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Math Test Post-Assessment

Answers and Explanations

A. 3

B. 6

C. 21

D. 529

Session 1, Question 1

1. What is the value of 52 – 22?

A. 2

B. 6

C. 9

D. 18

Session 1, Question 2

2. What is the greatest common factor that could be used to reduce ?36

90

Use prime factorization to solve for the GCF

A. 4 (n + 7)

B. 7 (n + 4)

C. 7n + 4

D. n (4 + 7)

Session 1, Question 3

3. A phrase is shown.

Which expression represents the phrase?

seven times the sum of a number, n, and four

A. Point A

B. Point B

C. Point C

D. Point D

Session 1, Question 4

4. Which point on the number line below represents the value ?16

6

Point B is between –2 and –3

A. 18 − 2x

B. 10x − 18

C. −2x − 18

D. 10x − 18

Session 1, Question 5

5. Which of the following expressions is equal to the expression 4x − 2 (3x − 9)?

Follow the order of operations with PEMDAS:

A. 26x + 270 ≥ 1,325

B. 26x + 270 ≤ 1,325

C. 270x + 26 ≥ 1,325

D. 270x + 26 ≤ 1,325

Session 1, Question 6

6. Annie is planning a business meeting for her company. She has a budget of $1,325 for renting a

meeting room at a local hotel and providing lunch. She expects 26 people to attend the meeting. The

cost of renting the meeting room is $270. Which inequality shows how to find the amount, x, Annie can

spend on lunch for each person? The amount Annie has left to spend on lunch for 26 people is

found by subtracting the fixed cost of the room from the

total budget. She can spend less than or equal to this amount

on lunch, but not more:

$1,325 $270

26x

26 1,325 270x

26 270 1,325x

A. 162

B. 163

C. 166

D. 167

Session 1, Question 7

7. Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity

walk. The company that makes the caps charges $6 per cap plus a $25 flat shipping fee. Laura has a

budget of $1,000. What is the greatest number of caps she can buy?

Laura cannot buy half a cap; therefore, she can buy a maximum of

162 complete caps.

A. Step 1

B. Step 2

C. Step 3

D. Step 4

Session 1, Question 8

8. Ray made an error while solving the following equation.

In which step did Ray make an error?

Equation: Step 1:Step 2:Step 3:Step 4:

3( 6) 8

3 18 2 8

5 18 8

5 10

2

x x x

x x

x

x

x

Step 1: distribute 3 and combine like terms – YES!

Step 2: subtract 2x from both sides – NO!

Step 3: subtract -18 from both sides – YES!

Step 4: divide both sides by 5 to solve for x - YES!

Ray added 2x to both sides in Step 2, rather than

subtract two from both sides, so he made a mistake

in Step 2.

A. x < 0

B. x > 0

C. x < 12

D. x < 4

Session 1, Question 9

9. Solve for x: 12 (x − 2) < 24.

A. 54

B. 46

C. 36

D. –36

Session 1, Question 10

10. On April 1 of this year, the high temperature in Northville was 46 degrees Fahrenheit. Then a

sudden snowstorm arose, and the temperature dropped sharply to a low of −8 degrees Fahrenheit.

What was the magnitude of the change in temperature on that day?

Session 2, Question 1

1. Hartley opened a food truck business to sell food on the street. On day 2, the business earned

$112. On day 5, the business earned $367. Hartley assumes that the earnings will continue to

increase at the same rate. How much will the business earn on day 10?

Find the rate of change, write an equation, and evaluate the equation when d = 10.

Rate of change = slope

Day 2, $112 (2, 112)

Day 5, $367 (5, 367)

y = mx + b

112 = 85 (2) = b

b = –58

y = 85x – 58

when x = 10: y = 85 (10) – 58

y = 850 – 58

y = 792

A. 649

B. 707

C. 734

D. 792

2 1

2 1

367 11285

5 2

y ym

x x

A. $337.04

B. $359.84

C. $513.00

D. $622.04

Session 2, Question 2

2. Dominic earns $285 per week plus an 8% commission rate on all his sales. If Dominic sells $4,213

worth of merchandise in one week, how much will his total earnings for the week be?

