Free Printable Unit 2 Calculus Review

1.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

2.

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

a)

38 m/s/s

b)

27 m/s/s

c)

16 m/s/s

d)

49 m/s/s

3.

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

a)

v(t) = -2

b)

v(t) = -2t - 1

c)

v(t) = t³

d)

v(t) = -t

4.

When velocity and acceleration are both negative, then the particle is _____________

a)

slowing down

b)

speeding up

c)

changing direction

d)

swagging

5.

If velocity is positive and speed is decreasing, then acceleration is _____________.

a)

positive

b)

negative

c)

zero

d)

unknown

6.

Where is the graph not differentiable?

a)

x = -2, -1, 0, 1

b)

x = -2, -1, 1

c)

x = -2, -1

d)

x = -1,

7.

The graph below represents the velocity (v) in feet per second, of a particle moving along the x-axis over the time interval from t=0 to t=9 seconds. Over what time interval is the particle's speed increasing?

a)

(0,3) & (5,6)

b)

(0,3)

c)

(5,6)

d)

(0,5)

8.

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?

a)

2

b)

4

c)

6.5

d)

7

9.

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

10.

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

a)

2

b)

4

c)

6

d)

8

11.

An objects distance from its starting point at time t is given by the equation
s(t) = t³ - 6t² - 4.
What is the speed of the object when its acceleration is 0?

a)

2

b)

-24

c)

22

d)

44

12.

An objects distance from its starting point at time t is given by the equation
s(t) = t³ - 6t² - 4.
What is the speed of the object when its acceleration is 0?

a)

12

b)

-24

c)

22

d)

44

13.

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

14.

Given the graph of the position function, which graph below shows the velocity of the function?

a)

b)

c)

d)

15.

If velocity is positive and speed is decreasing, then acceleration is ______?

a)

negative

b)

positive

c)

zero

d)

none of the above

16.

If velocity is negative and increasing, the speed is _____________?

a)

decreasing

b)

increasing

c)

constant

d)

none of the above

17.

Find the limit
$\lim_{h\rightarrow0}\frac{\left(3+h\right)^2-\left(3\right)^2}{h}$

a)

3

b)

4

c)

6

d)

8

18.

Find the derivative of the given equation
f(x) = -4x

a)

4

b)

x

c)

-4

d)

0

19.

a)

A

b)

B

c)

C

d)

D

20.

At which point(s) will the slopes of the tangent line are zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

21.

$f\left(x\right)=\left(2x+3\right)^2$

Calculate the derivative of $f\left(x\right).$

a)

$4x^2+9$

b)

$8x$

c)

$8x+12$

d)

$4x^2+12x+9$

22.

What is the derivative of cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

23.

At what point will the slope of y = -x² + 4 is zero?

a)

(0, 4)

b)

(1, 4)

c)

(4, 0)

d)

(1, 0)

24.

What is the equation of the line tangent to the curve y = x² at x = 1?

a)

y = 2x + 1

b)

y = 2x - 1

c)

y = -2x + 1

d)

y = x - 1

25.

Use the given function or the graph to find the average rate of change

a)

5

b)

-1/5

c)

-5

d)

15

26.

Find the instantaneous rate of change for f(x) at x = 8 for $f\left(x\right)\ =-\frac{3}{4}x+2$

a)

-8

b)

- $\frac{3}{2}$

c)

8

d)

- $\frac{3}{4}$

27.

#8

a)

f′(x) = 1/x + 1/7

b)

f′(x) = 7/x + 7

c)

f′(x) = 1/e^x + 7

d)

f′(x) = 1/x + 7

28.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

29.

What is the derivative of cot(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

30.

What is the derivative of sec(x)?

a)

sec(x)tan(x)

b)

-csc(x)cot(x)

c)

-sec(x)tan(x)

d)

csc(x)cot(x)

31.

What is the derivative of csc(x)?

a)

sec(x)tan(x)

b)

-csc(x)cot(x)

c)

-sec(x)tan(x)

d)

csc(x)cot(x)

32.

The three situations where derivatives fail to exist are at corners or cusps, at a vertical tangent, and...

a)

horizontial tangent

b)

discontinuity

c)

curve

d)

intercepts

33.

Use the chart to find f'(3) for f(x) = g(x)/[2h(x)]

a)

(2π+3)/9

b)

-(3+2π)/9

c)

-(6+4π)/9

d)

-2(3+4π)/9

34.

Find b'(2) if f(x) = g'(x) and g(x)=h'(x)

a)

-232/9

b)

0

c)

17/3

d)

-221/3

35.

f(x) = xln(x)
Find f'(x)

a)

1

b)

1+ln(x)

c)

1+xln(x)

d)

ln(x)

36.

Differentiate y=(3x⁴- 7)(5x²+ 1)

a)

(12x³)(10x)

b)

(3x⁴ - 7)(10x) + (12x³)(5x² + 1)

c)

(3x⁴ - 7)(10x) - (12x³)(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

37.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

38.

Which if the following is not a correct notation for 'derivative?'

a)

f'(x)

b)

y'

c)

dy

d)

dy/dx

39.

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

a)

The function is increasing

b)

The function is decreasing

40.

What's the definition of derivative?

a)

Instantaneous rate of change

b)

Slope of tangent line

c)

41.

f' is given, which could be f?

a)

A

b)

B

c)

C

42.

a)

15x²

b)

(5/4)x⁴

c)

indeterminate

d)

∞

43.

f'(x)=

a)

$\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$

b)

$\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

c)

$\frac{\text{d}y}{\text{d}x}$

d)

an equation for the slope of the tangent line

44.

$\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)$

a)

2

b)

4

c)

6

d)

8

45.

$\lim_{x\rightarrow\infty}x^2+3x-5$

a)

$-\infty$

b)

2

c)

0

d)

$\infty$

46.

Differentiate with respect to x.

a)

b)

c)

d)

47.

Find the derivative for $y=\sqrt{x^5}$

a)

$\frac{5}{2}x^{\frac{7}{2}}$

b)

$\frac{5}{2}x^{\frac{1}{2}}$

c)

$\frac{1}{2}x^{\frac{3}{2}}$

d)

$\frac{5}{2}x^{\frac{3}{2}}$

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

A

b)

B

c)

C

d)

D

50.

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

a)

200x³+36x²-30x+4

b)

600x² +72x -26

c)

600x² +72x -30

d)

600x² +72x -36

51.

Find $f^{'''}\left(x\right)$ if $f\left(x\right)=\cos x+x^2-2x$

a)

$-\sin x+2x-2$

b)

$-\cos x+2$

c)

$-\cos x$

d)

$\sin x$

52.

Is the function continuous, differentiable, both, or neither?

a)

continuous

b)

differentiable

c)

both

d)

neither

53.

Is the function continuous, differentiable, both, or neither?

a)

continuous

b)

differentiable

c)

both

d)

neither

54.

$\frac{d}{dx}\left(x-3\sin x\right)=$

a)

$1-3\cos x$

b)

$1+3\cos x$

c)

$1-3\sin x$

d)

$1+3\sin x$

55.

Find the derivative for $f\left(x\right)=\left(x+2\right)\left(x^2-3\right)$

a)

$f'\left(x\right)=3x^2-3+4x$

b)

$f'\left(x\right)=3x^2-3x+4x-6$

c)

$f'\left(x\right)=3x^2-3+4x-6$

d)

$f'\left(x\right)=x^3-3x+2x^2-6$

Unit 2 Calculus Review

Total questions: 55

Worksheet time: 3hrs 39mins

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