TEST PREP

AP Precalculus Study Guide

A practical, exam-focused plan for AP Precalculus: exactly what is on the test, a prioritized topic checklist for all four units, a 6-week study schedule, the mistakes that cost the most points, and the highest-value practice order — so every study hour counts.

By FiboTutors Math Team Math-reviewed Updated October 2026 9 min read

QUICK ANSWER

The AP Precalculus exam consists of 40 multiple-choice questions and 4 free-response questions, taken over about 3 hours. Units 1–3 — polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions — carry the majority of the points. The fastest way to raise your score: close algebra gaps first, work unit-by-unit through the checklist below, and finish with timed mixed practice.

Who This Guide Is For

This guide is for students currently enrolled in AP Precalculus who want a clear, exam-focused study plan for the May exam. It assumes you have seen the material in class and want to turn that knowledge into points on test day.

If you are deciding whether to take AP Precalculus next year, this guide still works as a preview: the unit breakdown shows exactly what the course demands, and the readiness section tells you which algebra skills to sharpen over the summer so you start the course ahead instead of behind.

One note on approach before you begin: AP Precalculus rewards fluency — fast, accurate work with functions, graphs, and models — more than clever tricks. Rote memorizing formulas without understanding when to use them is the most common way students waste study time. Everything in this plan is built around understanding first, then speed.

What’s on the Exam: The 4 Units

The course is organized into four units. Here is what each one covers and how to think about it:

Unit 1: Polynomial and Rational Functions. End behavior, zeros and multiplicity, asymptotes and holes in rational functions, function composition and transformations. This is the foundation everything else builds on.
Unit 2: Exponential and Logarithmic Functions. Growth and decay models, solving exponential equations, logarithm properties, logistic models. Heavy on algebra fluency.
Unit 3: Trigonometric and Polar Functions. The unit circle, sinusoidal graphs and equations, trig identities, polar coordinates and graphs. The biggest unit and the one most students underestimate.
Unit 4: Functions Involving Parameters, Vectors, and Matrices. Parametric equations, vector operations, matrix operations and linear systems. Real content, but a smaller footprint on the exam than the first three units.

The exam format is fixed: Section I has 40 multiple-choice questions (about 2 hours), and Section II has 4 free-response questions (about 1 hour) — roughly 3 hours of testing total. Like all AP exams, it is scored on the 1–5 scale. A graphing calculator is permitted on portions of the exam, but the free-response section includes questions where no calculator is allowed, so you need clean by-hand algebra alongside calculator skill.

Topic Checklist by Unit

Work through each unit top to bottom. Items marked HIGH earn the most exam points per study hour — master those before touching anything marked MEDIUM.

Unit 1: Polynomial and Rational Functions

Polynomial graphs: end behavior, zeros with multiplicity, turning points HIGH Practice polynomial operations
Function transformations (shifts, stretches, reflections) and composition HIGH Learn function transformations · Practice function transformations
Rational functions: vertical, horizontal, and slant asymptotes; holes; end behavior HIGH
Solving polynomial and rational inequalities (sign charts, test values) MEDIUM
Rates of change: average rate over an interval, interpreting it in context MEDIUM

Unit 2: Exponential and Logarithmic Functions

Exponential functions: properties, graphs, and transformations HIGH
Solving exponential equations by writing both sides with the same base HIGH Practice exponents
Logarithm properties (product, quotient, power) and solving logarithmic equations HIGH
Exponential models: growth and decay, doubling time, half-life HIGH
Logistic growth models: recognizing the carrying capacity and growth pattern MEDIUM

Unit 3: Trigonometric and Polar Functions

Unit circle values and reference angles — automatic recall, not derivation HIGH Learn trig ratios
Sinusoidal functions: amplitude, period, phase shift, midline; writing an equation from a graph HIGH Practice trig ratios
Solving trigonometric equations and verifying identities HIGH
Inverse trigonometric functions and their restricted domains MEDIUM
Polar coordinates and polar graphs MEDIUM

Unit 4: Parameters, Vectors, and Matrices

Parametric equations: eliminating the parameter, graphing, direction of motion MEDIUM
Vectors: addition, scalar multiplication, magnitude, simple applications MEDIUM
Matrices: operations, determinants, solving linear systems MEDIUM

The honest priority call: a student who fully masters the HIGH items in Units 1–3 will outscore a student who spreads the same hours evenly across all four units. Study Unit 4 in the final weeks, not first.

Fix Your Readiness Gaps First

Most lost AP Precalculus points trace back to shaky prerequisites, not to new material. Before starting Unit 1 review, make sure these are automatic — if any of them feel slow, drill them this week:

Factoring quadratics and higher-degree polynomials
Exponent and radical rules
Fraction and rational-expression manipulation
Function notation f(x), and evaluating composite functions
Unit circle values for sine and cosine at the standard angles

The two worked examples below are the kind of fluency the exam assumes. If either feels effortful, that is your signal to drill the prerequisites before moving on.

WORKED EXAMPLE

Solve 2^x = 32.

When both sides can be written with the same base, the exponents must be equal.

2^x = 32 → 2^x = 2⁵ → x = 5

This same-base move is the backbone of Unit 2 equation solving. On the exam it appears in harder forms (fractional or negative bases), but the logic never changes.