Find the commission by multiplying the sales by 0.08 and then adding the

commission to the amount of money he earns per week ($285):

commission: $4,213 × 0.08 = $337.04

total earnings: $337.04 + $285 = $622.04

Count the incidences of each number:

2 cars – one person

3 cars – three people

4 cars – three people

5 cars – two people

6 cars – one person

7 cars – one person

8 cars – one person

A.

B.

Session 2, Question 3

3. The data represents the number of cars that the sales staff at Templeton Motors sold this week.

4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3

Which line plot correctly displays the data?

C.

D.

A. –288

B. –180

C. 1,200

D. 3,600

Session 2, Question 4

4. What is the value of 36x – 8y2 when x = 3 and y = –6?

Evaluate the expression by substituting x and y into the

equation:

36x – 8y2 = 36 (3) – 8 (–6)2

= 108 – 8 (36)

= –180

A. $1,000

B. $4,800

C. $6,000

D. $24,000

Session 2, Question 5

5. Jason deposits $5,000 in a bank account that will pay him 4% simple interest annually. If Jason

deposits no more than the initial $5,000, how much money will be in the account at the end of five

years?

Use the simple interest formula: interest = principal × rate × time

I = prt

I = $5,000 (0.04) (5)

I = $1,000

Total amount = principal + interest

= $5,000 + $1,000

= $6,000

A.

B. 6,000 (3x – 10)

C.

D.

Session 2, Question 6

6. A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at

a different rate. This rate was less than 10 feet per hour less than twice the first rate. Which expression

represents the number of hours the mountaineer climbed?

6,000

3 10x

1,000 5,000

2 10x x

1,000 5,000

102x x

Session 2, Questions 7 and 8

Video Warehouse has divided the surrounding community into four advertising zones. The graph

shows the total number of customers from each zone for a three-week period.

A. between 900 and 1,000

B. between 1,000 and 1,100

C. between 1,100 and 1,200

D. between 1,200 and 1,300

Session 2, Question 7

7. During the three weeks, how many customers came from Zones 3 and 4?

A. 3 : 5

B. 3 : 2

C. 2 : 1

D. 1 : 2

Session 2, Question 8

8. Approximately what is the ratio of customers from Zone 1 to customers from Zone 3?

A. Add two data points to 4

B. Add one data point to 2 and one data

points to 3

C. Add one data point to 3 and two data

points to 4

D. Add one data point to 2 and one data

point to 4

Session 2, Question 99. A speech pathologist collects data from 10 people for an experiment. Each person answers 6 questions. The speech

pathologist records the number of questions that each person correctly answers and puts each person’s data in the line

plot. The median of the data is 3.5, and the mode of the data is 2. Which steps will complete the line plot so the plot

matches the pathologist’s data?

Think backwards to answer this question:

1) If the mode is 2, then 2 must have the most data points, so

at least one point must be added to 2; eliminate answer

choices A and C

2) This gives us 9 data points so far, so we need one more.

After adding the extra data point at 2, the median is now 3.

Adding one data point to 4 will put the median in between 3

and 4, making the median 3.5. This matches answer choice (D).

Session 2, Questions 10 and 11

Anne owns an art supply store. Anne is analyzing the store’s expenses and income because she

wants to increase the store’s profits. The expenses including renting 1,250 square feet of space for

$13,750 per month. The store has only one employee, who is paid $8.00 per hour plus 8%

commission. Much of the store’s income comes from the sales of blank canvases and frames. The

table shows the prices of canvases and frames sold at the store.

A. 35 (8) + 0.08x < 400

B. 35 (8) + 0.08x > 400

C. 35 (0.08) + 8x < 400

D. 35 (0.08) + 8x > 400

Session 2, Question 10

10. The store employee works 35 hours per week. Which inequality can be used to find the dollar

value, x, of weekly sales that the employee must make to earn more than $400 per week?

