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ACAP Review - 7th Grade 2024

Total questions: 50

Worksheet time: 50mins

Name
Class
Date
1.

A vehicle used 1 1/8 gallons of gasoline to travel 13 1/2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?

a)

A. 16/243

b)

B. 4/3

c)

C. 12

d)

D. 13

2.

A factory makes rectangular sheets of cardboard, each with an area of 2½ square feet. Each sheet of cardboard can be cut into smaller pieces of cardboard measuring 16\frac{1}{6} square feet. How many smaller pieces of cardboard does each sheet of cardboard provide?

a)

15

b)

18

c)

22

d)

16

3.

Which representation shows a proportional relationship between x and y?

a)

Graph A

b)

Graph B

c)

Table C

d)

Table D

4.

The furniture store is having a weekend sale on chairs. If you buy 2 chairs, then you can get a third chair for ¾ off of the regular price.

Eric buys 3 chairs, each regularly priced at $128. 


After the discount, what is the price Eric paid for the third chair?

a)

$32

b)

$96

c)

$64

d)

$128

5.

The furniture store is having a weekend sale on chairs. If you buy 2 chairs, then you can get a third chair for ¾ off of the regular price.

Eric buys 3 chairs, each regularly priced at $128. 

What is his total cost for the chairs?

a)

$256

b)

$352

c)

$384

d)

$400

6.

Parker was able to pay for 44% of his college tuition with his scholarship. If the remaining amount he paid with a student loan was $10,054.52, what was the total cost of Parker's tuition?

a)

A) $17,954.50

b)

B) $18,305.00

c)

C) $28,400.00

d)

D) $23,283.91

7.

Clayton and Riley played a game where they threw plastic discs across a field into baskets. Each player earned a point for landing a disc in a basket and lost a point for missing a basket. Clayton ended with -12 points. Riley ended with 12 more points than Clayton. 

How many points did Riley end with?

a)

0

b)

24

c)

-24

d)

12

8.

Point P is shown on the number line below. The distance between point Q and point P is 6½ units. Which number could represent the location of point Q?

a)

A. -9½

b)

B. 1½

c)

C. 2½

d)

D. 10½

9.

Which expression is equivalent to 4 - (-7)?

a)

7 + 4

b)

4 - 7

c)

-7 - 4

d)

-4 + 7

10.

A man on a boat is sitting 9 feet above sea level. A bird flies at an altitude of 54 feet above sea level, and a fish swims below at an altitude of 8 feet below sea level. The ocean floor sits 75 feet below the surface of the ocean.

What is the distance between the man and the fish?

a)

17 feet

b)

63 feet

c)

1 feet

d)

9 feet

11.

A man on a boat is sitting 9 feet above sea level. A bird flies at an altitude of 54 feet above sea level, and a fish swims below at an altitude of 8 feet below sea level. The ocean floor sits 75 feet below the surface of the ocean.

What is the distance between the bird and the man?

a)

45 feet

b)

63 feet

c)

75 feet

d)

8 feet

12.

Each time that Samantha rides the commuter train, she spends $4 for her fare. How much money will she spend after 13 days if she rides the train to and from work?

a)

A) $52

b)

B) $104

c)

C) $26

d)

D) $13

13.

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?

a)

A) 10 months

b)

B) 11 months

c)

C) 12 months

d)

D) 13 months

14.

What will the sensor read after 5 minutes if the hose fills the aquarium at a constant rate of 15 liters per minute and the initial reading was 225 liters?

a)

300 liters

b)

150 liters

c)

375 liters

d)

250 liters

15.

A restaurant bill is $21. You leave a 15% tip. How much do you pay including the tip?

a)

A) $3.15

b)

B) $21

c)

C) $24.15

d)

D) $36

16.

A furniture store pays a wholesale price for a mattress. Then, the store marks up the retail price to 150% of the wholesale price. Later, they put the mattress on sale for 50% off of the retail price. A customer just bought the mattress on sale and paid $1,200.


What was the retail price of the mattress before the discount?

a)

$800

b)

$1,600

c)

$2,400

d)

$1,200

17.

Which expression is equivalent to 8m + 6 - 3m - 2?

a)

5m + 4

b)

5m + 8

c)

11m + 4

d)

11m + 8

18.

Which expression is equivalent to -8(10x - 3)?

a)

-80x - 24

b)

-80x + 24

c)

-80x + 3

d)

-80x - 3

19.

