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Common Core Mathematics
Prealgebra
01. Variables, Expressions, and Integers
1.1 Expressions of Variables
1.2 Powers and Exponents
1.3 Order of Operations
1.4 Comparing and Ordering Integers
1.5 Adding Integers
1.6 Subtracting Integers
1.7 Multiplying and Dividing Integers
1.8 The Coordinate Plane
02. Solving Equations
2.1 Properties of Operations
2.2 The Distributive Property
2.3 Simplifying Variable Expressions
2.4 Variables and Equations
2.5 Solving Equations Using Addition or Subtraction
2.6 Solving Equations Using Multiplication or Division
2.7 Decimal Operations and Equations with Decimals
03. Multi-step Equations and Inequalities
3.1 Solving Two-step Equations
3.2 Solving Equations Having Like Terms and Parentheses
3.3 Solving Equations with Variables on Both Sides
3.4 Solving Inequalities Using Addition or Subtraction
3.5 Solving Inequalities Using Multiplication or Division
3.6 Solving Multi-step Inequalities
04. Factors, Fractions, and Exponents
4.1 Factors and Prime Factorization
4.2 Greatest Common Factor
4.3 Equivalent Fractions
4.4 Least Common Multiple
4.5 Rules of Exponents
4.6 Negative and Zero Exponents
4.7 Scientific Notation
05. Rational Numbers and Equations
5.1 Rational Numbers
5.2 Adding and Subtracting Like Fractions
5.3 Adding and Subtracting Unlike Fractions
5.4 Multiplying Fractions
5.5 Dividing Fractions
5.6 Using Multiplicative Inverses to Solve Equations
5.7 Equations and Inequalities with Rational Numbers
06. Ratio, Proportion, and Probability
6.1 Ratios and Rates
6.2 Writing and Solving Proportions
6.3 Solving Proportions Using Cross Products
6.4 Similar and Congruent Figures
6.5 Similarity and Measurement
6.6 Scale Drawings
6.7 Probability and Odds
6.8 The Counting Principle
07. Percents
7.1 Percents and Fractions
7.2 Percents and Proportions
7.3 Percents and Decimals
7.4 The Percent Equation
7.5 Percent of Change
7.6 Percent Applications
7.7 Simple and Compound Interest
08. Linear Functions
8.1 Relations and Functions
8.2 Linear Equations in Two Variables
8.3 Using Intercepts
8.4 The Slope of a Line
8.5 Slope-Intercept Form
8.6 Writing Linear Equations
8.7 Function Notation
8.8 Systems of Linear Equations
8.9 Graphs of Linear Inequalities
09. Real Numbers and Right Triangles
9.1 Square Roots
9.2 Simplifying Square Roots
9.3 The Pythagorean Theorem
9.4 Real Numbers
9.5 The Distance and Midpoint Formulas
9.6 Special Right Triangles
9.7 The Tangent Ratio
9.8 The Sine and Cosine Ratios
10. Measurement, Area, and Volume
10.1 Triangles
10.2 Polygons and Quadrilaterals
10.3 Areas of Parallelograms and Trapezoids
10.4 Circumference and Area of a Circle
10.5 Surface Areas of Prisms and Cylinders
10.6 Surface Areas of Pyramids and Cones
10.7 Volumes of Prisms and Cylinders
10.8 Volumes of Pyramids and Cones
11. Data Analysis and Probability
11.1 Stem-and-Leaf Plots and Histograms
11.2 Box-and-whisker Plots
11.3 Using Data Displays
11.4 Collecting Data
11.5 Interpreting Data
11.6 Permutations
11.7 Combinations
11.8 Probabilities of Disjoint and Overlapping Events
11.9 Independent and Dependent Events
12. Polynomials and Nonlinear Functions
12.1 Polynomials
12.2 Adding and Subtracting Polynomials
12.3 Multiplying Monomials and Polynomials
