AP Calculus Exam Questions And
Correct Answer Updated
the graph of f is shown, for which of the following values of x is f'x positive and
increasing? - Answer -✔✔e
let f b a function that is continuous on the closed interval [2,4] with f(2)=10 and f(4)=20.
Which of the following is guaranteed by the Intermediate Value Theorem? - Answer -
✔✔f(x)=13 has at least one solution in the open interval (2,4)
the graph of (e^tanx)-2 crosses the x-axis at one point in the interval [0,1]. What is the
slope of the graph at this point? - Answer -✔✔2.961
a particle moves along the x axis. the velocity of the particle at time t is given by v(t),
and the acceleration of the particle at time t is given by a(t). which of the following gives
the average velocity of the particle from t=0 to t=8 - Answer -✔✔1/8!v(t)dt from 0 to 8
the graph of f' is shown above. which of the following statements must be true? bell
graph - Answer -✔✔I and III only
water is pumped into a tank at a rate of r(t)=30(1-e^-.16t) gallons per minute. if the tank
contained 800 gallons of water when the pump was turned on, how much water to the
nearest gallon is in the tank after 20 minutes? - Answer -✔✔1220 gallons
if f'= the square root of (x^4+1)+x^3-3x, then f has a local maximum at x= - Answer -
✔✔.350
the graph above gives the velocity in ft/sec of a car for 0<t<8, where t is the time in
seconds. Of the following, which is the best estimate of the distance traveled by the car
from t=0 until the car comes to a complete stop? - Answer -✔✔210ft
for -1.5<x<1.5, let f be a function with first derivative given by f'x= e^(x^(4)-2x^(2)+1)-2.
Which of the following are all intervals on which the graph of f is concave down? -
Answer -✔✔(-1.5,-1) and (0,1)
the graph f' is shown in the figure above. the function f has a local maximum at
x=?mountain looking graph crosses the x axis at x=1 - Answer -✔✔-3
if f'>0 for all real numbers x and the integral from 4 to 7
f(t)dt=0, which of the following could be a table of values for the function f? - Answer -
✔✔x f(x)
4 -4
5 -2
, 75
the graph of f'' is shown above for -2<x<4, what are all intervals on which the graph of
the function f is concave down? - Answer -✔✔-2<x<-1 ND 1<X<3
a person whose height is 6 feet is walking away from the base of a streetlight along a
straight path at a rate of 4 ft/sec. IF the height of the streetlight is 15 feet, what is the
rate at which the person's shadow is lengthening? - Answer -✔✔2.667 ft/sec
a particle moves along a line so that its acceleration for t>0 is given by
a(t)=(t+3)/(t^(3)+1)^1/2. if the particles velocity at t=0 is 5, what is the velocity of the
particle at t=3? - Answer -✔✔.713
let f be a function such that the integral from 6 to 12 f(2x)dx =10. Which of he following
must be true? - Answer -✔✔the integral from 12 to 24 f(t)dt=20
let f be a polynomial function with values of f' at selected values of x given in the table
above. which of the following must be true for -2<x<6? - Answer -✔✔the graph of f has
at least two points of inflection
a particle moves along a straight line so that at time t>0 the position of the particle is
given by s(t), the velocity is given by v(t), and the acceleration is given by a(t). Which of
the following expressions gives the average velocity of the particle on the interval [2,8]?
- Answer -✔✔[s(8)-s(2)]/6
if sin(1/x^2 +1) is an antiderivative for fx, then the integral from 1 to 2 of fxdt = - Answer
-✔✔-.281
the function is differentiable and increasing for all real numbers x, and the graph of f has
exactly one point of inflection. Of the following, which could be the graph of f'? - Answer
-✔✔the graph with the sharp point
the table above gives selected values of a function f. THe function is twice differentiable
with f'' >0. What is the value of f'(3) - Answer -✔✔.7
really fun waterslide graph.the figure above shows the graph f', for -6<x<8. which best
describes the graph of f on the same interval? - Answer -✔✔1 relative minimum, 1
relative maximum, 3 points of inflection
The regions A,B, and C in the figure above are bounded by the graph of the function f
and the x-axis. The area of region A is 14, the area of region b is 16, and the area of
region c is 50. What is the average value of f on the interval [0,8] - Answer -✔✔6
Correct Answer Updated
the graph of f is shown, for which of the following values of x is f'x positive and
increasing? - Answer -✔✔e
let f b a function that is continuous on the closed interval [2,4] with f(2)=10 and f(4)=20.
