AP Exams · Calculus AB · Calculus BC
Build AP Calculus readiness with original limits, derivatives, integrals, series, representations, and exam-strategy questions.
This page combines AP Calculus AB and AP Calculus BC preparation in one canonical hub. It provides five short practice sets with 10 original questions each, covering limits, continuity, differentiation, integration, differential equations, parametric and polar functions, vector-valued functions, infinite series, and mathematical communication.
College Board describes AP Calculus AB around limits, differentiation, integration, differential equations, and applications. AP Calculus BC includes the AB foundation and adds parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series. This page keeps AB and BC on one URL while clearly labeling BC-only practice.
College Board’s current AP Calculus information also notes a hybrid digital exam with multiple-choice questions viewed in Bluebook and handwritten free-response answers returned in paper booklets. Exam timing, question counts, calculator rules, and other administration details can change, so check the current course and exam description before test day. College Board reports updates effective with the May 2027 exams.
Start with one untimed set to identify a topic gap, then use timed sets to build pacing. For every missed item, identify the representation and theorem or rule involved, read the explanation, and solve a new similar problem.
These questions are original supplemental practice. They are not official College Board questions, secure AP Exam content, a score predictor, an AP Classroom assignment, or a substitute for current AP policies and course materials.
For current scope and preparation, review the AP Calculus AB course page, the AP Calculus AB exam page, the AP Calculus BC overview, the AP Calculus AB and BC Course and Exam Description, and the AP calculator policy.
For more study options, visit AP Exam Tests or explore College Readiness Tests, High School Course Tests, and Pomodoro.
2. Test
A 10-question AP Calculus AB and BC practice set on ap calculus ab and bc: differentiation and applications, with answers and explanations.
Read the function, graph, table, series, or scenario carefully. Choose the best answer and review the explanation after each response.
Please select an answer first.
Correct answer: C
The correct answer is 3x².
The power rule gives f′(x) = 3x².
Please select an answer first.
Correct answer: D
The correct answer is cos x.
The derivative of sin x is cos x.
Please select an answer first.
Correct answer: A
The correct answer is eˣ.
The exponential function eˣ is its own derivative.
Please select an answer first.
Correct answer: B
The correct answer is Chain Rule.
The outer fifth power is applied to the inner function x² + 1, so use the Chain Rule.
Please select an answer first.
Correct answer: C
The correct answer is The slope of the tangent line to f at x = a.
The derivative at a gives the instantaneous slope at that point.
Please select an answer first.
Correct answer: D
The correct answer is 10.
Velocity is s′(t) = 2t + 4, so s′(3) = 10.
Please select an answer first.
Correct answer: A
The correct answer is A local maximum may occur.
A positive-to-negative derivative sign change indicates a local maximum.
Please select an answer first.
Correct answer: B
The correct answer is There is c in (a,b) with f′(c) = [f(b)-f(a)]/(b-a).
The theorem matches an instantaneous slope with the average slope on the interval.
Please select an answer first.
Correct answer: C
The correct answer is Related rates.
Related-rates problems differentiate a relationship among variables that change with time.
Please select an answer first.
Correct answer: D
The correct answer is Use the constraint to write the quantity as a function of one variable.
A one-variable objective makes critical-point and endpoint analysis possible.
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Yes. It uses one canonical page and labels BC extensions such as parametric, polar, vector-valued functions, and infinite series.
BC includes the AB foundation and additional topics including parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series.
No. These are original supplemental questions. Use AP Classroom, Bluebook previews, AP Central, and current College Board course materials for official preparation.
Calculator rules depend on the exam part and current College Board policy. Review the current calculator policy and approved-device information before test day.
Students should check the current Course and Exam Description because College Board has announced updates for the May 2027 exams.