12.4 Multiplying Binomials
12.5 Other Rules of Exponents
12.6 Quadratic Functions
12.7 Exponential Growth and Decay
12.8 Sequences
13. Angle Relationships and Transformations
13.1 Angle Relationships
13.2 Angles and Parallel Lines
13.3 Angles and Polygons
13.4 Translations
13.5 Reflections and Symmetry
13.6 Rotations and Symmetry
13.7 Dilations
Algebra I
01. Foundations for Algebra
1.1 Variable and Expressions
1.2 Order of Operations and Evaluating Expressions
1.3 Real Numbers and the Number Line
1.4 Properties of Real Numbers
1.5 Adding and Subtracting Real Numbers
1.6 Multiplying and Dividing Real Numbers
1.7 The Distributive Property
1.8 An Introduction to Equations
1.9 Patterns, Equations, and Graphs
02. Solving Equations
2.1 Solving One-step Equations
2.2 Solving Two-step Equations
2.3 Solving Multi-step Equations
2.4 Solving Equations with Variables on Both Sides
2.5 Literal Equations and Formulas
2.6 Ratios, Rates, and Conversions
2.7 Solving Proportions
2.8 Proportions of Similar Figures
2.9 Percents
2.10 Change Expressed as a Percent
03. Solving Inequalities
3.1 Inequalities and Their Graphs
3.2 Solving Inequalities Using Addition or Subtraction
3.3 Solving Inequalities Using Multiplication or Division
3.4 Solving Multi-step Inequalities
3.5 Working with Sets
3.6 Compound Inequalities
3.7 Absolute Value Equations and Inequalities
3.8 Unions and Intersections of Sets
04. An Introduction to Functions
4.1 Using Graphs to Relate Two Quantities
4.2 Patterns and Linear Functions
4.3 Patterns and Nonlinear Functions
4.4 Graphing a Function Rule
4.5 Writing a Function Rule
4.6 Formalizing Relations and Functions
4.7 Arithmetic Sequences
05. Linear Functions
5.1 Rate of Change and Slope
5.2 Direct Variation
5.3 Slope-Intercept Form
5.4 Point-Slope Form
5.5 Standard Form
5.6 Parallel and Perpendicular Lines
5.7 Scatter plots and Trend Lines
5.8 Graphing Absolute Value Functions
06. Systems of Equations and Inequalities
6.1 Solving Systems by Graphing
6.2 Solving Systems by Substitution
6.3 Solving Systems by Elimination
6.4 Applications of Linear Systems
6.5 Linear Inequalities
6.6 Systems of Linear Inequalities
07. Exponents and Exponential Functions
7.1 Zero and Negative Exponents
7.2 Multiplying Powers with the Same Base
7.3 More Multiplication Properties of Exponents
7.4 Division Properties of Exponents
7.5 Rational Exponents and Radicals
7.6 Exponential Functions
7.7 Exponential Growth and Decay
7.8 Geometric Sequences
08. Polynomials and Factoring
8.1 Adding and Subtracting Polynomials
8.2 Multiplying and Factoring
8.3 Multiplying Binomials
8.4 Multiplying Special Cases
8.5 Factoring x^2 + bx +c
8.6 Factoring ax^2 + bx +c
8.7 Factoring Special Cases
8.8 Factoring by Grouping
09. Quadratic Functions and Equations
9.1 Quadratic Graphs and Their Properties
9.2 Quadratic Functions
9.3 Solving Quadratic Equations
9.4 Factoring to Solve Quadratic Equations
9.5 Completing the Square
9.6 The Quadratic Formula and the Discriminant
9.7 Linear, Quadratic, and Exponential Models
9.8 Systems of Linear and Quadratic Equations
10. Radical Expressions and Equations
10.1 The Pythagorean Theorem
10.2 Simplifying Radicals
10.3 Operations with Radical Expressions
10.4 Solving Radical Equations
10.5 Graphing Square Root Functions
