Free Printable Unit 1 Review

1.

WRITE AN EQUATION TO REPRESENT THE SITUATION

Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day.

a)

400 - 75x = 1,000 + 25x

b)

400 + 75x = 1,000 – 25x

c)

400x - 75 = 1,000x + 25

d)

400x + 75 = 1,000x – 25

2.

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

a)

80+9.50x > 120+7.50x

b)

80+9.50x < 120+7.50x

c)

80x+9.50 > 120x+7.50

d)

80x+9.50 < 120x+7.50

3.

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. Which equation could be used to determine how many miles would have to be driven in one day for both rental agencies to cost the same amount to rent?

a)

30 + 0.15x = 36 + 0.10x

b)

30 - 0.15x = 36 - 0.10x

c)

30 + 36 = 0.10x + 0.36x

d)

36 - 30 = 0.36x + 0.10x

4.

I can join video club A for $25.00 and rent videos for $1.00 each. Or, I can join video club B for $15.00 and rent videos for $2.00 each. Write an equation that could be used to determine how many rentals would be needed for the price to be equal.

a)

25 - x = 15 - 2x

b)

25 + 15 = x + 2x

c)

25x + 1 = 15x + 2

d)

25 + x = 15 + 2x

5.

Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has $50 and she spends $3.25 every day. Write an inequality that shows when Sue's account will be more than Troy's.

a)

25 - 2.5d > 50 - 3.25d

b)

25 - 2.5d < 50 - 3.25d

c)

25 + 2.5d > 50 + 3.25d

d)

25 + 2.5d < 50 + 3.25d

6.

At the beginning of the year, Ethan has $800 in his savings account and Faith has $1,280 in her savings account. Each month, Ethan deposits and additional $25 in his account, while Faith withdraws $15 from her account. Write an equation to show after how many months will Ethan’s account have a greater balance than Faith’s account?

a)

800 - 25x < 1280 - 15x

b)

800 + 25x < 1280 - 15x

c)

800 + 25x > 1280 - 15x

d)

800 + 25x > 1280 + 15x

7.

A local bakery has a daily operating cost of $1800 plus a cost of $10 per cake they make. If a cake sells for $15, which problem could be used to determine the minimum number of cakes, c, they must sell each day to earn a profit?

a)

15c < 1800 + 10c

b)

15c > 1800 + 10c

c)

15c = 1800 + 10c

d)

10c < 1800 + 15c

8.

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

a)

2 hours

b)

3 hours

c)

4 hours

d)

5 hours

9.

Which situation can be represented by the equation
1500 - 50x = 2000 - 100x

a)

There are two water tanks in the city. One tank has 1500 gallons and gains 50 gallons each hour. The other tank has 2000 gallons and gains 100 gallons each hour. When will the tanks have the same amount of water?

b)

There are two water tanks in the city. One tank has 1500 gallons and loses 50 gallons each hour. The other tank has 2000 gallons and gains 100 gallons each hour. When will the tanks have the same amount of water?

c)

There are two water tanks in the city. One tank has 1500 gallons and loses 50 gallons each hour. The other tank has 2000 gallons and loses 100 gallons each hour. When will the tanks have the same amount of water?

d)

There are two water tanks in the city. One tank has 1500 gallons and loses 50 gallons each hour. The other tank has 2000 gallons and loses 100 gallons each hour. When will the bigger tank have more water?

10.

Veronica is ordering trophies for her school. Company P charges $3.50 for each trophy and a one-time engraving fee of $25. Company R charges $7.50 for each trophy and a one-time engraving fee of $17. Which inequality can be used to find x, the minimum number of trophies that can be ordered so that the total charge at company P is less than the total charge at Company R?

a)

3.5 + 25x < 7.5 + 17x

b)

3.5 + 25x > 7.5 + 17x

c)

3.5x + 25 < 7.5x + 17

d)

3.5x + 25 > 7.5x + 17

11.

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

a)

5x + 10 ≥ 100

b)

5x - 100 ≥ 10

c)

10x + 5 ≤ 100

d)

5x + 10 > 100

12.

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

a)

125x + 55 ≤ 600

b)

125x + 55 ≥ 600

c)

125x + 55 > 600

d)

125x + 55 < 600

13.

a)

30x < 330 + 50x

b)

50x > 330 + 30x

c)

30x > 330 + 50x

d)

50x < 330 + 30x

14.

a)

2.5v + 5 < 5v

b)

2.5v + 5 > 5v

c)

7.5v < 5v

d)

7.5v > 5v

15.

The two figures have the same perimeter. Write an equation to determine the value of x?

a)

3.5x – 5 = 13.5x

b)

23.5x + 2 = 13.5x - 3

c)

23.5x – 2 = 13.5x + 3

d)

3.25x + 1 = 5.5x + 3

16.

