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• Equations & Inequalities

• Systems of Equations

• Functions & Graphs

• Polynomial & Rational Functions

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Equations and Inequalities 

Learn how to solve and graph different kinds of equations and inequalities, including quadratic ones. 

• Graphing and Writing Linear Equations

• Equations of Parallel and Perpendicular Lines

• Solving Quadratic Equations Using Algebra

• Analyzing and Solving Equations Graphically

• Applying Equations to Real-World Problems

• Understanding and Graphing Linear Inequalities

Systems of Equations and Inequalities 

Find ways to solve multiple equations together and work with matrices.

• Solving Systems in Two and Three Variables

• Introduction to Matrices and Their Applications

• Performing Matrix Operations

• Using Matrices to Model Motion

• Understanding Determinants and Inverses

• Solving Linear Inequalities and Optimizing with Linear Programming

Functions and Graphing

Understand different types of functions, how they behave, and how to graph and transform them. 

• Exploring Functions and Their Key Properties

• Operations with Multiple Functions

• Graphing Piecewise Functions

• Transforming Graphs of Functions

• Recognizing and Analyzing Twelve Fundamental Functions

Graphs and Relationships

Explore patterns in graphs, learn about inverse functions, and work with rational functions. 

• Symmetry and Patterns in Graphs

• Families of Graphs and Their Characteristics

• Graphing Nonlinear Inequalities

• Understanding Inverse Functions and Relations

• Graphs of Rational Functions and Their Variations

• Direct, Inverse, and Joint Variations

Polynomial and Rational Functions

Practice advanced skills like dividing polynomials, finding roots, and simplifying rational equations. 

• Dividing Polynomials and Using the Remainder Theorem

• Applying the Factor Theorem and Rational Root Theorem

• Locating Zeros of Polynomial Functions

• Working with Complex Numbers in Equations

• Simplifying Rational Equations and Partial Fractions

• Solving Radical Equations and Inequalities

Exponential and Logarithmic Functions

Study exponential and logarithmic functions, solve related equations, and learn about the number e. 

• Properties of Exponents and Radicals

• Exponential Functions, Including Base e

• Graphing and Analyzing Logarithmic Functions

• Applying the Laws of Logarithms

• Solving Exponential and Logarithmic Equations

Trigonometric Concepts

Work with angles, the unit circle, and basic trigonometric functions.

• Angles in Degrees and Radians

• Trigonometric Ratios in Right Triangles

• Trigonometric Functions on the Unit Circle

• Solving Problems with Trigonometric Applications

Trigonometric Graphs and Equations

Graph trigonometric functions and use identities to solve equations.

• Graphing Sine, Cosine, and Other Trigonometric Functions

• Amplitude, Period, and Phase Shifts

• Graphing Composite and Inverse Trigonometric Functions

• Solving Trigonometric Equations Using Identities

Advanced Trigonometric Identities

Learn and use trigonometric identities and solve more complex equations.

• Applying the Law of Sines and Law of Cosines

• Verifying Basic and Complex Trigonometric Identities

• Using Sum, Difference, Double-Angle, and Half-Angle Identities

• Advanced Trigonometric Equations

• Distance Calculations and Linear Equations

Vectors, Parametric Equations, and Polar Coordinates

Understand vectors in three dimensions, parametric equations, and polar graphs.

• Geometric and Algebraic Vectors

• Dot Products and Working with 3D Vectors

• Parametric Equations and Polar Coordinates

• Polar Equations and Applying De Moivre’s Theorem

Conics and Three-Dimensional Geometry

Study shapes like circles, ellipses, and hyperbolas, and learn about 3D graphing.

• Circles, Parabolas, Ellipses, and Hyperbolas

• Conics and Rotations

• Graphing Polar Equations of Conics

• Three-Dimensional Coordinate Systems

Statistics and Probability

Analyze data, calculate probabilities, and understand normal distributions.

• Basic Statistics and Measures of Central Tendency

• Probability and Calculating Outcomes

• Normal Distributions and Their Applications

Sequences, Series, and Mathematical Induction

Work with patterns in sequences and series, and learn mathematical induction.

• Arithmetic and Geometric Sequences and Series

• Infinite Series and Convergence

• Sigma Notation and the Binomial Theorem

Calculus 

Get familiar with limits, derivatives, and the basics of finding areas under curves.

• Exploring Limits and Continuity

• Understanding Limits Involving Infinity

• Introduction to Derivatives and Antiderivatives

• Calculating Area Under a Curve

• Understanding the Fundamental Theorem of Calculus