10.6 Trigonometric Ratios
11. Rational Expressions and Functions
11.1 Simplifying Rational Expressions
11.2 Multiplying and Dividing Rational Expressions
11.3 Dividing Polynomials
11.4 Adding and Subtracting Rational Expressions
11.5 Solving Rational Equations
11.6 Inverse Variation
11.7 Graphing Rational Functions
12. Data Analysis and Probability
12.1 Organizing Data Using Matrices
12.2 Frequency and Histograms
12.3 Measures of Central Tendency and Dispersion
12.4 Box-and-whisker Plots
12.5 Samples and Surveys
12.6 Permutations and Combinations
12.7 Theoretical and Experimental Probability
12.8 Probability of Compound Events
Geometry
01. Tools of Geometry
1.1 Nets and Drawings for Visualizing Geometry
1.2 Points, Lines, and Planes
1.3 Measuring Segments
1.4 Measuring Angles
1.5 Exploring Angle Pairs
1.6 Basic Constructions
1.7 Midpoint and Distance in the Coordinate Plane
1.8 Perimeter, Circumference, and Area
02. Reasoning and Proof
2.1 Patterns and Inductive Reasoning
2.2 Conditional Statements
2.3 Biconditionals and Definitions
2.4 Deductive Reasoning
2.5 Reasoning in Algebra and Geometry
2.6 Proving Angles Congruent
03. Parallel and Perpendicular Lines
3.1 Lines and Angles
3.2 Properties of Parallel Lines
3.3 Proving Lines Parallel
3.4 Parallel and Perpendicular Lines
3.5 Parallel Lines and Triangles
3.6 Constructing Parallel and Perpendicular Lines
3.7 Equations of Lines in the Coordinate Plane
3.8 Slopes and Parallel and Perpendicular Lines
04. Congruent Triangles
4.1 Congruent Figures
4.2 Triangle Congruence by SSS and SAS
4.3 Triangle Congruence by ASA and AAS
4.4 Using Corresponding Parts of Congruent Triangles
4.5 Isosceles and Equilateral Triangles
4.6 Congruence in Right Triangles
4.7 Congruence in Overlapping Triangles
05. Relationships Within Triangles
5.1 Midsegments of Triangles
5.2 Perpendicular and Angle Bisectors
5.3 Bisectors in Triangles
5.4 Medians and Altitudes
5.5 Indirect Proof
5.6 Inequalities in One Triangle
5.7 Inequalities in Two Triangles
06. Polygons and Quadrilaterals
6.1 The Polygon Angle-Sum Theorems
6.2 Properties of Parallelograms
6.3 Proving That a Quadrilateral is a Parallelogram
6.4 Properties of Rhombuses, Rectangles, and Squares
6.5 Conditions for Rhombuses, Rectangles, and Squares
6.6 Trapezoids and Kites
6.7 Polygons in the Coordinate Plane
6.8 Applying Coordinate Geometry
6.9 Proofs Using Coordinate Geometry
07. Similarity
7.1 Ratios and Proportions
7.2 Similar Polygons
7.3 Proving Triangles Similar
7.4 Similarity in Right Triangles
7.5 Proportions in Triangles
08. Right Triangles and Trigonometry
8.1 The Pythagorean Theorem
8.2 Special Right Triangles
8.3 Trigonometry
8.4 Angles of Elevation and Depression
8.5 Laws of Sines
8.6 Laws of Cosines
09. Transformations
9.1 Translations
9.2 Reflections
9.3 Rotations
9.4 Compositions and Isometries
9.5 Congruence Transformations
9.6 Dilations
9.7 Similarity Transformations
10. Area
10.1 Areas of Parallelograms and Triangles
10.2 Areas of Trapezoids, Rhombuses, and Kites
10.3 Areas of Regular Polygons
10.4 Perimeters and Areas of Similar Figures
10.5 Trigonometry and Area
10.6 Circles and Arcs
10.7 Areas of Circles and Sectors
10.8 Geometric Probability
11. Surface Area and Volume
11.1 Space Figures and Cross Sections
