Answer Key
AP Calculus AB Pre-Exam
The Calculus Pre-Exam is a tool for evaluating whether a student is ready to take the AP Calculus AB
Course offered by Patrick Henry College Preparatory Academy. After taking the exam, students or their
parents may download the Pre-Exam Answer Key to grade the exam. A student should be able to score at
least 80% on the exam before signing up for the course.
This test covers (1) basic algebraic skills, (2) basic skills involving functions, and (3) basic trigonometric
skills. A student should be able to effectively use mathematical skills in all three of these areas before
taking AP Calculus AB.
For each of the following questions, choose the best response.
Problems (1) – (10) test basic algebraic skills:
1.
If and are integers and
incorrect?
(A)
·
(B)
·
and
are real numbers, which of the following statements is
(C)
(D)
Correct answer
·
(E)
2.
The expression
can be simplified to which of the following choices?
(A)
(B)
(C)
(D)
Correct answer
(E)
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
3.
which of the following choices?
(A)
(B)
(C)
(D)
Correct answer
(E)
4.
Which of the following is a correct factoring of the expression
5
(A)
5
25
(B)
(C)
4
6
(D)
6
4
If
(A)
2
(B)
5
(C)
12
(D)
3
(E)
10
6.
If
(A)
2
(B)
–3
(C)
4
(D)
–4
(E)
0
4
Correct answer
5
5
5
(E)
5.
24
5
4 , what is the value of y when
2?
Correct answer
,
cannot be evaluated for what value of ?
Correct answer
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
25
?
7.
What are the values of
(A)
2, 1, and 1
(B)
2, 1, and
(C)
1 and 2
(D)
1 and 2
(E)
0, 1, and 2
8.
1
for which the following is it true:
2
1
0?
Correct answer
The solution of the equation
4
is which of the following?
2
(A)
(B)
1
(C)
1
(D)
4
(E)
Correct answer
9.
One number is 5 more than another and the sum of the two numbers is 25. What is the smaller of
the two numbers?
(A)
5
(B)
10
(C)
15
(D)
8
(E)
12
10.
Let
Correct answer
2
(A)
4
(B)
2
(C)
2
(D)
0
(E)
0
4. For what value or values of
is
0?
Correct answer
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
Problems (11) – (20) test basic skills involving the concept of functions:
11.
2
(A)
as a function of ?
1
2
(B)
(C)
3
(D)
2
2
(E)
2
1
12.
3. What is
1 and
Suppose
Correct answer
and
Suppose
. Which of the following is not true?
(A)
when
1
(B)
when
0
(C)
when
0
Correct answer
(D)
(E)
13.
Suppose
(A)
and
when
(C)
when
0
0
(E)
14.
Suppose
2
(B)
0.5
(C)
1
(E)
1
1
Correct answer
when
(A)
(D)
. Which of the following is not true?
0.
is not defined at
(B)
(D)
1
when
2 and
1
1. For what
value is it true that
–
Correct answer
1
0.5
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
0?
15.
Suppose
and
(A)
0
(B)
0
(C)
0 and
1
(D)
3 and
1
values is it true that
?
Correct answer
(E)
no
16.
Consider the function
values satisfy the condition
(A)
2 and
2
(B)
2 and
2
(C)
all values of
(D)
no values of
– 4. For what
is it true that
0?
Correct answer
2
(E)
17.
Let
(A)
2
(B)
3
(C)
4
(D)
–3
(E)
0
18.
Suppose
(A)
1
(B)
. For what
;
is not defined for which of the following values of ?
Correct answer
2
1 . For which of the following x values is it true that
1
(C)
1 and
(D)
1 and
(E)
no values of
1
1
Correct answer
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
0?
19.
Suppose
value?
4
and
. For what
value do these functions map into the same
2
(A)
(B)
1
(C)
1
(D)
4
(E)
20.
Correct answer
A rectangle has a height , width
, and a perimeter of length 30. Express
as a function of
.
(A)
(B)
15
(C)
30
(D)
30
(E)
√30
Correct answer
2
Problems (21) – (30) test basic skills involving trigonometry:
Problems 21, 22, and 23 refer to the following figure showing triangle
with angles , , and ; sides
,
, and
; and the line
which is perpendicular to side
. We will indicate length of lines with
a pair of vertical lines. Thus, | | is the length of side
.
B
c
a
C
D
A
21.
Which of the following is sin
(A)
sin
|
|
|
|
(B)
sin
|
|
|
|
(C)
sin
|
|
|
|
(D)
sin
|
| |
|
(E)
sin
|
| |
|
?
Correct answer
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
22.
Which of the following is cos
(A)
cos
|
|
|
|
(B)
cos
|
|
|
|
(C)
cos
|
|
|
|
(D)
cos
|
| |
|
(E)
cos
|
| |
|
23.
Which of the following is tan
(A)
tan
|
|
|
|
(B)
tan
|
|
|
|
(C)
tan
|
|
|
|
(D)
tan
|
|
|
|
(E)
tan
|
| |
24.
For which angle
(A)
0°
(B)
180°
(C)
90°
(D)
360°
(E)
tan
25.
Let
Correct answer
?
Correct answer
|
is tan
not defined?
Correct answer
is defined for all .
be some angle for which cos
(A)
0°
(B)
135°
(C)
45°
(D)
225°
(E)
?
sin 45° . For which of the following θ values is this true?
Correct answer
none of the above.
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
26.
It is known that tan 45°
(A)
0°
(B)
135°
(C)
45°
(D)
225°
1. For which of the following
Correct answer
(E)
none of the above.
27.
What is the minimum value of cos
(A)
0
(B)
(C)
(D)
(E)
values is it also true that tan
45° ?
√
1
1
Correct answer
√
28.
Which of the following is not true?
(A)
tan
sin
(B)
sin
cos
(C)
cos
sin 90°
(D)
cos
(E)
cos
29.
Suppose
cos
1
90°
sin
cos
cos
(A)
90°
(B)
360°
(C)
100°
(D)
180°
(E)
200°
Correct answer
and
is an integer. Which of the following is true?
Correct answer
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam
1?
30.
Consider the function cos 3
(A)
0°
(B)
60°
(C)
30°
(D)
45°
(E)
. For which of the following
values is this function equal to 0?
Correct answer
none of the above
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
AP Calculus AB Pre-Exam