and extrema of sinusoidal functions
        • Finding amplitude and midline of sinusoidal functions from their formulas
        • Period of sinusoidal functions
        • Graphing sinusoidal functions
        • Constructing sinusoidal functions
      • Trigonometric equations and identities
        • The inverse trigonometric functions
        • Solving basic sinusoidal equations
        • Solving advanced sinusoidal equations
        • Solving sinusoidal models
        • Introduction to the trigonometric angle addition identities
        • Using trigonometric identities to solve problems
        • Challenging trigonometry problems
    • Statistics and probability
      • Analyzing categorical data
        • Analyzing one categorical variable
        • Two-way tables
        • Distributions in two-way tables
      • Displaying and comparing quantitative data
        • Displaying quantitative data with graphs
        • Describing and comparing distributions
        • More on data displays
      • Summarizing quantitative data
        • Measuring center in quantitative data
        • More on mean and median
        • Interquartile range (IQR)
        • Variance and standard deviation of a population
        • Variance and standard deviation of a sample
        • More on standard deviation
        • Box and whisker plots
        • Other measures of spread
      • Modeling data distributions
        • Percentiles
        • Z-scores
        • Effects of linear transformations
        • Density curves
        • Normal distributions and the empirical rule
        • Normal distribution calculations
      • Exploring bivariate numerical data
        • Introduction to scatterplots
        • Correlation coefficients
        • Introduction to trend lines
        • Least-squares regression equations
        • Assessing the fit in least-squares regression
        • More on regression
      • Study design
        • Statistical questions
        • Sampling and observational studies
        • Sampling methods
        • Types of studies (experimental vs. observational)
        • Experiments
      • Probability
        • Basic theoretical probability
        • Probability using sample spaces
        • Basic set operations
        • Experimental probability
        • Randomness, probability, and simulation
        • Addition rule
        • Multiplication rule for independent events
        • Multiplication rule for dependent events
        • Conditional probability and independence
      • Counting, permutations, and combinations
        • Counting principle and factorial
        • Permutations
        • Combinations
        • Combinatorics and probability
      • Random variables
        • Discrete random variables
        • Continuous random variables
        • Transforming random variables
        • Combining random variables
        • Binomial random variables
        • Binomial mean and standard deviation formulas
        • Geometric random variables
        • More on expected value
        • Poisson distribution
      • Sampling distributions
        • What is a sampling distribution?
        • Sampling distribution of a sample proportion
        • Sampling distribution of a sample mean
      • One-sample confidence intervals
        • Introduction to confidence intervals
        • Estimating a population proportion
        • Estimating a population mean
      • One-sample z and t significance tests
        • The idea of significance tests
        • Tests about a population proportion
        • Tests about a population mean
      • Two-sample inference for the difference between groups
        • Comparing two proportions
        • Comparing two means
      • Inference for categorical data (chi-square tests)
        • Chi-square goodness-of-fit tests
        • Chi-square tests for homogeneity and association/independence
      • Advanced regression (inference and transforming)
        • Nonlinear regression
      • Analysis of variance (ANOVA)
        • Analysis of variance (ANOVA)
    • High school statistics
      • Scatterplots
        • Creating and interpreting scatterplots
        • Estimating with trend lines
      • Data distributions
        • Displays of distributions
        • Summarizing center of distributions (central tendency)
        • Summarizing spread of distributions
        • Box and whisker plots
        • Comparing distributions
      • Two-way tables
        • Two-way frequency tables
        • Two-way relative frequency tables
      • Study design
        • Samples and surveys
        • Observational studies and experiments
      • Probability
        • Probability basics
        • Counting with permutations
        • Counting with combinations
        • Probability with counting, permutations, combinations
        • Multiplication rule for independent events
        • Multiplication rule for dependent events
        • Addition rule for probability
        • Conditional probability
        • Simulation and randomness
        • Expected value
      • Binomial probability
        • Binomial probability
      • Normal distributions
        • Normal distributions
    • AP Statistics
      • Analyzing categorical data
        • Welcome to AP Statistics
        • Analyzing one categorical variable
        • Two-way tables
        • Distributions in two-way tables
      • Displaying and comparing quantitative data
        • Frequency tables and dot plots
        • Histograms and stem-and-leaf plots
        • Describing and comparing distributions
      • Summarizing quantitative data
        • Measuring center in quantitative data
        • More on mean and median
        • Measuring spread in quantitative data
        • More on standard deviation
        • Box and whisker plots
      • Modeling data distributions
        • Percentiles (cumulative relative frequency)
        • Z-scores
        • Effects of linear transformations
        • Density curves
        • Normal distributions and the empirical rule
        • Normal distribution calculations
      • Exploring bivariate numerical data
        • Introduction to scatterplots
        • Correlation coefficients
        • Least-squares regression equations
        • Assessing the fit in least-squares regression
      • Study design
        • Sampling and observational studies
        • Sampling methods
        • Types of studies (experimental vs. observational)
        • Experiments
      • Probability
        • Randomness, probability, and simulation
        • Addition rule
        • Multiplication rule
        • Conditional probability
      • Random variables
        • Discrete random variables
        • Continuous random variables
        • Transforming random variables
        • Combining random variables
        • Binomial random variables
        • Binomial mean and standard deviation formulas
        • Geometric random variables
      • Sampling distributions
        • What is a sampling distribution?
        • Sampling distribution of a sample proportion
        • Sampling distribution of a sample mean
      • One-sample confidence intervals
        • Introduction to confidence intervals
        • One-sample z interval for a proportion
    • Precalculus
      • Trigonometry
        • The inverse trigonometric functions
        • Solving basic sinusoidal equations
        • Solving advanced sinusoidal equations
        • Solving sinusoidal models
        • Introduction to the trigonometric angle addition identities
        • Using trigonometric identities to solve problems
      • Conic sections
        • Introduction to conic sections
        • The features of a circle
        • Standard equation of a circle
        • Expanded equation of a circle
        • Center and radii of an ellipse
        • Foci of an ellipse
        • Focus and directrix of a parabola
        • Introduction to hyperbolas
        • Foci of a hyperbola
        • Hyperbolas not centered at the origin
        • Identifying conic sections from their expanded equations
        • Challenging conic section problems (IIT JEE)
      • Vectors
        • Vector basics
        • Magnitude of vectors
        • Scalar multiplication
        • Vector addition and subtraction
        • Combined vector operations
        • Unit vectors
        • Magnitude and direction form of vectors
        • Component form of vectors
        • Adding vectors in magnitude and direction form
        • Applications of vectors
      • Matrices
        • Introduction to matrices
        • Representing linear systems of equations with augmented matrices
        • Elementary matrix row operations
        • Row-echelon form and Gaussian elimination
        • Adding and subtracting matrices
        • Multiplying matrices by scalars
        • Properties of matrix addition & scalar multiplication
        • Multiplying matrices by matrices
        • Properties of matrix multiplication
        • Matrices as transformations
        • The determinant of a 2x2 matrix
        • Introduction to matrix inverses
        • Finding the inverse of a matrix using its determinant
        • Practice finding the inverses of 2x2 matrices
        • Solving equations with inverse matrices
        • Model real-world situations with matrices
      • Complex numbers
        • What are the imaginary numbers?
        • What are the complex numbers?
        • The complex plane
        • Adding and subtracting complex numbers
        • Distance and midpoint of complex numbers
        • Multiplying complex numbers
        • Complex conjugates and dividing complex numbers
        • Absolute value and angle of complex numbers
        • Polar form of complex numbers
        • Multiplying and dividing complex numbers in polar form
        • Challenging complex number problems
      • Probability and combinatorics
        • Basic probability
        • Venn diagrams and the addition rule
        • Compound probability of independent events using diagrams
        • Compound probability of independent events using the multiplication rule
        • Dependent events
        • Permutations
        • Combinations
        • Probability using combinatorics
      • Series
        • Arithmetic sequences
        • Basic sigma notation
        • Finite arithmetic series
        • Geometric sequences
        • Finite geometric series
        • Finite geometric series applications
    • Differential calculus
      • Limits basics
        • Limits introduction
        • One-sided limits
        • Formal definition of limits (epsilon-delta)
        • Review: Limits basics
      • Continuity
        • Continuity at a point
        • Limits of combined & composite functions
        • Continuous functions
        • Intermediate value theorem
        • Review: Continuity
      • Limits from equations
        • Limits from equations (direct substitution)
        • Limits from equations (factoring & rationalizing)
        • Squeeze theorem
        • Limits of trigonometric functions
        • Limits of piecewise functions
        • Removable discontinuities
        • Review: Limits from equations
      • Infinite limits
        • Unbounded limits (vertical asymptotes)
        • Limits at infinity (horizontal asymptotes)
        • Review: Infinite limits
      • Derivative introduction
        • Introduction to differential calculus
        • Derivative as slope of tangent line
        • Derivative as instantaneous rate of change
        • Secant lines
        • Derivative as a limit
        • Formal definition of derivative
        • Using the formal definition of derivative
        • Differentiability
        • Derivative as a function
        • Review: Derivative basics
      • Basic differentiation
        • Basic differentiation rules
        • Power rule
        • Polynomial functions differentiation
        • Rational functions differentiation (intro)
        • Radical functions differentiation (intro)
        • Sine & cosine derivatives
        • eˣ and ln(x) derivatives
        • Review: Basic differentiation
      • Product, quotient, & chain rules
        • Product rule
        • Chain rule
        • Chain rule proof
        • Quotient rule
        • Review: Product, quotient, & chain rule
      • Differentiating common functions
        • Rational functions differentiation
        • Radical functions differentiation
        • Trigonometric functions differentiation
        • Exponential functions differentiation
        • Logarithmic functions differentiation
        • Derivatives capstone
      • Advanced differentiation
        • Implicit differentiation introduction
        • Implicit differentiation (advanced examples)
        • Inverse trig functions differentiation
        • Derivatives of inverse functions
        • Disguised derivatives
        • Proofs for the derivatives of eˣ and ln(x)
        • Logarithmic differentiation
        • Parametric & vector-valued function differentiation
        • Review: Advanced differentiation
        • Higher-order derivatives
        • Higher-order derivatives (parametric & vector-valued functions)
      • Analyzing functions with calculus
        • Critical points
        • Increasing & decreasing intervals
        • Relative minima & maxima
        • Absolute minima & maxima
        • Review: Increasing/decreasing intervals & extrema
        • Concavity
        • Points of inflection
        • Sketching graphs using calculus
        • Review: Concavity & points of inflection
      • Derivative applications
        • Linear approximation
        • Rectilinear motion
        • Planar motion
        • Related rates
        • Optimization
        • Applied rates of change
        • Mean value theorem
        • L'Hôpital's rule
        • Review: Derivative applications
    • Integral calculus
      • Indefinite integrals
        • Antiderivatives
        • Indefinite integrals intro
        • Indefinite integrals of common functions
        • Review: Indefinite integrals & antiderivatives
      • Definite integrals introduction
        • Definite integral as area
        • Definite integral properties
        • Review: Definite integral basics
      • Riemann sums
        • Riemann sums
        • Riemann sums with sigma notation
        • Trapezoidal rule
        • Definite integral as the limit of a Riemann sum
        • Review: Riemann sums
      • Fundamental theorem of calculus
        • Functions defined by integrals
        • Fundamental theorem of calculus
        • Fundamental theorem of calculus: chain rule
      • Definite integral evaluation
        • Definite integral evaluation
        • Definite integrals of piecewise functions
        • Improper integrals
      • Integration techniques
        • Integration by parts
        • u-substitution
        • Reverse chain rule
        • Partial fraction expansion
        • Integration using trigonometric identities
        • Trigonometric substitution
      • Area & arc length using calculus
        • Area between curves
        • Arc length
        • Area defined by polar graphs
        • Arc length of polar graphs
      • Integration applications
        • Area & net change
        • Rectilinear motion
        • Average value of a function
      • Volume using calculus
        • Solids with known cross sections
        • Disc method
        • Washer method
        • Shell method
      • Sequences & series intro
        • Sequences review
        • Infinite sequences
        • Series review
        • Finite geometric series
        • Partial sums
        • Infinite geometric series
        • Series basics challenge
      • Series convergence & estimation
        • Basic convergence tests
        • Comparison tests
        • Ratio & alternating series tests
        • Estimating infinite series
      • Power series
        • Power series intro
        • Taylor & Maclaurin polynomials intro
        • Maclaurin series of sin(x), cos(x), and eˣ
        • Power series function representation
        • Challenge series exercises
    • AP Calculus AB
      • Limits and continuity
        • About the course
        • Analyzing limits graphically
        • Analyzing limits numerically
        • One-sided limits
        • Continuity
        • Limit rules for sums, differences, products, quotients, & composites
        • Determining limits using direct substitution
        • Determining limits by factoring & rationalizing
        • Trigonometric limits & squeeze theorem
        • Infinite limits intro
        • Analyzing limits at infinity
        • Analyzing functions for discontinuities
        • Strategy in finding limits
        • Optional videos
      • Derivatives introduction
        • The derivative: An intuitive introduction
        • Estimating derivatives with secant lines and average rate of change
        • Secant lines & average rate of change with arbitrary points
        • Formal definition of the derivative as a limit
        • Differentiability
        • Tangent lines and local linearity
        • Optional videos
      • Derivative rules
        • Basic differentiation rules
        • Power rule
        • Polynomial functions differentiation
        • Derivatives of negative and fractional powers with power rule
        • Derivatives of sin(x) and cos(x)
        • Product rule
        • Quotient rule
        • Rational functions differentiation
        • Chain rule
        • Radical functions differentiation
        • Trigonometric functions differentiation
        • Strategy in differentiating functions
        • Optional videos
      • Advanced derivatives
        • Differentiating using multiple rules
        • Second derivatives
        • Implicit differentiation
        • Derivatives of inverse functions
        • Derivatives of inverse trigonometric functions
        • Derivatives of exponential functions
        • Derivatives of logarithmic functions
        • Optional videos
      • Existence theorems
        • Intermediate and extreme value theorems
        • Mean value theorem
      • Using derivatives to analyze functions
        • L'Hôpital's rule
        • Justifying properties of functions using the first derivative
        • Critical points & intervals of increase or decrease
        • Finding relative extrema (first derivative test)
        • Finding absolute extrema
        • Concavity & inflection points intro
        • Justifying properties of functions using the second derivative
        • Finding inflection points & analyzing concavity
        • Connecting ƒ, ƒ’, and ƒ’’
        • Optional videos
      • Applications of derivatives
        • Rates of change in applied contexts
        • Related rates intro
        • Related rates problems
        • Optimization
        • Motion problems
      • Accumulation and Riemann sums
        • Definite integrals intro
        • Left & right Riemann sums
        • Midpoint & trapezoidal sums
        • Summation notation
        • Riemann sums in summation notation
        • Definite integral as the limit of a Riemann sum
        • Definite integrals properties
        • Functions defined by integrals
      • Antiderivatives and the fundamental theorem of calculus
        • Antiderivatives and indefinite integrals intro
        • Fundamental theorem of calculus
        • Indefinite integrals: reverse power rule
        • Indefinite integrals of sin(x), cos(x), eˣ, and 1/x
        • Finding definite integrals
        • 𝘶-substitution
        • Average value of a function
        • Interpreting behavior of 𝑔 from graph of 𝑔'=ƒ
        • Optional videos
      • Differential equations
        • Differential equations intro
        • Separable differential equations
        • Differential equations: specific solutions
        • Slope fields
        • Exponential models
      • Applications of definite integrals
        • Word problems involving definite integrals
        • Motion problems (with integrals)
        • Area: vertical areas between curves
        • Area: horizontal areas between curves
        • Volume: known cross sections
        • Volume: disc method
        • Volume: washer method
        • Volume: shell method (optional)
      • AP Calculus AB solved exams
        • AP Calculus AB 2017
        • AP Calculus AB 2015
        • AP Calculus AB 2011
    • AP Calculus BC
      • Limits and continuity
        • About the course
        • Analyzing limits graphically
        • Analyzing limits numerically
        • One-sided limits
        • Continuity
        • Limit rules for sums, differences, products, quotients, & composites
        • Determining limits using direct substitution
        • Determining limits by factoring & rationalizing
        • Trigonometric limits & squeeze theorem
        • Infinite limits intro
        • Analyzing limits at infinity
        • Analyzing functions for discontinuities
        • Strategy in finding limits
        • Optional videos
      • Derivatives introduction
        • The derivative: An intuitive introduction
        • Estimating derivatives with secant lines and average rate of change
        • Secant lines & average rate of change with arbitrary points
        • Formal definition of the derivative as a limit
        • Differentiability
        • Tangent lines and local linearity
        • Optional videos
      • Derivative rules
        • Basic differentiation rules
        • Power rule
        • Polynomial functions differentiation
        • Derivatives of negative and fractional powers with power rule
        • Derivatives of sin(x) and cos(x)
        • Product rule
        • Quotient rule
        • Rational functions differentiation
        • Chain rule
        • Radical functions differentiation
        • Trigonometric functions differentiation
        • Strategy in differentiating functions
        • Optional videos
      • Advanced derivatives
        • Differentiating using multiple rules
        • Second derivatives
        • Implicit differentiation
        • Derivatives of inverse functions
        • Derivatives of inverse trigonometric functions
        • Derivatives of exponential functions
        • Derivatives of logarithmic functions
        • Parametric & vector-valued function differentiation
        • Polar functions differentiation
        • Optional videos
      • Existence theorems
        • Intermediate and extreme value theorems
        • Mean value theorem
      • Using derivatives to analyze functions
        • L'Hôpital's rule
        • Justifying properties of functions using the first derivative
        • Critical points & intervals of increase or decrease
        • Finding relative extrema (first derivative test)
        • Finding absolute extrema
        • Concavity & inflection points intro
        • Justifying properties of functions using the second derivative
        • Finding inflection points & analyzing concavity
        • Connecting ƒ, ƒ’, and ƒ’’
        • Optional videos
      • Applications of derivatives
        • Rates of change in applied contexts
        • Related rates intro
        • Related rates problems
        • Optimization
        • Planar motion
      • Accumulation and Riemann sums
        • Definite integrals intro
        • Left & right Riemann sums
        • Midpoint & trapezoidal sums
        • Summation notation
        • Riemann sums in summation notation
        • Definite integral as the limit of a Riemann sum
        • Definite integrals properties
        • Functions defined by integrals
      • Antiderivatives and the fundamental theorem of calculus
        • Antiderivatives and indefinite integrals intro
        • Fundamental theorem of calculus
        • Indefinite integrals: reverse power rule
        • Indefinite integrals of sin(x), cos(x), eˣ, and 1/x
        • Finding definite integrals
        • Improper integrals
        • 𝘶-substitution
        • Integration by parts
        • Partial fraction expansion
        • Average value of a function
        • Interpreting behavior of 𝑔 from graph of 𝑔'=ƒ
        • Optional videos
      • Differential equations
        • Differential equations intro
        • Separable differential equations
        • Differential equations: specific solutions
        • Slope fields
        • Euler's Method
        • Exponential models
        • Logistic models
      • Applications of definite integrals
        • Word problems involving definite integrals
        • Motion problems (with integrals)
        • Area: vertical areas between curves
        • Area: horizontal areas between curves
        • Area: polar curves
        • Arc length
        • Volume: known cross sections
        • Volume: disc method
        • Volume: washer method
        • Volume: shell method (optional)
      • Series
        • Infinite sequences
        • Finite geometric series
        • Partial sums
        • Infinite geometric series
        • Basic convergence tests
        • Comparison tests
        • Ratio & alternating series tests
        • Estimating infinite series
        • Power series intro
        • Taylor & Maclaurin polynomials intro
        • Maclaurin series of sin(x), cos(x), and eˣ
        • Power series function representation
        • Optional videos
      • AP Calculus BC solved exams
        • AP Calculus BC 2017
        • AP Calculus BC 2015
        • AP Calculus BC 2011
        • AP Calculus BC 2008
    • Multivariable calculus
      • Thinking about multivariable functions
        • Introduction to multivariable calculus
        • Skill check
        • Visualizing scalar-valued functions
        • Visualizing vector-valued functions
        • Transformations
        • Visualizing multivariable functions (articles)
      • Derivatives of multivariable functions
        • Skill checks
        • Partial derivatives
        • Gradient and directional derivatives
        • Partial derivative and gradient (articles)
        • Differentiating parametric curves
        • Multivariable chain rule
        • Curvature
        • Partial derivatives of vector-valued functions
        • Differentiating vector-valued functions (articles)
        • Divergence
        • Curl
        • Divergence and curl (articles)
        • Laplacian
        • Jacobian
      • Applications of multivariable derivatives
        • Tangent planes and local linearization
        • Quadratic approximations
        • Optimizing multivariable functions
        • Optimizing multivariable functions (articles)
        • Lagrange multipliers and constrained optimization
        • Constrained optimization (articles)
      • Integrating multivariable functions
        • Line integrals for scalar functions (videos)
        • Line integrals for scalar functions (articles)
        • Line integrals in vector fields (videos)
        • Line integrals in vector fields (articles)
        • Double integrals (videos)
        • Double integrals (articles)
        • Triple integrals (videos)
        • Triple integrals (articles)
        • Surface integral preliminaries (videos)
        • Surface integrals (videos)
        • Surface integrals (articles)
        • Flux in 3D (videos)
        • Flux in 3D (articles)
      • Green's, Stokes', and the divergence theorems
