Free AP Precalculus Course: Lessons, Practice Questions and Full Exams
Learn every topic in AP Precalculus with this free course: 12 step-by-step lessons, 305 practice questions, 31 topic quizzes, 10 timed mini-exams and 12 full-length practice exams. Every question comes with a worked explanation, and you can start right now without creating an account.
A complete, free AP Precalculus course
AP Precalculus teaches you to see functions as models, not just formulas: how inputs determine outputs, how a table or graph reveals the type of function behind it, and where a model stops making sense. This free course follows the official course framework in order, from rates of change and polynomials to exponential, logarithmic and trigonometric functions. Each of the 12 lessons explains its topic with worked examples, then links to matching quizzes so you can practice right away. When a unit feels solid, timed mini-exams and full-length practice exams prepare you for the real test.
The AP exam rewards reasoning as much as algebra. You will need to tell linear from exponential behavior in a table, keep track of domain restrictions, and connect a formula to its graph and to the situation it models. That is why every practice question comes with a full explanation of the reasoning, not only the final answer. Use the course alongside your class, as a self-study path, or as a focused review before the May exam. It is also the best foundation for AP Calculus AB and BC.
AP Precalculus exam format at a glance
The AP Precalculus exam is a hybrid digital exam: you answer multiple-choice questions in the Bluebook app and handwrite your free-response answers on paper. Here is how it is set up for the May 2027 exam, according to the College Board:
| Section I: Multiple choice | 42 questions, 1 hour 45 minutes, 62.5% of the score |
|---|---|
| Part A (no calculator) | 29 questions in 65 minutes |
| Part B (graphing calculator required) | 13 questions in 40 minutes |
| Section II: Free response | 4 questions, 1 hour 10 minutes, 37.5% of the score |
| Part A (graphing calculator required) | 2 questions in 35 minutes: Function Concepts and Modeling a Non-Periodic Context |
| Part B (no calculator) | 2 questions in 35 minutes: Modeling a Periodic Context and Symbolic Manipulations |
| Units on the exam | Units 1 to 3; Unit 4 is taught in the course but not assessed |
| Scoring | AP score from 1 to 5; many colleges award credit for a 3 or higher |
Most of the multiple-choice section is calculator-free, so you need to handle function rules, logarithm properties and trigonometric values by hand. The free-response section also expects clear reasoning, such as explaining why a model is exponential, so practice writing out your thinking, not just the answer.
All 12 free AP Precalculus lessons
The lessons follow the four official AP Precalculus units in order. Each one pairs a clear explanation with matching quizzes in the question bank.
Unit 1: Polynomial and Rational Functions (30–40% of multiple choice)
Unit 2: Exponential and Logarithmic Functions (25–40%)
Unit 3: Trigonometric and Polar Functions (30–35%)
Unit 4: Parameters, Vectors, and Matrices (not on the AP exam)
Ready to test yourself?
Jump into 305 free AP Precalculus questions with full explanations.
Try 5 free AP Precalculus sample questions
These original questions show the style and level of the course, covering every unit on the AP exam. Pick an answer to see whether you are right, then read the step-by-step explanation.
What is the average rate of change of f(x) = x2 on the interval [1, 4]?
Correct answer: A. 5
The average rate of change is the change in output divided by the change in input: (f(4) − f(1)) / (4 − 1) = (16 − 1) / 3 = 15/3 = 5. Choice B stops at the change in output and forgets to divide by the change in input, 3.
The function g is defined by g(x) = (x2 − 4)/(x − 2). Which statement describes the graph of g at x = 2?
Correct answer: B. A hole at the point (2, 4)
Factor the numerator: (x − 2)(x + 2)/(x − 2). The factor x − 2 cancels, so g(x) = x + 2 everywhere except x = 2, where g is undefined. Because the factor cancels, there is a hole rather than an asymptote, located at y = 2 + 2 = 4. The domain restriction stays even after canceling, which is exactly what choice A gets wrong.
