AP CALCULUS EXAM 5 QUESTIONS
WITH CORRECT ANSWERS
If a trapezoidal sum overapproximates ∫0 to 4 f(x)dx, and a right Riemann sum
underapproximates ∫0 to 4 f(x)dx, which of the following could be the graph of y=f(x)? -
ANSWER-A- The one with a y intercept at three that is concave up and decreasing
Let f be the function given by f(x)=9^x. If four subintervals of equal length are used,
what is the value of the right Riemann sum approximation for ∫0 to 2 f(x)dx? - ANSWER-
C- 60
t(sec)-0-2-4-6
a(t)(ft^2/sec)-5-2-8-3
The data for the acceleration a(t) of a car from 0 to 6 seconds are given in the table
above. If the velocity at t=0 is 11 feet per second, the approximate value of the velocity
at t=6, computed using a left-hand Riemann sum with three subintervals of equal length,
is - ANSWER-E- 41 ft/sec
Calculate the approximate area of the shaded region in the figure by the trapezoidal
rule, using divisions at x=4/3 and x=5/3. - ANSWER-D-127/54
If G(x) is an antiderivative for f(x) and G(2)=−7, then G(4)= - ANSWER-E- -7+ ∫2 to
4f(t)dt
Let f and g be continuous functions such that ∫0 to 10f(x)dx=21, ∫0 to 10 1/2g(x)dx=8,
and ∫3 to 10(f(x)−g(x))dx=2. What is the value of ∫0 to 3 (f(x)-g(x))dx? - ANSWER-A- 3
Which of the following is an antiderivative of f(x)=sqr(1+x^3) - ANSWER-E- ∫0 to x
sqr(1+t^3)dt
If the function f is defined by f(x)=sqr(x^3+2) and g is an antiderivative of f such that g(3)
= 5, then g(1) = - ANSWER-B- -1.585
The function f is given by f(x)=∫1 to x sqr(t^3+2)dt. What is the average rate of change of
f over the interval [0,3]? - ANSWER-E- 2.694
Let g be the function given by g(x)=∫1 to x 100(t^2−3t+2)e^-t^2dt. Which of the following
statements about g must be true?
I. g is increasing on (1, 2).
II. g is increasing on (2, 3).
III. g(3) > 0 - ANSWER-B- II only
WITH CORRECT ANSWERS
If a trapezoidal sum overapproximates ∫0 to 4 f(x)dx, and a right Riemann sum
underapproximates ∫0 to 4 f(x)dx, which of the following could be the graph of y=f(x)? -
ANSWER-A- The one with a y intercept at three that is concave up and decreasing
Let f be the function given by f(x)=9^x. If four subintervals of equal length are used,
what is the value of the right Riemann sum approximation for ∫0 to 2 f(x)dx? - ANSWER-
C- 60
t(sec)-0-2-4-6
a(t)(ft^2/sec)-5-2-8-3
The data for the acceleration a(t) of a car from 0 to 6 seconds are given in the table
above. If the velocity at t=0 is 11 feet per second, the approximate value of the velocity
at t=6, computed using a left-hand Riemann sum with three subintervals of equal length,
is - ANSWER-E- 41 ft/sec
Calculate the approximate area of the shaded region in the figure by the trapezoidal
rule, using divisions at x=4/3 and x=5/3. - ANSWER-D-127/54
If G(x) is an antiderivative for f(x) and G(2)=−7, then G(4)= - ANSWER-E- -7+ ∫2 to
4f(t)dt
Let f and g be continuous functions such that ∫0 to 10f(x)dx=21, ∫0 to 10 1/2g(x)dx=8,
and ∫3 to 10(f(x)−g(x))dx=2. What is the value of ∫0 to 3 (f(x)-g(x))dx? - ANSWER-A- 3
Which of the following is an antiderivative of f(x)=sqr(1+x^3) - ANSWER-E- ∫0 to x
sqr(1+t^3)dt
If the function f is defined by f(x)=sqr(x^3+2) and g is an antiderivative of f such that g(3)
= 5, then g(1) = - ANSWER-B- -1.585
The function f is given by f(x)=∫1 to x sqr(t^3+2)dt. What is the average rate of change of
f over the interval [0,3]? - ANSWER-E- 2.694
Let g be the function given by g(x)=∫1 to x 100(t^2−3t+2)e^-t^2dt. Which of the following
statements about g must be true?
I. g is increasing on (1, 2).
II. g is increasing on (2, 3).
III. g(3) > 0 - ANSWER-B- II only