        • Formal definitions of div and curl (optional reading)
        • Green's theorem (videos)
        • Green's theorem (articles)
        • 2D divergence theorem
        • Stokes' theorem (videos)
        • Stokes' theorem (articles)
        • 3D divergence theorem (videos)
        • Divergence theorem (articles)
        • Proof of Stokes' theorem
        • Types of regions in three dimensions
        • Divergence theorem proof
    • Differential equations
      • First order differential equations
        • Intro to differential equations
        • Slope fields
        • Euler's Method
        • Separable equations
        • Exponential models
        • Logistic models
        • Exact equations and integrating factors
        • Homogeneous equations
      • Second order linear equations
        • Linear homogeneous equations
        • Complex and repeated roots of characteristic equation
        • Method of undetermined coefficients
      • Laplace transform
        • Laplace transform
        • Properties of the Laplace transform
        • Laplace transform to solve a differential equation
        • The convolution integral
    • Linear algebra
      • Vectors and spaces
        • Vectors
        • Linear combinations and spans
        • Linear dependence and independence
        • Subspaces and the basis for a subspace
        • Vector dot and cross products
        • Matrices for solving systems by elimination
        • Null space and column space
      • Matrix transformations
        • Functions and linear transformations
        • Linear transformation examples
        • Transformations and matrix multiplication
        • Inverse functions and transformations
        • Finding inverses and determinants
        • More determinant depth
        • Transpose of a matrix
      • Alternate coordinate systems (bases)
        • Orthogonal complements
        • Orthogonal projections
        • Change of basis
        • Orthonormal bases and the Gram-Schmidt process
        • Eigen-everything
    • 6th grade (Ontario)
      • Number Sense and Numeration
        • Ratios, rates and percentages
        • Fractions
        • Multiplication and division
        • Place value and decimal operations
        • Factors and multiples
        • Properties of numbers
      • Measurement
        • Unit conversion
        • Area
        • Volume
      • Geometry and Spatial Sense
        • Coordinate plane
        • Angles and polygons
        • Transformations
      • Patterning and Algebra
        • Number patterns
        • Variables and expressions
      • Data Management and Probability
        • Data management
        • Statistics
        • Probability
    • 6th grade (WNCP)
      • Number
        • Place value and decimals
        • Prime numbers, factors and multiples
        • Mixed numbers and improper fractions
        • Ratios and percentages
        • Integers negative numbers
        • Multiplication and division
        • Properties of numbers and order of operations
      • Patterns and Relations
        • Number patterns
        • Variables and equations
      • Shape and Space
        • Angles
        • Perimeter and Area
        • Volume
        • Triangles and Polygons
        • Coordinate plane
        • Transformations
      • Statistics and Probability
        • Data
        • Probability
    • 3rd grade (Eureka Math/EngageNY)
      • Module 1: Properties of multiplication and division and solving problems with units of 2–5 and 10
        • Topic A: Multiplication and the meaning of the factors
        • Topic B: Division as an unknown factor problem
        • Topic C: Multiplication using units of 2 and 3
        • Topic D: Division using units of 2 and 3
        • Topic E: Multiplication and division using units of 4
        • Topic F: Distributive property and problem solving using units of 2–5 and 10
      • Module 2: Place value and problem solving with units of measure
        • Topic A: Time measurement and problem solving
        • Topic B: Measuring weight and liquid volume in metric units
        • Topic C: Rounding to the nearest ten and hundred
        • Topic D: Two- and three-digit measurement addition using the standard algorithm
        • Topic E: Two- and three-digit measurement subtraction using the standard algorithm
      • Module 3: Multiplication and division with units of 0, 1, 6–9, and multiples of 10
        • Topic A: The properties of multiplication and division
        • Topic B: Multiplication and division using units of 6 and 7
        • Topic C: Multiplication and division using units up to 8
        • Topic D: Multiplication and division using units of 9
        • Topic E: Analysis of patterns and problem solving including units of 0 and 1
      • Module 4: Multiplication and area
        • Topic A: Foundations for understanding area
        • Topic B: Concepts of area measurement
        • Topic C: Arithmetic properties using area models
        • Topic D: Applications of area using side lengths of figures
      • Module 5: Fractions as numbers on the number line
        • Topic A: Partitioning a whole into equal parts
        • Topic B: Unit fractions and their relation to the whole
        • Topic C: Comparing unit fractions and specifying the whole
        • Topic D: Fractions on the number line
        • Topic E: Equivalent fractions
        • Topic F: Comparison, order, and size of fractions
      • Module 6: Collecting and displaying data
        • Topic A: Generate and analyze categorical data
        • Topic B: Generate and analyze measurement data
      • Module 7: Geometry and measurement word problems
        • Topic A: Solving word problems
        • Topic B: Attributes of two-dimensional figures
        • Topic C: Problem solving with perimeter
        • Topic D: Recording perimeter and area data on line plots
        • Topic E: Problem solving with perimeter and area
    • 4th grade (Eureka Math/EngageNY)
      • Module 1: Place value, rounding, and algorithms for addition and subtraction
        • Topic A: Place value of multi-digit whole numbers
        • Topic B: Comparing multi-digit whole numbers
        • Topic C: Rounding multi-digit whole numbers
        • Topic D: Multi-digit whole number addition
        • Topic E: Multi-digit whole number subtraction
        • Topic F: Addition and subtraction word problems
      • Module 2: Unit conversions and problem solving with metric measurement
        • Topic A: Metric unit conversions
        • Topic B: Application of metric unit conversions
      • Module 3: Multi-digit multiplication and division
        • Topic A: Multiplicative comparison word problems
        • Topic B: Multiplication by 10, 100, and 1,000
        • Topic C: Multiplication of up to four digits by single-digit numbers
        • Topic D: Multiplication word problems
        • Topic E: Division of tens and ones with successive remainders
        • Topic F: Reasoning with divisibility
        • Topic G: Division of thousands, hundreds, tens, and ones
        • Topic H: Multiplication of two-digit by two-digit numbers
      • Module 4: Angle measure and plane figures
        • Topic A: Line and angles
        • Topic B: Angle measurement
        • Topic C: Problem solving with the addition of angle measures
        • Topic D: Two-dimensional figures and symmetry
      • Module 5: Fraction equivalence, ordering, and operations
        • Topic A: Decomposition and fraction equivalence
        • Topic B: Fraction equivalence using multiplication and division
        • Topic C: Fraction comparison
        • Topic D: Fraction addition and subtraction
        • Topic E: Extending fraction equivalence to fractions greater than 1
        • Topic F: Addition and subtraction of fractions by decomposition
        • Topic G: Repeated addition of fractions as multiplication
        • Topic H: Exploring a fraction pattern
      • Module 6: Decimal fractions
        • Topic A: Exploration of tenths
        • Topic B: Tenths and hundredths
        • Topic C: Decimal comparison
        • Topic D: Addition with tenths and hundredths
        • Topic E: Money amounts as decimal numbers
      • Module 7: Exploring measurement with multiplication
        • Topic A: Measurement conversion tables
        • Topic B: Problem solving with measurement
        • Topic C: Investigation of measurements expressed as mixed numbers
    • 5th grade (Eureka Math/EngageNY)
      • Module 1: Place value and decimal fractions
        • Topic A: Multiplicative patterns on the place value chart
        • Topic B: Decimal fractions and place value patterns
        • Topic C: Place value and rounding decimal fractions
        • Topic D: Adding and subtracting decimals
        • Topic E: Multiplying decimals
        • Topic F: Dividing decimals
      • Module 2: Multi-digit whole number and decimal fraction operations
        • Topic A: Mental strategies for multi-digit whole number multiplication
        • Topic B: The standard algorithm for multi-digit whole number multiplication
        • Topic C: Decimal multi-digit multiplication
        • Topic D: Measurement word problems with whole number and decimal multiplication
        • Topic E: Mental strategies for multi-digit whole number division
        • Topic F: Partial quotients and multi-digit whole number division
        • Topic G: Partial quotients and multi-digit decimal division
        • Topic H: Measurement word problems with multi-digit division
      • Module 3: Addition and subtractions of fractions
        • Topic A: Equivalent fractions
        • Topic B: Making like units pictorially
        • Topic C: Making like units numerically
        • Topic D: Further applications
      • Module 4: Multiplication and division of fractions and decimal fractions
        • Topic A: Line plots of fraction measurements
        • Topic B: Fractions as division
        • Topic C: Multiplication of a whole number by a fraction
        • Topic D: Fraction expressions and word problems
        • Topic E: Multiplication of a fraction by a fraction
        • Topic F: Multiplication with fractions and decimals as scaling and word problems
        • Topic G: Division of fractions and decimal fractions
        • Topic H: Interpretation of numerical expressions
      • Module 5: Addition and multiplication with volume and area
        • Topic A: Concepts of volume
        • Topic B: Volume and the operations of multiplication and addition
        • Topic C: Area of rectangular figures with fractional side lengths
        • Topic D: Drawing, analysis, and classification of two-dimensional shapes
      • Module 6: Problem solving with the coordinate plane
        • Topic A: Coordinate systems
        • Topic B: Patterns in the coordinate plane and graphing number patterns from rules
        • Topic C: Drawing figures in the coordinate plane
        • Topic D: Problem solving in the coordinate plane
    • 6th grade (Eureka Math/EngageNY)
      • Module 1: Ratios and unit rates
        • Topic A: Representing and reasoning about ratios
        • Topic B: Collections of equivalent ratios
        • Topic C: Unit rates
        • Topic D: Percents
      • Module 2: Arithmetic operations including dividing by a fraction
        • Topic A: Dividing fractions by fractions
        • Topic B: Multi‐digit decimal operations—adding, subtracting, and multiplying
        • Topic C: Dividing whole numbers and decimals
        • Topic D: Number theory—thinking logically about multiplicative arithmetic
      • Module 3: Rational numbers
        • Topic A: Understanding positive and negative numbers on the number line
        • Topic B: Order and absolute value
        • Topic C: Rational numbers and the coordinate plane
      • Module 4: Expressions and equations
        • Topic A: Relationships of the operations
        • Topic B: Special notations of operations
        • Topic C: Replacing letters and numbers
        • Topic D: Expanding, factoring, and distributing expressions
        • Topic E: Expressing operations in algebraic form
        • Topic F: Writing and evaluating expressions and formulas
        • Topic G: Solving equations
        • Topic H: Applications of equations
      • Module 5: Area, surface area, and volume problems
        • Topic A: Area of triangles, quadrilaterals, and polygons
        • Topic B: Polygons on the coordinate plane
        • Topic C: Volume of right rectangular prisms
        • Topic D: Nets and surface area
      • Module 6: Statistics
        • Topic A: Understanding distributions
        • Topic B: Summarizing a distribution that is approximately symmetric using the mean and mean absolute deviation
        • Topic C: Summarizing a distribution that is skewed using the median and the interquartile range
        • Topic D: Summarizing and describing distributions
    • 7th grade (Eureka Math/EngageNY)
      • Module 1: Ratios and proportional relationships
        • Topic A: Proportional relationships
        • Topic B: Unit rate and constant of proportionality
        • Topic C: Ratios and rates involving fractions
        • Topic D: Ratios of scale drawings
      • Module 2: Rational numbers
        • Topic A: Addition and subtraction of integers and rational numbers
        • Topic B: Multiplication and division of integers and rational numbers
        • Topic C: Applying operations with rational numbers to expressions and equations
      • Module 3: Expressions and equations
        • Topic A: Use properties of operations to generate equivalent expressions
        • Topic B: Solve problems using expressions, equations, and inequalities
        • Topic C: Use equations and inequalities to solve geometry problems
      • Module 4: Percent and proportional relationships
        • Topic A: Finding the whole
        • Topic B: Percent problems including more than one whole
        • Topic C: Scale drawings
        • Topic D: Population, mixture, and counting problems involving percents
      • Module 5: Statistics and probability
        • Topic A: Calculating and interpreting probabilities
        • Topic B: Estimating probabilities
        • Topic C: Random sampling and estimating population characteristics
        • Topic D: Comparing populations
      • Module 6: Geometry
        • Topic A: Unknown angles
        • Topic B: Constructing triangles
        • Topic C: Slicing solids
        • Topic D: Problems involving area and surface area
        • Topic E: Problems involving volume
    • 8th grade (Eureka Math/EngageNY)
      • Module 1: Integer exponents and scientific notation
        • Topic A: Exponential notation and properties of integer exponents
        • Topic B: Magnitude and scientific notation
      • Module 2: The concept of congruence
        • Topic A: Definitions and properties of the basic rigid motions
        • Topic B: Sequencing the basic rigid motions
        • Topic C: Congruence and angle relationships
        • Topic D: The Pythagorean theorem
      • Module 3: Similarity
        • Topic A: Dilation
        • Topic B: Similar figures
        • Topic C: The Pythagorean theorem
      • Module 4: Linear equations
        • Topic A: Writing and solving linear equations
        • Topic B: Linear equations in two variables and their graphs
        • Topic C: Slope and equations of lines
        • Topic D: Systems of linear equations and their solutions
      • Module 5: Examples of functions from geometry
        • Topic A: Functions
        • Topic B: Volume
      • Module 6: Linear functions
        • Topic A: Linear functions
        • Topic B: Bivariate numerical data
        • Topic C: Linear and nonlinear models
        • Topic D: Bivariate categorical data
      • Module 7: Introduction to irrational numbers using geometry
        • Topic A: Square and cube roots
        • Topic B: Decimal expansions of numbers
        • Topic C: The Pythagorean theorem
        • Topic D: Applications of radicals and roots
    • Algebra I (Eureka Math/EngageNY)
      • Module 1: Relationships between quantities and reasoning with equations and their graphs
        • Topic A: Lessons 1-3: Piecewise, quadratic, and exponential functions
        • Topic A: Lessons 4-5: Analyzing graphs
        • Topic B: Lessons 6-7: Distributive, commutative, and associative properties
        • Topic B: Lesson 8: Adding and subtracting polynomials
        • Topic B: Lesson 8: Adding and subtracting polynomials with 2 variables
        • Topic B: Lesson 9: Multiplying monomials
        • Topic B: Lesson 9: Multiplying monomials by polynomials
        • Topic B: Lesson 9: Multiplying binomials
        • Topic C: Lessons 10-13: Solving Equations
        • Topic C: Lesson 14: Solving inequalities
        • Topic C: Lessons 15-16 Compound inequalities
        • Topic C: Lessons 17-19: Advanced equations
        • Topic C: Lesson 20: Solution sets to equations with two variables
        • Topic C: Lesson 21: Solution sets to inequalities with two variables
        • Topic C: Lesson 22: Solution sets to simultaneous equations
        • Topic C: Lesson 23: Solution sets to simultaneous equations
        • Topic C: Lesson 24: Applications of systems of equations and inequalities
        • Topic D: Creating equations to solve problems
      • Module 2: Descriptive statistics
        • Topic A: Lesson 1: Dot plots and histograms
        • Topic A: Lesson 1: Box plots and shape
        • Topic A: Lesson 2: Describing the center of a distribution
        • Topic A: Lesson 3: Estimating centers and interpreting the mean as a balance point
        • Topic B: Lesson 4: Summarizing deviations from the mean
        • Topic B: Lessons 5-6: Standard deviation and variability
        • Topic B: Lesson 7: Measuring variability for skewed distributions (interquartile range)
        • Topic B: Lesson 8: Comparing distributions
        • Topic C: Lessons 9-10: Bivariate categorical data
        • Topic C: Lesson 11: Conditional relative frequencies and association
        • Topic D: Lessons 12-13: Relationships between two numerical variables
        • Topic D: Lesson 14: Modeling relationships with a line
        • Topic D: Lessons 15-18: Residuals
        • Topic D: Lesson 19: Interpreting correlation
      • Module 3: Linear and exponential functions
        • Topic A: Lessons 1-3: Arithmetic sequence intro
        • Topic A: Lessons 1-3: Geometric sequence intro
        • Topic A: Lessons 1-3: Arithmetic sequence formulas
        • Topic A: Lessons 1-3: Geometric sequence formulas
        • Topic A: Lessons 4-6: Exponential growth
        • Topic A: Lesson 7: Exponential decay
        • Topic B: Lessons 8-12: Functions intro
        • Topic B: Lessons 8-12: Function domain and range
        • Topic B: Lessons 8-12: Recognizing functions
        • Topic B: Lesson 13: Interpreting the graph of a function
        • Topic B: Lesson 14: Linear and exponential Models—comparing growth rates
        • Topic C: Lesson 15: Piecewise functions
        • Topic C: Lessons 16-20: Graphing absolute value functions
        • Topic D: Using functions and graphs to solve problems
      • Module 4: Polynomial and quadratic expressions, equations, and functions
        • Topic A: Lessons 1-2: Factoring monomials
        • Topic A: Lessons 1-2: Common factor
        • Topic A: Lessons 1-2: Factoring binomials intro
        • Topic A: Lessons 3-4: Special forms
        • Topic A: Lessons 3-4: Factoring by grouping
        • Topic A: Lesson 5: The zero product property
        • Topic A: Lessons 6-7: Solving basic one-variable quadratic equations
        • Topic A: Lessons 8-10: Parabolas intro
        • Topic B: Lessons 11-13: Completing the square
        • Topic B: Lessons 14-15: The quadratic formula
        • Topic B: Lesson 16: Graphing quadratic equations from the vertex form
        • Topic B: Lesson 17: Graphing quadratic functions from the standard form
        • Topic C: Lessons 18-19: Translating graphs of functions
        • Topic C: Lessons 20-22: Scaling and transforming graphs
        • Topic C: Lessons 23–24: Modeling with quadratic functions
      • Module 5: A synthesis of modeling with equations and functions
        • Module 5: A synthesis of modeling with equations and functions
    • Geometry (Eureka Math/EngageNY)
      • Module 1: Congruence, proof, and constructions
        • Topic A: Basic constructions
        • Topic B: Lesson 6: Solve for unknown angles—angles and lines at a point
        • Topic B: Lesson 7: Solve for unknown angles—transversals
        • Topic B: Lesson 8: Solve for unknown angles—angles in a triangle
        • Topic B: Lessons 9-11: Unknown angle proofs
        • Topic C: Lesson 12: Transformations—The next level
        • Topic C: Lesson 13: Rotations
        • Topic C: Lesson 14: Reflections
        • Topic C: Lesson 15: Rotations, reflections, and symmetry
        • Topic C: Lesson 16: Translations
        • Topic C: Lessons 17-21: Applications of transformations
        • Topic D: Lessons 22-25: Congruence criteria
        • Topic D: Lessons 26-27: Triangle congruency proofs
        • Topic E: Proving properties of geometric figures
        • Topic F: Advanced constructions
        • Topic G: Axiomatic systems
      • Module 2: Similarity, proof, and trigonometry
        • Topic A: Scale drawings
        • Topic B: Dilations
        • Topic C: Lessons 12-14: Similarity intro
        • Topic C: Lessons 15-17: Triangle similarity
        • Topic C: Lessons 18-20: Similarity applications
        • Topic D: Applying similarity to right triangles
        • Topic E: Lessons 25-26: Trigonometry intro
        • Topic E: Lesson 27: Sine and cosine of complementary angles and special angles
        • Topic E: Lesson 34: Unknown angles
        • Topic E: Lessons 28-31: Trigonometry applications
        • Topic E: Lessons 32-33: Laws of sines and cosines
      • Module 3: Extending to three dimensions
        • Topic A: Area
        • Topic B: Lessons 5-9: Volume properties
        • Topic B: Lessons 10-13: Volume formulas
      • Module 4: Connecting algebra and geometry through coordinates
        • Topic A: Rectangular and triangular regions defined by inequalities
        • Topic B: Perpendicular and parallel lines in the Cartesian plane
        • Topic C: Perimeters and areas of polygonal regions in the Cartesian plane
        • Topic D: Partitioning and extending segments and parameterization of lines
      • Module 5: Circles with and without coordinates
        • Topic A: Central and inscribed angles
        • Topic B: Lessons 7-8: Angles and arcs
        • Topic B: Lessons 9-10: Arc length and sector area
        • Topic C: Secants and tangents
        • Topic D: Equations for circles and their tangents
        • Topic E: Cyclic quadrilaterals and Ptolemy’s theorem
    • Algebra II (Eureka Math/EngageNY)
      • Module 1: Polynomial, rational, and radical relationships
        • Topic A: Polynomials—from base ten to base X
        • Topic B: Lessons 12-13: Factorization
        • Topic B: Lesson 14: Graphing factored polynomials
        • Topic B: Lesson 15: Structure in graphs of polynomial functions
        • Topic B: Lessons 16-21: Remainder theorem and modeling
        • Topic C: Lessons 22-23: Simplifying rational expressions
        • Topic C: Lesson 24: Multiplying and dividing rational expressions
        • Topic C: Lesson 25: Adding and subtracting rational expressions
        • Topic C: Lessons 26-27: Rational equations
        • Topic C: Lessons 28-29: Radical equations
        • Topic C: Lesson 30: Linear systems in three variables
        • Topic C: Lesson 31: Systems of equations
        • Topic C: Lesson 32: Graphing systems of equations
        • Topic C: Lessons 33-35: Parabolas
        • Topic D: Lesson 37: Complex numbers intro
        • Topic D: Lesson 37: Complex number operations
        • Topic D: Lessons 38-40: Complex roots and the fundamental theorem of algebra
      • Module 2: Trigonometric functions
        • Topic A: Lessons 1-7: Unit circle definition of trig functions
        • Topic A: Lessons 8-10: Trigonometric graphs and radians
        • Topic B: Lesson 11: Graphing sinusoidal functions
        • Topic B: Lesson 11: Features of sinusoidal graphs
        • Topic B: Lessons 12-13: Modeling with sinusoidal functions
        • Topic B: Lesson 14: Graphing the tangent function
        • Topic B: Lessons 15-17: Trigonometric identities
      • Module 3: Exponential and logarithmic functions
        • Topic A: Lesson 1: Integer exponents
        • Topic A: Lesson 2: Scientific notation
        • Topic A: Lessons 3-6: Rational exponents
        • Topic B: Lessons 7-9: Logarithms intro
        • Topic B: Lessons 10-12: Logarithm properties
        • Topic B: Lesson 13: Changing the base
        • Topic B: Lessons 13-15: Logarithms and equations
        • Topic C: Lesson 16: Rational and Irrational Numbers
        • Topic C: Lessons 17-22: Graphs of exponential and logarithmic functions
        • Topic D: Lessons 23-24: Solving exponential models
        • Topic D: Lessons 25-28: Modeling with exponential functions
        • Topic E: Lesson 29: Geometric series
        • Topic E: Lesson 29: Arithmetic series
        • Topic E: Lessons 30-33: Series applications
      • Module 4: Inferences and conclusions from data
        • Topic A: Lesson 1: Chance experiments, sample spaces, and events
        • Topic A: Lessons 2-4: Two-way tables, conditional probability, and independence
        • Topic A: Lessons 5-7: Venn diagrams and probability rules
        • Topic B: Lesson 8: Distributions—Center, shape, and spread
        • Topic B: Lesson 9: Using a curve to model a data distribution
        • Topic B: Lessons 10-11: Normal distributions
        • Topic C: Lesson 12: Types of statistical studies
        • Topic C: Lesson 13: Using sample data to estimate a population characteristic
        • Topic C: Lessons 14-17: Sample proportions, sampling variability, margin of error
        • Topic C: Lessons 18-19: Sampling variability in the sample mean
        • Topic C: Lessons 20-22: Margin of error with sample means; evaluating reports with sample data
        • Topic D: Lesson 23: Experiments and the role of random assignment
        • Topic D: Lessons 24-27: Ruling out differences due to random assignment
        • Topic D: Lessons 28-29: Drawing a conclusion from an experiment
        • Topic D: Lesson 30: Evaluating reports based on data from an experiment
    • Precalculus (Eureka Math/EngageNY)
      • Module 1: Complex numbers and transformations
        • Topic A: Lessons 1-6: Complex numbers review
        • Topic A: Lessons 7-8: Complex number division
        • Topic B: Lessons 9-12: Distance and midpoint of complex numbers
        • Topic B: Lesson 13: Trigonometry and complex numbers
        • Topic B: Lessons 14-17: Multiplying and dividing complex numbers in polar form
        • Topic C: Lessons 18-19: Exploiting the connection to trigonometry
        • Topic C: Lessons 21-23: Transforming vectors with matrices
        • Topic C: Lesson 24: Matrix notation encompasses new transformations!
