Free Printable Calculus Review

1.

Find f(2).

a)

1

b)

-1

c)

5

d)

DNE

2.

Find the limit of the function as x approaches 2.

a)

1

b)

-1

c)

5

d)

DNE

3.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

4.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

5.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

6.

Evaluate

a)

-7

b)

0

c)

1

d)

DNE

7.

Differentiate f(x) =(2/x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10x^-6

8.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

9.

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

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

10.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

11.

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

12.

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

13.

What will be true at an inflection point? (select the best answer)

a)

f(x)=0

b)

f'(x)=0

c)

f''(x)=0

d)

The function is undefined

14.

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

15.

a)

Mean value theorem

b)

Instantaneous Rate of Change

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

16.

a)

Intermediate Value Theorem

b)

Instantaneous Rate of Change

c)

Average Rate of Change

d)

Average Value of f

17.

a)

Average Rate of Change

b)

Instantaneous Rate of Change

c)

Intermediate Value Theorem

d)

Average Value of f

18.

What is this expression equivalent to?

a)

f '(g'(x))

b)

f '(x)g'(x)

c)

f '(g(x))g'(x)

d)

f '(g(x)

19.

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? (Choose the correct set-up.)

a)

(5)3 + (12)b' = (13)0

b)

(5)a' + (12)3 = (13)0

c)

(5)a' + (12)0 = (13)3

d)

(5)0 + (12)b' = (13)3

20.

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)

21.

Where does the function, f(x) = 2x³ - 9x²+ 12x -3 have relative max/min values?

a)

Rel max x = -1, Rel min x = 2

b)

Rel min x = 1, Rel min x = 2

c)

Rel max x = 1, Rel min x = 2

d)

Rel max x = 2, Rel min x = 1

22.

Which choice below represents this slope field?

a)

$\frac{dy}{dx}=2x$

b)

$\frac{dy}{dx}=-x$

c)

$\frac{dy}{dx}=x$

d)

$\frac{dy}{dx}=x^2$

23.

Which differential equation is represented by the slope field?

a)

$\frac{dy}{dx}=-y$

b)

$\frac{dy}{dx}=1$

c)

$\frac{dy}{dx}=-1$

d)

$\frac{dy}{dx}=-x$

24.

Which slope field below is $\frac{dy}{dx}=-\frac{x}{y}?$

a)

b)

c)

d)

25.

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s. How fast is the distance between the rocket and Devin changing after 2s?

a)

-2.5 m/s

b)

2.5 m/s

c)

3.2 m/s

d)

-3.2 m/s

26.

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

a)

100ft x 200ft

b)

102ft x 196 ft

c)

50 ft x 300 ft

d)

50 ft x 175 ft

27.

a)

-cos(x⁶)

b)

sin(x⁶)

c)

2x sin(x³)

d)

2x sin(x⁶)

28.

a)

0

b)

-3

c)

3

d)

6

29.

a)

-3

b)

3

c)

-5

d)

8

30.

a)

-4<x<-2, 4<x<5

b)

3<x<4

c)

-2<x<0, 5<x<7

d)

0<x<3, 10<x<12

31.

a)

-4<x<0, 4<x<5

b)

3<x<4

c)

-2<x<0, 5<x<7

d)

0<x<3, 10<x<12

32.

Suppose f(x) = x³ – x.

Use a linear approximation at x = 2 to estimate f(2.5).

a)

10.5

b)

11

c)

11.5

d)

12

33.

Suppose f (x) = 3x² is graphed in the x-y plane. Will any linear approximations to f overestimate or underestimate the actual function values?

a)

overestimate

b)

underestimate

34.

$\int\left(\frac{3}{x+1}\right)dx$

a)

$3\left(x+1\right)+c$

b)

$\ln\left(3x+1\right)+c$

c)

$\ln\left(x+1\right)+c$

d)

$3\ln\left(x+1\right)+c$

35.

a)

b)

c)

d)

e)

36.

What should be used for u in the integral?

a)

tanx

b)

tan⁴x

c)

no u needed

d)

tanx secx

37.

What should be used for u in the integral?

a)

no u needed

b)

4t²

c)

t³

d)

1/4t²

Calculus Review

Total questions: 37

Worksheet time: 1hrs 5mins

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