AB Calculus - Hardtke
Quiz Practice Exam II: Mult Choice
SOLUTIONS
No Calculator. MULTIPLE CHOICE. Fill in the best answer on the scan form. (1 pt each)
1. ∫
=
A.
B.
D. 0
E.
C.
2. If f(x) = e2x and g(x) = ln x, then the derivative of f( g(x) ) at x = e is
2
2
A. 2e
D. 2
3. If
B. e
E. undefined
∫
=
A.
D.
C. 2e
B.
√
√
C.
√
E. The limit does not exist.
4. The area of the region bounded by the lines x = 1 and y = 0 and the curve
A.
B.
D. e – 1
E.
C. 1 – e
5. What is
A.
B.
C.
D.
E. The limit does not exist.
6. A particle starts at time t = 0 and moves along a number line so that
3
its position, at time t ≥ 0, is given by x(t) = (t – 2) (t – 6). The particle
is moving to the right for
A. t ≥ 0
D. 2 < t < 6
B. t > 5
E. never
C. 0 < t < 5
is
∫
7.
√
=
A. 3
D.
B. 9
C. 4
E. None of the above.
5
4
8. On which of the following intervals, is the curve y = x – 5x + 10x + 15 concave up?
I. x < 0
II. 0 < x < 3
III. x > 3
A. I only
D. I and II only
B. II only
E. II and III only
C. III only
9. The slope of the tangent line to the curve 2xy + sin y = 2π at the point where y = π is
B. – 2π
E. π
A. 2π
D. 0
10. The derivative of
A.
⁄
D.
√
√
⁄
⁄
C. – π
is
B.
⁄
E.
⁄
⁄
⁄
12.
A. – sin x
D. cos x
B. – 1
E. 2
(
)
⁄
⁄
11. If the function G is defined for all real numbers by G(x) =∫
A. – 2
D. 1
⁄
C.
C. 0
=
2
B. – cosx
C. – csc x
E. does not exist
(
)
, then
(√ ) =
13. A graph of the function f is shown at the right. Which of the
Following statements are true?
I. f(2) > f ’ (2.5)
II. ∫ ( )
f ’ (5)
III.
(
)
A. I only
D. II and III only
( )
<
( )
( )
B. II only
E. I , II and III
C. I and II only
14. The function f is continuous and differentiable on the closed interval [1, 7].
The table below gives selected values of f on this interval. Which of the
Following statements MUST be TRUE?
1 2 3 4 5 6 7
x
f(x) 8 12 7 – 2 1 2 4
A. f ‘(x) > 0 for 1 < x < 2
B. f ‘‘ (x) < 0 for 2 < x < 4
C. There exists a number c, 1 < c < 7 for which f(c) = 0.
D. The maximum value of f on [1, 7] must be 12.
E. 5 is a critical number of f(x)
15. An equation of the normal to the graph of f(x) =
A. x + 3y = 2
D. 3x + y = 2
B. x – 3y = 4
E. 3x + y = 4
at (1, f(1)) is
C. x – 3y = – 2
EXTRA CREDIT – 1 pt each
2
16. The average value of sec x over the interval 0 ≤ x ≤
A. 1
B.
C.
D.
E. none of the above
is
y = f(x)