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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.
1c− os2(2x)
1. lim 2 =
x 0 (2x)
(A) 0
(B) 1
4
(C) 1
2
(D) 1
2 for1x <−
fx()= x
2
xx−−3for 12
43xx−>for2
2. Let f be the function defined above. At what values of x, if any, is f 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.
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AP Calculus AB and BC Course and Exam Description Exam Information V.1
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00762-114-CED-Calculus-AB/BC_Exam Information.indd 228 3/12/19 1:44 PM
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 functions f 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
3 2 dy
4. If x - 2xy + 3y = 7, then dx =
2
(A) 34xy+
2x
2
(B) 32xy−
26xy−
3x2
(C)
26xy−
3x2
(D)
26− y
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 h
of the cylinder?
2
(The volume V of a cylinder with radius r and height h is V = πr h.)
(A) -20πr
(B) -2πrh
2
(C) 4πrh - 5πr
2
(D) 4πrh + 5πr
AP Calculus AB and BC Course and Exam Description Exam Information V.1 | 229
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6. Which of the following is equivalent to the definite integral 6 xdx?
2
n 44
(A) n
k 1
(B)
n
(C)
k 1
(D)
O 12345678
Graph of g
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) = x gt()dt . On wh
3 at intervals is h
increasing?
(A) [2, 5]only
(B) [1, 7]
(C) [0, 1] and [3, 7]
(D) [1, 3] and [7, 8]
8. x dx =
2
19− x
1 2
(A) −−19xC+
9
1 2
(B) −−ln 19xC+
18
(C) 1arcsin(3xC)+
3
x
(D) 3arcsin(3xC)+
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ents
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00762-114-CED-Calculus-AB/BC_Exam Information.indd 230 3/12/19 1:44 PM
y
3
2
1
–3 –2 –1 1 2 3 x
–1
–2
–3
9. Shown above is a slope field for which of the following differential equations?
(A) dy = y−2
dx 2
dy y2 −4
(B) dx = 4
(C) dy = x −2
dx 2
dy x2 −4
(D) dx = 4
y
10. Let R be the region bounded by the graph of x = e , the vertical line x = 10, and
the horizontal lines y = 1 and y = 2. Which of the following gives the area of R?
2 y
(A) edy
1
e2
xd
(B) e ln x
2 y
(C) 1(10)−edy
10
( n1
(D) e l xd− ) x
AP Calculus AB and BC Course and Exam Description Exam Information V.1 | 231
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00762-114-CED-Calculus-AB/BC_Exam Information.indd 231 3/12/19 1:44 PM
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