A table shows the values y = 3, 6, 12, 24 for x = 0, 1, 2, 3. Which function models the table?
Correct answer: C. y = 3(2)x
Over equal steps in x, each output is multiplied by the same factor: 6/3 = 12/6 = 24/12 = 2. A constant ratio signals exponential behavior, with initial value 3 (when x = 0) and base 2. Choice A would need constant differences, but the differences 3, 6, 12 keep growing. Choice B gives y = 2 at x = 0.
What value of x satisfies log3(x + 1) = 2?
Correct answer: D. 8
Rewrite the logarithm in exponential form: x + 1 = 32 = 9, so x = 8. Check the domain: x + 1 = 9 is positive, so the solution is valid. Choice A finds 32 but forgets to subtract 1, and choice B multiplies 3 by 2 instead of raising 3 to the power 2.
What are the amplitude and period of f(θ) = 4 sin(2θ) + 1?
Correct answer: A. Amplitude 4, period π
For a sin(bθ) + d, the amplitude is |a| = 4 and the period is 2π/b = 2π/2 = π. The +1 moves the midline up to y = 1 but does not change the amplitude, which is the mistake in choice C. Choice B multiplies 2π by 2 instead of dividing.
How to study for the AP Precalculus exam with this course
- Follow the units in order. Each unit builds on the function ideas from the one before, so start with rates of change and polynomials.
- Practice by topic. After each lesson, take its quizzes and read every explanation, including the ones you got right.
- Write down restrictions first. Before solving, note where denominators are zero and where logarithm inputs must be positive.
- Work without a calculator. Most of the multiple-choice section is calculator-free, so do the majority of your practice by hand.
- Build speed. Use the 10 timed mini-exams to get used to the pace of about two and a half minutes per multiple-choice question.
- Simulate exam day. Take full practice exams in one sitting, then go back to the lessons for any topic you still miss.
Focus most of your exam review on Units 1 to 3, since Unit 4 is not assessed. Starting two to three months before the May exam, with a few sessions per week, leaves time to cover every unit and still save the final weeks for full practice exams.
AP Precalculus course: frequently asked questions
Is this AP Precalculus course really free?
Yes. All 12 lessons, 31 quizzes, 305 practice questions, 10 timed mini-exams and 12 full practice exams are free, and you do not need an account to start.
What is the format of the AP Precalculus exam?
Section I has 42 multiple-choice questions in 1 hour 45 minutes and counts for 62.5% of the score. Section II has 4 free-response questions in 1 hour 10 minutes and counts for 37.5%. It is a hybrid digital exam: you answer multiple choice in the Bluebook app and handwrite free-response answers in a paper booklet.
Can I use a calculator on the AP Precalculus exam?
Only on some parts. A graphing calculator is required for Part B of the multiple-choice section and Part A of the free-response section, and it is not allowed on the other two parts. Most of the multiple-choice section is calculator-free, so practice both ways.
Which units are on the AP Precalculus exam?
Units 1 to 3 are assessed: Polynomial and Rational Functions, Exponential and Logarithmic Functions, and Trigonometric and Polar Functions. Unit 4, Functions Involving Parameters, Vectors, and Matrices, is part of the course but is not on the AP exam. Lessons 10 to 12 in this course cover Unit 4 for class and future courses.
How is the AP Precalculus exam scored?
Your multiple-choice and free-response results are combined into an AP score from 1 to 5, where 5 means extremely well qualified. Many colleges grant credit or placement for a 3 or higher, though policies vary by school. Scores on our practice exams are feedback, not official AP scores.
Should I take AP Precalculus before AP Calculus?
For most students, yes. AP Precalculus builds the function skills that AP Calculus AB and BC rely on, including rates of change, exponential and logarithmic models, and trigonometric functions. The AP Calculus AB and BC courses on this site pick up where this course ends.
Start your free AP Precalculus course today
12 lessons, 305 questions, 12 full practice exams. No sign-up required.