        • Topic C: Lesson 25: Properties of matrix addition
        • Topic C: Lesson 25: Properties of matrix multiplication
        • Topic C: Lessons 26-30: Matrix inverses
      • Module 2: Vectors and matrices
        • Topic A: Networks and matrices
        • Topic B: Linear transformations of planes and space
        • Topic C: Systems of linear equations
        • Topic D: Lessons 17-18: Vectors in the coordinate plane
        • Topic D: Lesson 19: Directed line segments and vectors
        • Topic D: Lessons 20: Vectors and stone bridges
        • Topic D: Lessons 21-22: Vectors and linear transformations
        • Topic D: Lessons 23-24: Why are vectors useful?
        • Topic E: First-person video games—projection matrices
      • Module 3: Rational and exponential functions
        • Topic A: Lesson 1: Solutions to polynomial equations
        • Topic A: Lessons 2-3: Roots of complex numbers
        • Topic A: Lessons 4-5: The binomial theorem
        • Topic A: Lessons 6-7: Ellipses
        • Topic A: Lesson 8: Hyperbolas
        • Topic A: Lesson 9: Volume and Cavalieri’s principle
        • Topic B: Lessons 10-11: Simplifying rational expressions
        • Topic B: Lessons 10-11: Multiplying & dividing rational expressions
        • Topic B: Lessons 10-11: Adding & subtracting rational expressions
        • Topic B: Lessons 12-13: End behavior and asymptotes of rational functions
        • Topic B: Lessons 14-15: Graphing rational functions
        • Topic B: Lessons 16-17: Function composition
        • Topic C: Lesson 18: Inverse functions
        • Topic C: Lesson 19: Restricting the domain
        • Topic C: Lessons 20-21: Inverse relationship of exponentials and logarithms
      • Module 4: Trigonometry
        • Topic A: Lessons 1-2: Special values and properties of trigonometric functions
        • Topic A: Lessons 3-4: Addition and subtraction formulas
        • Topic A: Lessons 5-6: Tangent lines and wave functions
        • Topic B: Trigonometry and triangles
        • Topic C: Inverse trigonometric functions
      • Module 5: Probability and statistics
        • Topic A: Lesson 1: The general multiplication rule
        • Topic A: Lesson 2: Counting rules—The fundamental counting principle and permutations
        • Topic A: Lesson 3: Counting rules—Combinations
        • Topic A: Lesson 4: Using permutations and combinations to compute probabilities
        • Topic B: Lessons 5-6: Discrete random variables
        • Topic B: Lessons 7-8: Expected value
        • Topic B: Lessons 9-12: Creating probability distributions
        • Topic C: Lessons 13-19: Applications of expected value and probability
    • 3rd grade foundations (Eureka Math/EngageNY)
      • Module 1: Foundations
        • Topic A, B, C, D, E, & F: Foundations
      • Module 2: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D & E: Foundations
      • Module 3: Foundations
        • Topic A, C, D, & E: Foundations
        • Topic B: Foundations
        • Topic F: Foundations
      • Module 4: Foundations
        • Topic A: Foundations
        • Topic B, C, & D: Foundations
      • Module 5: Foundations
        • Topic A, B, C, D, E, & F: Foundations
      • Module 6: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
      • Module 7: Foundations
        • Topic A, B, C, D, & E: Foundations
    • 4th grade foundations (Eureka Math/EngageNY)
      • Module 1: Foundations
        • Topic A & B: Foundations
        • Topic C: Foundations
        • Topic D, E, & F: Foundations
      • Module 2: Foundations
        • Topic A & B: Foundations
      • Module 3: Foundations
        • Topic A: Foundations
        • Topic B & C: Foundations
        • Topic D: Foundations
        • Topic E: Foundations
        • Topic F: Foundations
        • Topic G: Foundations
        • Topic H: Foundations
      • Module 4: Foundations
        • Topic A: Foundations
        • Topic C: Foundations
      • Module 5: Foundations
        • Topic A, D, & F: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic E: Foundations
        • Topic H: Foundations
      • Module 6: Foundations
        • Topic A: Foundations
        • Topic B, C, & D: Foundations
      • Module 7: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
    • 5th grade foundations (Eureka Math/EngageNY)
      • Module 1: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D & F: Foundations
        • Topic E: Foundations
      • Module 2: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
        • Topic E: Foundations
        • Topic F: Foundations
        • Topic G: Foundations
        • Topic H: Foundations
      • Module 3: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 4: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
        • Topic E: Foundations
        • Topic F: Foundations
        • Topic G: Foundations
      • Module 5: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 6: Foundations
        • Topic A: Foundations
        • Topic B & D: Foundations
        • Topic C: Foundations
        • Topic E: Foundations
    • 6th grade foundations (Eureka Math/EngageNY)
      • Module 1: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
      • Module 2: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 3: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
      • Module 4: Foundations
        • Topic A & D: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic E & F: Foundations
        • Topic G: Foundations
        • Topic H: Foundations
      • Module 5: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 6: Foundations
        • Topics A, B, C, & D: Foundations
    • 7th grade foundations (Eureka Math/EngageNY)
      • Module 1: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 2: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
      • Module 3: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
      • Module 4: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C & D: Foundations
      • Module 5: Foundations
        • Topic A, B, C, & D: Foundations
      • Module 6: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic D: Foundations
        • Topic E: Foundations
    • 8th grade foundations (Eureka Math/EngageNY)
      • Module 1: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
      • Module 2: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 3: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
      • Module 4: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
      • Module 5: Foundations
        • Topic A: Foundations
        • Topic B: Foundations
      • Module 6: Foundations
        • Topic A: Foundations
        • Topic B & C: Foundations
      • Module 7: Foundations
        • Topic A & B: Foundations
        • Topic C: Foundations
        • Topic D: Foundations
    • Mathematics I
      • Solving equations & inequalities
        • Linear equations with variables on both sides
        • Linear equations with parentheses
        • Analyzing the number of solutions to linear equations
        • Linear equations with unknown coefficients
        • Multi-step inequalities
        • Compound inequalities
      • Working with units
        • Rate conversion
        • Appropriate units
        • Word problems with multiple units
      • Linear equations & graphs
        • Two-variable linear equations intro
        • x-intercepts and y-intercepts
        • Slope
        • Horizontal & vertical lines
        • Intro to slope-intercept form
        • Graphing slope-intercept equations
        • Writing slope-intercept equations
        • Point-slope form
        • Standard form
        • Summary: Forms of two-variable linear equations
      • Functions
        • Evaluating functions
        • Inputs and outputs of a function
        • Functions and equations
        • Interpreting function notation
        • Introduction to the domain and range of a function
        • Determining the domain of a function
        • Recognizing functions
        • Maximum and minimum points
        • Intervals where a function is positive, negative, increasing, or decreasing
        • Interpreting features of graphs
        • Average rate of change
        • Average rate of change word problems
      • Linear word problems
        • Interpreting linear functions and equations
        • Comparing linear functions
        • Constructing linear models for real-world relationships
        • Linear models word problems
      • Systems of equations
        • Systems of equations overview
        • Introduction to systems of equations
        • Equivalent systems of equations and the elimination method
        • Solving systems of equations with substitution
        • Manipulating expressions with unknown variables
        • Number of solutions to systems of equations
        • Solving any system of linear equations
        • Systems of equations word problems
      • Inequalities (systems & graphs)
        • Checking solutions of two-variable inequalities
        • Graphing two-variable inequalities
        • Modeling with linear inequalities
      • Scatterplots
        • Creating and interpreting scatterplots
        • Estimating with trend lines
      • Data distributions
        • Displays of distributions
        • Summarizing center of distributions (central tendency)
        • Box and whisker plots
        • Comparing distributions
      • Two-way tables
        • Two-way frequency tables
        • Two-way relative frequency tables
      • Sequences
        • Introduction to arithmetic sequences
        • Constructing arithmetic sequences
        • Introduction to geometric sequences
        • Constructing geometric sequences
        • Modeling with sequences
        • General sequences
      • Rational exponents & radicals
        • Exponent properties review
        • Radicals
        • Rational exponents intro
        • Properties of exponents (rational exponents)
        • Advanced exponent & radical evaluation
        • Simplifying square roots
        • Simplifying radicals (higher-index roots)
      • Exponential growth & decay
        • Exponential vs. linear growth
        • Exponential expressions
        • Graphs of exponential growth
        • Exponential vs. linear growth over time
        • Exponential decay
        • Exponential functions from tables & graphs
      • Geometry transformations
        • Introduction to rigid transformations
        • Translations
        • Rotations
        • Reflections
        • Rigid transformations overview
        • Dilations
        • Properties & definitions of transformations
        • Symmetry
      • Congruence
        • Transformations & congruence
        • Triangle congruence
        • Theorems concerning triangle properties
        • Working with triangles
        • Theorems concerning quadrilateral properties
        • Proofs of general theorems that use triangle congruence
        • Constructing bisectors of lines & angles
      • Analytic geometry
        • Distance and midpoints
        • Dividing line segments
        • Problem solving with distance on the coordinate plane
        • Parallel & perpendicular lines on the coordinate plane
        • Equations of parallel & perpendicular lines
        • Coordinate plane proofs
    • Mathematics II
      • Absolute value & piecewise functions
        • Graphs of absolute value functions
        • Piecewise functions
      • Polynomials
        • Intro to polynomials
        • Adding & subtracting polynomials
        • Adding & subtracting polynomials: two variables
        • Multiplying monomials
        • Multiplying monomials by polynomials
        • Multiplying binomials
        • Multiplying binomials by polynomials
        • Special products of binomials
        • Polynomials word problems
        • Long division of polynomials
        • Synthetic division of polynomials
        • Practice dividing polynomials with remainders
      • Factorization
        • Introduction to factorization
        • Factoring monomials
        • Factoring polynomials by taking common factors
        • Evaluating expressions with unknown variables
        • Factoring quadratics intro
        • Factoring quadratics by grouping
        • Factoring polynomials with quadratic forms
        • Factoring quadratics: Difference of squares
        • Factoring quadratics: Perfect squares
        • Strategy in factoring quadratics
        • Factoring polynomials with special product forms
        • Polynomial Remainder Theorem
      • Quadratics
        • Parabolas intro
        • Quadratic factored form
        • Solving quadratics by taking square roots
        • Quadratic vertex form
        • Solving quadratics by factoring
        • Completing the square
        • The quadratic formula
        • Quadratic standard form
        • Features & forms of quadratic functions
        • Transforming parabolas
      • Irrational numbers
        • Irrational numbers
        • Sums & products of rational/irrational numbers
        • Proofs concerning irrational numbers
      • Complex numbers
        • What are the imaginary numbers?
        • What are the complex numbers?
        • The complex plane
        • Adding & subtracting complex numbers
        • Multiplying complex numbers
      • Exponential growth & decay
        • Equivalent forms of exponential expressions
        • Exponential equations: properties of exponents
        • Interpreting the rate of change of exponential models
        • Constructing exponential models according to rate of change
        • Advanced interpretation of exponential models
        • Distinguishing between linear and exponential growth
      • Modeling with algebra
        • Modeling with one-variable equations & inequalities
        • Manipulating formulas
      • Similarity
        • Definitions of similarity
        • Introduction to triangle similarity
        • Solving similar triangles
        • Angle bisector theorem
        • Solving problems with similar & congruent triangles
        • Solving modeling problems with similar & congruent triangles
      • Right triangles & trigonometry
        • Pythagorean theorem
        • Pythagorean theorem proofs
        • Pursuit of a Pythagorean proof (optional)
        • Special right triangles
        • Introduction to the trigonometric ratios
        • Solving for a side in a right triangle using the trigonometric ratios
        • Solving for an angle in a right triangle using the trigonometric ratios
        • Modeling with right triangles
        • Trigonometric ratios & similarity
        • Sine & cosine of complementary angles
      • Solid geometry
        • Solid geometry intro
        • Density
        • 2D vs. 3D objects
      • Circles
        • Circle basics
        • Arc measure
        • Arc length (degrees)
        • Introduction to radians
        • Arc length (radians)
        • Sectors
        • Inscribed angles
        • Inscribed shapes problem solving
        • Properties of tangents
        • Area of inscribed triangle
        • Constructing regular polygons inscribed in circles
        • Constructing circumcircles & incircles
        • Constructing a line tangent to a circle
      • Conic sections
        • Introduction to conic sections
        • Features of a circle
        • Standard equation of a circle
        • Expanded equation of a circle
        • Focus & directrix of a parabola
      • Probability
        • Probability basics
        • Counting with combinations
        • Probability with counting, permutations, combinations
        • Multiplication rule for independent events
        • Multiplication rule for dependent events
        • Addition rule for probability
        • Conditional probability
        • Simulation and randomness
        • Expected value
    • Mathematics III
      • Functions
        • Combining functions
        • Composing functions
        • Modeling situations by combining & composing functions
        • Shifting functions
        • Stretching functions
        • Introduction to inverses of functions
        • Finding inverse functions
        • Verifying that functions are inverses
        • Determining whether a function is invertible
      • Polynomials
        • Binomial theorem
        • Understanding the binomial theorem
        • Advanced polynomial factorization methods
        • Proving polynomial identities
        • Polynomial identities with complex numbers
        • Quadratic equations with complex numbers
        • Fundamental theorem of Algebra
        • Finding zeros of polynomials
        • Zeros of polynomials and their graphs
        • End behavior of polynomial functions
        • Graphs of polynomials
        • Introduction to symmetry of functions
        • Symmetry of polynomial functions
      • Radical relationships
        • Square-root equations
        • Extraneous solutions of radical equations
        • Cube-root equations
        • Domain of radical functions
        • Graphs of radical functions
      • Rational relationships
        • Simplifying rational expressions
        • Multiplying & dividing rational expressions
        • Adding & subtracting rational expressions
        • Nested fractions
        • Rational equations
        • Direct and inverse variation
        • End behavior of rational functions
        • Discontinuities of rational functions
        • Graphs of rational functions
        • Modeling with rational functions
      • Exponentials & logarithms
        • Introduction to logarithms
        • The constant e and the natural logarithm
        • Properties of logarithms
        • Change of base formula for logarithms
        • Exponential equations: logarithms
        • Solving exponential models
        • Graphs of exponential functions
        • Graphs of logarithmic functions
        • Logarithmic scale (optional)
      • Trigonometry
        • Law of sines
        • Law of cosines
        • Solving general triangles
        • Introduction to radians
        • Unit circle definition of sine, cosine, & tangent
        • Graphs of sine, cosine, & tangent
        • Basic trigonometric identities
        • Trigonometric values of special angles
        • Pythagorean identity
        • Introduction to amplitude, midline, & extrema of sinusoidal functions
        • Finding amplitude & midline from formula
        • Period of sinusoidal functions
        • Graphing sinusoidal functions
        • Constructing sinusoidal functions
      • Advanced equations & functions
        • Solving equations by graphing
        • Systems of quadratic equations
        • Interpreting the symmetry of algebraic models
        • Interpreting the end behavior of algebraic models
        • Interpreting the periodicity of algebraic models
        • Comparing features of functions
      • Series
        • Basic sigma notation
        • Finite arithmetic series
        • Finite geometric series
        • Finite geometric series applications
      • Study Design
        • Samples and surveys
        • Observational studies and experiments
      • Binomial probability
        • Binomial probability
      • Normal distributions
        • Normal distributions
    • Arithmetic (all content)
      • Addition and subtraction
        • Basic addition and subtraction
        • Making 10
        • Addition and subtraction word problems within 10
        • Addition and subtraction within 20
        • Word problems within 20
        • Word problems with "more" and "fewer"
        • Intro to addition with 2-digit numbers
        • Intro to subtraction with 2-digit numbers
        • Strategies for adding and subtracting within 100
        • Addition within 100
        • Subtraction within 100
        • Word problems within 100
        • Adding 1s, 10s, and 100s
        • Subtracting 1s, 10s, and 100s
        • Strategies for adding 2- and 3-digit numbers
        • Addition with regrouping within 1000
        • Subtraction with regrouping within 1000
        • Addition and subtraction missing value problems
        • Addition and subtraction greater than 1000
      • Multiplication and division
        • Multiplication intro
        • Multiplication facts
        • Properties of multiplication
        • Multiplying by tens
        • Multiplication by 10s, 100s, and 1000s
        • Multiplication: place value and area models
        • Multi-digit multiplication
        • Relating multiplication and division
        • Division intro
        • Division facts
        • Division problems that work out nicely
        • Division: place value and area
        • Multi-digit division (no remainders)
        • Remainders
        • Multi-digit division (remainders)
        • Multiplication and division word problems
      • Negative numbers
        • Intro to negative numbers
        • Number opposites
        • Absolute value
        • Intro to adding negative numbers
        • Intro to subtracting negative numbers
        • Adding & subtracting negative numbers
        • Adding & subtracting with negatives on the number line
        • Multiplying & dividing negative numbers
      • Fractions
        • Fractions intro
        • What fractions mean
        • Fractions on the number line
        • Fractions and whole numbers
        • Comparing fractions
        • Equivalent fractions 1
        • Equivalent fractions on the number line
        • Equivalent fractions 2
        • Common denominators
        • Decomposing fractions
        • Adding and subtracting fractions with like denominators
        • Mixed numbers
        • Adding and subtracting mixed numbers
        • Visually adding and subtracting fractions with unlike denominators
        • Adding and subtracting fractions with unlike denominators
        • Adding and subtracting mixed number with unlike denominators
        • Adding and subtracting fractions with unlike denominators word problems
        • Multiplying unit fractions and whole numbers
        • Multiplying whole numbers and fractions
        • Multiplication as scaling
        • Multiplying fractions
        • Multiplying mixed numbers
        • Multiplying fractions word problems
        • Fractions as division
        • Dividing unit fractions by whole numbers
        • Dividing whole numbers by unit fractions
        • Dividing fractions by fractions
        • Dividing fractions word problems
      • Decimals
        • Intro to decimals
        • Decimal place value intro
        • Decimals on the number line
        • Rewriting decimals as fractions
        • Adding decimals
        • Adding decimals: standard algorithm
        • Subtracting decimals
        • Subtracting decimals: standard algorithm
        • Adding and subtracting decimals word problems
        • Multiplying decimals
        • Multiplying decimals: standard algorithm
        • Dividing decimals
        • Dividing decimals: standard algorithm
        • Significant figures
    • Algebra (all content)
      • Introduction to algebra
        • Overview and history of algebra
        • Introduction to variables
        • Substitution and evaluating expressions
        • Evaluating expressions word problems
        • Writing algebraic expressions introduction
        • Introduction to equivalent algebraic expressions
        • Dependent & independent variables
        • Combining like terms
        • Interpreting linear expressions
        • Irrational numbers
        • Sums and products of rational and irrational numbers
        • Proofs concerning irrational numbers
        • Division by zero
        • Binary and hexadecimal number systems
      • Solving basic equations & inequalities (one variable, linear)
        • Algebraic equations basics
        • Why we do the same thing to both sides of an equation
        • One-step addition & subtraction equations
        • One-step multiplication & division equations
        • Two-steps equations intro
        • Two-step equation word problems
        • Linear equations with variables on both sides
        • Linear equations with parentheses
        • Analyzing the number of solutions to linear equations
        • Linear equations word problems
        • Linear equations with unknown coefficients
        • Old school equations with Sal
        • Introduction to inequalities with variables
        • One-step inequalities
        • Two-step inequalities
        • Multi-step inequalities
        • Compound inequalities
      • Linear equations, functions, & graphs
        • Two-variable linear equations intro
        • x-intercepts and y-intercepts
        • Slope
        • Horizontal & vertical lines
        • Intro to slope-intercept form
        • Graphing slope-intercept equations
        • Writing slope-intercept equations
        • Point-slope form
        • Standard form
        • Summary: Forms of two-variable linear equations
        • Interpreting linear functions and equations
        • Comparing linear functions
        • Constructing linear models for real-world relationships
        • Linear models word problems
      • Sequences
        • Introduction to arithmetic sequences
        • Constructing arithmetic sequences
        • Introduction to geometric sequences
        • Constructing geometric sequences
        • Modeling with sequences
        • General sequences
      • System of equations
        • Systems of equations overview
        • Introduction to systems of equations
        • Equivalent systems of equations and the elimination method
        • Solving systems of equations with substitution
        • Manipulating expressions with unknown variables
        • Number of solutions to systems of equations
        • Solving any system of linear equations
        • Systems of equations word problems
        • Solving equations by graphing (Algebra 2 level)
        • Systems with three variables
      • Two-variable inequalities
        • Checking solutions of two-variable inequalities
        • Constraining solutions of two-variable inequalities
        • Graphing two-variable inequalities
        • Modeling with linear inequalities
      • Functions
        • Evaluating functions
        • Inputs and outputs of a function
        • Functions and equations
        • Interpreting function notation
        • Introduction to the domain and range of a function
        • Determining the domain of a function
        • Recognizing functions
        • Piecewise functions
        • Maximum and minimum points
        • Intervals where a function is positive, negative, increasing, or decreasing
        • Interpreting features of graphs
        • Average rate of change
        • Average rate of change word problems
        • Combining functions
        • Composing functions (Algebra 2 level)
        • Shifting functions
        • Stretching functions
        • Modeling situations by combining and composing functions (Algebra 2 level)
        • Introduction to inverses of functions (Algebra 2 level)
        • Finding inverse functions (Algebra 2 level)
        • Verifying that functions are inverses (Algebra 2 level)
        • Determining whether a function is invertible (Algebra 2 level)
        • Determining the domain of advanced functions (Algebra 2 level)
        • Determining the range of a function (Algebra 2 level)
        • Graphing nonlinear piecewise functions (Algebra 2 level)
        • Interpreting the symmetry of algebraic models (Algebra 2 level)
        • Interpreting the end behavior of algebraic models (Algebra 2 level)
        • Interpreting the periodicity of algebraic models (Algebra 2 level)
        • Comparing features of functions (Algebra 2 level)
        • Two-variable functions
      • Absolute value equations, functions, & inequalities
        • Graphs of absolute value functions
        • Solving absolute value equations
        • Solving absolute value inequalities
      • Quadratic equations & functions
        • Parabolas intro
        • Quadratic factored form
        • Solving quadratics by taking square roots
        • Quadratic vertex form
        • Solving quadratics by factoring
        • Completing the square
        • The quadratic formula
        • Quadratic standard form
        • Features & forms of quadratic functions
        • Transforming parabolas
        • Systems of quadratic equations
        • Quadratic inequalities
      • Polynomial expressions, equations, & functions
        • Intro to polynomials
        • Adding & subtracting polynomials
        • Adding & subtracting polynomials: two variables
        • Multiplying monomials
        • Multiplying monomials by polynomials
        • Multiplying binomials
        • Special products of binomials
        • Multiplying binomials by polynomials
        • Polynomials word problems
        • Introduction to factorization
        • Factoring monomials
        • Factoring polynomials by taking common factors
        • Evaluating expressions with unknown variables
        • Factoring quadratics intro
        • Factoring quadratics by grouping
        • Factoring polynomials with quadratic forms
        • Factoring quadratics: Difference of squares
        • Factoring quadratics: Perfect squares
        • Strategy in factoring quadratics
        • Factoring polynomials with special product forms
        • Long division of polynomials
        • Synthetic division of polynomials
        • Practice dividing polynomials with remainders
        • Polynomial Remainder Theorem
        • Binomial theorem
        • Understanding the binomial theorem
        • Advanced polynomial factorization methods
        • Proving polynomial identities
        • Polynomial identities with complex numbers
        • Quadratic equations with complex numbers
        • Fundamental Theorem of Algebra
        • Finding zeros of polynomials
        • Zeros of polynomials and their graphs
        • End behavior of polynomial functions
        • Graphs of polynomials
        • Introduction to symmetry of functions
        • Symmetry of polynomial functions
      • Exponential & logarithmic functions
        • Exponent properties review
        • Radicals
        • Rational exponents intro
        • Properties of exponents (rational exponents)
        • Advanced exponent & radical evaluation
        • Simplifying square roots
        • Simplifying radicals (higher-index roots)
        • Radicals (miscellaneous videos)
        • Exponential vs. linear growth
        • Exponential expressions
        • Graphs of exponential growth
        • Exponential vs. linear growth over time
        • Exponential decay
        • Exponential functions from tables & graphs
        • Equivalent forms of exponential expressions
        • Solving exponential equations using properties of exponents
        • Introduction to rate of exponential growth and decay
        • Interpreting the rate of change of exponential models (Algebra 2 level)
        • Constructing exponential models according to rate of change (Algebra 2 level)
        • Advanced interpretation of exponential models (Algebra 2 level)
        • Distinguishing between linear and exponential growth (Algebra 2 level)
        • Introduction to logarithms (Algebra 2 level)
        • The constant e and the natural logarithm (Algebra 2 level)
        • Properties of logarithms (Algebra 2 level)
        • The change of base formula for logarithms (Algebra 2 level)
        • Logarithmic equations (Algebra 2 level)
        • Solving exponential equations with logarithms (Algebra 2 level)
        • Solving exponential models (Algebra 2 level)
        • Graphs of exponential functions (Algebra 2 level)
        • Graphs of logarithmic functions (Algebra 2 level)
        • Logarithmic scale (Algebra 2 level)
      • Radical equations & functions
        • Solving square-root equations
        • Extraneous solutions of radical equations
        • Solving cube-root equations
        • Domain of radical functions
        • Graphs of radical functions
      • Rational expressions, equations, & functions
        • Intro to rational expressions
        • Simplifying rational expressions
        • Multiplying & dividing rational expressions
        • Adding & subtracting rational expressions
        • Nested fractions
        • Solving rational equations
        • Direct and inverse variation
        • End behavior of rational functions
        • Discontinuities of rational functions
        • Graphs of rational functions
        • Modeling with rational functions
        • Rational inequalities
        • Partial fraction expansion
      • Trigonometric functions
        • Introduction to radians
        • The unit circle definition of sine, cosine, & tangent
        • The graphs of sine, cosine, & tangent
        • Basic trigonometric identities
        • Trigonometric values of special angles
        • Pythagorean identity
        • Introduction to amplitude, midline, & extrema of sinusoidal functions
        • Finding amplitude & midline of sinusoidal functions from their formulas
        • Period of sinusoidal functions
        • Graphing sinusoidal functions
        • Constructing sinusoidal functions
        • The inverse trigonometric functions
        • Solving basic sinusoidal equations
        • Solving advanced sinusoidal equations
        • Solving sinusoidal models
        • Introduction to the trigonometric angle addition identities
        • Using trigonometric identities to solve problems
        • Parametric equations
      • Algebraic modeling
        • Rate conversion
        • Appropriate units
        • Word problems with multiple units
        • Modeling with one-variable equations & inequalities
        • Manipulating formulas
      • Complex numbers
        • What are the imaginary numbers?
