APĀ® Calculus AB Practice Tests & Questions
Ace APĀ® Calculus AB with practice test questions from our Question Bank (QBank) and earn college credit on your schedule and budget.
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Try These AP Calc AB Practice Test Questions
Question
The graph of f ā², the derivative of the function f, is shown in the graph above. The function f is concave up on (2, 4).
| A. True | |
| B. False |
Explanation
The given graph shows the first derivative of the function f. Concavity is given by the second derivative, so the slope of f′ gives the concavity of f. The graph of f′ is increasing on (2, 3) but decreasing on (3, 4). Therefore, f is concave down on part of the interval (2, 4), and the given statement is false.
Question
What is the area of the region R bounded by the graphs of x = y2 − y + 1 and x = y + 1 ?
| A.
4
3
|
|
| B.
8
3
|
|
| C.
4
|
|
| D.
20
3
|
Explanation
The area between the given functions is equal to the integral of the right function minus the left function between the y-values of their intersection points, so it is necessary to determine which are the right and left functions and to find the intersection points.
The quadratic function has a positive leading coefficient, so the parabola opens to the right. All the choices are finite values, so the linear function must cross to the right of the quadratic (graph). Set the expressions equal and solve for y to find where they intersect.
| y2 ā y + 1 = y + 1 | Set functions equal |
| y2 ā 2y = 0 | Subtract y and 1 from both sides |
| y(y ā 2) = 0 | Factor out GCF |
| y = 0 and y = 2 | Apply zero product property |
Therefore, the right function is f(y) = y + 1 and the left function is g(y) = y2 ā y + 1, and they intersect at y = 0 and y = 2.
Integrate the difference between the functions on the interval of their intersection points to find the area of region R.
| Area of region R | |
| Substitute functions and values | |
| Combine like terms | |
| Integrate | |
| Apply FTC | |
| Simplify terms | |
| Subtract |
Therefore, the area of region R is .
Question
The graphs of the functions f (x) = 2x3 − x + 2 and g (x) = −2x3 + 3x + 2 are shown above. The graphs of f and g intersect at x = −1, x = 0, and x = 1. What is the area between the graphs of f and g on [−1, 1] ?
| A. 0 | |
| B. 1 | |
| C. 2 | |
| D. 4 |
Explanation
To find the area between the graphs offandgon the interval [−1, 1], write two integrals that meet at the inner intersection point at x = 0.
The given graph shows that f (x) ≥ g (x) on [−1, 0], so the integrand of the integral on this interval is f (x) − g (x). Write the integral for the first interval and evaluate.
| Area between f and g on [a, b] | |
| Substitute functions, a = -1, and b = 0 | |
| Combine like terms | |
| Integrate | |
| Apply FTC | |
| Simplify | |
| Subtract |
The area on the first interval [−1, 0] is 1.
The given graph shows that g (x) ≥ f (x) on [0, 1], so the integrand of the integral on this interval is g (x) −f (x). Write the integral for the second interval and evaluate.
| Area between f and g on [a, b] | |
| Substitute functions, a = 0, and b = 1 | |
| Combine like terms | |
| Integrate | |
| Apply FTC | |
| Simplify | |
| Subtract |
The area on the second interval [0, 1] is also 1.
The total area between the graphs of the given functions on [−1, 1] is the sum of the values of the two integrals, so the total area is 1 + 1 = 2.
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AP Calculus AB Practice Test Reviews
UWorlds multiple choice questions are similar to the ones on the official AP exam and allowed me to time myself for each question. This was very helpful for me as I was able to answer questions faster and could finish the questions on the actual exam. The explanations for each question went in-depth and gave important details pertaining to events in the timeline. Through this, I was able to gain important skills for the exam and get a 5.
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Before, I had a hard time studying and staying focused because it was just boring, but now with UWorld, not only can I focus, but I actually feel motivated to learn!
The explanations were clear and I could practice the question based on units. I got a 5 in the end!! So, I think itās very helpful and Iāll be using it to study for my future exams š You guys provide so many different functions to help students like me, and I really appreciate it, itās really worth the money.
See MoreAP Calc AB Practice Tests: Frequently Asked Questions (FAQs)
How closely do UWorld's AP Calculus AB practice tests mirror the actual exam?
Our AP Calculus AB practice tests are meticulously designed to replicate the format, difficulty, and content of the real exam. Written by in-house experts, our multiple-choice and free-response questions align with what you’ll encounter on test day including the specific problem types, multi-step reasoning, and justification skills youāll need to master. Every AP Calculus AB practice problem features a detailed, step-by-step solution so you understand the logic, methodology and mathematics behind every answer, not just the final number.
