Math 8: Review of Pre-Diagnostic Skills for Unit 4

Equivalent
Expressions

Find the
Missing Value

Write an
Equation

Word
Problems

Mystery

100

Which expression is equivalent to equation below?

12(3 + m)

(a) 36m

(b) 36 + m

(d) 3m + 12m

100

What value makes the equation true?

17 + b = 60

b = 43

100

Kyle spends a total of $44 for four sweatshirts. Each sweatshirt costs the same amount of money.

Which bar model could be used to show the situation?

100

Kyle is saving money to buy a phone. She has $45.50 in her savings account and saves 15% of her babysitting money each week. After 10 weeks, she has $90.50 in her savings account. Let k represent the amount she earns each week from her babysitting job.

True or False?

Each week, Kyle saves $5.00.

False.

Each week, Kyle saves $4.50.

100

Select the value of r that makes the equation below true.

8r = 24

(a) 7

(b) 16

(d) 3

200

True or False?

6x + y

is equivalent to

3x + 3(x + y).

False.

6x + 3y

is equivalent to

3x + 3(x + y).

200

What value makes the equation true?

y + 4/7 = 6/7

y = 2/7

200

David and Ted are walking a trail. Ted walks 3.1 km farther than David.

Which equation for the number of km David walks, d, if Ted walks 5.4 km?

d = 5.4 - 3.1

200

David wants to join a fitness club. The fitness club charges an initial membership fee of $65 and a monthly fee of $20.50. He has $200 to spend on a membership at the club. How many months can he be a member?

(a) 7 months

(b) 3 months

(d) 6 months

200

Notebooks cost $2.95 each, and 2 pens cost $1.95. A set of colored pencils and 4 pens have the same cost as 3 notebooks. How much does a set of colored pencils cost?

(a) $4.95

(b) $8.85

(d) $2.95

(a) $4.95

300

Which expressions are equivalent to the equation below?

4d + 6 +2d

(a) 2(3d + 3)

(b) 6(d + 6)

(d) (3d + 3)

(a) 2(3d + 3) and (c) (3d + 3) + (3d + 3)

300

Sierra has 11.5 yards of yarn. She uses a certain amount for a project, leaving 5.25 yards of yarn. The equation

11.5 - x = 5.25

represents this situation, where x is the amount of yarn Sierra used for her project.

How much yarn did Sierra use for her project?

(a) 5.25 yards

(b) 5.75 yards

(d) 6.5 yards

300

True or False?

David and Ted are walking a trail. Ted walks 3.1 kilometers farther than David. The number of kilometers David walks, d, if Ted walks 5.4 kilometers can be written as the equation,

3.1 - t = 4.9.

False.

The equation can be written as,

t - 3.1 = 4.9.

300

A phone sells for $245. It is now on sale for

1/5

off the original price. April has a coupon for an extra 10% off the sale price.

To the nearest dollar, how much less than the original price will April pay for the phone?

(a) $25

(b) $49

(d) $69

300

What is the first step in solving the following equation?

3x + 5 = 20

Subtract both sides by 5.

400

Write an expression equivalent to

5x2 - 15x

that is a product of two expressions.

Fill in the blanks with numbers, variables, or expressions.

_____ (_____ - _____)

5x(x - 3)

400

Harry solves the equation

18t = 108.

He says the solution is 6.

Is his solution correct?

Possible Answer:

Harry is correct because is you solve for t, you get 6 as your solution.

400

Suki is trying to solve the equation

62.75 + x = 92.

Can she think, "x is the difference between 92 and 62.75"?

Yes

400

Julie bought 5 pairs of shoes and 4 blouses. The shoes were priced at $19 per pair and the blouses cost $16.50 each. Which equation can be used to find the total cost, t, she spent on the shoes and blouses?

(a) 5(16.50) + 4(19) = t

(b) 5(16.50) - 4(19) = t

(d) 4(16.50) - 5(19) = t

400

For the expression below, combine like terms and write an equivalent expression with fewer terms.

5+2x+7+4x

6x + 9

500

Clara states that

r2 + 5r + 3r

is an equivalent expression to

9r.

Is Clara's statement correct or incorrect?

Explain your reasoning.

Possible Answer:

Clara's statement is incorrect. The expression

r2 + 5r + 3r

simplifies to

r2 + 8r,

which is not equivalent to

9r.

500

Write a real-world problem that you could represent with the equation

20 - n = 4.

Possible answer:

Stacy has 20 cupcakes. After selling n cupcakes, Stacy has 4 left. How many cupcakes did Stacy sell?

500

Write an equation and find the weight of the unknown fish on a balance scale.
One side of the scale: 12 pounds and 23 pounds.
Other side of the scale: 13 pounds and n pounds.
The scale is equally balanced.

12 + 23 = 13n

n=22

500

Mr. Ford’s kitchen is in the shape of a rectangle with a width of 25.5 feet. He is buying tile to border the room on all sides. He wants to buy 5 extra feet of border to make sure he has enough. He buys 90.5 feet in all.

What is the length of the kitchen?

(a) 17.25 feet

(b) 32.5 feet

(d) 16 feet

(a) 17.25 feet

500

David wants to join a fitness club. The fitness club charges an initial membership fee of $65 and a monthly fee of $20.50. He has $200 to spend on a membership at the club. Which equation can he used to solve how many months he can be a member?

(a) 65x + 20.50 = 200

(b) 20.50x + 65 = 200