        • What are the complex numbers?
        • The complex plane
        • Adding & subtracting complex numbers
        • Multiplying complex numbers
        • Complex conjugates & dividing complex numbers
        • Absolute value & angle of complex numbers
        • Distance & midpoint of complex numbers
        • Polar form of complex numbers
        • Multiplying & dividing complex numbers in polar form
        • Challenging complex number problems
      • Conic sections
        • Introduction to conic sections
        • The features of a circle
        • Standard equation of a circle
        • Expanded equation of a circle
        • Center and radii of an ellipse
        • Foci of an ellipse
        • Focus and directrix of a parabola
        • Introduction to hyperbolas
        • Foci of a hyperbola
        • Hyperbolas not centered at the origin
        • Identifying conic sections from their expanded equations
        • Challenging conic section problems (IIT JEE)
      • Series & induction
        • Basic sigma notation
        • Arithmetic series
        • Geometric sequences
        • Finite geometric series
        • Finite geometric series applications
        • Advanced sigma notation
        • Infinite geometric series
        • Infinite geometric series applications
        • Deductive and inductive reasoning
        • Induction
      • Vectors
        • Vector basics
        • Magnitude of vectors
        • Scalar multiplication
        • Vector addition & subtraction
        • Combined vector operations
        • Unit vectors
        • Magnitude & direction form of vectors
        • Component form of vectors
        • Adding vectors in magnitude & direction form
        • Applications of vectors
      • Matrices
        • Introduction to matrices
        • Representing linear systems of equations with augmented matrices
        • Elementary matrix row operations
        • Row-echelon form & Gaussian elimination
        • Adding & subtracting matrices
        • Multiplying matrices by scalars
        • Properties of matrix addition & scalar multiplication
        • Multiplying matrices by matrices
        • Properties of matrix multiplication
        • Matrices as transformations
        • Determinant of a 2x2 matrix
        • Introduction to matrix inverses
        • Finding the inverse of a matrix using its determinant
        • Practice finding the inverses of 2x2 matrices
        • Determinants & inverses of large matrices
        • Solving equations with inverse matrices
        • Model real-world situations with matrices
    • Geometry (all content)
      • Lines
        • Lines, line segments, and rays
        • Measuring segments
        • Parallel and perpendicular
        • Points, lines, & planes
        • Geometric definitions
        • The golden ratio
      • Angles
        • Angle introduction
        • Measuring angles
        • Constructing angles
        • Angles in circles
        • Angle types
        • Vertical, complementary, and supplementary angles
        • Angles between intersecting lines
        • Sal's old angle videos
      • Shapes
        • Properties of shapes
        • Classifying geometric shapes
        • Angles with polygons
        • Geometric solids (3D shapes)
      • Triangles
        • Triangle types
        • Triangle angles
        • Triangle inequality theorem
        • Perpendicular bisectors
        • Angle bisectors
        • Medians & centroids
        • Altitudes
        • Bringing it all together
      • Quadrilaterals
        • Quadrilateral types
        • Quadrilateral proofs & angles
      • Coordinate plane
        • Coordinate plane: quadrant 1
        • Coordinate plane: 4 quadrants
        • Quadrants on the coordinate plane
        • Reflecting points on coordinate plane
        • Quadrilaterals on the coordinate plane
        • Drawing polygons in the coordinate plane
      • Area and perimeter
        • Count unit squares to find area
        • Area of rectangles
        • Perimeter
        • Area of parallelograms
        • Area of triangles
        • Area of shapes on grids
        • Area of trapezoids & composite figures
        • Area and circumference of circles
        • Advanced area with triangles
      • Volume and surface area
        • Volume of rectangular prisms
        • Volume with fractions
        • Surface area
        • Volume of cones, cylinders, and spheres
        • Solid geometry
        • Surface and volume density
        • Cross sections of 3D objects
        • Koch snowflake fractal
        • Heron's formula
      • Pythagorean theorem
        • Pythagorean theorem
        • Pythagorean theorem application
        • Pythagorean theorem and distance between points
        • Pythagorean theorem proofs
      • Transformations
        • Introduction to rigid transformations
        • Translations
        • Rotations
        • Reflections
        • Rigid transformations overview
        • Dilations
        • Properties and definitions of transformations
        • Symmetry
        • Old transformations videos
      • Congruence
        • Transformations and congruence
        • Triangle congruence
        • Theorems concerning triangle properties
        • Working with triangles
        • Theorems concerning quadrilateral properties
        • Proofs of general theorems that use triangle congruence
      • Similarity
        • Definitions of similarity
        • Introduction to triangle similarity
        • Solving similar triangles
        • Angle bisector theorem
        • Solving problems with similar and congruent triangles
        • Solving modeling problems with similar and congruent triangles
      • Trigonometry
        • Special right triangles
        • Introduction to the trigonometric ratios
        • Solving for a side in a right triangle using the trigonometric ratios
        • Solving for an angle in a right triangle using the trigonometric ratios
        • Modeling with right triangles
        • Trigonometric ratios and similarity
        • Sine and cosine of complementary angles
        • The reciprocal trigonometric ratios
        • The law of sines
        • The law of cosines
        • Solving general triangles
      • Circles
        • Circle basics
        • Arc measure
        • Arc length (degrees)
        • Introduction to radians
        • Arc length (radians)
        • Sectors
        • Inscribed angles
        • Inscribed shapes problem solving
        • Properties of tangents
        • Area of inscribed triangle
        • Standard equation of a circle
        • Expanded equation of a circle
      • Analytic geometry
        • Distance and midpoints
        • Dividing line segments
        • Problem solving with distance on the coordinate plane
        • Parallel and perpendicular lines on the coordinate plane
        • Equations of parallel and perpendicular lines
        • Challenge: Distance between a point and a line
      • Geometric constructions
        • Constructing bisectors of lines and angles
        • Constructing regular polygons inscribed in circles
        • Constructing circumcircles and incircles
        • Constructing a line tangent to a circle
      • Miscellaneous
        • Worked examples
    • Calculus (all content, first year)
      • Limits and continuity
        • Limits introduction
        • Limits from tables
        • Limits from graphs
        • One-sided limits
        • Formal definition of limits (epsilon-delta)
        • Review: Limits basics
        • Continuity at a point
        • Limits of combined and composite functions
        • Continuous functions
        • Intermediate value theorem
        • Review: Continuity
        • Limits from equations (direct substitution)
        • Limits from equations (factoring & rationalizing)
        • Squeeze theorem
        • Limits of trigonometric functions
        • Limits of piecewise functions
        • Removable discontinuities
        • Review: Limits from equations
        • Unbounded limits (vertical asymptotes)
        • Limits at infinity (horizontal asymptotes)
        • Review: Infinite limits
        • Limits skill checks
      • Taking derivatives
        • Introduction to differential calculus
        • Derivative as slope of tangent line
        • Derivative as instantaneous rate of change
        • Secant lines
        • Derivative as a limit
        • Formal definition of derivative
        • Using the formal definition of derivative
        • Differentiability
        • Derivative as a function
        • Review: Derivative basics
        • Basic differentiation rules
        • Power rule
        • Polynomial functions differentiation
        • Rational functions differentiation (intro)
        • Radical functions differentiation (intro)
        • Sine & cosine derivatives
        • eˣ and ln(x) derivatives
        • Review: Basic differentiation
        • Product rule
        • Chain rule
        • Chain rule proof
        • Quotient rule
        • Review: Product, quotient, & chain rule
        • Rational functions differentiation
        • Radical functions differentiation
        • Trigonometric functions differentiation
        • Exponential functions differentiation
        • Logarithmic functions differentiation
        • Derivatives capstone
        • Implicit differentiation introduction
        • Implicit differentiation (advanced examples)
        • Inverse trig functions differentiation
        • Derivatives of inverse functions
        • Disguised derivatives
        • Proofs for the derivatives of eˣ and ln(x)
        • Logarithmic differentiation
        • Parametric & vector-valued function differentiation
        • Review: Advanced differentiation
        • Higher-order derivatives
        • Higher-order derivatives (parametric & vector-valued functions)
        • Taking derivatives skill checks
        • Polar curve differentiation
      • Derivative applications
        • Critical points
        • Increasing & decreasing intervals
        • Relative minima & maxima
        • Absolute minima & maxima
        • Review: Increasing/decreasing intervals & extrema
        • Concavity
        • Points of inflection
        • Sketching graphs using calculus
        • Review: Concavity & points of inflection
        • Linear approximation
        • Rectilinear motion
        • Planar motion
        • Related rates
        • Optimization
        • Applied rates of change
        • Mean value theorem
        • L'Hôpital's rule
        • Review: Derivative applications
        • Derivative applications skill check
      • Integration
        • Antiderivatives
        • Indefinite integrals intro
        • Indefinite integrals of common functions
        • Review: Indefinite integrals & antiderivatives
        • Definite integral as area
        • Definite integral properties
        • Review: Definite integral basics
        • Riemann sums
        • Riemann sums with sigma notation
        • Trapezoidal rule
        • Definite integral as the limit of a Riemann sum
        • Review: Riemann sums
        • Functions defined by integrals
        • Fundamental theorem of calculus
        • Fundamental theorem of calculus: chain rule
        • Definite integral evaluation
        • Definite integrals of piecewise functions
        • Improper integrals
      • Integration techniques
        • Integration by parts
        • u-substitution
        • Reverse chain rule
        • Partial fraction expansion
        • Integration using trigonometric identities
        • Trigonometric substitution
      • Integration applications
        • Area between curves
        • Area defined by polar graphs
        • Arc length
        • Arc length of polar graphs
        • Average value of a function
        • Area & net change
        • Rectilinear motion (integral calc)
        • Solids with known cross sections
        • Disc method
        • Washer method
        • Shell method
      • Series
        • Sequences review
        • Infinite sequences
        • Series review
        • Finite geometric series
        • Partial sums
        • Infinite geometric series
        • Series basics challenge
        • Basic convergence tests
        • Comparison tests
        • Ratio & alternating series tests
        • Estimating infinite series
        • Power series intro
        • Taylor & Maclaurin polynomials intro
        • Maclaurin series of sin(x), cos(x), and eˣ
        • Power series function representation
        • Challenge series exercises
      • AP Calculus practice questions
        • AP Calculus AB questions
        • AP Calculus BC questions
    • Math for fun and glory
      • Doodling in Math and more
        • Spirals, Fibonacci and being a plant
        • Doodling in math
        • Hexaflexagons
        • About pi and tau
        • Singing (and noises)
        • Mobius strips
        • Thanksgiving math
        • Infinity . . .
        • Other cool stuff
      • Puzzles
        • Brain teasers
        • Transformation Puzzles
        • Lights Puzzles
      • AMC 10
        • 2013 AMC 10 A
      • AIME
        • 2003 AIME
      • Math warmups
        • Expectation warmup
        • Random sampling warmup
        • Distribution warmup
        • Arithmetic warmups
    • Class 8 (India)
      • Rational numbers
        • Introduction to rational numbers
      • Linear equations in one variable
        • Solving equations with linear expressions on one side and numbers on the other
        • Some applications
        • Solving linear equations with variables on both sides
        • Reducing equations to simpler form
        • Some more applications
        • Algebraic equations review
      • Understanding quadrilaterals
        • Polygons
        • Sum of the measures of the exterior angles of a polygon
        • Kinds of quadrilaterals
        • Quadrilateral proofs & angles
      • Data handling
        • Organizing data
        • Grouping Data
        • Circle Graphs or Pie Charts
        • Chance and Probability
      • Squares and square roots
        • Squares
        • Square roots
        • Estimating square roots
      • Cubes and cubes roots
        • Cube roots
      • Algebraic expressions and identities
        • What are expressions?
        • Addition and subtraction of algebraic expressions
        • Multiplying a monomial by a monomial
        • Multiplying a monomial by a polynomial
        • Multiplying a polynomial by a polynomial
        • Standard identities
      • Visualising solid shapes
        • Mapping space around us
      • Mensuration
        • Let us recall
        • Area of a trapezium
        • Area of general quadrilaterals
        • Area of polygons
        • Surface area
        • Volume of cube, cuboid, and cylinder
      • Exponents and powers
        • Powers with negative exponents
        • Laws of exponents
        • Use of Exponents to Express Small Numbers in Standard Form
      • Direct and inverse proportions
        • Direct and inverse proportions
      • Factorization
        • Introduction to factorization
        • Factoring polynomials by taking common factors
        • Factoring quadratics 1
        • Factoring quadratics using identities: Difference of squares
        • Factoring quadratics using identities: Perfect squares
        • Factoring quadratics by grouping
      • Introduction to graphs
        • Bar graphs and histograms review
        • Linear graphs
        • Intro to the coordinate plane
        • Coordinate plane word problems
        • Dependent & independent variables
        • Some applications
      • Playing with numbers
        • Numbers in general form
        • Tests of divisibility
    • Math - Indian curriculum
    • 1ère primaire
      • Nombres
        • Plus grand ….plus petit… comparaison de quantités
        • Les symboles égal ou pas égal
        • L'ordinalité
        • Dénombrer la quantité 1 à 5
        • Additions et soustractions de 1 à 5
        • Décomposer et recomposer les nombres de 1à 5 (ex : 5 c'est 1+1+3 ou 5 c'est 2 +2+1)
        • Reconnaître et ordonner des quantités jusque 10
        • Additionner et soustraire jusqu'à 10
        • L'arbre de 10
        • Découverte de la multiplication
        • Décomposition additive de nombre plus grands que 10
        • La découverte de la division
        • Ordonner des nombres jusque 20
        • Additionner soustraire jusque 20
      • Solides et figures
        • Situer ma position
        • Reconnaitre des figures
      • Grandeurs
        • Comparaison : plus petit, plus grand
      • Traitement de données
        • Le tableau à double entrée
        • Opérations habillées sur l'addition et la soustraction
    • 2ème primaire
      • Nombres
        • Révisions additions
        • Additions de dizaines (D+D)
        • Comptage par 10
        • Les tables de multiplication de 2 à 9
        • Valeur et position des chiffres dans un nombre à 2 chiffres
        • Les nombres 25 et 42
        • D + U = DU U +D = DU (sans passage de la dizaine)
        • D-U (sans passage de la dizaine)
        • Du +Du =D
        • DU-DU ou U (avec passage)
        • DU+U/U+DU/DU+U
        • DU + DU(avec passage)
        • DU-DU = D, DU-DU=DU(avec passage)
        • Soustraire avec 2 nombres ou plus
        • Introduction à la multiplication
        • Table de 2 de division
        • Table de division
        • Initiation aux fractions
        • Divisions avec reste (ex : 37 : 5 = 7 reste 2)
        • Classement des nombres jusque 100
      • Solides et figures
        • Reconnaître et comparer des solides
      • Traitement de données
        • Opérations habillées pour l'addition
        • Opérations habillées pour la soustraction
        • Additions ET soustractions habillées
    • 3ème primaire
      • Nombres
        • Révisions signe =
        • Ecrire et lire les nombres de 0 à 1000
        • Les classer dans un abaque (CDU et MCDU)
        • Situer des nombres de 0 à 100 sur une droite graduée
        • Décomposition des nombres 100 et 1000
        • Multiplier et diviser par 10, 100 et 1000
        • Addition écrite sans et avec report (nombres à deux et trois chiffres)
        • Soustraction écrite (avec emprunt/compensation, nombres à deux et trois chiffres)
        • Multiplication écrite sans/avec une retenue (multiplicateur à un chiffre)
        • Division écrite (diviseur à un chiffre)
        • Calcul mental : addition et soustraction avec compensation
        • Calcul mental : addition et soustraction avec décomposition
      • Solides et figures
        • Droite, ½ droite, segment
        • Droites parallèles, sécantes, perpendiculaires
        • Tracer et mesurer des segments
        • Notion d’angle ; angles droits, aigus, obtus
        • Tracer des angles
        • Connaître le vocabulaire (faces, arêtes, sommets) des solides
        • Classement des triangles selon la longueur des côtés et les amplitudes d’angles
        • Distinguer les polygones des non polygones
      • Grandeurs
        • Lire les heures et les ½ heures
        • Mesurer des durées (heures et minutes)
        • Mesurer des longueurs et conversion via abaque (cm, dm, m, dam, hm, km)
        • Mesurer des capacités (litre et fractions simples - ½, ¼-du litre, dl, cl)
        • Mesurer des masses (kg, ½ kg, ¼ kg, g, t)
        • Proportionnalité directe simple (multiplier les ingrédients dans une recette ou calculer l’échelle d’un plan ; x 4, : 4, p ex)
      • Traitement de données
        • Dans un problème : sélectionner les informations utiles et organiser ces informations
        • Manipuler les € dans des achats
        • Lecture et construction de graphiques (températures, par exemple)
        • Lecture d’un tableau à double entrée (programmes TV, par exemple)
    • 4ème primaire
      • Nombres
        • Ecrire et lire les nombres jusqu’à 100000
        • Nombres décimaux (jusqu’à deux chiffres après la virgule)
        • Ecriture décimale des nombres fractionnaires dont le dénominateur est 10 ou 100
        • Placer des fractions ou des nombres décimaux sur une droite graduée
        • Diviseurs et multiples
        • Critères de divisibilité par 2, 4, 5, 10, 25 et 100
        • Addition, soustraction écrites avec des nombres jusqu’à 100000
        • Multiplication, division écrites avec deuxième facteur à 2 ou 3 chiffres
        • Calcul mental : multiplication avec décomposition
        • Commutativité, associativité, distributivité
      • Solides et figures
        • Caractéristiques des quadrilatères (carré, rectangle, losange, parallélogramme et trapèze)
        • Se repérer, se déplacer sur un quadrillage : introduction des coordonnées
        • Symétrie orthogonale : l’axe de symétrie d’une figure
      • Grandeurs
        • Mesurer des durées (heures, minutes et introduction de la seconde)
        • Utilisation du rapporteur
        • Aire d'un triangle
        • Proportionnalité directe simple : la règle de 3
        • Fractions inférieures/supérieures à 1
        • Fraction d’un nombre (Ex : ½ de 8) – multiplier une fraction par un nombre
        • Fractions équivalentes (suite) : passer d’une fraction réductible à son équivalent irréductible
        • Représentations semi-abstraites des fractions (bandelettes, disque,…)
        • Addition et soustraction de deux fractions ayant même dénominateur
        • Introduction aux pourcentages (représentation sur des quadrillages 10 x 10, relation avec fraction ayant un dénominateur égal à 100, calcul de ristournes)
      • Traitement de données
        • Introduction aux histogrammes et tableaux à double entrée et graphes
    • 5ème primaire
      • Nombres
        • Ecriture décimale des nombres fractionnaires
        • Décomposition d’un nombre en produits de facteurs premiers
        • Critères de divisibilité par 3, 9, 8, 125, 1000
        • Comparaison de nombres décimaux
        • Addition, soustraction, multiplication et division écrites avec des nombres décimaux
      • Solides et figures
        • Caractéristiques de l’octogone
      • Grandeurs
        • Comparaison de fractions (même numérateur/même dénominateur)
      • Traitement de données
        • Introduction aux graphiques circulaires
    • 6ème primaire
      • Nombres
        • Priorité des opérations
        • Le PGCD et le PPCM
        • Introduction à la notion de division
        • Quotients multiples de 10
        • Introduction à la division avec reste non nul
        • Introduction aux longues divisions
        • Problèmes avec des multiplications ou des divisions
        • Addition des nombres décimaux
        • Soustraire des nombres décimaux
        • Soustraire des nombres décimaux-Exemple 2
        • Additionner ou soustraire des nombres décimaux dans un exercice concret
        • Multiplier un nombre entier par un nombre décimal
        • Poser une multiplication de nombres décimaux
        • Pousser la division après la virgule
        • Exercices : Diviser des nombres décimaux
      • Grandeurs
        • Première approche de la notion d'aire
        • Le périmètre
        • L'aire du rectangle
        • Calculs d'aires et distributivité de la multiplication sur l'addition
        • Aire et périmètre
        • Aire d'un triangle
        • Rayon, diamètre et circonférence d'un cercle
        • L'aire d'un étrange quadrilatère
        • Volume, aire, longueur: comment mesure-t-on ?
