Free Printable ap calc review ws 86-89

1.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

2.

In the following picture, what does the

+

mean about the graph of

f\left(x\right)

a)

$f\left(x\right)$ is increasing

b)

$f\left(x\right)$ is decreasing

c)

$f\left(x\right)$ is positive

d)

$f\left(x\right)$ is negative

3.

Consider the $f'\left(x\right)$ sign chart. What can you conclude about the point $x=2$ on $f\left(x\right)$ ?

a)

local maximum

b)

local minimum

c)

stationary point/platuae point

4.

f''(x) is pictured. Which x values are inflection points of f(x)?

a)

x=-5 and -1

b)

x=-3

c)

x=4

d)

no inflection points

5.

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

6.

7.

a)

(A)

b)

(B)

c)

(C)

d)

(D)

7.

f' is given, which could be f?

a)

A

b)

B

c)

C

8.

Which of the following statements must be true?

I. f has a relative Min at x=-3.

II. The graph of f has a point of inflection at x=2.

III. The graph of f is concave down for 0 < x < 4.

a)

I only

b)

II only

c)

III only

d)

I and II only

e)

I and III only

9.

Find the critical points of f(x) = 2x⁴- 4x² + 1

a)

x= 0

b)

x = -1, 1

c)

x = -1, 0, 1

d)

no critical points

10.

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

a)

0

b)

-1

c)

2

d)

5

11.

Find the derivative: h(x)=(3x+2)(5x³+2x)

a)

(3x+2)(15x²+2x)+(5x³+2x)(3)

b)

(3x+2)(15x²+2)(5x³+2x)(3)

c)

(3x+2)(15x²+2)+(5x³+2x)(3)

d)

60x³+30x²+12x+4

12.

Find h'(3)

a)

-2

b)

0

c)

1

d)

3

13.

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

a)

7

b)

0

c)

7x

d)

14

14.

What is the derivative of sin(x)?

a)

-sin(x)

b)

-cos(x)

c)

cos(x)

d)

sin(x)

15.

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

a)

2

b)

4

c)

6

d)

8

16.

If Distance is a function of Time, what is the average rate of change from 6 to 9 seconds?

a)

3.3 feet per second

b)

-10 feet per second

c)

-3.3 feet per second

d)

10 feet per second

17.

What is the total distance of the object represented in this motion graph?

a)

0 meters

b)

300 meters

c)

450 meters

d)

600 meters

18.

What is the total displacement of the object represented in this motion graph?

a)

0 meters

b)

300 meters

c)

450 meters

d)

600 meters

19.

A particle's speed is decreasing if

a)

it's acceleration is positive

b)

it's velocity is positive

c)

it's velocity and acceleration have the same sign

d)

it's velocity and acceleration have different signs

20.

What is the slope of the line normal to the curve y = x² + x at x = 1?

a)

-1

b)

-1/2

c)

-1/3

d)

-1/4

21.

What is the equation of the tangent line at x = 1 $of$ $f\left(x\right)=\ \sqrt{x}$

a)

$y=\frac{1}{2}x-\frac{1}{2}$

b)

$y=\frac{1}{2}x+\frac{1}{2}$

c)

$y=2x-1$

d)

$y=2x$

22.

If (a,b) is a local minimum, then what will be true about f''(a)?

a)

It's postive

b)

It's negative

c)

It's zero

d)

Cannot be determined

23.

If (a,b) is a local minimum, then what will be true about f'(a)?

a)

It's positive

b)

It's negative

c)

It's zero

d)

Cannot be determined

24.

If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?

a)

It's constant

b)

It's increasing

c)

It's decreasing

d)

Cannot be determined

25.

a)

Mean value theorem

b)

Instantaneous Rate of Change

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

26.

a)

Intermediate Value Theorem

b)

Instantaneous Rate of Change

c)

Average Rate of Change

d)

Average Value of f

27.

a)

Average Rate of Change

b)

Instantaneous Rate of Change

c)

Intermediate Value Theorem

d)

Average Value of f

28.

Based on the table, use LRAM and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

29.

What is the integral of f(x)=sin(2x)+1/x

a)

-2cos(2x)+ln(x)+c

b)

ln(|x|)−cos(2x)/2+C

c)

ln(|x|)−cos(2x)/2

d)

ln(|x|)+cos(2x)/2+C

30.

what is the limit as x approaches infinity of the function f(x)= (3x-5)/(5x²+4)

a)

infinity

b)

negative infinity

c)

0

d)

1

31.

