Review AP Precalculus with study guides for all four units, practice questions, and FRQ practice across functions, graphs, tables, and equations. Use these AP Precalculus resources to build fluency with polynomial, rational, exponential, logarithmic, trigonometric, polar, parametric, and matrix models.
AP Precalculus develops your ability to model change using polynomial, rational, exponential, logarithmic, trigonometric, polar, parametric, and matrix functions while reasoning across graphs, tables, equations, and words.
Get the big picture: what AP Pre-Calculus covers, how it is scored, and how the units connect.
read the overviewAnswer a quick mix of questions to see which units need the most review.
start a diagnosticOpen the unit you are studying now and review its guides, practice, and key terms.
browse all 4 unitsAP Precalculus, often searched as AP Pre-Calc, develops your understanding of function families by focusing on how quantities change and how to model real situations. You work with polynomial, rational, exponential, logarithmic, trigonometric, polar, parametric, vector-valued, and matrix functions. The course pushes you to analyze each function type through graphs, tables, equations, and verbal descriptions, then test and refine models using data. It is designed to be the equivalent of a first-semester college precalculus course.
The content is organized into four units that build on one another, moving from polynomial and rational functions through exponential and logarithmic functions, into trigonometric and polar functions, and finishing with parameters, vectors, and matrices. Along the way you interpret key features like long-run behavior, periodic patterns, inverses, and rates of change. The reasoning habits you build here are exactly what you need for calculus, so consistent practice across all four representations pays off all year.
Analyze polynomial and rational functions, including zeros, end behavior, holes, and asymptotes
Model growth and decay with exponential and logarithmic functions and validate competing models
Build and transform sinusoidal functions and work with polar coordinates and graphs
Use parametric equations, vectors, and matrices to describe motion and transformations
Move fluently between graphical, numerical, analytical, and verbal representations of functions
Communicate mathematical reasoning and justify conclusions about models and assumptions
The AP Precalculus exam is 3 hours long with 40 multiple-choice questions and 4 free-response questions. Here is how the sections, timing, and calculator rules break down.
| Section | Questions | Time | % of Score |
|---|---|---|---|
| Section I – Multiple Choice | 40 | 120 min | 63% |
| Section II – Free Response | 4 | 60 min | 38% |
Total timed testing time: 180 minutes.
The course is organized into 4 units. The percentages below are the College Board exam weights, so you can see which units carry the most multiple-choice points. Open each unit for its study guide, topic pages, key terms, and practice questions.
AP Precalculus Unit 1 is about how two quantities change together, and it uses polynomial and rational functions as the lab for studying that change.
AP Pre-Calc Unit 2 is about functions that change by repeated multiplication instead of repeated addition.
AP Precalculus Unit 3 is about functions that repeat.
AP Precalculus Unit 4 covers parametric functions, vectors, and matrices, three tools that let you describe motion and change in two dimensions instead of one.
These trends come from real Fiveable practice data, so you can see what students are reviewing, which topics need extra attention, and how written practice can improve over time.
Miss rate is based on high-volume AP Pre-Calculus multiple-choice practice.
Average MCQ accuracy by student practice volume across 1,780 AP Pre-Calculus students.
Among AP Pre-Calculus FRQ responses that students retried on Fiveable, average scores rose from 43% on the first attempt to 66% on the latest attempt.
practice AP Pre-Calculus FRQs →These guides collect important exam skills, big ideas, essay tasks, and other subject-specific resources.
Work through the units in order, because gaps in polynomial or exponential fluency will slow you down in trigonometry and Unit 4. For every function type, practice all four representations: graph, table, equation, and verbal description. Since most of the exam is no-calculator, build algebraic manipulation until it feels automatic, then drill the calculator tasks like regression, zeros, and intersections so they are fast on test day. Do full free-response problems and write out clear reasoning, not just final answers. Start cumulative review four to six weeks out, revisiting Units 1 and 2 while you finish Units 3 and 4 in class.
Week 1: Review Unit 1 polynomial and rational functions, focusing on end behavior, zeros, and asymptotes with no-calculator practice
Week 2: Work Unit 2 exponential and logarithmic functions, including inverses, log rules, and data modeling
Week 3: Study Unit 3 sinusoidal functions, transformations, and polar graphs, then practice FRQ 3 periodic modeling
Week 4: Cover Unit 4 parametric functions, vectors, and matrices, and review FRQ 4 symbolic manipulation skills
Week 5: Take a timed multiple-choice set across all units, splitting no-calculator and calculator parts
Week 6: Complete a full set of 4 FRQs under timing and review scoring against your work
Use the question types below to plan written-response practice and connect exam guides to timed FRQs. Open an example prompt to practice that question type right away.
| Question | Focus | Points | % of Score | Example prompt |
|---|---|---|---|---|
| FRQ 1 | Function Concepts (Calculator) | 6 | 9% | Composite functions and function composition analysis |
| FRQ 2 | Modeling a Non-Periodic Context (Calculator) | 6 | 9% | Quadratic function maximum determines realistic domain boundary |
| FRQ 3 | Modeling a Periodic Context (No Calculator) | 6 | 9% | Sinusoidal function parameters from graph analysis |
| FRQ 4 | Symbolic Manipulations (No Calculator) | 6 | 9% | Logarithmic equations with multiple terms |
AP Precalculus is moderately challenging. The toughest part is not any single topic but the demand to move fluidly between graphs, tables, equations, and verbal descriptions for every function type. If you finished Algebra 2 with solid skills, the early units feel like a natural extension. Keeping up week to week and practicing problems regularly, not just reading notes, makes it very manageable.
Start with Unit 1 and work through the units in order, since each one builds on the last. For every function type, practice all four representations: graph, table, equation, and verbal description. Build no-calculator algebra fluency first because most of the exam is no-calculator, then practice calculator tasks like regression and finding zeros. Do timed practice questions to lock in your skills.
In the multiple-choice section, Unit 3 (Trigonometric and Polar Functions) carries the most weight at 30 to 35 percent, followed by Unit 2 (Exponential and Logarithmic Functions) at 22 to 28 percent and Unit 1 (Polynomial and Rational Functions) at 20 to 25 percent. The exam assesses Units 1, 2, and 3, so prioritize trig while keeping Units 1 and 2 solid.
There are 4 free-response questions, each worth six points and weighted equally. FRQ 1 covers function concepts and FRQ 2 models a non-periodic context; both require a graphing calculator. FRQ 3 models a periodic (sinusoidal) context and FRQ 4 tests symbolic manipulations; both are no-calculator. You have 30 minutes for the two calculator FRQs and 30 minutes for the two no-calculator FRQs.
Yes. You need a graphing calculator for Part B of the multiple-choice section and Part A of the free-response section. Practice tasks like graphing functions, building tables, finding zeros and intersections, running regression models, and matrix operations. Keep your calculator in radian mode. Most of the exam is no-calculator, though, so build strong algebraic manipulation skills first and use technology strategically.