        • Des volumes et des fractions
      • Traitement de données
        • Intérêt, taux, capital
        • Les différents types de diagrammes - révision
  • Science
    • Physics
      • One-dimensional motion
        • Skill check for one-dimensional motion
        • Introduction to physics
        • Displacement, velocity, and time
        • Acceleration
        • Kinematic formulas and projectile motion
        • Old videos on projectile motion
      • Two-dimensional motion
        • Skill check for two-dimensional motion
        • Two-dimensional projectile motion
        • Optimal angle for a projectile
      • Forces and Newton's laws of motion
        • Skill check for Forces and Newton's Laws of motion
        • Newton's laws of motion
        • Normal force and contact force
        • Balanced and unbalanced forces
        • Slow sock on Lubricon VI
        • Inclined planes and friction
        • Tension
        • Treating systems
      • Centripetal force and gravitation
        • Skill check for centripetal force and gravitation
        • Circular motion and centripetal acceleration
        • Centripetal forces
        • Newton's law of gravitation
      • Work and energy
        • Skill check for work and energy
        • Work and energy
        • Springs and Hooke's law
        • Mechanical advantage
      • Impacts and linear momentum
        • Skill check for Impacts and linear momentum
        • Momentum and Impulse
        • Elastic and inelastic collisions
        • Center of mass
      • Torque and angular momentum
        • Skill check: Moments, torque, and angular momentum
        • Rotational kinematics
        • Torque, moments, and angular momentum
      • Oscillations and mechanical waves
        • Skill check: Oscillations and mechanical waves
        • Simple harmonic motion
        • Simple harmonic motion (with calculus)
        • Introduction to mechanical waves
        • Sound
        • The Doppler effect
        • Wave interference
      • Fluids
        • Skill check for fluids
        • Density and Pressure
        • Buoyant Force and Archimedes' Principle
        • Fluid Dynamics
      • Thermodynamics
        • Skill check for thermodynamics
        • Temperature, kinetic theory, and the ideal gas law
        • Specific heat and heat transfer
        • Laws of thermodynamics
      • Electric charge, field, and potential
        • Skill check: Electric charge, field, and electric potential
        • Charge and electric force (Coulomb's law)
        • Electric field
        • Electric potential energy, electric potential, and voltage
      • Circuits
        • Skill Check: Circuits
        • Ohm's law and circuits with resistors
        • Circuits with capacitors
      • Magnetic forces, magnetic fields, and Faraday's law
        • Skill check for Magnetic fields, forces, and Faraday's law
        • Magnets and Magnetic Force
        • Magnetic field created by a current
        • Electric motors
        • Magnetic flux and Faraday's law
      • Electromagnetic waves and interference
        • Skill Check: Electromagnetic waves and interference
        • Introduction to electromagnetic waves
        • Interference of electromagnetic waves
      • Geometric optics
        • Skill check: Geometric optics
        • Reflection and refraction
        • Mirrors
        • Lenses
      • Special relativity
        • Michelson and Morley's luminiferous ether experiment
        • Minkowski spacetime
        • Lorentz transformation
        • Einstein velocity addition
      • Quantum Physics
        • Photons
        • Atoms and electrons
        • Quantum numbers and orbitals
        • Nuclei
      • Discoveries and projects
        • Discovery of magnetism
        • Discovery of magnetic fields
        • Measuring magnetic fields
        • Discovery of batteries
        • Discovery of electromagnetism
        • Discovery of resistors
        • Electric motor
        • Electrostatics
        • Projectile launcher
        • Thermo can
        • Simple machines explorations
      • Review for AP Physics 1 exam
        • AP Physics 1 concept review
        • AP Physics 1 free response questions 2015
    • AP Physics 1
      • One-dimensional motion
        • Introduction to physics
        • Displacement, velocity, and time
        • Acceleration
        • Kinematic formulas and projectile motion
        • Old videos on projectile motion
      • Two-dimensional motion
        • Two-dimensional projectile motion
        • Optimal angle for a projectile
      • Forces and Newton's laws of motion
        • Newton's laws of motion
        • Normal force and contact force
        • Balanced and unbalanced forces
        • Slow sock on Lubricon VI
        • Inclined planes and friction
        • Tension
        • Treating systems
      • Centripetal force and gravitation
        • Circular motion and centripetal acceleration
        • Centripetal forces
        • Newton's law of gravitation
      • Work and energy
        • Work and energy
        • Springs and Hooke's law
        • Mechanical advantage
      • Impacts and linear momentum
        • Momentum and Impulse
        • Elastic and inelastic collisions
        • Center of mass
      • Torque and angular momentum
        • Rotational kinematics
        • Torque, moments, and angular momentum
      • Oscillations and mechanical waves
        • Simple harmonic motion
        • Simple harmonic motion (with calculus)
        • Introduction to mechanical waves
        • Sound
        • The Doppler effect
        • Wave interference
      • Electric charge, field, and potential
        • Charge and electric force (Coulomb's law)
        • Electric field
        • Electric potential energy, electric potential, and voltage
      • Circuits
        • Ohm's law and circuits with resistors
        • Circuits with capacitors
      • Review for AP Physics 1 exam
        • AP Physics 1 concept review
        • AP Physics 1 free response questions 2015
    • AP Physics 2
      • Fluids
        • Density and Pressure
        • Buoyant Force and Archimedes' Principle
        • Fluid Dynamics
      • Thermodynamics
        • Temperature, kinetic theory, and the ideal gas law
        • Specific heat and heat transfer
        • Laws of thermodynamics
      • Electric charge, field, and potential
        • Charge and electric force (Coulomb's law)
        • Copy of Electric field
        • Electric potential energy, electric potential, and voltage
      • Magnetic forces, magnetic fields, and Faraday's law
        • Magnets and Magnetic Force
        • Magnetic field created by a current
        • Electric motors
        • Magnetic flux and Faraday's law
      • Electromagnetic waves and interference
        • Introduction to electromagnetic waves
        • Interference of electromagnetic waves
      • Geometric optics
        • Reflection and refraction
        • Mirrors
        • Lenses
      • Quantum Physics
        • Photons
        • Atoms and electrons
        • Quantum numbers and orbitals
        • Nuclear physics
    • Class 11 Physics (India)
      • Physical world
        • Physics and its laws
      • Units and measurement
        • Physical quantities and their measurement
        • Scientific notation
        • Significant figures
      • Basic math concepts for physics (Prerequisite)
        • Introduction to logarithms
        • The constant e and the natural logarithm
        • Slope
        • Basics of trigonometry
        • The unit circle definition of sine, cosine, and tangent
        • The graphs of sine, cosine, and tangent
        • Basic trigonometric identities
        • Evaluating functions
        • Inputs and outputs of a function
        • Maximum and minimum points
        • Intervals where a function is positive, negative, increasing, or decreasing
        • Interpreting features of graphs
      • Differentiation for physics (Prerequisite)
        • Slope
        • Introduction to differential calculus
        • Secant lines
        • Limit basics
        • Derivative as a limit
        • Using the formal definition of derivative
        • Derivative as a function
        • Basic differentiation rules
        • Power rule
        • Polynomial functions differentiation
        • Sine & cosine derivatives
        • Product rule
        • Chain rule
      • Integration for physics (Prerequisite)
        • Antiderivatives
        • Indefinite integrals of common functions
        • Definite integral as area
        • Riemann sums
        • Definite integral evaluation
        • u-substitution
        • Area & net change
      • Motion in a straight line
        • Skill check for one-dimensional motion
        • Displacement, velocity, and time
        • Acceleration
        • Kinematic formulas and projectile motion
        • Rectilinear motion (integral calc)
      • Vectors (Prerequisite)
        • Vector basics
        • Magnitude of vectors
        • Scalar multiplication
        • Vector addition and subtraction
        • Combined vector operations
        • Unit vectors
        • Magnitude and direction form of vectors
        • Component form of vectors
        • Adding vectors in magnitude and direction form
        • Applications of vectors
      • Motion in a plane
        • Skill check for two-dimensional motion
        • Two-dimensional projectile motion
        • Review: Unit vectors
        • Optimal angle for a projectile
        • Circular motion and centripetal acceleration
      • Laws of motion
        • Skill check for Forces and Newton's Laws of motion
        • Newton's laws of motion
        • Impulse, momentum and Newton's second law
        • Normal force and contact force
        • Balanced and unbalanced forces
        • Slow sock on Lubricon VI
        • Inclined planes and friction
        • Tension
        • Treating systems
        • Centripetal forces
      • Work, energy and power
        • Skill check for work and energy
        • Work and energy
        • Conservative and non conservative forces
        • Springs and Hooke's law
        • Power
        • Elastic and inelastic collisions
      • System of particles and rotational motion
        • Skill check: Moments, torque, and angular momentum
        • Centre of mass
        • Cross product
        • Rotational kinematics
        • Torque, moments, and angular momentum
      • Gravitation
        • Newton's law of gravitation
      • Mechanical properties of fluid
        • Skill check for fluids
        • Density and pressure
        • Buoyant force and Archimedes' principle
        • Fluid dynamics
        • Viscosity
        • Surface tension
      • Thermal properties of matter
        • Skill check for thermodynamics
        • Temperature, kinetic theory, and the ideal gas law
        • Specific heat and heat transfer
      • Thermodynamics
        • Zeroth and first law of thermodynamics
        • Work from PV graph and internal energy
        • Thermodynamic processes and Carnot cycle
      • Kinetic theory
        • Ideal gas equation
        • Kinetic molecular theory of gases
      • Oscillations
        • Simple harmonic motion
        • Simple harmonic motion (with calculus)
      • Waves
        • Skill check: Oscillations and mechanical waves
        • Introduction to mechanical waves
        • Sound
        • The Doppler effect
        • Wave interference
    • Class 12 Physics (India)
      • Electric charges and field
        • Skill check: Electric charge, field, and electric potential
        • Charge and electric force (Coulomb's law)
        • Electric field
      • Electrostatic potential and capacitance
        • Electric potential energy, electric potential, and voltage
        • Circuits with capacitors
      • Current electricity
        • Skill Check: Circuits
        • Electric current and voltage
        • Ohm's law and power
        • Circuit networks
      • Moving charges and magnetism
        • Skill check for Magnetic fields, forces, and Faraday's law
        • Cross product (Prerequisite)
        • Magnets and magnetic force
        • Magnetic field created by a current
        • Electric motors
      • Electromagnetic induction
        • Magnetic flux and Faraday's law
      • Electromagnetic waves
        • Introduction to electromagnetic waves
      • Ray optics and optical instruments
        • Skill check: Geometric optics
        • Reflection and refraction
        • Mirrors
        • Lenses
      • Wave optics
        • Skill Check: Electromagnetic waves and interference
        • Introduction to electromagnetic waves
        • Interference of electromagnetic waves
      • Dual nature of radiation and matter
        • Photons
      • Atoms
        • History of atomic structure
        • Atoms and electrons
      • Nuclei
        • Nuclear physics
        • Half life and decay rate
    • Chemistry
      • Atoms, compounds, and ions
        • Skill check for atoms, compounds, and ions
        • Introduction to the atom
        • Ions and compounds
        • Names and formulas of ionic compounds
        • Mass spectrometry
      • Chemical reactions and stoichiometry
        • Skill check for chemical reactions and stoichiometry
        • Balancing chemical equations
        • Stoichiometry
        • Limiting reagent stoichiometry
        • Molecular composition
        • Types of chemical reactions
      • Electronic structure of atoms
        • Skill checks for electronic structure of atoms
        • History of atomic structure
        • Bohr's model of the hydrogen atom
        • Quantum numbers and orbitals
        • Electron configurations
      • Periodic table
        • Skill checks for the periodic table
        • Introduction to the periodic table
        • Periodic table trends
      • Chemical bonds
        • Skill checks for chemical bonds
        • Types of chemical bonds
        • Dot structures and molecular geometry
        • Hybridization and hybrid orbitals
      • Gases and kinetic molecular theory
        • Ideal gas equation
        • Non-ideal gas behavior
      • States of matter and intermolecular forces
        • States of matter
        • Introduction to intermolecular forces
        • Mixtures and solutions
      • Chemical equilibrium
        • Equilibrium constant
        • Factors that affect chemical equilibrium
      • Acids and bases
        • Skill checks for acids and bases
        • Acids, bases, and pH
        • Acid-base equilibria
      • Buffers, titrations, and solubility equilibria
        • Skill checks for buffers, titrations, and solubility equilibria
        • Buffer solutions
        • Titrations
        • Solubility equilibria
      • Thermodynamics
        • Internal energy
        • Enthalpy
        • Entropy
        • Gibbs free energy
      • Redox reactions and electrochemistry
        • Skill checks on redox reactions and electrochemistry
        • Oxidation-reduction reactions
        • Galvanic cells
        • Standard cell potentials
        • Electrochemistry, thermodynamics, and equilibrium
        • Cell potentials under nonstandard conditions
        • Electrolytic cells and electrolysis
      • Kinetics
        • Skill checks for kinetics
        • Reaction rates and rate laws
        • Relationship between reaction concentrations and time
        • Arrhenius equation and reaction mechanisms
        • Spectrophotometry
      • Nuclear chemistry
        • Radioactive decay
      • Studying for the AP Chemistry exam?
        • 2015 AP Chemistry free response questions
      • Meet the chemistry professional
        • Meet the chemistry professional
    • AP Chemistry
      • Atoms, compounds, and ions
        • Introduction to the atom
        • Compounds and ions
        • Mass Spectrometry
      • Stoichiometry and molecular composition
        • Balancing chemical equations
        • Stoichiometry
        • Limiting reagent stoichiometry
        • Molecular composition
      • Chemical reactions
        • Types of chemical reactions
      • Electronic structure of atoms
        • History of atomic structure
        • Bohr's model of the hydrogen atom
        • Electron configurations
      • Periodic table
        • Introduction to the periodic table
        • Periodic table trends
      • Chemical bonds
        • Types of chemical bonds
        • Dot structures and molecular geometry
        • Hybridization and hybrid orbitals
      • States of matter and intermolecular forces
        • States of matter
        • Introduction to intermolecular forces
        • Mixtures and solutions
      • Gases and kinetic molecular theory
        • Ideal gas equation
      • Kinetics
        • Reaction rates and rate laws
        • Relationship between reaction concentrations and time
        • Arrhenius equation and reaction mechanisms
        • Spectrophotometry
      • Thermodynamics
        • Internal energy
        • Enthalpy
        • Entropy
        • Gibbs free energy
      • Chemical equilibrium
        • Equilibrium constant
        • Factors that affect chemical equilibrium
      • Acids and bases
        • Acids, bases, and pH
        • Acid-base equilibria
      • Buffers, titrations, and solubility equilibria
        • Buffer solutions
        • Titrations
        • Solubility equilibria
      • Redox reactions and electrochemistry
        • Oxidation-reduction reactions
        • Galvanic cells
        • Standard cell potentials
        • Electrochemistry, thermodynamics, and equilibrium
        • Cell potentials under nonstandard conditions
        • Electrolytic cells and electrolysis
      • Studying for the AP Chemistry exam?
        • 2015 AP Chemistry free response questions
    • Organic chemistry
      • Structure and bonding
        • Dot structures
        • Hybridization
        • Bond-line structures
        • Electronegativity
      • Resonance and acid-base chemistry
        • Counting electrons
        • Resonance structures
        • Organic acid-base chemistry
      • Alkanes, cycloalkanes, and functional groups
        • Naming alkanes
        • Naming alkanes, cycloalkanes, and bicyclic compounds
        • Conformations of alkanes
        • Conformations of cycloalkanes
        • Functional groups
      • Stereochemistry
        • Chirality
        • Enantiomers
        • Stereoisomeric relationships
      • Substitution and elimination reactions
        • Free radical reaction
        • Nucleophilicity and basicity
        • Elimination reactions
        • Sn1/Sn2/E1/E2
        • Sn1 and Sn2
        • E1 and E2 reactions
        • Sn1/Sn2/E1/E2
      • Alkenes and alkynes
        • Naming alkenes
        • Alkene reactions
        • Alkene nomenclature
        • Alkene reactions
        • Naming and preparing alkynes
        • Alkyne reactions
        • Synthesis using alkynes
      • Alcohols, ethers, epoxides, sulfides
        • Alcohol nomenclature and properties
        • Synthesis of alcohols
        • Reactions of alcohols
        • Nomenclature and properties of ethers
        • Synthesis and cleavage of ethers
        • Nomenclature and preparation of epoxides
        • Ring-opening reactions of epoxides
        • Thiols and sulfides
      • Conjugated systems and pericyclic reactions
        • Diels-Alder reaction
      • Aromatic compounds
        • Naming benzene derivatives
        • Reactions of benzene
        • Aromatic stability
        • Electrophilic aromatic substitution
        • Directing effects
        • Other reactions and synthesis
        • Nucleophilic aromatic substitution
      • Aldehydes and ketones
        • Introduction to aldehydes and ketones
        • Reactions of aldehydes and ketones
      • Carboxylic acids and derivatives
        • Naming carboxylic acids
        • Formation of carboxylic acid derivatives
        • Nomenclature and reactions of carboxylic acids
        • Nomenclature and reactions of carboxylic acid derivatives
      • Alpha carbon chemistry
        • Formation of enolate anions
        • Aldol condensations
      • Amines
        • Naming amines
      • Spectroscopy
        • Infrared spectroscopy
        • UV/Vis Spectroscopy
        • Proton NMR
    • Biology
      • Intro to biology
        • Intro to biology skill check
        • Welcome to biology!
        • The science of biology
      • Chemistry of life
        • Chemistry of life skill checks
        • Elements and atoms
        • Electron shells and orbitals
        • Chemical bonds and reactions
      • Water, acids, and bases
        • Properties of water skill check
        • Hydrogen bonding in water
        • Cohesion and adhesion
        • Temperature and state changes in water
        • Acids, bases, and pH
      • Properties of carbon
        • Properties of carbon skill check
        • Carbon
        • Hydrocarbon structures and functional groups
      • Macromolecules
        • Macromolecules skill check
        • Introduction to macromolecules
        • Carbohydrates
        • Lipids
        • Nucleic acids
        • Proteins
      • Energy and enzymes
        • Skill check: Energy and enzymes
        • Energy in metabolism
        • Laws of thermodynamics
        • Free energy
        • ATP and reaction coupling
        • Introduction to enzymes
        • Enzyme regulation
      • Structure of a cell
        • Skill check: Structure of a cell
        • Introduction to cells
        • Prokaryotic and eukaryotic cells
        • Tour of a eukaryotic cell
        • Extracellular structures and cell-cell junctions
      • Membranes and transport
        • Membranes and transport skill checks
        • The plasma membrane
        • Diffusion and osmosis
        • Passive transport
        • Active transport
        • Bulk transport
      • Cellular respiration
        • Cellular respiration skill check
        • Introduction to cellular respiration
        • Steps of cellular respiration
        • Glycolysis
        • Pyruvate oxidation and the citric acid cycle
        • Oxidative phosphorylation
        • Variations on cellular respiration
      • Photosynthesis
        • Photosynthesis skill check
        • Intro to photosynthesis
        • The light-dependent reactions
        • The Calvin cycle
        • Photorespiration: C3, C4, and CAM plants
      • Cell signaling
        • Skill check: Cell signaling
        • How cells signal to each other
        • Communication in single-celled organisms
      • Cell division
        • Skill check: Cell division
        • Introduction to cell division
        • The cell cycle and mitosis
        • Meiosis
        • Cell cycle regulation, cancer, and stem cells
      • Classical and molecular genetics
        • Skill check: Classical genetics
        • Mendelian genetics
        • Variations on Mendelian genetics
        • Chromosomal basis of genetics
        • Sex linkage, chromosomal mutations, & non-nuclear inheritance
        • Molecular basis of genetics
      • DNA as the genetic material
        • DNA skill checks
        • Structure of DNA
        • Discovery of DNA
        • DNA replication
      • Central dogma (DNA to RNA to protein)
        • Central dogma skill check
        • Central dogma and the genetic code
        • Transcription
        • Translation
      • Gene regulation
        • Gene regulation in bacteria
        • Gene regulation in eukaryotes
      • Biotechnology
        • Skill check: Biotechnology
        • Intro to biotechnology
        • DNA cloning
        • DNA analysis methods
        • Stem cells
      • Developmental biology
        • Development & differentiation
        • Signaling & transcription factors in development
        • Apoptosis
      • Bacteria and archaea
        • Prokaryotes skill check
        • Prokaryote structure
        • Prokaryote metabolism and ecology
      • Viruses
        • Viruses
      • Evolution and the tree of life
        • Skill check: Evolution and natural selection
        • Evolution and natural selection
        • Population genetics
        • Speciation and evolutionary trees
      • History of life on Earth
        • Formation of Earth and early life
        • The diversification of life
        • Radiometric dating
      • Ecology
        • Intro to ecology
        • Intro to population ecology
        • Population growth & regulation
        • Intro to community ecology
        • Community structure & diversity
        • Intro to ecosystems
        • Biogeochemical cycles
        • Biogeography
      • Biodiversity and conservation
        • Ecosystems & ecosystem services
        • Global distribution of biodiversity
        • Threats to biodiversity
        • Protecting biodiversity
        • Levels of biodiversity
      • Behavioral biology
        • Animal behavior
      • Principles of physiology
        • Body structure & homeostasis
        • Metabolism & thermoregulation
      • Human biology
        • Circulatory and pulmonary systems
        • The neuron and nervous system
        • The kidney and nephron
        • Muscles
        • Immunology
      • Plant biology
        • Plant responses to light
      • Crash Course: Biology and Ecology
        • Crash Course: Biology
        • Crash Course: Ecology
      • Meet the biology professional
        • Meet the biology professional
    • AP Biology
      • Intro to biology
        • Welcome to biology!