11.2 Surface Areas of Prisms and Cylinders
11.3 Surface Areas of Pyramids and Cones
11.4 Volumes of Prisms and Cylinders
11.5 Volumes of Pyramids and Cones
11.6 Surfaces Areas and Volumes of Spheres
11.7 Areas and Volumes of Similar Solids
12. Tangent Lines
12.1 Tangent Lines
12.2 Chords and Arcs
12.3 Inscribed Angles
12.4 Angle Measures and Segment Lengths
12.5 Circles in the Coordinate Plane
12.6 Locus: A Set of Points
13. Probability
13.1 Experimental and Theoretical Probability
13.2 Probability Distributions and Frequency Tables
13.3 Permutations and Combinations
13.4 Compound Probability
13.5 Probability Models
13.6 Conditional Probability Formulas
13.7 Modeling Randomness
Algebra II
01. Expressions, Equations, and Inequalities
1.1 Patterns and Expressions
1.2 Properties of Real Numbers
1.3 Algebraic Expressions
1.4 Solving Equations
1.5 Solving Inequalities
1.6 Absolute Value Equations and Inequalities
02. Functions, Equations, and Graphs
2.1 Relations and Functions
2.2 Direct Variation
2.3 Linear Functions and Slope-Intercept Form
2.4 More About Linear Equations
2.5 Using Linear Models
2.6 Families of Functions
2.7 Absolute Value Functions and Graphs
2.8 Two-Variable Equations
03. Linear Systems
3.1 Solving Systems Using Tables and Graphs
3.2 Solving Systems Algebraically
3.3 Systems of Inequalities
3.4 Linear Programming
3.5 Systems with Three Variables
3.6 Solving Systems Using Matrices
04. Quadratic Functions and Equations
4.1 Quadratic Functions and Transformations
4.2 Standard Form of a Quadratic Function
4.3 Modeling with Quadratic Functions
4.4 Factoring Quadratic Expressions
4.5 Quadratic Equations
4.6 Completing the Square
4.7 The Quadratic Formula
4.8 Complex Numbers
4.9 Quadratic Systems
05. Polynomials and Polynomial Functions
5.1 Polynomial Functions
5.2 Polynomials, Linear Factors, and Zeros
5.3 Solving Polynomial Equations
5.4 Dividing Polynomials
5.5 Theorems about Roots of Polynomial Functions
5.6 The Fundamental Theorem of Algebra
5.7 The Binomial Theorem
5.8 Polynomial Models in the Real World
5.9 Transforming Polynomial Functions
06. Radical Functions and Rational Exponents
6.1 Roots and Radical Expressions
6.2 Multiplying and Dividing Radical Expressions
6.3 Binomial Radical Expressions
6.4 Rational Exponents
6.5 Solving Square Root and Other Radical Equations
6.6 Function Operations
6.7 Inverse Relations and Functions
6.8 Graphing Radical Functions
07. Exponential and Logarithmic Functions
7.1 Exploring Exponential Models
7.2 Properties of Exponential Functions
7.3 Logarithmic Functions as Inverses
7.4 Properties of Logarithms
7.5 Exponential and Logarithmic Equations
7.6 Natural Logarithms
08. Rational Functions
8.1 Inverse Variation
8.2 The Reciprocal Function Family
8.3 Rational Functions and Their Graphs
8.4 Rational Expressions
8.5 Adding and Subtracting Rational Expressions
8.6 Solving Rational Equations
09. Sequences and Series
9.1 Mathematical Patterns
9.2 Arithmetic Sequences
9.3 Geometric Sequences
9.4 Arithmetic Series
9.5 Geometric Series
10. Quadratic Relations and Conic Sections
10.1 Exploring Conic Sections
10.2 Parabolas
10.3 Circles
10.4 Ellipses
10.5 Hyperbolas
10.6 Translating Conic Sections
11. Probability and Statistics
11.1 Permutations and Combinations
