AP Calculus AB: 2012 Released Exam, Section I (Non-Calculator)

If y = x sin x, then dy/dx =

• sin x + cos x

• sin x + x cos x

• sin x - x cos x

• x(sin x + cos x)

• x(sin x - cos x)

Let f be the function given by f(x) = 300x - x³. On which of the following intervals is the function f increasing?

• (-∞, -10] and [10, ∞)

• [-10, 10]

• [0, 10]

• [0, 10√3]

• [0, ∞)

∫sec x tan x dx =

• sec x + C

• tan x + C

• (sec² x)/2 + C

• (tan² x)/2 + C

• (sec² x tan² x)/2 + C

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

• 4
• 5
• 6
• 7
• 8

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

• lim_x->2 f(x) exists.

• lim_x->3 f(x) exists.

• lim_x->4 f(x) exists.

• lim_x->5 f(x) exists.

• The function f is continuous at x=3.

A particle moves along the x-axis. The velocity of the particle at time t is 6t - t². What is the total distance traveled by the particle from time t=0 to t=3?

• 3

• 6

• 9

• 18

• 27

If y = (x³-cos x)⁵, then y' =

• 5(x³-cos x)⁴

• 5(3x²+sin x)⁴

• 5(3x²+sin x)

• 5(3x²+sin x)⁴(6x+cos x)

• 5(x³-cos x)⁴(3x²+sin x)

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 and data from the table, what is the approximation of the number of liters of oil that are in the tank at time t = 15 hours?

• 64.9

• 68.2

• 114.9

• 116.6

• 118.2

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

• 0

• 1

• 2

• 3

• 5

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

• 2e-2

• 2e

• e/2-1

• (e - 1)/2

• e-1