        • The science of biology
      • Chemistry of life
        • Elements and atoms
        • Electron shells and orbitals
        • Chemical bonds and reactions
      • Water, acids, and bases
        • Hydrogen bonding in water
        • Cohesion and adhesion
        • Temperature and state changes in water
        • Acids, bases, and pH
      • Properties of carbon
        • Carbon
        • Hydrocarbon structures and functional groups
      • Macromolecules
        • Introduction to macromolecules
        • Carbohydrates
        • Lipids
        • Nucleic acids
        • Proteins
      • Energy and enzymes
        • Energy in metabolism
        • Laws of thermodynamics
        • Free energy
        • ATP and reaction coupling
        • Introduction to enzymes
        • Enzyme regulation
      • Structure of a cell
        • Introduction to cells
        • Prokaryotic and eukaryotic cells
        • Tour of a eukaryotic cell
        • Extracellular structures and cell-cell junctions
      • Membranes and transport
        • The plasma membrane
        • Diffusion and osmosis
        • Passive transport
        • Active transport
        • Bulk transport
      • Cellular respiration
        • Introduction to cellular respiration
        • Steps of cellular respiration
        • Glycolysis
        • Pyruvate oxidation and the citric acid cycle
        • Oxidative phosphorylation
        • Variations on cellular respiration
      • Photosynthesis
        • Intro to photosynthesis
        • The light-dependent reactions
        • The Calvin cycle
        • Photorespiration: C3, C4, and CAM plants
      • Cell signaling
        • How cells signal to each other
        • Communication in single-celled organisms
      • Cell division
        • Introduction to cell division
        • The cell cycle and mitosis
        • Meiosis
        • Cell cycle regulation, cancer, and stem cells
      • Classical and molecular genetics
        • Mendelian genetics
        • Variations on Mendelian genetics
        • Chromosomal basis of genetics
        • Sex linkage, chromosomal mutations, & non-nuclear inheritance
        • Molecular basis of genetics
      • DNA as the genetic material
        • Structure of DNA
        • Discovery of DNA
        • DNA replication
      • Central dogma (DNA to RNA to protein)
        • Central dogma and the genetic code
        • Transcription
        • Translation
      • Gene regulation
        • Gene regulation in bacteria
        • Gene regulation in eukaryotes
      • Biotechnology
        • Intro to biotechnology
        • DNA cloning
        • DNA analysis methods
        • Stem cells
      • Developmental biology
        • Development & differentiation
        • Signaling & transcription factors in development
        • Apoptosis
      • Bacteria and archaea
        • Prokaryote structure
        • Prokaryote metabolism and ecology
      • Viruses
        • Viruses
      • Evolution and the tree of life
        • Evolution and natural selection
        • Population genetics
        • Speciation and evolutionary trees
      • History of life on Earth
        • Formation of Earth and early life
        • The diversification of life
        • Radiometric dating
      • Ecology
        • Intro to ecology
        • Intro to population ecology
        • Population growth & regulation
        • Intro to community ecology
        • Community structure & diversity
        • Intro to ecosystems
        • Biogeochemical cycles
        • Biogeography
      • Biodiversity and conservation
        • Ecosystems & ecosystem services
        • Global distribution of biodiversity
        • Threats to biodiversity
        • Protecting biodiversity
        • Levels of biodiversity
      • Behavioral biology
        • Animal behavior
      • Principles of physiology
        • Body structure & homeostasis
        • Metabolism & thermoregulation
      • Human biology
        • Circulatory and pulmonary systems
        • The neuron and nervous system
        • The kidney and nephron
        • Muscles
        • Immunology
      • Plant biology
        • Plant responses to light
      • Meet the biology professional
        • Meet the biology professional
    • Cosmology and astronomy
      • Scale of the universe
        • Scale of earth, sun, galaxy and universe
        • Time scale of the cosmos
        • Light and fundamental forces
        • Big bang and expansion of the universe
      • Stars, black holes and galaxies
        • Life and death of stars
        • Quasars and galactive collisions
        • Stellar parallax
        • Cepheid variables
      • Earth geological and climatic history
        • Plate tectonics
        • Seismic waves and how we know earth's structure
        • Earth's rotation and tilt
        • Moon phases and eclipses
      • Life on earth and in the universe
        • History of life on earth
        • Humanity on earth
        • Measuring age on earth
        • Life in the universe
    • Electrical engineering
      • Introduction to electrical engineering
        • Getting started
      • Circuit analysis
        • Circuit elements
        • Resistor circuits
        • DC circuit analysis
        • Natural and forced response
        • AC circuit analysis
      • Amplifiers
        • Operational amplifier
      • Semiconductor devices
        • Diode
      • Electrostatics
        • Electric force and electric field
        • Fields, potential, and voltage
      • Signals and systems
        • Fourier series
      • Home-made robots
        • All about Spout
        • Spout Bot with Solder
        • Spout Bot without Solder
        • Spider Bot
        • Bit-zee Bot
      • Lego robotics
        • Introduction
        • Light guitar
        • Coin detector
        • Ant bot
        • Programming basics
      • Reverse engineering
        • Household items
        • Hair dryer
        • DVD player
        • Digital camera
    • Health and medicine
      • Human anatomy and physiology
        • Circulatory system introduction
        • Respiratory system introduction
        • Urinary system introduction
        • Hematologic system introduction
        • Immunologic system introduction
        • Gastrointestinal system introduction
        • Nervous system introduction
        • Muscular system introduction
        • Skeletal system introduction
        • Endocrine system introduction
        • Integumentary system introduction
        • Lymphatic system introduction
        • Reproductive system introduction
        • Pregnancy and pregnancy complications
      • Advanced circulatory system physiology
        • Circulatory system introduction
        • Blood pressure
        • Blood pressure control
        • Fetal circulation
        • Blood vessels
        • Arterial stiffness
        • Heart muscle contraction
        • Heart depolarization
        • Nerve regulation of the heart
        • Preload and afterload
        • Pressure volume loops
        • Changing the PV loop
      • Circulatory system diseases
        • Coronary artery disease
        • Atherosclerosis, arteriosclerosis, and arteriolosclerosis
        • Stroke
        • Hypertension
        • Heart failure
        • Aortic dissection and aneurysm
        • Myocarditis and pericarditis
        • Cardiomyopathy
        • Cardiac dysrhythmias and tachycardias
        • Heart valve diseases
        • Acyanotic heart diseases
        • Cyanotic heart diseases
        • Shock
        • Vasculitis
        • Hypertension
      • Advanced respiratory system physiology
        • Respiratory system introduction
        • Gas exchange
        • Breathing control
      • Respiratory system diseases
        • Introduction to pulmonary diseases
        • Asthma
        • Emphysema (COPD)
        • Chronic Bronchitis (COPD)
        • Cystic fibrosis
        • Occupational lung diseases
        • Pulmonary hypertension
        • Pneumonia
        • Pleural Effusion
        • Lung cancer
        • Nose, sinus, and upper respiratory conditions
        • Throat conditions
        • Laryngeal conditions
        • Bronchiolitis
      • Advanced hematologic system physiology
        • Hematologic system introduction
        • Bleeding and impaired hemostasis
      • Hematologic system diseases
        • Anemia
        • Leukemia
        • Iron deficiency anemia and anemia of chronic disease
        • Plasma cell dyscrasias
        • Myeloproliferative disorders
      • Advanced endocrine system physiology
        • Endocrine system introduction
        • Biological basis of behavior: Endocrine system
      • Endocrine system diseases
        • Diabetes
      • Advanced nervous system physiology
        • Nervous system introduction
        • Neural cells and neurotransmitters
        • Neuron membrane potentials
        • Sensory perception
        • Sight (vision)
        • Sound (Audition)
        • Somatosensation
        • Taste (gustation) and smell (olfaction)
      • Nervous system diseases
        • Parkinson's disease
        • Multiple sclerosis
      • Advanced gastrointestinal physiology
        • Gastrointestinal system introduction
      • Gastrointestinal system diseases
        • Gastroenteritis
        • Inflammatory bowel disease
        • Celiac disease
        • Colon diseases
      • Advanced muscular-skeletal system physiology
        • Muscular system introduction
        • Skeletal system introduction
      • Muscular-skeletal diseases
        • Arthritis and rheumatoid arthritis
      • Executive systems of the brain
        • Cognition
        • Attention and language
        • Sleep and consciousness
        • Memory
        • Emotion
      • Mental health
        • Drug abuse and drug addictions
        • Depression and related disorders
        • Anxiety
        • Psychotic disorders
        • Dementia, delirium, and Alzheimer's
        • Neurodevelopmental disorders
      • Infectious diseases
        • Tuberculosis
        • Pertussis
        • Influenza
        • Polio
        • Sexually transmitted diseases
        • HIV and AIDS
        • Malaria
      • Lab values and concentrations
      • Current events in health and medicine
        • Antibiotics and antibiotic resistance
        • Ebola outbreak
      • Health care system
      • Miscellaneous
  • Economics and finance
    • Microeconomics
      • Supply, demand, and market equilibrium
        • Introduction to economics
        • The demand curve
        • The supply curve
        • Market equilibrium
        • What drives oil prices
      • Elasticity
        • Price elasticity
      • Consumer and producer surplus
        • Consumer and producer surplus
        • Deadweight loss
        • Public goods and externalities
        • Bonus articles: Pollution as a negative externality
        • Bonus articles: Innovation as a positive externality
      • Scarcity, possibilities, preferences and opportunity cost
        • Production possibilities frontier
        • Comparative advantage and gains from trade
        • Marginal utility and budget lines
      • Production decisions and economic profit
        • Economic profit and opportunity cost
        • Average costs (ATC, MC) and marginal revenue (MR)
        • Average fixed, variable and marginal costs
        • Labor and marginal product revenue
        • Price discrimination
      • Forms of competition
        • Perfect competition
        • Monopoly
        • Between perfect competition and monopoly
      • Game theory and Nash equilibrium
        • Nash equilibrium
        • Why parties in a cartel will cheat
    • Macroeconomics
      • GDP: Measuring national income
        • Introduction to economics
        • GDP and the circular flow of income and expenditures
        • Components of GDP
        • Real and nominal GDP
        • National income and inequality
      • Inflation - measuring the cost of living
        • Measuring cost of living – inflation and the consumer price index
        • Real and nominal return
        • Deflation
        • Inflationary and deflationary scenarios
        • The Phillips curve: Inflation and unemployment
      • Aggregate demand and aggregate supply
        • Aggregate demand and aggregate supply
        • Historical circumstances explained by AD/AS
        • The business cycle
        • Monetary and fiscal policy
        • Keynesian thinking
      • The monetary system
        • Fractional reserve banking
        • Money supply
        • Fractional reserve accounting
        • Interest as the price of money
        • Functions of money
      • Income and expenditure: Keynesian cross and IS-LM model
        • Marginal propensity to consume (MPC)
        • Consumption function
        • Keynesian cross
        • IS-LM model
        • Articles on the Keynesian perspective
      • Foreign exchange and trade
        • Balance of payments- current account and capital account
        • Currency reserves
    • AP Microeconomics
      • Basic Economic Concepts
        • Introduction to economics
        • Production possibilities frontier
        • Comparative advantage and gains from trade
      • Supply, demand, and market equilibrium
        • The demand curve
        • The supply curve
        • Market equilibrium
        • What drives oil prices
        • Price elasticity of demand
        • Elasticity and total revenue
        • Cross-price elasticity of demand
        • Price elasticity of supply
        • Consumer and producer surplus
        • Deadweight loss
      • Theory of consumer choice
        • Total utility and marginal utility
        • Income and substitution effects
      • Production and costs
        • Average costs (ATC, MC) and marginal revenue (MR)
        • Average fixed, variable and marginal costs
        • Price discrimination
      • Firm behavior and market structure
        • Economic profit and opportunity cost
        • Perfect competition
        • Monopoly
        • Between perfect competition and monopoly
        • Nash equilibrium
        • Why parties in a cartel will cheat
      • Factor markets
        • Labor and marginal product revenue
      • Market failure and the role of government
        • Public goods and externalities
        • Bonus articles: Pollution as a negative externality
        • Bonus articles: Innovation as a positive externality
    • AP Macroeconomics
      • Basic economic concepts
        • Introduction to economics
        • Production possibilities frontier
        • Comparative advantage and gains from trade
        • The demand curve
        • The supply curve
        • Market equilibrium
        • Macroeconomic issues: business cycle, unemployment, inflation, growth
      • Measurement of economic performance
        • GDP and the circular flow of income and expenditures
        • Components of GDP
        • Real and nominal GDP
        • Measuring cost of living – inflation and the consumer price index
        • Real and nominal return
        • Deflation
        • Inflationary and deflationary scenarios
        • Unemployment
      • National income and price determination
        • Aggregate demand and aggregate supply
        • Historical circumstances explained by AD/AS
        • The business cycle
        • Monetary and fiscal policy
        • Keynesian thinking
      • Financial sector
        • Definition of financial assets: money, stocks, bonds
        • Time value of money (present and future value)
        • Real and nominal return
        • Fractional reserve banking
        • Money supply
        • Fractional reserve accounting
        • Interest as the price of money
        • Central bank and control of the money supply
      • Stabilization policies
        • Marginal propensity to consume (MPC)
        • Consumption function
        • Articles on the Keynesian perspective
      • Open Economy: International Trade and Finance
        • Balance of payments- current account and capital account
        • Foreign exchange market
        • Currency reserves
    • Finance and capital markets
      • Interest and debt
        • Compound interest basics
        • Interest basics
        • Credit cards and loans
        • Continuous compound interest and e
        • Present value
        • Personal bankruptcy
      • Housing
        • Home equity and personal balance sheets
        • Renting vs. buying a home
        • Mortgages
        • Home buying process
      • Inflation
        • Inflation basics
        • Inflation scenarios
        • Real and nominal return
        • Capacity utilization and inflation
        • Deflation
      • Taxes
        • Personal taxes
        • Corporate taxation
      • Accounting and financial statements
        • Cash versus accrual accounting
        • Three core financial statements
        • Depreciation and amortization
      • Stocks and bonds
        • Introduction to stocks
        • Shorting stock
        • Understanding company statements and capital structure
        • Corporate metrics and valuation
        • Life of a company--from birth to death
        • Dilution
        • Mergers and acquisitions
        • Leveraged buy-outs
        • Bonds
        • Corporate bankruptcy
      • Investment vehicles, insurance, and retirement
        • Mutual funds and ETFs
        • Retirement accounts: IRAs and 401ks
        • Life insurance
        • Hedge funds
        • Investment and consumption
      • Money, banking and central banks
        • Banking and money
        • Quantitative easing
        • 2008 bank bailout
        • Geithner plan
        • Foreign exchange and trade
        • Chinese currency and U.S. debt
        • 2011-2012 Greek debt crisis
        • Bitcoin
      • Options, swaps, futures, MBSs, CDOs, and other derivatives
        • Put and call options
        • Forward and futures contracts
        • Mortgage-backed securities
        • Collateralized debt obligations
        • Credit default swaps
        • Interest rate swaps
        • Black-Scholes formula
      • Current economics
        • Unemployment
        • Housing price conundrum
        • Credit crisis
        • Paulson bailout
        • European Union
  • Arts and humanities
    • US history
      • The historian's toolkit
        • How to think like a historian
      • Worlds collide (1491-1607)
        • Before contact
        • Old and new worlds collide
        • Spanish colonization
      • Colonial America (1607-1754)
        • Early colonization projects
        • Chesapeake and Southern colonies
        • Colonial North America
      • The road to revolution (1754-1800)
        • The American Revolution
        • Creating a nation
      • The early republic (1800-1848)
        • Politics and society in the early nineteenth century
        • The age of Jackson
        • Culture and reform in the early nineteenth century
      • The Civil War era (1844-1877)
        • Sectional tension in the 1850s
        • The Civil War
        • Reconstruction
      • The Gilded Age (1865-1898)
        • The Gilded Age
        • The South after the Civil War
        • The American West
      • Rise to world power (1890-1945)
        • The age of empire
        • The United States in World War I
        • 1920s America
        • The Great Depression
        • World War II
      • The postwar era (1945-1980)
        • The postwar era, 1945-1950
        • 1950s America
        • The Civil Rights Movement
        • 1960s America
        • 1970s America
      • The modern era (1980-present)
        • 1980s America
        • 1990s America
        • The United States after 2000
      • American civics
        • American civics
      • Surveys of history
        • United States history overview
    • AP US History
      • AP US History skills and test strategies
        • Thinking like a historian
        • AP US History examples
      • Period 1: 1491-1607
        • Before contact
        • Old and new worlds collide
        • Spanish colonization
      • Period 2: 1607-1754
        • Early colonization projects
        • Colonial North America
      • Period 3: 1754-1800
        • The American Revolution
        • Creating a nation
      • Period 4: 1800-1848
        • Politics and society in the early nineteenth century
        • The age of Jackson
        • Culture and reform
      • Period 5: 1844-1877
        • Sectional tension in the 1850s
        • The Civil War
        • Reconstruction
      • Period 6: 1865-1898
        • The Gilded Age
        • The South after the Civil War
        • The American West
      • Period 7: 1890-1945
        • The age of empire
        • The United States in World War I
        • 1920s America
        • The Great Depression
        • World War II
      • Period 8: 1945-1980
        • The postwar era, 1945-1950
        • 1950s America
        • The Civil Rights Movement
        • 1960s America
        • The 1970s
      • Period 9: 1980-present
        • 1980s America
        • 1990s America
        • The United States after 2000
    • World history
      • Beginnings - 600 BCE
        • The origin of humans and early human societies
        • The Neolithic Revolution and the birth of agriculture
        • Ancient Mesopotamia
        • Ancient Egypt
        • Ancient art and artifacts
        • Ancient India
        • Shang China
        • Ancient Americas
        • Human innovation and the environment
      • 600 BCE - 600 CE Second-Wave Civilizations
        • Ancient Persia
        • Classical Greece
        • The rise and fall of empires
        • Empire of Alexander the Great
        • Rise of Rome
        • From Roman Republic to Roman Empire
        • The Roman Empire
        • Ancient and Imperial China
        • Early Judaism
        • Early Christianity
        • Early Americas
        • Empires in India
        • Early Hinduism
        • Early Buddhism
        • Syncretism
        • Women and families
        • Transregional Trade: the Silk Road
        • Survey of second-wave civilizations
      • 600 - 1450 Regional and interregional interactions
        • Byzantine Empire
        • European Middle Ages: feudalism and serfdom
        • Origins of Islam
        • Spread of Islam
        • Sunni and Shia Islam
        • Golden Age of Islam
        • The Great Schism
        • The Crusades
        • The Mongols
        • Song China
        • Medieval Japan
        • Maya, Aztec, and Inca
        • Environment and trade
        • Human migration
        • Development of new trading cities
        • Cultural interactions along trade routes
        • Development of financial institutions
        • Disease and demography
        • Social institutions in the Islamic world
      • 1450 - 1750 Renaissance and Reformation
        • Scientific Revolution and Enlightenment
        • Mughal rule in India
        • Sikhism
        • The Protestant Reformation
        • The Russian Empire
      • 1750 -1900 Enlightenment and Revolution
        • American Revolution
        • French Revolution
        • Napoleon Bonaparte
        • France's many revolutions and republics
        • Haitian Revolution
        • Latin American independence
        • Imperialism
      • The 20th century
        • Beginning of World War I
        • Other fronts of World War I
        • Western and Eastern fronts of World War I
        • Blockades and American entry
        • World War I shapes the Middle East
        • Aftermath of World War I
        • World War I Quiz
        • Rise of Hitler and the Nazis
        • Rise of Mussolini and Fascism
        • Overview of Chinese history 1911-1949
        • Overview of World War II
        • The Cold War
        • Human rights
    • AP World History
      • Beginnings - 600 BCE
        • What is World History?
        • The origin of humans and early human societies
        • The Neolithic Revolution and the birth of agriculture
        • Ancient Mesopotamia
        • Ancient Egypt
        • Ancient India
        • Shang China
        • Ancient art and artifacts
        • Human innovation and the environment
      • 600 BCE - 600 CE Second-Wave Civilizations
        • Ancient Persia
        • Classical Greece
        • The Rise and Fall of Empires
        • Ancient Rome
        • Ancient and Imperial China
        • Early Judaism
        • Early Christianity
        • Early Americas
        • Empires in India
        • Early Hinduism
        • Early Buddhism
        • Syncretism
        • Women and families
        • Transregional trade: the Silk Road
      • 600 - 1450 Regional and interregional interactions
        • Byzantine Empire
        • European Middle Ages: feudalism and serfdom
        • Origins of Islam
        • Spread of Islam
        • Sunni and Shia Islam
        • Golden Age of Islam
        • The Great Schism
        • The Crusades
        • The Mongols
        • Song China
        • Medieval Japan
        • Maya, Aztec, and Inca
        • Environment and trade
        • Human migration
        • Development of new trading cities
        • Cultural interactions along trade routes
        • Development of financial institutions
        • Disease and demography
        • Social institutions in the Islamic world
      • 1450 - 1750 Renaissance and Reformation
        • Scientific Revolution and Enlightenment
        • Mughal rule in India
        • Sikhism
        • The Protestant Reformation
        • The Russian Empire
      • 1750 - 1900 Enlightenment and Revolution
        • American Revolution
        • French Revolution
        • Napoleon Bonaparte
        • France's many revolutions and republics
        • Haitian Revolution
        • Latin American independence
        • Imperialism
      • The 20th century
        • Beginning of World War I
        • Other fronts of World War I
        • Western and Eastern fronts of World War I
        • Blockades and American entry
        • World War I shapes the Middle East
        • Aftermath of World War I
        • Rise of Hitler and the Nazis
        • Rise of Mussolini and Fascism
        • Overview of Chinese history 1911-1949
        • Overview of World War II
        • The Cold War
        • Human rights
    • Art history
    • AP Art History
      • Start here
      • Introduction to cultures and religions for the study of AP Art History
      • Global prehistory: 30,000-500 B.C.E.
