AP Precalculus: unit and topic map

The four units of the course, numbered as in College Board's Course and Exam Description (CED) so the map can be checked against it; topic names are our own wording. The exam assesses Units 1 to 3. Each of those unit pages has notes, worked examples, common traps and at least 8 original practice questions for every topic: multiple choice, and free response in the four exam question types (function concepts, non-periodic modeling, periodic modeling, symbolic manipulation) with 6-point scoring guides. Unit 4 is not on the exam; for classes that teach it, it has notes and at least 8 practice questions for every topic too.

538 questions in all. The Questions column counts the questions tagged with each topic (a free-response question counts for every topic its parts test).

Full practice exams

Full-length practice exams in the May 2027 exam format, made from these questions, each with its scoring guide. Practice exam 1 is free with a free account; Pro opens every one. See the practice exams

Not sure you're ready? Take the 12-question Ready for AP? check, or brush up in High school math.

Unit 1: Polynomial and rational functions

131 questions (127 multiple choice, 4 free response) · notes, worked examples and common traps

CED topic	Topic (our wording)	Questions
1.1	Quantities that change together	11
1.2	Average rate of change	12
1.3	Rates of change of linear and quadratic functions	11
1.4	Polynomials: extrema, inflection and rates	12
1.5	Zeros of polynomials, real and complex	16
1.6	End behavior of polynomials	9
1.7	End behavior of rational functions	12
1.8	Zeros of rational functions	11
1.9	Vertical asymptotes of rational functions	10
1.10	Holes in rational graphs	8
1.11	Equivalent forms of polynomial and rational expressions	10
1.12	Transformations of functions	10
1.13	Choosing a function model	11
1.14	Building and using a function model	12

Unit 2: Exponential and logarithmic functions

152 questions (148 multiple choice, 4 free response) · notes, worked examples and common traps

CED topic	Topic (our wording)	Questions
2.1	Arithmetic and geometric sequences	12
2.2	Linear versus exponential change	12
2.3	Exponential functions	11
2.4	Rewriting exponential expressions	12
2.5	Exponential models and data	14
2.6	Comparing models with residuals	11
2.7	Composite functions	11
2.8	Inverse functions	11
2.9	Logarithmic expressions	10
2.10	Exponentials and logarithms as inverses	11
2.11	Logarithmic functions	11
2.12	Rewriting logarithmic expressions	10
2.13	Exponential and logarithmic equations and inequalities	12
2.14	Logarithmic models	11
2.15	Semi-log plots	11

Unit 3: Trigonometric and polar functions

138 questions (134 multiple choice, 4 free response) · notes, worked examples and common traps

CED topic	Topic (our wording)	Questions
3.1	Periodic behavior	8
3.2	Sine, cosine and tangent of an angle	10
3.3	Exact values on the unit circle	9
3.4	Graphs of sine and cosine	11
3.5	Sinusoidal functions	11
3.6	Transforming sinusoidal functions	10
3.7	Sinusoidal models	11
3.8	The tangent function	10
3.9	Inverse trigonometric functions	10
3.10	Trigonometric equations and inequalities	12
3.11	Secant, cosecant and cotangent	10
3.12	Equivalent trigonometric expressions	11
3.13	Polar coordinates	12
3.14	Graphs of polar functions	10
3.15	Rates of change in polar functions	11

Unit 4: Functions involving parameters, vectors and matrices

Not on the AP exam · 117 questions (113 multiple choice, 4 free response) · notes and worked examples

CED topic	Topic (our wording)	Questions
4.1	Parametric functions	9
4.2	Parametric models of planar motion	9
4.3	Rates of change of parametric functions	9
4.4	Parametric circles and lines	8
4.5	Implicitly defined functions	8
4.6	Conic sections	9
4.7	Parametrizing implicit curves	9
4.8	Vectors	10
4.9	Vector-valued functions	9
4.10	Matrices	9
4.11	Inverse and determinant of a 2x2 matrix	9
4.12	Linear transformations	8
4.13	Matrices as functions	8
4.14	Matrix models	9