AP Calculus BC Review

If f(x) = (x² – 3)⁴, then f'(1) =

• –64

• –32

• –16

• 32

Tags

CCSS.HSF.IF.A.2

An object moves in the xy-plane so that its position at any time t is given by the parametric equations x(t) = t³ – 3t² + 2 and y(t) = √(t² + 16). What is the rate of change of y with respect to x when t = 3?

• 1/90

• 1/15

• 3/5

• 5/2

Tags

CCSS.HSF.IF.B.4

Snow is falling at a rate of r(t) = 2e^–0.1t inches per hour, where t is the time in hours since the beginning of the snowfall. Which of the following expressions gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours?

• 2e^–0.5 – 2

• 0.2 – 0.2e^–0.5

• 4 – 4e^–0.5

• 20 – 20e^–0.5

At time t ≥ 0, a particle moving in the xy-plane has a velocity vector given by v(t) = <cos(2t), e^3t>. Wha tis the acceleration vector of the particle?

• <–2sin(2t), 3e^3t>

• <–2sin(2t), e^3t>

• <1/2sin(2t), 1/3e^3t>

• <2sin(2t), 3e^3t>

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.C.10

If e^x – y = xy³ + e² – 18, what is the value of ^dy/_dx at the point (2, 2)?

• e² – 32

• (e² – 9)/24

• (e² – 8)/25

• e²/13

Answer the following.

• A

• B

• C

• D

Consider the function given.

• –2

• 2

• 8

• nonexistent

Tags

CCSS.HSF-IF.C.7B

Which of the following series can be used with the limit comparison test to determine whether the given series converges or diverges?

• Σ(1/n)

• Σ(1/n³)

• Σ(n/(n+1)

• Σ(1/(n² + 1))

Find the integral.

• (6e⁵ – 1) / 25

• (4e⁵ + 1) / 25

• (1 – e³) / 3

• e⁴

An object moves along a straight line so that at any time t its acceleration is given by a(t) = 6t. At time t = 0, the object's velocity is 10 and the object's position is 7. What is the object's position at time t = 2?

• 22

• 27

• 28

• 35

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.A.2