PCHBC Final Exam Review

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

Tags

CCSS.7.G.B.4

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Tags

CCSS.8.G.B.8

An observer stands 2400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 200 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 700 ft from the ground?

• 56 ft/sec

• 57 ft/sec

• 52 ft/sec

• 61 ft/sec

Tags

CCSS.8.G.B.8

A rectangle is bounded by the x-axis and the parabola  $y=12-x^2$ .  What length and width should the rectangle have so that its area is a maximum?  

Given the constraint equation above and the optimization equation  $A=2xy$  , choose the DERIVATIVE of the merged (combined) equation.

•  $A'=2xy$  

•  $A'=\ \ 24-6x^2$  

•  $A'=2x\left(12-x^2\right)$  

•  $A'=12-2x$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.7

CCSS.HSA.CED.A.3

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

Tags

CCSS.HSF.IF.B.4

Find the limit of the function as x approaches 2.

• 1
• -1
• 5
• DNE

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

Differentiate y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

If f'(x) = 0 what does that imply about the x value?

• It is a critical point, it is a possible max, min, or point of inflection.

• That the limit does not exist.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Differentiate y= x³ + 2x

• 3x³+2x
• 3x²+2
• 3x+2
• 3x