11.2 Probability
11.3 Probability of Multiple Events
11.4 Conditional Probability
11.5 Probability Models
11.6 Analyzing Data
11.7 Standard Deviation
11.8 Samples and Surveys
11.9 Binomial Distributions
11.10 Normal Distributions
12. Matrices
12.1 Adding and Subtracting Matrices
12.2 Matrix Multiplication
12.3 Determinants and Inverses
12.4 Inverse Matrices and Systems
12.5 Geometric Transformations
12.6 Vectors
13. Periodic Functions and Trigonometry
13.1 Exploring Periodic Data
13.2 Angles and the Unit Circle
13.3 Radian Measure
13.4 The Sine Function
13.5 The Cosine Function
13.6 The Tangent Function
13.7 Translating the Sine and Cosine Functions
13.8 Reciprocal Trigonometric Functions
14. Trigonometric Identities and Equations
14.1 Trigonometric Identities
14.2 Solving Trigonometric Equations Using Inverses
14.3 Right Triangles and Trigonometric Ratios
14.4 Area and the Law of Sines
14.5 The Law of Cosines
14.6 Angle Identities
14.7 Double-Angle and Half-Angle Identities
Precalculus
01. Functions and Their Graphs
1.1 Rectangular Coordinates
1.2 Graphs of Equations
1.3 Linear Equations in Two Variables
1.4 Functions
1.5 Analyzing Graphs of Functions
1.6 A Library of Parent Functions
1.7 Transformations of Functions
1.8 Combinations of Functions: Composite Functions
1.9 Inverse Functions
1.10 Mathematical Modelling and Variation
02. Polynomial and Rational Functions
2.1 Quadratic Functions and Models
2.2 Polynomial Functions of Higher Degree
2.3 Polynomial and Synthetic Division
2.4 Complex Numbers
2.5 Zeros of Polynomial Functions
2.6 Rational Functions
2.7 Nonlinear Inequalities
03. Exponential and Logarithmic Functions
3.1 Exponential Functions and Their Graphs
3.2 Logarithmic Functions and Their Graphs
3.3 Properties of Logarithms
3.4 Exponential and Logarithmic Equations
3.5 Exponential and Logarithmic Models
04. Trigonometry
4.1 Radian and Degree Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications and Models
05. Analytic Trigonometry
5.1 Using Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Solving Trigonometric Equations
5.4 Sum and Difference Formulas
5.5 Multiple-Angle and Product-to-Sum Formulas
06. Additional Topics in Trigonometry
6.1 Law of Sines
6.2 Law of Cosines
6.3 Vectors in the Plane
6.4 Vectors and Dot Products
6.5 The Complex Plane
6.6 Trigonometric Form of a Complex Number
07. Systems of Equations and Inequalities
7.1 Linear and Nonlinear Systems of Equations
7.2 Two-Variable Linear Systems
7.3 Multivariable Linear Systems
7.4 Partial Fractions
7.5 Systems of Inequalities
7.6 Linear Programming
08. Matrices and Determinants
8.1 Matrices and Systems of Equations
8.2 Operations with Matrices
8.3 The Inverse of a Square Matrix
8.4 The Determinant of a Square Matrix
8.5 Applications of Matrices and Determinants
09. Sequences, Series, and Probability
9.1 Sequences and Series
9.2 Arithmetic Sequences and Series
9.3 Geometric Sequences and Series
9.4 Mathematical Induction
9.5 The Binomial Theorem
9.6 Counting Principles
9.7 Probability
10. Topics in Analytic Geometry
10.1 Lines
10.2 Introduction to Conics: Parabolas
10.3 Ellipses
10.4 Hyperbolas
10.5 Rotation of Conics
10.6 Parametric Equations
10.7 Polar Coordinates
10.8 Graphs of Polar Equations
10.9 Polar Equation of Conics