        • Paleolithic, Mesolithic and Neolithic
      • Ancient Mediterranean: 3500 B.C.E.-300 C.E.
        • Ancient Near East
        • Ancient Egypt
        • Ancient Greece
        • Ancient Etruria
        • Ancient Rome
      • Early Europe and Colonial Americas: 200-1750 C.E.
        • Medieval art in Europe
        • Art of the Islamic world in the medieval era
        • Renaissance Art in Europe
        • Protestant Reformation and Catholic Counter-Reformation
        • Colonial Americas
      • Later Europe and Americas: 1750-1980 C.E.
        • Enlightenment and revolution
        • Modern and contemporary art
      • Indigenous Americas
      • Africa: 1100-1980 C.E.
      • West and central Asia: 500 B.C.E.-1980 C.E.
      • South, East, and Southeast Asia: 300 B.C.E. - 1980 C.E.
        • India
        • China
        • Korea
        • Japan
        • Cambodia
        • Indonesia
      • The Pacific
      • Global contemporary: 1980-present
    • Grammar
      • Introduction to grammar
        • Welcome to grammar!
      • Parts of speech: the noun
        • Introduction to nouns
        • Types of nouns
        • Irregular plural nouns: base plurals and irregular endings
        • Irregular plural nouns: mutant and foreign plurals
      • Parts of speech: the verb
        • Introduction to verbs
        • The tenses
        • Linking and helping verbs
        • Irregular verbs
        • Verb aspect: simple, progressive, and perfect
        • Verb aspect and modal verbs
      • Parts of speech: the pronoun
        • Introduction to pronouns
        • Possessive and reflexive pronouns
        • Relative pronouns
        • Subject, object, person, and number
        • Indefinite pronouns, pronoun vagueness, and emphatic pronouns
      • Parts of speech: the modifier
        • Introduction to adjectives and articles
        • Introduction to adverbs
        • Adjective order and commas with adjectives
        • Comparative, superlative, intensifiers, and adverbs of degree
      • Parts of speech: the preposition and the conjunction
        • Introduction to prepositions
        • Types of prepositions and phrases
        • Introduction to conjunctions
        • Correlative conjunctions and starting sentences
      • Punctuation: the comma and the apostrophe
        • Introduction to commas
        • Commas in space and time
        • More ways to use commas
        • Apostrophes and contractions
        • Introduction to the possessive
        • Its vs. it's
      • Punctuation: the colon, semicolon, and more
        • Introduction to colons
        • Introduction to semicolons
        • Formatting styles
        • Hyphens, dashes, and ellipses
      • Syntax: sentences and clauses
        • Introduction to sentences
        • Types of sentences
        • Subjects and predicates
        • Phrases and clauses
      • Syntax: conventions of standard English
        • Subject-verb agreement and pronoun-antecedent agreement
        • Fragments and run-ons
        • Dangling modifiers and parallel structure
      • Usage and Style
        • Frequently confused words
        • Common expressions
        • Style!
    • Music
      • Music basics
        • Notes and rhythm
        • Reading music
      • Masterpieces old and new
        • Ludwig van Beethoven: Symphony No. 5
        • Pyotr Ilyich Tchaikovsky: Symphony No.4
        • Robert Schumann: Symphony No. 3 "Rhenish"
        • Johannes Brahms: Academic Festival Overture
        • Antonín Dvořák: Symphony No. 9 "From the New World"
        • Gustav Mahler: Symphony No. 2 – 1st Movement
        • Igor Stravinsky: Suite from The Firebird
        • Maurice Ravel: Suite No. 2 from Daphnis et Chloe
        • Dmitri Shostakovich: Symphony No. 5
        • Introduction to Philip Glass' "Harmonium Mountain"
        • Bernard Rands: Adieu
        • Augusta Read Thomas: Of Paradise and Light
        • Bright Sheng: "Black Swan", the composer and his work
        • Richard Danielpour: Piano Concerto No. 4, Movement III
        • David Stock: Blast!
        • Ellen Taaffe Zwilich: Avanti!
        • Joseph Schwantner: The Poet's Hour
      • Instruments of the orchestra
        • Strings
        • Woodwinds
        • Brass
        • Percussion
    • Special topics in art history
      • ARCHES (At Risk Cultural Heritage Education Series)
        • A beginner's guide
        • Endangered heritage: The Americas
        • Endangered heritage: Europe and West Asia
        • Endangered heritage: Southeast Asia
        • Endangered heritage: Pacific islands
        • Endangered heritage: Africa
      • Creating & conserving
        • The conservator's eye
        • What is conservation?
        • About color
        • Painting materials
        • Painting conservation
        • How to paint like...
        • Painting terms in action
        • Sculpture
        • Printmaking
        • Drawing and manuscripts
        • Photographs
        • Ceramics and lacquer
        • Mosaic, metalwork and glass
        • Textiles
        • Frames
        • Architecture
        • Quiz: materials and techniques
    • Art history basics
      • First things first
      • Tools for understanding art
      • Art 1010
    • Prehistoric art in Europe and West Asia
      • Paleolithic art
      • Neolithic art
      • Quiz: prehistoric art
    • Art of the ancient Mediterranean
      • Ancient Near East
        • The Ancient Near East, an introduction
        • Sumerian
        • Akkadian
        • Babylonian
        • Assyrian
        • Persian
        • Quiz: Ancient Near Eastern art
      • Egyptian art and culture
        • A beginner's guide to ancient Egypt
        • Predynastic and Old Kingdom
        • Middle Kingdom and New Kingdom
        • Ptolemaic
      • Aegean art
        • Cycladic
        • Mycenaean
      • Greek art
        • A beginner's guide to ancient Greece
        • Pottery
        • Daedalic and Archaic
        • Early classical
        • Classical
        • Late classical (4th century)
        • Hellenistic
        • Greek art
      • Nabataean
      • Etruscan
      • Roman
        • A beginner's guide to ancient Rome
        • Wall painting
        • Republic
        • Early empire
        • Middle empire
        • Late empire
        • Ancient Rome (quiz)
      • Palmyra
      • Judaism and art
    • Art of Medieval Europe
      • A beginner's guide to medieval Europe
      • Books in medieval Europe
        • Making the medieval book
        • Using the medieval book
      • Early Christian
      • Byzantine (late Roman Empire)
        • A beginner's guide to Byzantine art and culture
        • Constantinople and the East
        • Venice and Ravenna
        • Quiz: Byzantine art
      • Latin (Western) Europe
        • Early medieval
        • Carolingian
        • Ottonian
        • Romanesque
        • Gothic
    • Art of the Islamic world
      • A beginner's guide to the art of Islam
      • Early period
      • Medieval period
      • Late period
      • Arts of the Islamic world (quiz)
    • Renaissance & Reformation in Europe
      • Late Gothic art in Italy
        • A beginner's guide to the Late Gothic
        • Florence, the Late Gothic
        • Siena, the Late Gothic
        • Pisa and Rome, the Late Gothic
      • Northern Renaissance: 1400s
        • A beginner's guide to the Northern Renaissance
        • Claus Sluter and Claus de Werve
        • The Limbourg Brothers
        • Campin
        • Van Eyck
        • Christus
        • Van der Weyden
        • Van der Goes
        • Quarton (?)
        • Reliquaries and tapestries
      • Early Renaissance in Italy: 1400s
        • A beginner's guide to Renaissance Florence
        • Sculpture and architecture in Florence
        • Painting in Florence and Rome
        • Central Italy
      • High Renaissance: Florence and Rome
        • A beginner's guide to the High Renaissance
        • Leonardo da Vinci
        • Michelangelo
        • Raphael
        • Bramante
      • The Renaissance in Venice
        • Early Renaissance in Venice
        • Late Renaissance in Venice
      • Reformation and Counter-Reformation
      • Northern Renaissance: 1500s
        • A beginner's guide to the Northern Renaissance in the sixteenth century
        • Pacher and Grünewald
        • Hieronymus Bosch
        • Albrecht Dürer
        • Antwerp, Bruges and Brussels
        • Cranach and Altdorfer
        • Hans Holbein
        • England
        • Quiz: The Northern Renaissance in the 16th century
      • Renaissance in Spain
        • Introduction to the Renaissance in Spain
        • Renaissance architecture in Spain
      • Late Renaissance and Mannerism
    • Baroque to Neoclassical art in Europe
      • Baroque art
        • A beginner's guide to Baroque art
        • Italy
        • Flanders
        • Dutch Republic
        • Spain
        • France
        • England
      • Rococo
      • Neo-Classicism
      • British art in the 18th century
        • British art in the eighteenth century
        • Age of revolution (quiz)
    • Art of the Americas to World War I
      • A beginner's guide to the Art of the Americas
      • N. America before European colonization
        • Prehistoric Mexico
        • Clovis culture
        • Moundbuilders
        • Tlatilco
        • Olmec
        • Teotihuacan
        • Classic Veracruz culture
        • Maya
        • Ancestral Puebloan (formerly Anasazi)
        • Huastec
        • Mixtec
        • Aztec (Mexica)
      • S. America before European colonization
        • A beginner's guide
        • Cupisnique
        • Paracas and Nasca cultures
        • Chavín culture
        • Moche culture
        • Chimú culture
        • Sicán
        • Inka
        • Ancient Colombian chiefdoms
        • Amazonian peoples
      • Spanish colonies in the Americas
        • A beginner's guide
        • Viceroyalty of New Spain
        • Viceroyalty of Peru
        • Viceroyalty of New Granada
      • Native American art after 1600
        • A beginner's guide to Native American art after 1600
        • East
        • West
        • Southwest
        • Northwest coast
        • The Arctic
        • Contemporary art
      • British Colonies to the Early Republic
        • Colonial period
        • Early Republic
      • Art of the United States: 1800s
        • Romanticism in the United States
        • Realism in the United States
        • American Aestheticism and the Gilded Age
        • 19th century American sculpture, architecture and photography
      • Art of Mexico in the 18th and 19th centuries
    • Art in 19th century Europe
      • Introduction—Becoming Modern
      • Romanticism
        • Romanticism—an introduction
        • France
        • Spain
        • England (Blake and Fuseli)
        • England (Constable, Turner, Martin and Nash)
        • Germany
      • Early photography
      • Victorian art and architecture
        • Early Victorian
        • The Pre-Raphaelites and mid-Victorian art
        • Late Victorian
      • Realism, Impressionism and Post-Impressionism
        • Art and the French state
        • Realism
        • Impressionism
        • Post-Impressionism
        • Sculpture
      • Symbolism & Art Nouveau
      • Russia: The Wanderers
        • The Peredvizhniki (The Wanderers)
    • Expressionism to Pop Art
      • A beginner's guide to 20th century art
      • Early abstraction: Fauvism, Expressionism & Cubism
        • Fauvism and Matisse
        • Expressionism
        • Cubism and its impact
      • World War I, Futurism and Dada
        • Futurism and the Great War
        • Dada
      • Art between the wars: the avant-garde and the rise of totalitarianism
        • German art between the wars
        • The international avant-garde
        • Surrealism
        • Latin American Modernism
        • American art to World War II
      • Figuration & abstraction in post-war Britain
      • Art Brut
      • Abstract Expressionism & the New York School
        • Abstract Expressionism
        • New York School
      • Pop
      • Minimalism and Earthworks
      • Architecture and design
    • Global contemporary art
      • A beginner's guide to contemporary art
      • Identity, the body & the subversion of Modernism
        • United States
        • Asia, Africa, Europe, Latin America and the Middle East
      • Conceptual and Performance art
      • Global modernisms in the 21st century
    • Art of Asia
      • A beginner's guide to Asian art and culture
        • Hindu art and culture, an introduction
        • Buddhist art and culture, an introduction
      • China
        • Neolithic art in China
        • A beginner's guide to Imperial China
        • Shang dynasty (c. 1600-1050 B.C.E.)
        • Zhou dynasty (c. 1046 B.C.E.-256 B.C.E.)
        • Qin dynasty (221-206 B.C.E.)
        • Han dynasty (206 B.C.E–220 C.E.)
        • Later Zhao (319-351)
        • Northern Wei dynasty (386 - 534)
        • Northern Qi dynasty (550 - 577)
        • Sui dynasty (589-618)
        • Tang dynasty (618-907)
        • Liao Dynasty (907–1125)
        • Song dynasty (960-1279)
        • Yuan dynasty (1271-1368)
        • Ming dynasty (1368–1644)
      • Korea
        • A beginner's guide to Korean art
        • Proto-Three Kingdoms (300 B.C.E.-300 C.E.)
        • Three Kingdoms Period (57 B.C.E.-676 C.E.)
        • Goryeo dynasty (918-1392)
        • Joseon dynasty (1392–1910)
      • Japan
        • Beginner’s guide to Japanese Art
        • Kofun period (300-552 C.E.)
        • Nara period (710–794)
        • Heian period (794–1185)
        • Kamakura period (1185-1333)
        • Muromachi period (1392–1573)
        • Edo period (1615–1868)
      • South Asia
        • South Asia, an introduction
        • Hindu art in South Asia
        • Buddhist art in South Asia
        • Art in Afghanistan
      • Southeast Asia
        • A beginner's guide to Southeast Asian art
        • Cambodia
        • Myanmar
        • Indonesia
        • Bali
        • Thailand
      • The Himalayas
        • Nepal
        • Tibet
    • Art of Africa
      • African art, an introduction
      • East Africa and the Horn of Africa
        • Ethiopia
        • Tanzania
      • West Africa
        • Burkina Faso
        • Cameroon
        • Ghana
        • Guinea
        • Ivory Coast
        • Mali
        • Nigeria
        • Republic of Benin
        • Sierra Leone
      • North Africa
        • Algeria and Libya
      • Southern Africa
        • Namibia
        • South Africa
        • Zimbabwe
      • Central Africa
        • Cameroon
        • Democratic Republic of the Congo
        • Gabon
    • Art of Oceania
      • Lapita Culture
      • Polynesia
      • Melanesia
      • Micronesia
    • For teachers
      • Course materials
  • Computing
    • Computer programming
      • Intro to JS: Drawing & Animation
        • Test Yourself: Intro to JS: Drawing & Animation
        • Intro to programming
        • Drawing basics
        • Coloring
        • Variables
        • Animation basics
        • Interactive programs
        • Bonus: Resizing with variables
        • Text and strings
        • Functions
        • Logic and if Statements
        • Debugging programs
        • Looping
        • Writing clean code
        • Arrays
        • Objects
        • Object-Oriented Design
        • Becoming a better programmer
      • Intro to HTML/CSS: Making webpages
        • Intro to HTML
        • Intro to CSS
        • More HTML tags
        • CSS text properties
        • Web development tools
        • CSS layout
        • More CSS selectors
        • Other ways to embed CSS
        • Further learning
      • Intro to SQL: Querying and managing data
        • SQL basics
        • More advanced SQL queries
        • Relational queries in SQL
        • Modifying databases with SQL
        • Further learning in SQL
      • Advanced JS: Games & Visualizations
        • Intro to Games & Visualizations
        • Scene management
        • Buttons
        • Transformations
        • 3D Shapes
        • Making a Side Scroller: Hoppy Beaver
        • Making a Memory Game
      • Advanced JS: Natural Simulations
        • Intro to Natural Simulations
        • Randomness
        • Noise
        • Vectors
        • Forces
        • Angular Movement
        • Oscillations
        • Particle Systems
      • HTML/JS: Making webpages interactive
        • Test Yourself: HTML/JS: Making webpages interactive
        • Get ready to make your webpages interactive
        • JS and the DOM
        • DOM access methods
        • DOM modification
        • DOM events
        • DOM animation
        • Using JS libraries in your webpage
        • Further learning
      • HTML/JS: Making webpages interactive with jQuery
        • Welcome to jQuery
        • DOM access with jQuery
        • DOM modification with jQuery
        • jQuery techniques
        • DOM events with jQuery
        • Form processing with jQuery
        • DOM animation & effects with jQuery
        • Further learning
      • Meet the professional
      • Browse Projects
      • Project Feedback
      • Processing.js Documentation
      • Webpage Documentation
      • SQL Documentation
    • Computer science
      • Algorithms
        • Intro to algorithms
        • Binary search
        • Asymptotic notation
        • Selection sort
        • Insertion sort
        • Recursive algorithms
        • Towers of Hanoi
        • Merge sort
        • Quick sort
        • Graph representation
        • Breadth-first search
        • Further learning
      • Journey into cryptography
        • Ancient cryptography
        • Ciphers
        • Cryptography challenge 101
        • Modern cryptography
        • Modular arithmetic
        • Primality test
        • Randomized algorithms
      • Journey into information theory
        • Ancient information theory
        • Modern information theory
      • Internet 101
        • How the internet works
    • Hour of Code
      • Drawing with code
      • Creating webpages
      • Creating SQL databases
      • Hour of Code (for teachers and parents)
      • Drawing with code
  • Test prep
    • SAT
      • Full-length SAT
        • Online SAT Tests
        • Paper SAT Tests
      • SAT Math practice
        • Heart of algebra
        • Passport to advanced mathematics
        • Problem solving and data analysis
        • Additional topics in math
      • SAT Reading and Writing practice
        • Reading
        • Writing: Passages
        • Writing: Grammar
      • SAT Tips & Strategies
        • About the SAT
        • About Official SAT Practice on Khan Academy
        • General SAT Strategies
        • About the SAT Reading Test
        • SAT Reading Test Strategies
        • About the SAT Writing and Language Test
        • SAT Writing and Language Test Strategies
        • About the SAT Math Test
        • SAT Math Test Strategies
        • About the SAT Essay
        • SAT Essay Strategies
        • How to Prep for the SAT
        • SAT Coach Tools
        • SAT Reading & Writing lesson plans for teachers, by teachers
        • SAT Math lesson plans for teachers, by teachers
    • MCAT
      • Critical analysis and reasoning skills practice questions
        • Critical analysis and reasoning skills (CARS) practice questions
      • Biological and Biochemical Foundations of Living Systems Passages
        • Biological sciences practice passage questions
      • Chemical and Physical Foundations of Biological Systems Passages
        • Chemical and physical sciences practice passage questions
      • Psychological, Social, and Biological Foundations of Behaviors Passages
        • Social sciences practice passage questions
      • Biomolecules
        • Amino acids and proteins
        • Enzyme structure and function
        • Enzyme kinetics
        • DNA
        • Gene control
        • Genetic mutations
        • Mendelian genetics
        • DNA technology
        • Chromosomal inheritance
        • Evolution and population dynamics
        • Principles of bioenergetics
        • Overview of metabolism
        • Carbohydrates
        • Carbohydrate Metabolism
        • Krebs (citric acid) cycle and oxidative phosphorylation
        • Fat and protein metabolism
        • Endocrine system
        • Hormonal regulation
      • Cells
        • Cell membrane overview
        • Cell-cell interactions
        • Transport across a cell membrane
        • Cell theory
        • Eukaryotic cells
        • Cytoskeleton
        • Prokaryotes/bacteria
        • Viruses
        • Cellular division
        • Cellular development
        • Embryology
      • Organ systems
        • Biological basis of behavior: The nervous system
        • Neural cells
        • Neuron membrane potentials
        • Neuronal synapses
        • Biosignaling
        • Endocrine system
        • Circulatory system
        • Hematologic system
        • Respiratory system
        • Lymphatic system
        • Immune system
        • Renal system
        • Renal regulation of blood pressure
        • Gastrointestinal system
        • Muscular system
        • Skeletal system
        • Integumentary system
        • Reproductive system
      • Physical processes
        • Vectors and scalars
        • Speed and velocity
        • Acceleration
        • Newton's laws and equilibrium
        • Normal forces
        • Force of tension
        • Forces on inclined planes
        • Work and energy
        • Fluids at rest
        • Fluids in motion
        • Gas phase
        • Kinetic molecular theory of gases
        • Electrostatics
        • Current and resistance
        • Capacitors
        • Magnetism
        • Electrochemistry
        • Sound
        • Light and electromagnetic radiation
        • Infrared and Ultraviolet/Visible spectroscopy
        • Proton nuclear magnetic resonance
        • Thin lenses
        • Spherical mirrors
        • Reflection and refraction
        • Atomic nucleus
        • Electronic structure
        • Periodic table
        • Stoichiometry
        • Balancing chemical equations
        • Redox reactions
      • Chemical processes
        • Acid/base equilibria
        • Titrations
        • Solubility equilibria
        • Dot structures
        • Stereochemistry
        • Covalent bonds
        • Separations and purifications
        • Nucleic acids, lipids, and carbohydrates
        • Amino acids, peptides, proteins
        • Proteins
        • Carbohydrates
        • Alpha-carbon chemistry
        • Aldehydes and ketones
        • Alcohols and phenols
        • Carboxylic acids
        • Carboxylic acid derivatives
        • Enzymes
        • Kinetics
        • Equilibrium
        • Bioenergetics
        • Thermodynamics
        • Thermochemistry
      • Processing the environment
        • Sensory perception
        • Sight (vision)
        • Sound (Audition)
        • Somatosensation
        • Taste (gustation) and smell (olfaction)
        • Sleep and consciousness
        • Drug dependence
        • Attention
        • Memory
        • Cognition
        • Language
        • Emotion
        • Stress
      • Behavior
        • Biological basis of behavior: Nervous system
        • Human development
        • Behavior and genetics
        • Motivation and attitudes
        • Theories of personality
        • Psychological disorders
        • Social psychology
        • Normative and non-normative behavior
        • Learning
        • Theories of attitude and behavior change
      • Individuals and society
        • Self-identity
        • Perception, prejudice, and bias
        • Attributing behavior to persons or situations
        • Social behavior
        • Social interactions
        • Self-presentation and interacting with others
        • Biological explanations of social behavior in animals
        • Discrimination
      • Society and culture
        • Social structures
        • Demographics
        • Culture
      • Social inequality
        • Social inequality
    • NCLEX-RN
      • NCLEX-RN practice questions
        • NCLEX-RN questions
      • Circulatory system physiology
        • Circulatory system introduction
        • Blood pressure
        • Blood pressure control
        • Fetal circulation
        • Blood vessels
        • Arterial stiffness
        • Heart muscle contraction
        • Heart depolarization
        • Nerve regulation of the heart
        • Preload and afterload
        • Pressure volume loops
        • Changing the PV loop
      • Circulatory system diseases
        • Hypertension
        • Coronary artery disease
        • Stroke
        • Heart failure
        • Cardiac dysrhythmias and tachycardias
        • Acyanotic heart diseases
        • Cyanotic heart diseases
        • Vasculitis
        • Cardiomyopathy
        • Myocarditis and pericarditis
        • Aortic dissection and aneurysm
        • Heart valve diseases
        • Shock
      • Respiratory system physiology
        • Respiratory system introduction
        • Gas Exchange
        • Breathing Control
      • Respiratory system diseases
        • Introduction to pulmonary diseases
        • Asthma
        • Emphysema (COPD)
        • Chronic bronchitis (COPD)
        • Cystic fibrosis
        • Bronchiolitis
        • Lung cancer
        • Pneumonia
        • Pleural effusion
        • Nose, sinus, and upper respiratory track infections
        • Laryngeal conditions
        • Occupational lung diseases
        • Pulmonary hypertension
        • Throat conditions
        • Pertussis
      • Hematologic system diseases
        • Anemia
        • Leukemia
        • Plasma cell dyscrasias
        • Iron deficiency anemia and anemia of chronic disease
        • Myeloproliferative disorders
      • Endocrine system physiology
        • Endocrine system introduction
      • Endocrine system diseases
        • Diabetes
      • Lymphatic system physiology
        • Lymphatic system
      • Immune system physiology
        • Immune system
      • Renal system physiology
        • Renal system introduction
        • Renal regulation of blood pressure
      • Gastrointestinal system physiology
        • Gastrointestinal system
      • Gastrointestinal system diseases
        • Gastroenteritis
        • Inflammatory bowel disease
        • Celiac disease
      • Muscular-skeletal system physiology
        • Muscular system
        • Skeletal system
      • Muscular-skeletal diseases
        • Arthritis and rheumatoid arthritis
      • Nervous system physiology
        • Neural cells
        • Neuron membrane potentials
        • Neuronal synapses
        • Biosignaling
      • Nervous system diseases
        • Parkinson's disease
        • Multiple sclerosis
      • Integumentary system physiology
        • Integumentary system
      • Reproductive system physiology
        • Reproductive system
        • Pregnancy and pregnancy complications
      • Infectious diseases
        • Sexually transmitted diseases
        • Polio
        • HIV and AIDS
        • Malaria
        • Tuberculosis
      • Mental health
        • Drug abuse and drug addictions
        • Depression and related disorders
        • Anxiety
        • Psychotic disorders
        • Dementia, delirium, and Alzheimer's
        • Neurodevelopmental disorders
    • GMAT
      • Problem solving
      • Data sufficiency
    • CAHSEE
      • CAHSEE
    • IIT JEE
      • IIT JEE
  • KA Educator
  • Partner content
    • The Metropolitan Museum of Art
      • 82nd & Fifth
        • Body and mind
        • Books, music, and literature
        • Devotion
        • Dining
        • Family and community
        • Intersections
        • Nature
        • Observations
        • Power
        • Puzzles and surprises
        • The art of dress
        • Transformations
        • War and conquest
      • Extravagant Inventions
      • Making, finding, and conserving
      • #MetKids: Made for, with, and by kids
        • Q&A
        • Celebrate
        • Made by kids
        • Create
    • Tate
      • Get started and The Big Question
        • Welcome to Tate on Khan Academy
      • Conflict and Contradiction in Art
        • Activities
        • Art and Conflict
        • Documenting Conflict
        • Challenging the State
        • Creating Contradiction
      • Women in Art and Art History
        • Activities
        • A Brief History of Women in Art
        • Women as Artists
        • Women's Issues in Art
      • Global Modernisms
        • Pop art around the world
        • Africa
        • Latin America
        • Asia
        • The Middle East
      • Meet 500 years of British art
        • Welcome to 500 years of British art
        • 16th to 18th century: Dynasty, revolution, and the Classical Age
        • 19th century: Romanticism and the Victorian Era
        • Early 20th century: War and dynamism
        • Mid-century to today: Modernism and its legacy
      • Meet the artist: JMW Turner
        • Activities
        • Turner: The Artist and His Work
        • Visit Turner's Gallery
        • Learn to paint like Turner
      • Archives, Memory, and Conservation
        • Activities
        • What is an archive?