Logan is at an amusement park. She bought 16 tickets and each ride requires 2 tickets.
Which expression gives the number of tickets Logan has left in terms of x, the number of rides she has already gone on?

a)

16 - x

b)

16 + x

c)

16 - 2x

d)

16 / x

20.

Logan is at an amusement park. She bought 16 tickets and each ride requires 2 tickets.

Using the expression 16 - 2x, how would the numbers in the expression be interpreted in terms of tickets and rides?

a)

The number 16 represents the total number of tickets, and -2 represents the used tickets per ride.

b)

The number 16 represents the number of rides, and x represents the number of tickets per ride.

c)

The number 16 represents the number of tickets per ride, and x represents the total number of rides.

d)

The number 16 represents the number of tickets left, and x represents the number of rides Logan can still go on.

21.

The taxi fare in New York City is $2.40 for the first  ½ mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. 

How many miles can you ride for $10?

(a)  

22.

Which 3 of the following expressions represents the amount a customer pays including the tip of 15% if the bill was b dollars? 

A.   0.15b

B.   15b

C.   b + 0.15b

D.   1.15b

E.    b + (15/100)b

a)

A

b)

B

c)

C

d)

D

e)

E

23.

Ms. Miller bought x number of shirts for the new members of her basketball team. The cost for x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25. There was not sales tax on the purchase.
Which equation could be used to find x?

a)
  1. 3.99(x + 12.25) = 77.49

b)
  1. 3.99x + 12.25 = 77.49  

c)

12.25(x + 3.99) = 77.49

d)

 12.25x + 3.99 = 77.49

24.

Solve for x:

 12.25x + 3.99 = 77.49

(a)  

25.

Solve for x:

 12.25x + 3.99 = 77.49

(a)  

26.

Martha participated in a charity walk in which each kilometer walked raised $10 for charity. Her goal was to raise more than $300 on Saturday and Sunday. She raised $150 on Saturday. Write an inequality that could be used.

a)
  1. 150 + 10x > 300 

b)
  1. 150 + 10x < 300 

c)
  1. 150x + 10 > 300 

d)
  1. 150x + 10 < 300 

27.

A city council member wanted to know how her constituents felt about a planned rezoning. She randomly selected 75 names from the city phone directly and conducted a phone survey.  Which of the choices below correctly describes the population and sample of this data. 

a)
  1. The population is everyone listed in the city phone 

directory; the sample is the 75 people selected.

b)
  1. The population is the residents of the city; 

the sample is the registered voters in the city. 

c)
  1. The population is registered voters in the city; 

the sample is everyone listed in the city phone directory. 

28.

Select three valid comparisons.

a)

The data sets have similar variabilities. 

b)

The distribution of each data set is symmetric. 

c)

The distribution of each data set is skewed. 

d)

The difference in the medians is about 1.5 times the IQR. 

e)

Values in data set A are generally less than the values in data set

29.

A bowling team participates in a two-day tournament and records the scores for each team on both days on the box plots. 

Which conclusion can be drawn from the box plots?

a)
  1. The scores on Friday and the scores on Saturday have the same median and interquartile range.

b)

The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.

c)
  1. The scores on Friday have a greater interquartile range than 

the scores on Saturday, but both data sets have the same median.

d)
  1. The scores on Friday have a greater median than the scores 

on Saturday, but both data sets have the same interquartile range.

30.

Malika and Adrian prepared containers of potato salad at a deli. Each container was supposed to have a weight of one pound. The manager selected a random of containers prepared by each employee to check the weight of each container. The results are shown in the table below.

a)
  1. Malika will produce more containers with a weight of exactly one pound than Adrian will.

b)

Adrian will produce more containers with a weight of exactly one pound than malika will.

c)
  1. Most of Malika’s containers will have a weight closer to one pound than most of Adrian’s containers.

d)

Most of Adrian’s containers will have a weight closer to one pound than most of Malika’s containers.

31.

A large company has offices in cities across the county. The facilities director of the company was asked to survey employees about their office furniture. Rather than survey all employees in the company, the director decided to take a sample of employees. Which groups would be most representative of the opinions of all employees in the company?

Select three correct answers.

a)

 Employees with office phone numbers ending in 3 or 7 

(assume every employee has an office phone)

b)

 Randomly selected employees in the cafeteria of one of the offices

c)

Employees who have worked for the company for more than 10 years.

d)

5% of randomly selected employees from each office location

e)

Employees who are randomly selected by a computer from a list of all company employees

32.