Why should I use UWorldās AP Calculus AB practice tests instead of free online materials?
There are free AP Calc AB practice test resources available to help you study but they tend to focus on teaching the general concepts with limited solution and explanation sets. Our AP Calculus AB practice questions are authored by experienced educators and closely reflect the current exam.
With UWorld you get a comprehensive AP Calculus AB practice exam system that includes:
- Exam-level AP Calc AB questions with detailed, step-by-step solutions.
- Customizable quizzes to target specific units, like derivatives or integration.
- Performance tracking to pinpoint your conceptual weak spots.
- Timed modes to simulate the pressure of the AP Calculus AB practice exam.
You’re not just practicing; you’re getting a complete platform designed to help you master the material and improve your score.
Do your AP Calculus AB practice questions cover all the required units and topics?
Yes. Our AP Calculus AB question bank provides comprehensive coverage of all 8 units outlined in the official College Board course and exam description:
- Unit 1: Limits and Continuity
- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration
You can create AP Calc AB practice tests from all topics or build focused quizzes on specific units where you need the most review.
What's the best way to use AP Calculus AB practice tests to aim for a 5?
Start by using topic-specific quizzes to solidify your understanding as you learn new units in class. Before the next unit, create and take at least one AP Calculus AB practice test to then review the step-by-step solutions for every single problem, even the ones you got right. This helps you master the underlying concepts, learn efficient problem-solving methods, and recognize common pitfalls. Use your performance dashboard to identify your weakest units, then create additional AP Calc AB practice tests and quizzes to drill those specific areas.
When is the right time to start using AP Calculus practice questions?
Ideally, you should start using AP Calculus AB practice questions as soon as you begin learning the material in class. Practicing topics and solution techniques like the chain rule or the fundamental theorem of calculus while they are fresh helps reinforce your learning and identifies misunderstandings early. If you’re starting later in the year, don’t worry. Focus on high-yield topics and use our customizable AP Calc AB practice exam generator to target your weakest areas. Consistent, focused practice even 4–6 weeks before the exam can still lead to significant score improvements.
Can I build custom AP Calc AB practice tests focused on specific topics?
Absolutely. Our platform allows you to create customizable AP Calc AB practice tests tailored to your exact study needs. You can focus on broad units, like “Applications of Integration,” or drill down into specific sub-topics. You can set the number of questions to fit your study schedule, allowing you to efficiently target the areas where you need the most practice. After every AP Calc AB practice exam or quiz you can review the integrated performance tracker to track your progress on specific concepts over time.
What score on an AP Calculus AB practice test indicates Iām ready for the real exam?
While there’s no single magic number, a good benchmark is consistently scoring 70% or higher on UWorld’s full-length AP Calculus AB practice tests (across both MCQ and FRQ sections). This is a strong indicator that you are on track for a 4 or 5. If you’re not at 70% yet, don’t panic. Use the performance dashboard data to see exactly which units (e.g., “Differential Equations”) are holding you back, then create targeted quizzes to improve in those areas.
Do these AP Calculus AB practice tests include both Multiple-Choice and Free-Response Questions?
Yes. UWorld’s AP Calculus AB preparation includes hundreds of multiple-choice questions and a robust set of free-response questions (FRQs). You can practice realistic AP Calculus AB exam questions that model the format and style of the real FRQs and our detailed solutions and scoring guidelines teach you how to structure your answers and show your work to earn maximum points, just as an AP grader would expect.
How many full-length AP Calculus AB mock exams should I take before test day?
We recommend that every student take at least one full-length AP Calculus AB mock exam before test day. Practicing under realistic timed conditions is the best way to build stamina, manage your pacing across the different sections and reduce test-day anxiety. UWorld’s AP Calculus AB mock exams are built directly from our deep AB calculus question bank and will give you the realistic interface and style of questions you’ll see on exam day. Furthermore, coming in Spring 2026, we will also offer a pre-built, full-length AP Calculus AB mock exam as part of our AP Calculus AB Online Review Course.
Where can I find free AP Calculus AB practice questions?
You can try free AP Calculus AB practice questions by signing up for UWorld’s free 7-day trial. This will give you access to a sample of our high-quality MCQs and FRQs, complete with the detailed, step-by-step solutions that set our product apart. The free trial also provides a preview of our complete AP Calc AB Course, which includes video lessons and digital study guides to help you master the content.