AP
Pre-calculus · AP · High school · Math
Full College Board Course and Exam Description framework for Pre-calculus · AP, including course-scope topics not assessed on the AP Exam. Topics marked with an asterisk (*) are assessed on the exam. Click a topic for the full text and study materials.
Standards
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Unit 1: Polynomial and Rational Functions
- 1.1 * — Change in Tandem
- 1.2 * — Rates of Change
- 1.3 * — Rates of Change in Linear and Quadratic Functions
- 1.4 * — Polynomial Functions and Rates of Change
- 1.5 * — Polynomial Functions and Complex Zeros
- 1.6 * — Polynomial Functions and End Behavior
- 1.7 * — Rational Functions and End Behavior
- 1.8 * — Rational Functions and Zeros
- 1.9 * — Rational Functions and Vertical Asymptotes
- 1.10 * — Rational Functions and Holes
- 1.11 * — Equivalent Representations of Polynomial and Rational Expressions
- 1.12 * — Transformations of Functions
- 1.13 * — Function Model Selection and Assumption Articulation
- 1.14 * — Function Model Construction and Application
Unit 2: Exponential and Logarithmic Functions
- 2.1 * — Change in Arithmetic and Geometric Sequences
- 2.2 * — Change in Linear and Exponential Functions
- 2.3 * — Exponential Functions
- 2.4 * — Exponential Function Manipulation
- 2.5 * — Exponential Function Context and Data Modeling
- 2.6 * — Competing Function Model Validation
- 2.7 * — Composition of Functions
- 2.8 * — Inverse Functions
- 2.9 * — Logarithmic Expressions
- 2.10 * — Inverses of Exponential Functions
- 2.11 * — Logarithmic Functions
- 2.12 * — Logarithmic Function Manipulation
- 2.13 * — Exponential and Logarithmic Equations and Inequalities
- 2.14 * — Logarithmic Function Context and Data Modeling
- 2.15 * — Semi-log Plots
Unit 3: Trigonometric and Polar Functions
- 3.1 * — Periodic Phenomena
- 3.2 * — Sine, Cosine, and Tangent
- 3.3 * — Sine and Cosine Function Values
- 3.4 * — Sine and Cosine Function Graphs
- 3.5 * — Sinusoidal Functions
- 3.6 * — Sinusoidal Function Transformations
- 3.7 * — Sinusoidal Function Context and Data Modeling
- 3.8 * — The Tangent Function
- 3.9 * — Inverse Trigonometric Functions
- 3.10 * — Trigonometric Equations and Inequalities
- 3.11 * — The Secant, Cosecant, and Cotangent Functions
- 3.12 * — Equivalent Representations of Trigonometric Functions
- 3.13 * — Trigonometry and Polar Coordinates
- 3.14 * — Polar Function Graphs
- 3.15 * — Rates of Change in Polar Functions
Unit 4: Functions Involving Parameters, Vectors, and Matrices
- 4.1 — Parametric Functions
- 4.2 — Parametric Functions Modeling Planar Motion
- 4.3 — Parametric Functions and Rates of Change
- 4.4 — Parametrically Defined Circles and Lines
- 4.5 — Implicitly Defined Functions
- 4.6 — Conic Sections
- 4.7 — Parametrization of Implicitly Defined Functions
- 4.8 — Vectors
- 4.9 — Vector-Valued Functions
- 4.10 — Matrices
- 4.11 — The Inverse and Determinant of a Matrix
- 4.12 — Linear Transformations and Matrices
- 4.13 — Matrices as Functions
- 4.14 — Matrices Modeling Contexts
* Assessed on the AP Exam (per the Course and Exam Description). All topics listed; unmarked topics are course scope only.
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AP Course and Exam Description (College Board)
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