Free Printable M3 Unit 4 Review

1.

a)

A

b)

B

c)

C

d)

D

2.

a)

A

b)

B

c)

C

d)

D

3.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

4.

Which value of x makes the expression undefined?

a)

-2

b)

2

c)

-6

d)

-3

5.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

6.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

7.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

8.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

9.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

10.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

11.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

12.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

13.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

14.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

15.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

16.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

17.

Find the product

a)

A

b)

B

c)

C

d)

D

18.

Simplify.

a)

A

b)

B

c)

C

d)

D

19.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

20.

Subtract
$\frac{x-5}{3x+4}-\frac{3x-5}{3x+4}$

a)

$\frac{-2x-10}{3x+4}$

b)

$\frac{-2x}{3c+4}$

c)

$-2x$

d)

$-2x-10$

21.

Add
$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}$

c)

$\frac{12x^2-7x-2}{\left(x+2\right)\left(4x-1\right)}$

d)

$\frac{14x^2+7x+2}{\left(x+2\right)\left(4x-1\right)}$

22.

Subtract
$\frac{x}{2x+3}-\frac{2x+1}{2x-3}$

a)

$\frac{-2x^2-8x-3}{\left(2x-3\right)\left(2x+3\right)}$

b)

$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)}$

c)

$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)}$

d)

$\frac{-2x^2+3x+3}{\left(2x-3\right)\left(2x+3\right)}$

23.

Subtract
$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$

a)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}$

b)

$\frac{-x^2-3x-34}{\left(x+8\right)\left(x-4\right)}$

c)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}4$

d)

$\frac{-x^2+3x+46}{\left(x+8\right)\left(x-4\right)}$

24.

Subtract
$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$

a)

$\frac{x^2-2x-8}{2x+7}$

b)

$x^2-2x-8$

c)

$x^2-2x+2$

d)

$\frac{x^2-2x+2}{2x+7}$

25.

Simplify (add & divide)
$\frac{\frac{1}{2x}+\frac{2}{3x}}{\frac{x-1}{x-3}}$

a)

$\frac{7x-21}{6x^2-6x}$

b)

$\frac{7x+21}{6x^2-6x}$

c)

$\frac{7x^2-21x}{6x^3-6x^2}$

d)

$\frac{7x^2-21x}{6x^3-6x^2}$

26.

Add
$\frac{7x}{x^2-5x}+\frac{x^2}{x-5}$

a)

$\frac{x^3+7x}{x\left(x-5\right)}$

b)

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

c)

$\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)}$

d)

$\frac{x^4-5x^3-7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)}$

27.

Add
$\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}$

a)

$\frac{4x^2-6}{4x-7}$

b)

$\frac{4x^2-6x+9}{4x-7}$

c)

$\frac{4x-6}{4x^{ }-7}$

d)

$\frac{4x-6}{8x-14}$

28.

Add
$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$

a)

$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}$

b)

$\frac{x^3+6x^2-24x}{\left(x+6\right)\left(x^2-36\right)}$

c)

$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}$

d)

$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}$

29.

Add
$\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$

a)

$\frac{5x+9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}$

b)

$\frac{5x+11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}$

c)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}$

d)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}$

30.

Solve the equation for x: $\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

31.

Solve for x: $\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}$

a)

x = 5

b)

x = $\frac{4}{5}$

c)

x = 1

d)

x = - 4

32.

Solve: $\frac{2}{x-2}-\frac{1}{x+1}=\frac{2}{x^2-x-2}$

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

33.

Solve for y $\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}$

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

34.

$\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}$

a)

$-2$

b)

$5$

c)

$6$

d)

$\frac{61}{3}$

35.

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

a)

48 minutes

b)

50 minutes

c)

24 minutes

d)

12 minutes

36.

Joan can clean the store in five hours. If Dan helps, it takes them four hours. Without help, how long would it take Dan to complete this job ?

a)

10

b)

25

c)

20

d)

15

37.

Katherine can paint a room in 4 hours. Joe needs 6 hours to paint the same room. Which equation would you use to determine how long it takes them to paint the room if they work together?

a)

$\frac{1}{4}+\frac{1}{6}=\frac{1}{t}$

b)

$\frac{1}{4}+\frac{1}{t}=\frac{1}{6}$

c)

$\frac{1}{6}+\frac{1}{t}=\frac{1}{4}$

d)

$t=24$

38.

It takes Sarah the same amount of time to walk the 3 miles to school as it takes her to bike the 5 miles to work. Sarah’s biking speed is 4 miles per hour faster than her walking speed. Find Sarah’s walking speed in miles per hour.

(a)

39.

A boat goes 10 miles downstream in the same time it can go 3 miles upstream. The speed of the current is 2 miles per hour. Which equation could you use to find the speed of the boat in still water?

a)

$\frac{10}{2-x}=\frac{3}{2+x}$

b)

$\frac{10}{x-2}=\frac{3}{x+2}$

c)

$\frac{10}{x+2}=\frac{3}{x-2}$

d)

$\frac{10}{2+x}=\frac{3}{2-x}$

40.

A car travels 400 km in the same time that a freight train travels 300 km. The speed of the car is 25 km/h more than the speed of the train. Find the speed of the car and the speed of the train. (Hint set fractions equal rather than adding to a set time.)

a)

$\frac{400}{x-25}=\frac{300}{x+25}$

b)

$\frac{400}{x+25}=\frac{300}{x-25}$

c)

$\frac{400}{x+25}=\frac{300}{x}$

d)

$\frac{400}{x}=\frac{300}{x+25}$

41.

The time it takes for a canoe to go 4 miles upstream and back 4 miles downstream is 5 hours. The current in the lake is 2 mile per hour. Find the average speed (rate) of the canoe in still water.

a)

$\frac{4}{x+2}+\frac{4}{x-2}=5$

b)

$\frac{4}{2+x}+\frac{4}{2-x}=5$

c)

$\frac{4}{x+2}=\frac{5}{x-2}$

d)

$\frac{4}{2+x}=\frac{5}{2-x}$

42.

Bethany has scored 10 free throws out of 18 tries. She would really like to bring her free throw average up to at least 68%. How many consecutive free throws should she score in order to bring up her average to 68%?

a)

7

b)

10

c)

15

d)

who cares about Bethany?

43.

Determine the x-coordinate of the hole on the graph of
f(x)= (x²-2x + 1)/(x²+2x - 3)

a)

-1

b)

3

c)

1

d)

-3

44.

State the vertical asymptotes:
f(x) = 2 / (2x²+3x - 5)

a)

x = 1 , x = -5

b)

x = 1, x = -5/2

c)

x = -1/2, x = 5

d)

x = 0 , x = -5/2

45.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

end behavior

d)

none

46.

Name any holes of the function.

a)

x=0

b)

none

c)

x=3

d)

x=-3

47.

Solve and check for extraneous solutions.

a)

x=-1, x=-3 extraneous

b)

x=-1 extraneous, x=-2

c)

x=-1, x=-2 extraneous

d)

x=-1, x=2 extraneous

48.

a)

All Reals Except 0

b)

All Reals

c)

All Reals Except -3

d)

All Reals Except 0 and -3

49.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

50.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

M3 Unit 4 Review

Total questions: 50

Worksheet time: 3hrs 15mins

Similar Resources on Wayground