$8.00 per hour 35 hours × $8.00 per hour

x = weekly sales

commission 8% 0.08 × weekly sales 0.08x

more than $400 per week = > $400

35 (8) + 0.08x > 400 Answer choice (B)

A. 11

B. 132

C. 1,042

D. 12,500

Session 2, Question 11

11. What is the rental cost, in dollars per square foot, that Anne pays for the art store’s space?

A. –4 – 3

B. –4 + 3

C. | –4 – 3 |

D. | –4 + 3 |

Session 3, Question 1

1. A number line is shown. Which expression represents the distance between the two points, X and Y,

on the number line?

A. 3x3 − 3x2 +14 (−2y + 2x)

B. 5x3 − 3x2 + 14y − 2y − 2x

C. 3x3 − x + 4x2 + 12y

D. 5x3 − 4x2 − x + 12y

Session 3, Question 2

2. Simplify this polynomial:

3x3 + x + 2x3 − 4x2 +14y − 2 (y + x)

Session 3, Questions 3 and 4

A transit company operates commuter trains to

help people get to the city each day. Each train

travels on a straight route to and from the farthest

station, stopping at other stations along the route.

The graph shows the distance y miles the train is

from the station after x minutes.

A. 100

B. 80

C. 40

D. 20

Session 3, Question 3

3. What is the farthest distance, in miles, that the train is located from the station at any time?

Distance from the station is

located on the y-axis, so look for

the greatest y-value:

A. 15

B. 10

C. 2

D. 1.5

Session 3, Question 4

4. Based on the graph, what was the average speed, in miles per minute, of the train during the

interval of 30 to 40 minutes?

A. 2.5

B. 7.9

C. 23.7

D. 31.7

Session 3, Question 5

5. An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the

nearest tenth of a cubic inch, what is the volume of each drinking cup?

A. $2,080

B. $2,340

C. $2,600

D. $4,160

Session 3, Question 6

6. Together, Levy and Matthew earn $4,680 per month. Levy earns $520 more per month than

Matthew earns. How much does Levy earn per month?

Substitute (m + 520) in for l

A. 201

B. 402

C. 804

D. 3,215

Session 3, Question 7

7. A disco ball is shaped like a sphere with a diameter of 16 inches. To the nearest square inch, what is

the surface area of the disco ball?

A. 13

B. 16

C. 99

D. 198

Session 3, Question 8

8. Mr. Jovanovski is having wood flooring put in his rectangular living room. The area of the room is

234 square feet. The length of the room is 18 feet. What is the width, in feet, of the room?

A.

B.

C.

D.

Session 3, Question 9

9. Julia wants to spend $100 or less ordering shirts from an online company. The company charges a $5

shipping fee for any order. The inequality 5 + 15n ≤ 100 represents the number of shirts, n, Julia can order

from the online company. Which number line graphs all possible numbers of shirts Julia can buy?

Julia can only buy whole shirts (integer values)

less than or equal to 6

Session 3, Questions 10–12

A scientist is studying red maple tree growth in a state park. She measured the trunk diameters of a

sample of trees in the same month every other year. The tables show the data for two of the trees.

This the final year in which she will collect data. When her data collection is complete, she will predict

future red maple tree growth.

Session 3, Question 10

year 3 = 12.0

year 11 = 14.4

Session 3, Question 10

year 3 = 12.0

year 11 = 14.4

A. y = 0.6x + 18.6

B. y = 0.6x + 18.3

C. y = 0.3x + 18.6

D. y = 0.3x + 18.3

Session 3, Question 11

11. The scientist creates an equation that models her data for each tree so that she can predict the

diameter in the future. What is the linear equation that fits the data for tree 1, where x is the year and

y is the trunk diameter, in inches?

Plug in a point to solve for b:

A. 22

B. 44

C. 121

D. 261

Session 3, Question 12

12. In year 13, the scientist will put tree wrap around tree 1 to protect it from the winter snow. The

height of the tree wrap needs to be 45 inches. The wrap is priced by the square foot. To the nearest

square foot, how many square feet of wrap does she need?

The wrap will cover an area equal to the surface area of cylinder (minus the top and bottom).

From the charge, the diameter of the tree in year 13 is 22.2 inches.

2πr

h

h = 45in

d = 22.2 = 2r

r = 11.1in

A = 2πr x h

= 2π(11.1) x 45

= 3106in2