        • Art and Memory
        • Conservation: Behind the scenes
      • Performance and Participation
        • Performance art
        • Collaboration
        • Participation
      • The Art of Inspiration
        • Film meets art
        • Fashion meets art
        • Literature meets art
        • Art and appropriation
    • The Museum of Modern Art
      • Printmaking
      • 1913 Centennial Celebration
      • Behind the scenes at MoMA
      • Abstract Expressionism
      • Art terms in action
      • Artist interviews
      • Performance Art
      • MoMA Learning
      • Modern Art & Ideas
        • Modern Art & Ideas
      • Seeing Through Photographs
        • Seeing Through Photographs
    • The J. Paul Getty Museum
      • Antiquities
        • Ancient glassmaking
        • Ancient Greek vases
        • The Roman silversmith's craft
        • Gem carving in antiquity
        • Marble from antiquity to modern times
        • Inspiration from the classical past
      • Manuscripts
      • Art conservation
      • Paintings
      • Decorative arts
      • Sculpture
      • Photographs
        • Introducing photography
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        • Photographers
      • Drawings
      • For kids
    • California Academy of Sciences
      • Welcome to the world of biodiversity!
        • Welcome
      • Why is biodiversity important?
        • Biodiversity and ecosystem function
        • Biodiversity and ecosystem services
      • Where is biodiversity found?
        • Biodiversity Hotspots
        • Biodiversity distribution patterns
      • How is biodiversity studied?
        • Biodiversity fieldwork
        • Biodiversity analyses and unknowns
      • Why is biodiversity threatened?
        • Local threats to biodiversity
        • Global threats to biodiversity
      • How can biodiversity be protected?
        • Harnessing science and education for biodiversity conservation
        • Biodiversity champions
      • Where does biodiversity come from?
        • The evolutionary causes of biodiversity
        • Biodiversity patterns of speciation and extinction
      • What are the different levels of biodiversity?
        • Genetic and ecosystem biodiversity
        • Biodiversity and the tree of life
      • Exploring ecosystems
    • Exploratorium
      • Sound
        • Sound Introduction
        • Vocal Visualizer
      • Light and color
        • Light and Color Introduction
        • Soap Film on a Can
        • Soap Film Interference Model
        • CD Spectroscope
        • Colored Shadows
      • Chemistry
        • Chemistry introduction
        • Penny Battery
        • Ocean Acidification in a Cup
        • Indicating Electrolysis
      • Electromagnetism
        • Electromagnetism Introduction
        • Flying Tinsel
        • Turn Light into Sound
    • American Museum of Natural History
      • Dinosaurs
        • What is a dinosaur?
        • How do scientists study dinosaurs?
        • Dinosaur extinction
        • Dinosaur fossils
      • The Universe
        • Planets
        • Stars
        • Galaxies
        • Universe
      • Human Evolution
        • Darwin and evolution by natural selection (American Museum of Natural History)
        • Human evolution: The evidence (American Museum of Natural History)
        • Evolution and human health (American Museum of Natural History)
      • Earthquakes and Volcanoes
        • Plate Tectonics
        • Volcanoes
        • Earthquakes
    • Asian Art Museum
      • Overview
        • Overview
      • South Asia
        • South Asia
      • Southeast Asia
        • Cambodia and Myanmar (Burma)
        • Indonesia
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      • The Himalayas and the Tibetan Buddhist World
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      • China
        • China
      • Korea
        • Korea
      • Japan
        • Japan
      • Hinduism
        • Hinduism
      • Buddhism
        • Buddhism
      • Art conservation
        • Art Conservation
    • The British Museum
      • Africa
        • Introduction to Africa
        • Ancient Egypt
        • Aksum
        • Ife
        • Benin
        • Sierra Leone
      • The Americas
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        • Native North America
      • Asia
        • China
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      • Europe
        • Ancient Greece
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        • Ancient Near East
        • Islamic Middle East
      • Oceania
        • Polynesia
        • Melanesia
        • Micronesia
      • Contemporary Sculptors at the British Museum
    • All-Star Orchestra
      • Music basics
        • Notes and rhythm
        • Reading music
      • Masterpieces old and new
        • Ludwig van Beethoven: Symphony No. 5
        • Pyotr Ilyich Tchaikovsky: Symphony No.4
        • Robert Schumann: Symphony No. 3 "Rhenish"
        • Johannes Brahms: Academic Festival Overture
        • Antonín Dvořák: Symphony No. 9 "From the New World"
        • Gustav Mahler: Symphony No. 2 – 1st Movement
        • Igor Stravinsky: Suite from The Firebird
        • Maurice Ravel: Suite No. 2 from Daphnis et Chloe
        • Dmitri Shostakovich: Symphony No. 5
        • Introduction to Philip Glass' "Harmonium Mountain"
        • Bernard Rands: Adieu
        • Augusta Read Thomas: Of Paradise and Light
        • Bright Sheng: Black Swan
        • Richard Danielpour: Piano Concerto No. 4, Movement III
        • David Stock: Blast!
        • Ellen Taaffe Zwilich: Avanti!
        • Joseph Schwantner: The Poet's Hour
      • Instruments of the orchestra
        • Strings
        • Woodwinds
        • Brass
        • Percussion
    • Stanford School of Medicine
      • Tuberculosis
      • Influenza
      • Growth and Metabolism
      • Asthma
      • Breastfeeding
    • Wireless Philosophy
      • Critical thinking
        • Fundamentals
        • Fallacies
        • Cognitive biases
      • Metaphysics and epistemology
        • Metaphysics
        • Mind
        • Language
        • Theory of knowledge
        • Epistemology
        • Religion
      • Value theory
        • Ethics
        • Political
        • The good life
      • History of philosophy
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        • Hume
        • Kant
        • Contemporary
    • MIT+K12
      • Chemistry and biology
      • Engineering and electronics
      • Physics
      • Earth and space
      • Math
      • Materials
      • Measurement
    • LeBron asks
      • LeBron asks
    • The Brookings Institution
      • Introduction to health care in the U.S.
    • Pixar in a Box
      • Orientation
        • Start here
      • The art of storytelling
        • 1. We are all storytellers
        • 2. Character
        • 3. Story structure
        • 4. Visual language
        • 5. Film grammar
        • 6. Pitching and feedback
      • Simulation
        • Hair simulation 101
        • Code your own simulation
      • Color science
        • Introduction to color
        • Color spaces
      • Virtual cameras
        • How virtual cameras work
        • Mathematics of depth of field
      • Effects
        • Introduction to particle systems
        • The physics of particle systems
      • Patterns
        • Geometry of dinosaur skin
        • Painting with randomness
      • Rigging
        • Introduction to rigging
        • Code a character
      • Animation
        • Introduction to animation
        • Mathematics of animation curves
      • Environment modeling
        • Modeling grass with parabolas
        • Calculating parabolas
      • Character modeling
        • Modeling with subdivision surfaces
        • Mathematics of subdivision
      • Crowds
        • Building crowds
        • Counting crowds
      • Sets & staging
        • Geometric transformations
        • Mathematics of rotation
      • Rendering
        • Rendering 101
        • Mathematics of rendering
    • The Aspen Institute
      • The founding documents of the United States of America
        • The Declaration of Independence
        • The Articles of Confederation
        • The Constitution of the United States
      • The founding fathers of the United States of America
        • George Washington
        • Benjamin Franklin
        • James Madison
        • Alexander Hamilton
      • The founding mothers of the United States of America
        • Women in early America
        • An introduction to the founding mothers
        • Women and the expansion of America
      • Civil liberties, privacy, and the Constitution
        • The modern U.S. Supreme Court on privacy and civil liberties
        • How the Constitution deals with civil liberties and privacy in an age of technological change
        • The Reconstruction Amendments
      • The American Diplomatic Toolbox
        • Madeleine Albright, former Secretary of State
        • Joe Nye, American political scientist
        • General Colin Powell
        • Alec Ross, former senior advisor for innovation of the U.S. Department of State
        • Tara Sonenshine, former Under Secretary of State for Public Diplomacy and Public Affairs
        • Strobe Talbott, former Deputy Secretary of State
    • NASA
      • Welcome to NASA Mission Control
        • Welcome
      • Measuring the Universe
        • Modeling the solar system
        • Measuring the solar system
        • Orbital mechanics 1
        • Spectroscopy
      • Exploring the Universe
        • Mars: Modern exploration
        • Mars: Ancient observations
        • Curiosity rover: mission briefing
        • Curiosity rover: discoveries
    • NOVA Labs
      • Evolution
        • Evolution 101
      • Cybersecurity
        • Cybersecurity
      • RNA: the wonder molecule
      • The Sun and solar storms
      • Energy
      • Clouds
    • Big History Project
      • 1. What Is Big History?
        • 1.0—Welcome to Big History
        • 1.1—Scale
        • 1.2—Origin Stories
        • 1.3—What Are Disciplines?
        • 1.4—My Big History
        • Glossary
        • Other Materials
        • Resources
      • 2. The Big Bang
        • 2.0—How Did Our Understanding of the Universe Change?
        • 2.1—The Big Bang
        • 2.2—Claim Testing
        • Glossary
        • Other Materials
        • Resources
      • 3. Stars & Elements
        • 3.0—How Were Stars Formed?
        • 3.1—Creation of Complex Elements
        • 3.2—Way of Knowing: Stars and Elements
        • Glossary
        • Other Materials
        • Resources
      • 4. Our Solar System & Earth
        • 4.0—Earth & the Formation of Our Solar System
        • 4.1—What Was Young Earth Like?
        • 4.2—Why Is Plate Tectonics Important?
        • 4.3—Ways of Knowing: Our Solar System and Earth
        • Glossary
        • Other Materials
        • Resources
      • 5. Life
        • 5.0—What Is Life?
        • 5.1—How Did Life Begin and Change?
        • 5.2—How Do Earth and Life Interact? ?
        • 5.3—Ways of Knowing: Life
        • Glossary
        • Other Materials
        • Resources
      • 6. Early Humans
        • 6.0—How Our Ancestors Evolved
        • 6.1—Ways of Knowing: Early Humans
        • 6.2—Collective Learning
        • 6.3—How Did the First Humans Live?
        • Glossary
        • Other Materials
        • Resources
      • 7. Agriculture & Civilization
        • 7.0—The Rise of Agriculture
        • 7.1—The First Cities and States Appear
        • 7.2—Ways of Knowing: Agriculture and Civilization
        • Glossary
        • Other Materials
        • Resources
      • 8. Expansion & Interconnection
        • 8.0—Expansion
        • 8.1—Exploration & Interconnection
        • 8.2—Commerce & Collective Learning
        • Glossary
        • Other Materials
        • Resources
      • 9. Acceleration
        • 9.0—Acceleration
        • 9.1—The Anthropocene
        • 9.2—Changing Economies
        • Glossary
        • Other Materials
        • Resources
      • 10. The Future
        • 10.0—Looking Back
        • 10.1—The Biosphere
        • 10.2—Looking Forward
        • Glossary
        • Other Materials
        • Resources
    • Silicon Schools Fund and Clayton Christensen Institute
      • Introduction to blended learning
        • An overview of blended learning
        • Four different blended learning models
      • Teaching in a blended learning environment – rethinking the role of the teacher
        • An overview of the teacher experience
        • Case studies: teaching in a blended learning environment
        • The moves of a blended learning teacher
      • Redesigning a school toward blended learning
        • School redesign overview
        • Challenging existing assumptions
        • Leading change in blended learning
      • Making aligned hardware, software, and space decisions in a blended learning environment
        • Hardware, software and facilities decisions overview
        • Blended learning software
        • Blended learning hardware and infrastructure
        • Blended learning facilities and furniture
    • Dartmouth College
      • Learn Algorithms with Dartmouth College
    • Code.org
      • How the Internet Works
    • Breakthrough Junior Challenge
      • 2015 Challenge
        • 2015 Challenge — Mathematics
        • 2015 Challenge — Life sciences
        • 2015 Challenge — Physics
    • Science & engineering partners
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    • 49ers STEAM education
      • 49ers ask
        • 49ers ask
      • Science behind the game
        • Force and motion
        • Environmental sustainability
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        • How technology impacts the game
      • Gridiron engineering
        • Innovations in football equipment
        • Stadium structural engineering
      • Art in football
        • Elements of art & design in football
      • Geometry & statistics in football
        • The use of angles in the game
        • Statistics in football
      • Related Khan Academy videos
        • Related Khan Academy videos
    • 23andMe
      • Human prehistory
    • LearnStorm growth mindset activities
      • Activity #1: The truth about your brain
        • Get started!
      • Activity #2: Supercharge your growth
        • Get started!
      • Activity #3: Which voice will you hear?
        • Get started!
      • Activity #4: Turning mistakes into opportunities
        • Get started!
      • Activity #5: Overcoming frustration
        • Get started!
      • Activity #6: The path forward
        • Get started!
      • Growth mindset teacher resources
        • Growth mindset activity teacher resources
      • Growth mindset activity submission highlights
        • Growth mindset activity submission highlights
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    • Careers
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      • Serve your community
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    • Personal finance
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      • Auto
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      • Taxes
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        • Protecting your personal information
      • Paying for college
        • Introduction: Paying for college
        • Financial aid application process
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        • Work study
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      • Keeping your information safe
        • Password strength and other strategies
    • Entrepreneurship
      • Interviews with entrepreneurs
        • Sal chats with entrepreneurs
        • Richard Branson - Chairman of the Virgin Group
        • Marc Ecko - Founder of Ecko Unlimited
        • Philip Rosedale - Founder and Chairman of Second Life
        • Zach Kaplan - CEO of Inventables
        • T.A. McCann - Founder and CEO of Gist
        • Ben Milne - CEO of Dwolla
        • Giles Shih - President and CEO of BioResource International
        • Danny O'Neill - President of The Roasterie
        • Lara Morgan - Founder of Pacific Direct
        • Dave Smith - CEO & Founder of TekScape IT
        • Jason Christiansen - President & CEO of Rigid Industries
        • Linda Jeschofnig - Co-founder of Hands-On Labs
        • LaKeshia Grant - CEO & Founder of Virtual Enterprise Architects
        • Dave Gilboa & Neil Blumenthal - Co-founders & Co-CEOs of Warby Parker
        • Calvin Carter - Founder of Bottle Rocket Apps
        • Beth Schmidt - Founder of Wishbone.org
        • Toby Rush - CEO & Founder of EyeVerify
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    • Geometry < 160
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 161-178
      • Geometric Measurement and Relationships
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 179-191
      • Geometric Measurement and Relationships
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 192-202
      • Geometric Measurement and Relationships
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 203-212
      • Geometric Measurement and Relationships
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 213-219
      • Geometric Measurement and Relationships
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 220-223
      • Geometric Measurement and Relationships
      • Reason with Shapes, Attributes, & Coordinate Plane
    • Geometry 224-227
      • Geometric Measurement and Relationships
    • Geometry 228-230
      • Congruence, Similarity, Right Triangles, & Trig
      • Geometric Measurement and Relationships
    • Geometry > 231
      • Congruence, Similarity, Right Triangles, & Trig
      • Geometric Measurement and Relationships
    • Operations and Algebra < 160
      • Represent and Solve Problems
    • Operations and Algebra 161-178
      • Represent and Solve Problems
      • Expressions and Equations
    • Operations and Algebra 179-191
      • Represent and Solve Problems
      • Expressions and Equations
    • Operations and Algebra 192-202
      • Represent and Solve Problems
      • Analyze Patterns and Relationships
      • Expressions and Equations
    • Operations and Algebra 203-212
      • Represent and Solve Problems
      • Analyze Patterns and Relationships
      • Expressions and Equations
    • Operations and Algebra 213-219
      • Represent and Solve Problems
      • Analyze Patterns and Relationships
      • Expressions and Equations
      • Use Functions to Model Relationships
    • Operations and Algebra 220-223
      • Represent and Solve Problems
      • Expressions and Equations
    • Operations and Algebra 224-227
      • Represent and Solve Problems
      • Expressions and Equations
    • Operations and Algebra 228-230
      • Expressions and Equations
      • Use Functions to Model Relationships
    • Operations and Algebra > 231
      • Represent and Solve Problems
      • Expressions and Equations
      • Use Functions to Model Relationships
    • Measurement and Data < 160
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 161-178
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 179-191
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 192-202
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 203-212
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 213-219
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 220-223
      • Represent and Interpret Data
      • Geometric Measurement and Problem Solving
    • Measurement and Data 224-227
      • Geometric Measurement and Problem Solving
    • Numbers and Operations < 160
      • Understand Place Value, Counting, and Cardinality
    • Numbers and Operations 161-178
      • Understand Place Value, Counting, and Cardinality
      • Base Ten
    • Numbers and Operations 179-191
      • Understand Place Value, Counting, and Cardinality
      • Base Ten
    • Numbers and Operations 192-202
      • Understand Place Value, Counting, and Cardinality
      • Base Ten
      • Fractions
    • Numbers and Operations 203-212
      • Understand Place Value, Counting, and Cardinality
      • Base Ten
      • Fractions
    • Numbers and Operations 213-219
      • Understand Place Value, Counting, and Cardinality
      • Base Ten
      • Fractions
    • Numbers and Operations 220-223
      • Base Ten
      • Fractions
    • Numbers and Operations 224-227
      • Base Ten
      • Fractions
    • Real and Complex Numbers < 160
      • Extend and Use Properties
      • Perform Operations
    • Real and Complex Numbers 161-178
      • Extend and Use Properties
      • Perform Operations
    • Real and Complex Numbers 179-191
      • Perform Operations
      • Extend and Use Properties
    • Real and Complex Numbers 192-202
      • Extend and Use Properties
      • Perform Operations
    • Real and Complex Numbers 203-212
      • Extend and Use Properties
      • Perform Operations
      • Ratios and Proportional Relationships
    • Real and Complex Numbers 213-219
      • Perform Operations
      • Extend and Use Properties
      • Ratios and Proportional Relationships
    • Real and Complex Numbers 220-223
      • Extend and Use Properties
      • Perform Operations
      • Ratios and Proportional Relationships
    • Real and Complex Numbers 224-227
      • Ratios and Proportional Relationships
      • Perform Operations
    • Real and Complex Numbers 228-230
      • Extend and Use Properties
    • Real and Complex Numbers > 231
      • Extend and Use Properties
      • Perform Operations
    • Statistics and Probability 161-178
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability 179-191
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability 192-202
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability 203-212
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability 213-219
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability 220-223
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability 224-227
      • Using Sampling and Probability to Make Decisions
    • Statistics and Probability 228-230
      • Interpreting Categorical and Quantitative Data
    • Statistics and Probability > 231
      • Interpreting Categorical and Quantitative Data
      • Using Sampling and Probability to Make Decisions