AP map · Math Ladder
AP Precalculus
Functions as models of change: polynomial and rational, exponential and logarithmic, trigonometric and polar, then parameters, vectors and matrices.
Unit names: AP Precalculus course page and Course at a Glance (College Board), unit list, read October 16, 2026.
Units 1, 2 and 3 are on the AP Exam. Unit 4 is taught in the course but not assessed on the exam.
Unit 1 Polynomial and Rational Functions
- Average Rate of Change
- End Behavior of Polynomials
- Zeros and Multiplicity
- The Fundamental Theorem of Algebra
- Sketching Polynomial Graphs
- Polynomial and Rational Inequalities
- Asymptotes and Holes
- Graphing Rational Functions
- Slant Asymptotes
- Polynomial Long Division
- The Binomial Theorem
- Combining Transformations
- Even and Odd Functions
- Work-Rate and Average-Cost Models
8 mixed questions, with the steps after eachUnit 2 Exponential and Logarithmic Functions
- Arithmetic Sequences
- Geometric Sequences
- Linear vs Exponential Change
- Graphs of Exponential Functions
- Rewriting Exponential Expressions
- Exponential and Logarithmic Models
- Choosing a Function Model
- Composition of Functions
- Inverse Functions
- What a Logarithm Is
- Switching Between Log and Exponential Form
- Graphs of Logarithmic Functions
- Properties of Logarithms
- Solving Exponential Equations with Logs
- Solving Logarithmic Equations
- Logarithmic Scales
Semi-log plots come up in Logarithmic Scales; there is no separate topic on reading a semi-log plot yet.
8 mixed questions, with the steps after eachUnit 3 Trigonometric and Polar Functions
- Symmetry and Periodicity
- Radian Measure
- Sine and Cosine on the Unit Circle
- Exact Values at Special Angles
- Graphs of Sine and Cosine
- Amplitude and Period
- Phase Shift and Midline
- Modeling with Sinusoids
- Graphs of Tangent, Secant and Cosecant
- Inverse Trig Functions
- Solving Basic Trig Equations
- Trig Equations with Factoring and Multiple Angles
- All Six Trig Functions
- Reciprocal, Quotient and Pythagorean Identities
- Sum and Difference Formulas
- Double-Angle Formulas
- Polar Coordinates
- Converting Polar and Rectangular
- Graphs of Polar Equations
Rates of change in polar functions (whether r is growing or shrinking as θ turns) has no topic of its own yet.
8 mixed questions, with the steps after eachUnit 4 Functions Involving Parameters, Vectors, and Matrices
- Parametric Equations
- Projectile Motion with Parametric Equations
- Eliminating the Parameter
- Equation of a Circle
- Parabolas as Conics
- Ellipses
- Hyperbolas
- Vectors
- Vector Components and Magnitude
- Adding and Scaling Vectors
- The Dot Product and the Angle Between Vectors
- Vector-Valued Functions and Space Curves
- Matrices and Matrix Arithmetic
- Multiplying Matrices
- Determinants of 2 × 2 and 3 × 3 Matrices
- Inverse Matrices
- Matrices as Transformations
- Matrix Powers and Markov Chains
Not on the AP Exam. Vector-valued functions and matrices that model change over time (Markov chains) come from Calculus 3 and Linear Algebra, which go further than this unit.
8 mixed questions, with the steps after each