2(6x + 10) = 4(3x + 5)

a)

one solution

b)

no solutions

c)

infinitely many solutions

17.

8(x - 4) = 2(11 + 4x)

a)

one solution

b)

no solution

c)

infinitely many solutions

18.

3(2x + 5) = 4(x +6) +3

a)

one solution

b)

no solutions

c)

Infinitely many solutions

19.

IR = V

(solve for R)

a)

$R=IV$

b)

$R=\frac{I}{V}$

c)

$R=\frac{V}{I}$

d)

$R=V-I$

20.

A - B = C

(solve for A)

a)

A = C - B

b)

A = C + B

c)

A - C = B

d)

B = A - C

21.

Solve the formula for y. What is the 1st step?

a)

Subtract B from each side.

b)

Divide each side by Ax.

c)

Divide each side by B.

d)

Subtract Ax from each side.

22.

$cy=10$

Solve for y.

a)

$y=\frac{10}{c}$

b)

$y=10-c$

c)

$y=10c$

d)

$y=10+c$

23.

$Given\ ax-b=c,\ solve\ for\ x.\$

a)

$x\ =\ \frac{c+b}{a}$

b)

$x\ =\ \frac{c-b}{a}$

c)

$x\ =\ \frac{a+b}{c}$

d)

$x\ =\ \frac{c+a}{b}$

24.

$Solve\ y\ =\ mx\ +\ b\ for\ x.$

a)

$x=\frac{\left(y-b\right)}{m}$

b)

$x\ =\ y-\frac{b}{m}$

c)

$x=\frac{y}{m}-b$

25.

$A=\frac{bh}{2}$

Solve for b

a)

$b=2A-h$

b)

$b=\frac{2A}{h}$

c)

$b=\frac{Ah}{2}$

d)

$b=\frac{A-2}{h}$

26.

Solve the inequality.
- 3(9 + x) ≥ - 21

a)

x ≤ 2

b)

x ≥ 2

c)

x ≥ - 2

d)

x ≤ - 2

27.

Match the graph with its inequality.

a)

c > 9

b)

c < 9

c)

c ≥ 9

d)

c ≤ 9

28.

You want to spend at most $1200 on a new laptop. If you make a $400 down payment, then pay the same amount every month for 12 months. Which Inequality could be use to solve to find out how much you can pay each month.

a)

12x + 1200 > 400

b)

12x + 400 < 1200

c)

12x + 400 > 1200

d)

12x + 400 < 1200

29.

Which graph matches the inequality
k < 3?

a)

A

b)

B

c)

C

d)

D

30.

Graph the solution set of the inequality.

–4n + 1 > –23

a)

b)

c)

d)

31.

Choose the correct solution for the inequality:
$-3m+10>4-6m$

a)

b)

c)

d)

32.

Which of the following algebraic expressions best represents the perimeter of the given polygon?

a)

3x + 24

b)

2x + 10

c)

3x + 10

d)

3x + 2

33.

Which of the following best represents the perimeter of the given polygon?

a)

w + 3

b)

6w + 6

c)

2 - 6w

d)

6w + 2

34.

The given hexagon has all congruent sides. What expression may represent its perimeter?

a)

12x + 3

b)

(2x + 3)(2x + 3)

c)

12x + 18

d)

8x + 9

35.

Write the expression for the perimeter of the given rectangle. Choose the best answer.

a)

6x + 5

b)

12x + 10

c)

8x + 6

d)

16x + 12

36.

Evaluate the expression

-(3x + 5) - 4

a)

-3x + 5

b)

-3x + -5

c)

-3x + 9

d)

-3x +-9

37.

Simplify the expression

6(x + 2) - 4

a)

6x + 12

b)

6x + 8

c)

2x + 8

d)

14x

38.

Where was the 1st mistake made?
Given: 7 = 2(3x - 4)
Step 1: 2(3x - 4) = 7
Step 2: 6x - 6 = 7
Step 3: 6x = 13
Step 4: x = $\frac{6}{13}$

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

39.

What is the first step in solving the equation $2\left(3x-4\right)=3x+1$

a)

Distribute

b)

Subtract 3x from both sides

c)

Add 4 to both sides

d)

Combine Like Terms

40.

A student was solving the equation $8x\ +\ 4\ -6x\ +10=24$

Their work is below:
Step 1: 2x + 14 =24
Step 2: 2x = 38
Step 3: x = 19

What is their error?

a)

They combined like terms incorrectly

b)

They added 14 to both sides instead of subtracting

c)

They divided incorrectly

d)

There were no errors made

41.

Solve and graph the inequality.
77 ≤ 5 + 8n

a)

A

b)

B

c)

C

d)

D

Unit 1 Review

Total questions: 41

Worksheet time: 2hrs 29mins

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