AP Calculus Practice Exam and Solutions
[Pages:46]AP Calculus AB Practice Exam
Calculus AB
Section 1, Part A
Time - 55 minutes Number of questions - 28
A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM
Directions: Solve all of the problems that follow. Available space on the page may be used for
scratch work.
In this exam:
(1)
The domain of a function in this exam is assumed to be all real numbers for which the function is defined, unless specified otherwise.
(2)
The inverse notation
or the prefix "arc" may be used to indicate an inverse function.
x x For example, the inverse tangent of
may be written as arcsin( ) or as
.
Copyright ? 2015 by Lucid Education
Calculus AB
1. Using the substitution
A)
B) C) D) E)
, the integral
Section 1, Part A
is equivalent to
2.
A)
B) C) D) E)
. Find
.
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Calculus AB
Section 1, Part A
3. A line through the point (2, -2) is tangent to function f at the point (-2, 6). What is
?
A) -8
B) -2
C)
D) 6
E) Undefined
4. Grain is pouring out of an opening in the bottom of a grain silo. The rate at which the height,
h t , of the grain in the silo is changing with respect to time, , is proportional to the square root of
the height. Which of the following is a differential equation describing this situation?
A)
B)
C)
D) E)
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Calculus AB
5. Where is the graph of
A)
B)
concave up? C)
D)
Section 1, Part A
E)
f 6. Shown is a graph of function .
At which value of x f is continuous but not differentiable?
A) a
B) b
C) c
D) d
E) e
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Calculus AB
Section 1, Part A
7. The table shows values of
. Although f , the derivative of function
real numbers, only selected values of
are shown.
is continuous over all
x -2 -1 0 1 2 3 4
4.1
2.3
1.2
0
-0.6
-0.8
-2
56
0
1.5
If
f has exactly two real zeros, then
is increasing over which of the following intervals?
A)
B)
C)
only
D)
E)
8.
.
A)
B) C) D) E)
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Calculus AB
Section 1, Part A
9. At each point (x y f , ) on a graph of function , the graph has a slope equal to
f graph of
goes through the point (2, 3), then
A)
. If the
B)
C)
D) E)
g 10. The derivative of function is given by
A)
B) C) D) E)
g . When is increasing?
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Calculus AB
f 11. Function
is defined as
Which of the following statements is true:
f I.
is continuous at
.
II.
exists.
f III.
is differentiable at
A) None of the statements are true.
B) I only C) II only D) I and II only E) I, II, and III
Section 1, Part A
12.
A)
B)
C)
D)
E)
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