Have an account?
Skip to Content
Build your own quiz
Mathematics
10th -
Professional Development
AP Calculus Unit 2 Review
20 questions
Show Answers
See Preview
- 1. Multiple ChoiceFind dy/dx by Implicit Differentiation
x3 +y3 = 366 -x3x2 +3y2−x2/y20 - 2. Multiple ChoiceFind dy/dx
xy+y2=2-y/(x+2y)y/(x+2y)-3y/x-3x/y - 3. Multiple ChoiceRachel 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/sec7.2 ft/sec12
- 4. Multiple ChoiceBrandon 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/sec1/(4pi) cm/sec
- 5. Multiple ChoiceFind the second derivative of the function:
f (x) = 2x - 5x6f ''(x)= 2 - 30xf ''(x) = 2-30x5f ''(x) = -30x5f ''(x) = -150x4 - 6. Multiple ChoiceSet up the derivative of y=(3x4 - 7)*(5x2 + 1)(12x3)*(10x)(3x4 - 7)*(10x) + (12x3)*(5x2 + 1)(3x4 - 7)*(10x) - (12x3)*(5x2 + 1)(3x4 - 7)/(10x) + (12x3)/(5x2 + 1)
- 7. Multiple ChoiceFind the derivative of the given equation
f(x) = x4 + 4x3 - 2x2x3 + x2 - x4x3 + 12x2 + 4x4x + 12x - 4x4x3 + 12x2 - 4x - 8. Multiple ChoiceFind the derivative.x4 cosx - 4x3sinxx4 cosx + 4x3sinx4x3cosx-4x3cosx
- 9. Multiple Choice
Find the derivative f(x) = xex
f'(x) = ex
f'(x) = xex + xex
f'(x) = ex - xex
f'(x) = ex + xex
- 10. Multiple Choice
.
(3x2-2)cos(x3-2x)
-(3x2-2)cos(x3-2x)
cos(2x2-2)
sin(2x2-2)
- 11. Multiple ChoiceFind y' if y=e3xe3xe2x03e3x
- 12. Multiple Choice
Calculate the average rate of change from 20 to 40 minutes.
-2 minutes per gallon
-20 minutes per gallon
-2 gallons per minute
-20 gallons per minute
- 13. Multiple ChoiceFind the average rate of change over the given interval.477/33/7
- 14. Multiple ChoiceFind the slope of the line that passes through the points (2, 4) and (6, 12)1/2-1/22-2
- 15. Multiple ChoiceWhat does "m" represent in y=mx+b?y-interceptslopemacaroninothing
- 16. Multiple ChoiceFind the slope of the tangent line to f(x) = -3x2-6x at x = 1.m = 0f'(x) = -6x - 6f'(x) = 6xm = -12
- 17. Multiple ChoiceIf a function has a derivative that is negative, what does that tell you?The function is increasingThe function is decreasing
- 18. Multiple Choice
f(x) = ln x
f '(x) = x
f '(x) =ex
f '(x) =lnx
f '(x) = 1/x
- 19. Multiple Choice
d/dx ln(x3)
3/x
1/x3
ln(3x2)
1 / 3x2
- 20. Multiple ChoiceIf the position function for a particle is s(t) = -t2 - t, what is the instantaneous velocity function for the particle?v(t) = -2v(t) = -2t - 1v(t) = t3v(t) = -t
- Answer choicesTagsAnswer choicesTags