Laura collected data throughout the football season and used this data to determine the probabilities of different teams playing in the championship now. The probabilities of her four favorite teams playing in the championship game are shown.  

Which of these teams is least likely to play in the championship game?  

a)

Tigers

b)

Redbirds

c)

Bulldogs

d)

Titans

33.

Which probability corresponds to an event that is unlikely to occur?

a)

16%

b)

22%

c)

90%

d)

100%

34.

Every student in a class tosses a thumbtack several times. The tack lands point up 118 times and lands on its side 82 times. Predict the theoretical probability of the tack landing on its side.

a)

about 31%

b)

about 41%

c)

about 59%

d)

about 70%

35.

Liz and Sara ride their bikes every day. The table shows the number of miles Liz and Sara rode their bike during five randomly selected days.

Based on the data in the table, which is the best comparative statement about the number of miles each girl rides on a typical day?

a)

On a typical day, Liz rides farther than Sara because the mean of Liz’s data is greater than the mean of Sara’s data.

b)

On a typical day, Sara rides farther than liz because the mean of Sara’s data is greater than the mean of Liz’s data.

c)

On a typical day, Liz rides farther than Sara because the range of Liz’s data is greater than the range of Sara’s data.

d)

On a typical day, Sara rides farther than Liz because the range of Sara’s data is greater than the range of Liz’s data.

36.

The tables show your results of rolling a number cube n times. The graph shows your results of using technology to simulate 1000 rolls. How do the experimental results compare to the theoretical probability of rolling an odd number.

a)

When n = 20, experimental probability < theoretical probability

b)
  1. When n = 50, experimental probability < theoretical probability

c)

When n = 1000, experimental probability = theoretical probability

d)
  1. The experimental probability becomes farther from the theoretical probability as n increases.

37.

Alfie tossed a paper cup in the air 350 times and recorded whether it landed right side up, upside down, or on its side. The results of the experiment are shown in the table.
If Alfie tosses the paper cup 90 more times, what is the expected number of times that the cup will land on its side?

a)

30

b)

48

c)

54

d)

60

38.

What is the probability of the coin flip resulting in tails and the number cube roll resulting in an even number?

a)

1/2

b)

1/4

c)

1/6

d)

1/12

39.

There are 12 boys and 14 girls in Mr. Rowe’s class. Each week, Mr. Rowe puts pieces of paper with each student’s name in a box and randomly pulls one out. The chosen student spins the arrow on the spinner shown.

Which expression can be used to find the probability that this week a boy will be chosen and the arrow will land on “Free assignment”?

a)

12/14 + 1/4

b)

12/14 x 1/4

c)

12/26 + 1/4

d)

12/26 x 1/4

40.

A bag contains 20 different pieces of paper. One piece of paper is randomly drawn, not replaced, and then another piece of paper randomly drawn. How many unique outcomes are in the sample space for this situation?

a)

19

b)

20

c)

380

d)

400

41.

A scale drawing has a scale of 1 cm: 1 m. 

You want to reproduce the scale drawing to be larger than the original. Which of the following scales could you use?

a)

1 cm : 0.25 m

b)

1 cm : 2 m

c)

1 mm : 1 m

d)

1 mm : 3 m

42.

For each set of side lengths or angle measures in the table, organize them based on whether they define a unique triangle, more than one triangle, or no triangle.

Categorize the following

8in, 5in, 5in

80°, 80°, 40°

10in, 2in, 3in

72°, 34°, 74°

More Than One Triangle
No Triangle
Unique Triangle
43.

The intersection of a plane and which solid can be a circle?

a)

Cube

b)

Cone

c)

Rectangular Pyramid

d)

Triangular Prism

44.

If a circle has a diameter of 18, what is the area to the nearest tenth of a square inch? (Use 3.14 for pi.)

(a)  

45.

If a circle has a diameter of 18, what is the circumference to the nearest tenth of a square inch? (Use 3.14 for pi.)

(a)  

46.

What is the angle measure of VPQ?

(a)  

47.

If the two angles above are complementary angles, what is the measure of ∠DBC?

(a)  

48.

A solid figure is composed of a cube and a right triangular prism. What is the volume of the figure?

(a)  

49.

Match the following terms and definitions:

a)

Vertical Angles

1.

Angles are congruent (equal)

b)

Complementary Angles

2.

Angles add up to 90°

c)

Supplementary Angles

3.

Angles add up to 180°

50.
Solve and graph.
8a > -136
a)
A
b)
B
c)
C
d)
D