WORKED EXAMPLE

Find the vertex of y = x² − 6x + 5.

For y = ax² + bx + c, the vertex x-coordinate is −b/(2a).

−b/(2a) = −(−6)/(2·1) = 3
f(3) = 9 − 18 + 5 = −4

Vertex: (3, −4). Vertex form, axis of symmetry, and completing the square all show up in Unit 1 free-response questions.

TRY IT

Check your readiness in 3 minutes

Solve 3^x+1 = 81. (Write 81 as a power of 3, then equate exponents.)
Find the vertex of y = x² + 4x − 7. (Use −b/(2a), then evaluate.)

Answers: (1) 81 = 3⁴, so x + 1 = 4 and x = 3. (2) x = −4/2 = −2; f(−2) = 4 − 8 − 7 = −11, so the vertex is (−2, −11). If either took more than 90 seconds, add prerequisite drills to Week 1 of your schedule.

The 6-Week Study Schedule

Six weeks is a plan, not a law. If you have three weeks, compress to a 1-1-1 rhythm (gaps, Units 1–3, mixed review plus Unit 4). If you have ten, stretch Weeks 2–4 and double the timed practice in Week 6. The order matters more than the exact week count: gaps first, Units 1–3 next, Unit 4 late, timed practice last.

Week	Focus	What to do
1	Readiness gaps	Drill factoring, exponent rules, and unit circle values. Work through the Try-It problems above until they are fast.
2	Unit 1	Work the Unit 1 checklist top-down. Practice polynomial operations, then function transformations.
3	Unit 2	Exponential and logarithmic equations, log properties, growth and decay models. Exponents practice daily.
4	Unit 3	Sinusoidal graphs and equations, identities, trig equations. Review trig ratios, then the practice set.
5	Unit 4 + mixed review	Parametric equations, vectors, and matrices at medium priority. Begin 20-question mixed sets across Units 1–3.
6	Timed practice	Full mixed sets under time. Review your error log. Follow the day-before routine below.

The High-Value Practice Sequence

Not all practice is equal. This is the order that converts study time into points most efficiently:

Read the Learn page for one checklist topic — one topic, not a whole unit.
Do the matching targeted practice set untimed, with notes allowed. Understanding comes before speed.
Redo your misses after 48 hours. Spaced re-attempts beat same-day repetition.
Mix topics: 20-question mixed sets so your brain practices choosing the right tool, not just using it.
Time yourself: practice free-response-style writing under the clock, showing full work.
Keep an error log. Every missed problem gets one line: the problem type and the reason you missed it. Review it weekly — it becomes your personal checklist for the final week.

SKILL PATH

Your starting sequence (Units 1–2 foundations)

Begin the practice sequence here and follow it in order:

You: Learn function transformations→ Practice transformations→ Practice polynomial operations→ Practice exponents→ Practice trig ratios

Start with the function transformations lesson, then move through each practice set before advancing to the next unit.

Common Mistakes to Avoid

COMMON MISTAKE

Radian/degree mode mismatch

The exam uses radians for trigonometric work. Running a radian problem with your calculator in degree mode — or the reverse — silently produces wrong answers with no error message. Wrong: evaluating sin(π/6) in degree mode. Fix: before every trig practice set, check the mode. Make it a ritual, not a memory.

Using the calculator as a crutch. On no-calculator free-response questions, students who always reach for the calculator freeze on by-hand algebra. Practice the same problem types both ways during Weeks 2–4.
Misapplying logarithm rules. log(ab) = log a + log b — it is not log a × log b. And log(a + b) does not split at all. Write the three properties on a card and check against it until they are automatic.
Ignoring domain restrictions in log equations. Solving can produce extraneous roots, so always check solutions in the original equation. A “solution” that makes any logarithm’s argument zero or negative is not a solution.
Sign errors in completing the square and vertex work. Rushing −b/(2a) when b is negative is the single most common Unit 1 slip. Slow down for that one step; it costs five seconds and saves the whole problem.
Reversing composition order. (f∘g)(x) means f(g(x)) — innermost function first. Students who read left-to-right apply g last and get a wrong function.

The Day Before the Exam

No new topics. Re-read your error log and the HIGH-priority checklist items for Units 1–3 only.
Do 10–15 easy problems you know you can get right. This is confidence calibration, not learning — end the day feeling competent.
Pack tonight: graphing calculator with fresh batteries (plus spares), pencils, photo ID, and your admission ticket.
Sleep beats cramming. Plan to stop studying by early evening. A rested brain recalls unit circle values; a tired one does not.
Morning of: light breakfast, arrive early, and set your calculator to radian mode before the first question. Check it twice.

Key takeaways

The exam is 40 multiple-choice questions plus 4 free-response questions over about 3 hours.
Units 1–3 carry the majority of points — master their HIGH-priority topics first.
Fix algebra and trig-fluency gaps before starting unit review.
Follow the practice sequence: learn one topic, practice it, redo misses, mix topics, then time yourself.
Check your calculator mode before every trig set, and check log-equation solutions in the original equation.

Start the High-Value Practice Sequence

Begin where the plan begins: targeted Unit 1 practice. Work the set, log your errors, and move to the next step in the sequence.

Start Practicing: Polynomial Operations Review Transformations First