AP Calculus AB and BC - Sample Exam Questions - Section I: Multiple-Choice

Sep 20, 2026

Uploaded by Aurora

Sample AP Calculus AB and BC exam questions illustrating how the course framework maps to skills, learning objectives, and units. The document provides multiple-choice problems covering key topics such as limits, differentiability and continuity, derivatives and applications, related rates, definite integrals, slope fields, area between curves, and velocity-to-acceleration calculations. It includes answer choices and referenced exam information for both Section I (multiple-choice) and subsequent sections.

LanguageEnglish

CategoryExam

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Pages12

Reading Time30 min

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Section I: Multiple-Choice

Part A (AB or BC)

Part B (AB or BC)

Part A (BC only)

Sample AP Calculus AB and BC Exam Questions The sample exam questions that follow illustrate the relationship between the course framework and the AP Calculus AB and BC Exams and serve as examples of the types of questions that appear on the exams. After the sample questions is a table that shows which skill, learning objective(s), and unit each question relates to. The table also provides the answers to the multiple-choice questions. Section I: Multiple-Choice PART A (AB OR BC) Graphing calculators are not permitted on this part of the exam. 1. lim 1− cos2 (2x) x0 (2x)2 =(A) 0 (B) 14 (C) 12 (D) 1 2 f (x) = xx2 − 3 4x − 3 for x <−1 for − 1 x 2 for x > 2 2. Let f be the function defined above. At what values of x, if any, isf not differentiable? (A) x = -1 only (B) x = 2 only (C) x = -1 and x = -2 (D) f is differentiable for all values of x. AP Calculus AB and BC Course and Exam Description Exam Information V.1 | 228 Return to Table of Contents © 2019 College Board | x | f(x) | fʹ(x) | g(x) | gʹ(x) | | --- | --- | --- | --- | --- | | 1 | 2 | -4 | -5 | 3 | | 2 | -3 | 1 | 8 | 4 | 3. The table above gives values of the differentiable functionsf and g and their derivatives at selected values of x. If h is the function defined by h(x) =f(x)g(x) + 2g(x), then hʹ (1) = (A) 32 (B) 30 (C) -6 (D) -16 dy 4. If x3-2xy + 3y2 = 7, then ~~ ~~ = 2 dx 3x + 4y (A) 2x 2 (B) 3x2x~~ ~~2y6y 2 (C) 2x3~~ ~~6y 2 (D) 26y 5. The radius of a right circular cylinder is increasing at a rate of 2 units per second. The height of the cylinder is decreasing at a rate of 5 units per second. Which of the following expressions gives the rate at which the volume of the cylinder is changing with respect to time in terms of the radius r and height hof the cylinder? (The volume V ofa cylinder with radius r and height h is V = πr2h.) (A) -20πr (B) -2πrh (C) 4πrh-5πr2 (D) 4πrh + 5πr2 AP Calculus AB and BC Course and Exam Description Exam Information V.1 | 229 Return to Table of Contents © 2019 College Board 6 6. Which of the following is equivalent to the definite integral 2 x dx? (A) (B) (C) (D) Graph ofg 7. The figure above shows the graph of the continuous function g on the interval [0, 8]. Let h be the function defined by h(x) = x3 g (t ) dt . On what intervals is h increasing? (A) [2, 5]only (B) [1, 7] (C) [0, 1] and [3, 7] (D) [1, 3] and [7, 8] 8. ~~ ~~~~ ~~ dx = 1 (A) − ~~ ~~ 1− 9x2 + C 9 1 (B) − ~~ ~~ ln 1− 9x 2 + C 18 (C) 13arcsin(3x)+C (D) x3~~ ~~ arcsin(3x)+C AP Calculus AB and BC Course and Exam Description Exam Information V.1 | 230 Return to Table of Contents © 2019 College Board 9. Shown above is a slope field for which of the following differential equations? (A) dydx = y~~ ~~−2~~ ~~2 (B) dydx = y~~ ~~2~~ ~~4 (C) dydx = x~~ ~~−2~~ ~~2 (D) dydx = x~~ ~~2~~ ~~~~ ~~4 10. Let R be the region bounded by the graph ofx = ey, the vertical line x = 10, and the horizontal lines y = 1 andy = 2. Which of the following gives the area of R? 2 (A) ey dy 1 (B) (C) 2 e ln x dx e 2 1 (10− ey )dy 10 (D) (ln x − 1)dx e AP Calculus AB and BC Course and Exam Description Exam Information V.1 | 231 Return to Table of Contents © 2019 College Board PART B (AB OR BC) A graphing calculator is required on this part of the exam. y |
4 | | | | |
4
x | | --- | --- | --- | --- | --- | --- | | | | | | 3 | | | | | | | 2 | | | | | | | 1 | | | | | | | | | | –4 | –3 | –2 | –1 | O
1 | | | | | | | – | | | | | | | –2 | | | | | | | –3 | | | | | | | –4 | | Graph off 11. The graph of the functionf is shown in the figure above. The value of li f (x) is x 1 (A) -2 (B) -1 (C) 2 (D) nonexistent 12. The velocity of a particle moving along a straight line is given by v(t) = 1.3tln (0.2t + 0.4) for time t ≥ 0. What is the acceleration

FAQs

Are graphing calculators allowed in Section I of this sample AP Calculus exam?

Graphing calculators are not permitted on Part A of Section I. A graphing calculator is required on Part B of Section I.

What kinds of calculus concepts are tested in the multiple-choice questions?

The problems cover limits, differentiability and concavity, derivatives, related rates, definite integrals, area between curves, and slope fields, along with applications like velocity and acceleration.

How is the sample question set connected to course framework and learning objectives?

The questions are designed to illustrate the relationship between the course framework, the AP Calculus AB/BC exams, and specific skills, learning objectives, and units, with answers provided for multiple-choice items.

Sep 20, 2026

Uploaded by Aurora