AP CALCULUS SECOND SEMESTER
EXAM QUESTIONS WITH VERIFIED
ANSWERS
On a certain day, the rate at which material is deposited at a recycling center is
modeled by the function R, where R(t) is measured in tons per hour and t is the number
of hours since the center opened. Using a trapezoidal sum with the three subintervals
indicated by the data in the table, what is the approximate number of tons of material
deposited in the first 9 hours since the center opened? (Has table) - ANSWER-A. 68
The function g is defined by g(x)=x^2+bx, where b is constant. If the line tangent to the
graph of g at x=-1 is parallel to the line that contains the points (0, -2) and (3, 4), what is
the value of b? - ANSWER-D. 4
The function f is defined above (with two different equations in a bracket after "f(x)").
The value of the integral from [-5, 3] f(x)dx is: - ANSWER-A. -2
The graph of the function f, shown above (the V shaped graph), consists of three line
segments. If the function g is an antiderivative of f such that g(2)=5, for how many
values of c, where 0<(or equal to)c<(or equal to)6, does g(c)=3? - ANSWER-B. One
Which of the following could be a slope field for the differential equation dy/dx=x^2+y? -
ANSWER-B. (The lines are horizontal on the y-axis like this: -)
lim from x->e ((x^20-3x)-(e^20-3e))/(x-e)= - ANSWER-B. 20e^19-3
Let y=f(x) be the particular solution to the differential equation dy/dx+(x+1)/y with the
initial condition f(0)=-2. Which of the following is an expression for f(x)? - ANSWER-C. -
(square root)x^2+2x+4
Let R be the shaded region bounded by the graph of y=(square root)x, the graph of y=x-
2, and the x-axis , as shown in the figure above. Which of the following gives the volume
of the solid generated when R is revolved about the x-axis? - ANSWER-C. pi integral [0,
2] xdx + pi integral [2, 4] x-(x-2)^2dx
Let f be a function with first derivative defined by f'(x)=(3x^2-6)/(x^2) for x>0. It is known
that f(1)=9 and f(3)=11. What value of x in the open interval (1, 3) satisfies the
conclusion of the Mean Value Theorem for f on the closed interval [1, 3]? - ANSWER-B.
square root of 3
A hemispherical water tank, shown above, has a radius of 6 meters and is losing water.
The area of the surface of the water is A=12pih-pih^2 square meters, where h is the
depth, in meters, of the water in the tank. When h=3 meters, the depth of the water is
EXAM QUESTIONS WITH VERIFIED
ANSWERS
On a certain day, the rate at which material is deposited at a recycling center is
modeled by the function R, where R(t) is measured in tons per hour and t is the number
of hours since the center opened. Using a trapezoidal sum with the three subintervals
indicated by the data in the table, what is the approximate number of tons of material
deposited in the first 9 hours since the center opened? (Has table) - ANSWER-A. 68
The function g is defined by g(x)=x^2+bx, where b is constant. If the line tangent to the
graph of g at x=-1 is parallel to the line that contains the points (0, -2) and (3, 4), what is
the value of b? - ANSWER-D. 4
The function f is defined above (with two different equations in a bracket after "f(x)").
The value of the integral from [-5, 3] f(x)dx is: - ANSWER-A. -2
The graph of the function f, shown above (the V shaped graph), consists of three line
segments. If the function g is an antiderivative of f such that g(2)=5, for how many
values of c, where 0<(or equal to)c<(or equal to)6, does g(c)=3? - ANSWER-B. One
Which of the following could be a slope field for the differential equation dy/dx=x^2+y? -
ANSWER-B. (The lines are horizontal on the y-axis like this: -)
lim from x->e ((x^20-3x)-(e^20-3e))/(x-e)= - ANSWER-B. 20e^19-3
Let y=f(x) be the particular solution to the differential equation dy/dx+(x+1)/y with the
initial condition f(0)=-2. Which of the following is an expression for f(x)? - ANSWER-C. -
(square root)x^2+2x+4
Let R be the shaded region bounded by the graph of y=(square root)x, the graph of y=x-
2, and the x-axis , as shown in the figure above. Which of the following gives the volume
of the solid generated when R is revolved about the x-axis? - ANSWER-C. pi integral [0,
2] xdx + pi integral [2, 4] x-(x-2)^2dx
Let f be a function with first derivative defined by f'(x)=(3x^2-6)/(x^2) for x>0. It is known
that f(1)=9 and f(3)=11. What value of x in the open interval (1, 3) satisfies the
conclusion of the Mean Value Theorem for f on the closed interval [1, 3]? - ANSWER-B.
square root of 3
A hemispherical water tank, shown above, has a radius of 6 meters and is losing water.
The area of the surface of the water is A=12pih-pih^2 square meters, where h is the
depth, in meters, of the water in the tank. When h=3 meters, the depth of the water is