What are the vertical asymptotes of the function f(x)=(x²-9)/(x²+6x+9)

a)

x=3

b)

x=-3

c)

x=3,-3

d)

no vertical asymptote

32.

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

a)

4

b)

2

c)

3

d)

23/4

33.

What is the derivative of the function f(x)=∫₁^2x(6e^x)dx

a)

6e^2x

b)

12e^2x

c)

6e^2x-6e^x

d)

6e^2x

34.

a)

A

b)

B

c)

C

d)

D

35.

a)

speed

b)

acceleration

c)

displacement

d)

total distance

36.

a)

Volume using Shells

b)

Volume using Disks

c)

Volume using Washers

d)

Volume using Cross Sections

37.

a)

A

b)

B

c)

C

d)

E

38.

a)

A

b)

B

c)

C

d)

D

39.

Which of the following can be used to determine when a particle is at rest?

a)

x(t)=0

b)

v(t)=0

c)

a(t)=0

40.

v(t)>0 means

a)

the particle is moving to the right

b)

the particle is moving to the left

c)

the particle has positive position

d)

the particle is at rest

41.

The diagram shows the curve y = (x − 2)² and the line y + 2x = 7, which intersect at points A and B. Find the area of the shaded region.

a)

$10\ \frac{5}{7}$

b)

$10\ \frac{3}{4\ }$

c)

$10\ \frac{1}{3\ }$

d)

$10\ \frac{2}{3}$

42.

$\lim_{h\rightarrow0}\ \frac{f\left(2+h\right)-f\left(2\right)}{h}$ where $f\left(x\right)=3x-4$

a)

4

b)

0

c)

12

d)

3

43.

What integral would allow you to find the volume of the region bounded by y = 2x² and y = 8 around the line y = 11.

a)

Bounds: [0, 2]; π ∫(4x⁴ - 8)dx

b)

Bounds: [0, 2]; π ∫((11 - 2x²)² - 9)dx

c)

Bounds: [-2, 2]; π ∫((11 - 2x²)² - 9)dx

d)

Bounds: [-2, 2]; π ∫(4x⁴ - 8)dx

44.

The base of a solid is the region enclosed between the graphs of y=sinx and y=-sinx from x=0 to x= $\pi$ . Each cross section perpendicular to the x-axis is a semicircle with diameter connecting the two graphs. Find the volume of the solid.

a)

$\frac{\pi^2}{8}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi^2}{4}$

d)

$\frac{2\pi^2}{3}$

45.

Find the volume of the figure formed when a base, bounded by $x=y^2$ and $0\le x\le4$ , has cross-sections perpendicular to the x-axis that are squares.

a)

30

b)

$\frac{115}{4}$

c)

36

d)

32

46.

The derivative f'(x) of the function f(x) is shown. On what interval(s) is the FUNCTION f(x) increasing?

a)

(-∞, -1) only

b)

( 3, ∞) only

c)

(-∞, -1) and ( 3, ∞)

d)

(1, ∞)

47.

The population of a town grows at a rate of r(t) people per year (where t is time in years). What does $\int_2^4r\left(t\right)dt$ represent?

a)

The time it took for the town to grow from a population of 2 people to a population of 4 people.

b)

The number of people in the town on the fourth year.

c)

The average rate at which the population grew between the second and the fourth year.

d)

The change in the number of people between the second and the fourth year.

48.

The temperature in a room changes at a rate of $r\left(t\right)=\ln\left(t+1\right)\sin\left(t\right)$ degrees Celsius per hour (where t is the time in hours). At t = 1 hour, the temperature is 18 degrees Celsius.
What is the room's temperature at time t = 3 hours?

a)

1.571 degrees C

b)

19.571 degrees C

c)

19.323 degrees C

d)

1.323 degrees C

49.

Let f be the function given by f(x) = x³. What are all values of c that satisfy the conclusion of the Mean Value Theorem on the closed interval [-1, 2]? (No calculator)

a)

0 only

b)

1 only

c)

√3 only

d)

-1 and 1

50.

A particle moves along the x axis with its acceleration given by a(t) = t² – 2t for 0 < t < 6. At time t = 0, the velocity is 10. What is the maximum velocity of this particle on the specified interval?

a)

10

b)

26

c)

40

d)

46

ap calc review ws 86-89

Total questions: 50

Worksheet time: 2hrs 50mins

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