AP Calculus Review

A certain medical procedure requires that a balloon be inserted into the stomach and then inflated. Model the shape of the balloon by a sphere of radius r. If r is increasing at the rate of 0.3 cm/min, how fast is the volume changing when the radius is 4 cm?

• 15.08 cm³/min
• 268.08 cm³/min
• 60.32 cm³/min
• 6.03 cm³/min

A ladder 13 feet long rests against a vertical wall and is sliding down the wall at the rate of 3 ft/s at the instant the foot of the ladder is 5 feet from the base of the wall. At this instant, how fast is the foot of the ladder moving away from the wall?

• dz/dt = 36/5 ft/sec
• dx/dt = 36/5 ft/sec
• dy/dt = 36/5 ft/sec
• dx/dt = 36/5 ft²/sec

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec.  How long is the diameter when the diameter is changing at a rate of 3 cm/sec?

• .424 cm
• .651 cm
• 1.333 cm
• 1.155 cm

Tags

CCSS.HSA.CED.A.1

CCSS.HSG.GMD.A.3

A bug begins to crawl up a vertical wire at time t = 0.  The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction? 

• 2
• 4
• 6.5
• 7

Tags

CCSS.HSF.IF.B.4

• t = 0
• t = 2
• t = 3
• t = 6

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

• A only
• A and B
• A and C
• D

Tags

CCSS.HSF.IF.B.4

• A
• B
• C
• D

• 2.612
• 6.612
• 7.195
• 11.195

• speed
• acceleration
• displacement
• total distance

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.A.3

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing
• increasing
• concave up
• concave down

Tags

CCSS.HSF.IF.B.4