AP Calc AB 2012 MCQ Exam

If P(t) is the sie of a population at time t, which of the following differential equations describes linear growth in the size of the population?

dP/dt = 200

The graph of the function f is shown in the figure above. For which of the following values of x if f'(x) positive and increasing?

e

The graph of f', the derivative of the function f, is shown above. Which of the following statements must be true?

f has a relative minimun at x=-3 and The graph of f is concave down for 0<x<4

Let f be the function defined by f(x)=√abs(x-2) for all x. Which of the following statements is true?

f is continuous but not differentiable at x=2

Let f be 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?

f(x)=13 has at least one solution in the open interval (2,4)

Let f be a function such that (from 6 to 12) ∫f(2x)dx=10. Which of the following must be true?

from (12 to 24) ∫f(t)dt=20

Using the substitution u=√x, 1 to 4∫(e^√x)/(√x)dx is equal to which of the following?

from 1 to 2 2∫e^u du

Let g be a function with first derivative given by g'(x)= (from 0 to x) ∫e^-t^2 dt. Which of the following must be true on the interval 0<x<2?

g is increasing, and the graph of g in concave up

The graph of the differentiable function f is shown above. If h(x)= from 0 to x ∫f(t) dt, which of the following is true?

h(6)<h'(6)<h"(6)

The line y=5 is a horizontal asymptote to the graph of which of the following functions?

y=(20x^2-x)/(1+4x^2)

Which of the following is the solution to the differential equation dy/dx = 2sinx with the initial condition y(π) = 1

y=-2cosx-1

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 in concave down?

(-1.5,-1) and (0,1)

The function f is defined by f(x)=x/(x+2). what points (x,y) on the graph of f have the property that the line tangent to f at (x,y) has a slope 1/2

(0,0) and (-4,2)

For t≥0, the position of a particle moving along the x-axis is given by x(t)= sint-cost. What is the acceleration of the particle at the point where the velocity is first equal to 0?

-√2

Let R be the region in the first quadrant bounded below by the graph y=x^2 and above by the graph of y=√x. R is the base of the solid whose cross sections perpendicular to the x-axis are squares. What is the volume of the solid?

0.129

If f'(x)= √(x^4+1)+x^3-3x, then f has a local maximum at x=

0.350

The graph f', the derivative of f, is shown in the figure above. The function f has a local max at x=

1

If (x+2y)dy/dx= 2x-y, what is the value of d^2y/dx^2 at the point (3,0)

-10/3

The graph f", the second derivative of f, is shown above for -2≤x≤4. What are all intervals on which the graph of the function f is concave down?

-2<x<-1 and 1<x<3

Let g be the function given by g(x)=x^2e^kx, where k is a constant. For what value of k does g have a critical point at x=2/3

-3

as h goes to, 0 the lim((ln(4+h)-ln(4))/h is

1/4

Let f(x)=(2x+1)^3 and let g be the inverse function of f. Given that f(0)=1, what is the value of g'(1)

1/6

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 os the following gives the average velocity of the particle from time t=o to time t=8

1/8 (0 to 8) ∫v(t)dt

Let f be the function defined by f(x)=lnx/x. What is the absolute maximum value of f?

1/e

The function f is defined by f(x)= {2 for x<3 and x-1 for x≥3}. what is the value of from 1 to 5 ∫f(x) dx

10

A particle moves along a line so that its acceleration for t≥0 is given by a(t)=(t+3)/(√t^3+1). If the particle's velocity at t=0 is 5, what is the velocity of the particle at t=3?

11.710

A tank contains 50 liters of oil at time t=4 hours. Oil is being pumped into the tank at a rate R(t), where R(t) is measured in liters per hour, and t is measured in hours. Selected values of R(t) are given in the table above. Using a right Riemann sum with three subintervals from the data table, what is the approximation of the number of liters of oil that are in the tank at time t=15?

114.9

Water is pumped into a tank at a rate of r(t)=30(1-e^-0.16t) gallons per minute, where t is the number of minutes since the pump was turned on. if the tank contains 800 gallons of water when the pump was turned on, how much water, so the nearest gallon, is in the tank after 20 minutes

1220 gallons

A particle moves along the x-axis. The velocity of the particle at time t is 6t-t^2 What is the total distance traveled by the particle from time t=0 to t=3

18

A person whose height is 6 feet is talking 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?

2.667 ft/sec

The graph of y=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?

2.961

The graph above gives the velocity, v, 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?

210 ft

What is the area of the region in the first quadrant bounded by the graph y=e^(x/2) and the line x=2

2e-2

Let f be the function defined above. For what value of k is f continuous at x=2

5

If y=(x^3-cosx)^5, then y'=

5(x^3-cosx)^4(3x^2+sinx)

If f(x)=√x^2-4 and g(x)=3x-2, then the derivative of f(g(x)) at x=3 is

7/√5

If f(x)= 7x-3+lnx, then f'(1)=

8

Let f be a polynomial function with values of f'(x) at selected values of x given in the table abone. Which of the following must be true for -2<x<6?

The graph of f has at least two points of inflection

Let f be the function given by f(x)=300x-x^3. On which of the following intervals is the function f increasing?

[-10,10]

The figure above shows the graph of f. if f(x)= (from 2 to x) ∫g(t)dt, which of the following could be the graph of y= g(x)

horizontal line above x-axis

The graph of the function f is shown above. Which of the following statements is false?

lim(x->4) f(x) exists

∫secx tanx dx=

secx + C

if y=xsinx, then dy/dx=

sinx+xcosx

A particle moves along the x-axis with its position at time t given by x(t)= (t-a)(t-b), where a and b are constants and a≠b. For which of the following values of t is the particle at rest?

t=(a+b)/2

If f'(x)>0 for all real numbers x and (from 4 to 7) ∫f(t)dt=0, which of the following could be a table of values for the function f?

table with f(x) values of -4,-2,5