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Math and Computer SciencePrecalculus

AP Precalculus

Build a flexible understanding of functions and modeling across algebraic, exponential, logarithmic, trigonometric, polar, parametric, vector, and matrix settings.

Start with the course map All AP courses

Course map

Open a section, then choose the exact idea.

1Polynomial and Rational Functions14 topics

Connect rates of change, zeros, asymptotes, transformations, and equivalent forms to build and justify polynomial and rational models.

  1. 1.1Change in Tandem
  2. 1.2Rates of Change
  3. 1.3Rates of Change in Linear and Quadratic Functions
  4. 1.4Polynomial Functions and Rates of Change
  5. 1.5Polynomial Functions and Complex Zeros
  6. 1.6Polynomial Functions and End Behavior
  7. 1.7Rational Functions and End Behavior
  8. 1.8Rational Functions and Zeros
  9. 1.9Rational Functions and Vertical Asymptotes
  10. 1.10Rational Functions and Holes
  11. 1.11Equivalent Representations of Polynomial and Rational Expressions
  12. 1.12Transformations of Functions
  13. 1.13Function Model Selection and Assumption Articulation
  14. 1.14Function Model Construction and Application

2Exponential and Logarithmic Functions15 topics

Compare linear, exponential, and logarithmic change while using composition, inverses, equations, and data to select and validate models.

  1. 2.1Change in Arithmetic and Geometric Sequences
  2. 2.2Change in Linear and Exponential Functions
  3. 2.3Exponential Functions
  4. 2.4Exponential Function Manipulation
  5. 2.5Exponential Function Context and Data Modeling
  6. 2.6Competing Function Model Validation
  7. 2.7Composition of Functions
  8. 2.8Inverse Functions
  9. 2.9Logarithmic Expressions
  10. 2.10Inverses of Exponential Functions
  11. 2.11Logarithmic Functions
  12. 2.12Logarithmic Function Manipulation
  13. 2.13Exponential and Logarithmic Equations and Inequalities
  14. 2.14Logarithmic Function Context and Data Modeling
  15. 2.15Semi-log Plots

3Trigonometric and Polar Functions15 topics

Represent periodic behavior with trigonometric and polar functions, then analyze transformations, equations, identities, graphs, and rates of change.

  1. 3.1Periodic Phenomena
  2. 3.2Sine, Cosine, and Tangent
  3. 3.3Sine and Cosine Function Values
  4. 3.4Sine and Cosine Function Graphs
  5. 3.5Sinusoidal Functions
  6. 3.6Sinusoidal Function Transformations
  7. 3.7Sinusoidal Function Context and Data Modeling
  8. 3.8The Tangent Function
  9. 3.9Inverse Trigonometric Functions
  10. 3.10Trigonometric Equations and Inequalities
  11. 3.11The Secant, Cosecant, and Cotangent Functions
  12. 3.12Equivalent Representations of Trigonometric Functions
  13. 3.13Trigonometry and Polar Coordinates
  14. 3.14Polar Function Graphs
  15. 3.15Rates of Change in Polar Functions

4Functions Involving Parameters, Vectors, and Matrices14 topics · not assessed on the AP Exam

Extend function thinking to parametric and implicit relations, vectors, matrices, transformations, planar motion, and contextual models.

  1. 4.1Parametric Functions
  2. 4.2Parametric Functions Modeling Planar Motion
  3. 4.3Parametric Functions and Rates of Change
  4. 4.4Parametrically Defined Circles and Lines
  5. 4.5Implicitly Defined Functions
  6. 4.6Conic Sections
  7. 4.7Parametrization of Implicitly Defined Functions
  8. 4.8Vectors
  9. 4.9Vector-Valued Functions
  10. 4.10Matrices
  11. 4.11The Inverse and Determinant of a Matrix
  12. 4.12Linear Transformations and Matrices
  13. 4.13Matrices as Functions
  14. 4.14Matrices Modeling Contexts