• 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