Which of the following is guaranteed by the Intermediate Value Theorem? - Answer -
✔✔f(x)=13 has at least one solution in the open interval (2,4)
the graph of (e^tanx)-2 crosses the x-axis at one point in the interval [0,1]. What is the
slope of the graph at this point? - Answer -✔✔2.961
a particle moves along the x axis. the velocity of the particle at time t is given by v(t),
and the acceleration of the particle at time t is given by a(t). which of the following gives
the average velocity of the particle from t=0 to t=8 - Answer -✔✔1/8!v(t)dt from 0 to 8
the graph of f' is shown above. which of the following statements must be true? bell
graph - Answer -✔✔I and III only
water is pumped into a tank at a rate of r(t)=30(1-e^-.16t) gallons per minute. if the tank
contained 800 gallons of water when the pump was turned on, how much water to the
nearest gallon is in the tank after 20 minutes? - Answer -✔✔1220 gallons
if f'= the square root of (x^4+1)+x^3-3x, then f has a local maximum at x= - Answer -
✔✔.350
the graph above gives the velocity in ft/sec of a car for 0<t<8, where t is the time in
seconds. Of the following, which is the best estimate of the distance traveled by the car
from t=0 until the car comes to a complete stop? - Answer -✔✔210ft
for -1.5<x<1.5, let f be a function with first derivative given by f'x= e^(x^(4)-2x^(2)+1)-2.
Which of the following are all intervals on which the graph of f is concave down? -
Answer -✔✔(-1.5,-1) and (0,1)
the graph f' is shown in the figure above. the function f has a local maximum at
x=?mountain looking graph crosses the x axis at x=1 - Answer -✔✔-3
if f'>0 for all real numbers x and the integral from 4 to 7
f(t)dt=0, which of the following could be a table of values for the function f? - Answer -
✔✔x f(x)
4 -4
5 -2
, 75
the graph of f'' is shown above for -2<x<4, what are all intervals on which the graph of
the function f is concave down? - Answer -✔✔-2<x<-1 ND 1<X<3
a person whose height is 6 feet is walking away from the base of a streetlight along a
straight path at a rate of 4 ft/sec. IF the height of the streetlight is 15 feet, what is the
rate at which the person's shadow is lengthening? - Answer -✔✔2.667 ft/sec
a particle moves along a line so that its acceleration for t>0 is given by
a(t)=(t+3)/(t^(3)+1)^1/2. if the particles velocity at t=0 is 5, what is the velocity of the
particle at t=3? - Answer -✔✔.713
let f be a function such that the integral from 6 to 12 f(2x)dx =10. Which of he following
must be true? - Answer -✔✔the integral from 12 to 24 f(t)dt=20
let f be a polynomial function with values of f' at selected values of x given in the table
above. which of the following must be true for -2<x<6? - Answer -✔✔the graph of f has
at least two points of inflection
a particle moves along a straight line so that at time t>0 the position of the particle is
given by s(t), the velocity is given by v(t), and the acceleration is given by a(t). Which of
the following expressions gives the average velocity of the particle on the interval [2,8]?
- Answer -✔✔[s(8)-s(2)]/6
if sin(1/x^2 +1) is an antiderivative for fx, then the integral from 1 to 2 of fxdt = - Answer
-✔✔-.281
the function is differentiable and increasing for all real numbers x, and the graph of f has
exactly one point of inflection. Of the following, which could be the graph of f'? - Answer
-✔✔the graph with the sharp point
the table above gives selected values of a function f. THe function is twice differentiable
with f'' >0. What is the value of f'(3) - Answer -✔✔.7
really fun waterslide graph.the figure above shows the graph f', for -6<x<8. which best
describes the graph of f on the same interval? - Answer -✔✔1 relative minimum, 1
relative maximum, 3 points of inflection
The regions A,B, and C in the figure above are bounded by the graph of the function f
and the x-axis. The area of region A is 14, the area of region b is 16, and the area of
region c is 50. What is the average value of f on the interval [0,8] - Answer -✔✔6
