AP CALCULUS BC UNIT 2 PROGRESS CHECK MCQ PART
A FREQUENTLY TESTED ACTUAL EXAM QUESTIONS
WITH CORRECT ANSWERS
Question 1.
1. X | 0 | 1 F(x) | 1 | 2 Let f be the function given by f(x) = 2^(x^2). Selected values of f are
given in the table above. If the values in the table are used to approximate f'(0.5), what is the
difference between the approximation and the actual value of f'(0.5)?
A. 0
B. 0.176
C. 0.824
D. 1
ANSWER
B. 0.176
Question 2.
2. Let f be the function given by f(x) = (1/7)x^7 - (7/6)x^6
+ 3x^5 - (5/4)x^4 - (16/3)x^3 + 6x^2. Which of the following statements is true?
A. f'(-1.1) < f'(0.5) < f'(1.4)
B. f'(-1.1) < f'(1.4) < f'(0.5)
C. f'(0.5) < f'(1.4) < f'(-1.1)
D. f'(1.4) < f'(0.5) < f'(-1.1)
ANSWER
D. f'(1.4) < f'(0.5) < f'(-1.1)
Question 3.
3. X | 1 | 2 | 3 | 4 | 5 | 6 f(x) | -3 | -1 | 1 | 2 | 5 | 10 Selected values of a function f are shown in
the table above. What is the average rate of change of f over the interval [1, 6]?
A. (6-1)/[10-(-3)]
C. [10-(-3)]/(6-1)
D. [(-3) + (-1) + 1 + 2 + 5 + 10]/6
ANSWER
C. [10-(-3)]/(6-1)
1
, Question 4.
4. The graph of the function f, shown above, consists
of three line segments. What is the average rate of change of f over the interval 1 < x < 7?
(Should be less than or equal to)
A. -2
B. 0
C. 1/3
D. 3
ANSWER
B. 0
Question 5.
5. The function f is given by f(x) = 1 + 2sin(x). What is the
average rate of change of f over the interval [0, pi/2]?
A. 4/pi
B. 6/pi
C. 8/pi
D. 2
ANSWER
A. 4/pi
Question 6.
6. The derivative of a function f is given by f'(x) = 0.2x
+ e^(0.15x). Which of the following procedures can be used to determine the value of x at
which the line tangent to the graph of f has slope 2?
A. Evaluate 0.2x + e^(0.15x) at x=2
B. Evaluate d/dx (0.2x + e^(0.15x)) at x=2
C. Solve 0.2x + e^(0.15x)= 2 for x
D. Solve d/dx (0.2x + e^(0.15x) = 2) for x
ANSWER
C. Solve 0.2x + e^(0.15x)=
2 for x
Question 7.
+ 4 for all x, and f(-1) = 5. Which of the following is an equation for the line tangent to the
graph of f at x = -1?
A. y = -2x + 3
B. y = -2x + 4
C. y = 6x + 5
D. y = 6x + 11
ANSWER
D. y = 6x + 11
2
A FREQUENTLY TESTED ACTUAL EXAM QUESTIONS
WITH CORRECT ANSWERS
Question 1.
1. X | 0 | 1 F(x) | 1 | 2 Let f be the function given by f(x) = 2^(x^2). Selected values of f are
given in the table above. If the values in the table are used to approximate f'(0.5), what is the
difference between the approximation and the actual value of f'(0.5)?
A. 0
B. 0.176
C. 0.824
D. 1
ANSWER
B. 0.176
Question 2.
2. Let f be the function given by f(x) = (1/7)x^7 - (7/6)x^6
+ 3x^5 - (5/4)x^4 - (16/3)x^3 + 6x^2. Which of the following statements is true?
A. f'(-1.1) < f'(0.5) < f'(1.4)
B. f'(-1.1) < f'(1.4) < f'(0.5)
C. f'(0.5) < f'(1.4) < f'(-1.1)
D. f'(1.4) < f'(0.5) < f'(-1.1)
ANSWER
D. f'(1.4) < f'(0.5) < f'(-1.1)
Question 3.
3. X | 1 | 2 | 3 | 4 | 5 | 6 f(x) | -3 | -1 | 1 | 2 | 5 | 10 Selected values of a function f are shown in
the table above. What is the average rate of change of f over the interval [1, 6]?
A. (6-1)/[10-(-3)]
C. [10-(-3)]/(6-1)
D. [(-3) + (-1) + 1 + 2 + 5 + 10]/6
ANSWER
C. [10-(-3)]/(6-1)
1
, Question 4.
4. The graph of the function f, shown above, consists
of three line segments. What is the average rate of change of f over the interval 1 < x < 7?
(Should be less than or equal to)
A. -2
B. 0
C. 1/3
D. 3
ANSWER
B. 0
Question 5.
5. The function f is given by f(x) = 1 + 2sin(x). What is the
average rate of change of f over the interval [0, pi/2]?
A. 4/pi
B. 6/pi
C. 8/pi
D. 2
ANSWER
A. 4/pi
Question 6.
6. The derivative of a function f is given by f'(x) = 0.2x
+ e^(0.15x). Which of the following procedures can be used to determine the value of x at
which the line tangent to the graph of f has slope 2?
A. Evaluate 0.2x + e^(0.15x) at x=2
B. Evaluate d/dx (0.2x + e^(0.15x)) at x=2
C. Solve 0.2x + e^(0.15x)= 2 for x
D. Solve d/dx (0.2x + e^(0.15x) = 2) for x
ANSWER
C. Solve 0.2x + e^(0.15x)=
2 for x
Question 7.
+ 4 for all x, and f(-1) = 5. Which of the following is an equation for the line tangent to the
graph of f at x = -1?
A. y = -2x + 3
B. y = -2x + 4
C. y = 6x + 5
D. y = 6x + 11
ANSWER
D. y = 6x + 11
2
