AP Calc Unit 4 Review

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Tags

CCSS.8.G.B.8

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec.  How fast is the angle between the tip of the ladder and the house changing when the ladder is 5 ft high? Hint: Use a trig function.

• 1 deg/sec
• -.5 deg/sec
• .6 deg/sec
• The angle is not changing.

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Rachel is standing atop a 13ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3ft/sec. How fast is the angle changing between the base of the ladder and the ground when the ladder is 5 ft high?

• -0.6 rad/sec

• 1.5 rad/sec

• .5 rad/sec

• .65 rad/sec

Tags

CCSS.HSF.TF.A.1

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec.  How fast is the area of the outer circle changing when the diameter is 8 in?

• 80pi in/sec
• 20pi in/sec
• 60pi in/sec
• 4opi in/sec

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.1

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 fast is the diameter changing when the diameter is 8 cm?

• -1/(16pi) cm/sec
• -1/16 cm/sec
• -1/(4pi) cm/sec
• 1/(4pi) cm/sec

Tags

CCSS.HSG.GMD.A.3

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec
• 9/(8pi) ft/sec
• -8/(9pi) ft/sec
• 8/(9pi) f/tsec

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

CCSS.HSG.MG.A.1

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the radius changing when the water is 2 ft deep?

• 4/(3pi) ft/sec
• 3/(4pi)ft/sec
• -3/(4pi) ft/sec
• -4/(3pi) ft/sec

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GMD.A.3

(3 min) The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100 π square inches, what is the rate of increase, in cubic inches per second, in the volume V? SA = 4 π r² and V = (4/3) π r³

• 30π
• 10π
• 12π
• 25π

Tags

CCSS.HSG.GMD.A.3

The tire pressure can be modeled by the following equation:  $P\left(t\right)=35\left(2\right)^{-\frac{t}{20}}$  
where you can find an estimate of  $P'\left(t\right)=-1.5\left(2\right)^{-\frac{t}{20}}$  
Write the equation of the local linearization of P(t) at t = 20

•  $y=-0.75\left(x-20\right)+17.5$  

•  $y=-0.75\left(x-20\right)-17.5$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Given that f (-3) = 4 and f ' (-3) = 2, which of the following is the tangent line approximation of f (-3.1)?

• 4.2

• 4.1

• 3.9

• 3.8

Tags

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.6