SEVENTH GRADE MOCK ACT ASPIRE
Directions:
Today you will be taking a Mock ACT Aspire Mathematics Test
Read each question carefully. Some questions will ask you to choose one correct
answer, while other questions will ask you to show your thinking and explain your
process. Mark your answers by filling in the circles in your test booklet.
If you do not know the answer to a question, skip it and go on. If you finish the
test early, you may review your answers and any questions you may have
skipped.
You will have 60 minutes to complete this test. I will give you a 5 minute warning
to let you know there is five minutes left in the test. Are there any questions
before we begin?
Inside this test booklet are questions about mathematics. Some questions are
multiple choice. Others ask to you to write your answer.
Multiple Choice Questions:
 There is one correct answer.
 Read the question carefully and then choose the correct answer.
 In the answer document, completely fill in the circle that goes with the
answer you think is correct.
 If you decide to change your answer, erase your first answer completely.
 It is best to mark an answer for every question even if you are not sure
which answer is correct.
 Instructions for marking your answers are given in your answer document.
Constructive Response Questions:




Write your answer on the answer document.
Write your entire answer inside the box that goes with the question.
Give reasons in your answer.
Instructions for writing your answers are given in your answer document.
Please Note:
 Any writing in your test booklet will NOT be scored. Only your responses in
your answer document will be scored.
 Begin working on the test when you are told to do so.
 If you finish the test before time is called, you should use the remaining
time to review your work.
 When time is called, lay down your pencil immediately.
 You may NOT change answers in any way after time is called.
1. If a plant manufacturing carpet backing has a cylindrical tank that is 3
meters high and is 6 meters in diameter, what is the volume of the tank?
Assume 3.14 for pi.
a. 28.3 m3
b. 37.7 m3
c. 56.5 m3
d. 84.8 m3
e. 18.84 m3
2. The price of a gallon of gasoline was $1.65. The price rose y dollars. Then
the price dropped $0.15 and later rose again by $0.45. Which expression
below could be used to find the price of a gallon of the gasoline?
f. 1.9 + y
g. 1.95 + y
h. 2.0 + y
j. 2.1 + y
k. 2.25 + y
3. Simplify:
a. -16
b. -7
c. 7
d. 16
e. -10
−2(3)2 − 8 ÷ 2 + 6
4. Solve:
f.
g.
h.
j.
k.
𝑟
5
− 6 = −1
r=1
r=5
r=10
r=25
r= -35
5. The actual length of side t is 0.045 cm. Use the scale drawing to find the
actual length of side w.
a. 0.06 cm
b. 0.075 cm
c. 0.45 cm
d. 0.75 cm
e. 0.0075 cm
6. The scale drawing of a concrete pad has a length of 9.1 cm, a depth of 2.2
cm, and a width of 3.8 cm. What is the actual depth of the concrete pad if
the actual width is 418 cm?
f.
.1 cm
g.
242 cm
h.
112.2 cm
j.
668.8 cm
k.
15 cm
7. The five-number summaries for two sets of data are shown in the tale
below.
Part A. Which set is more dispersed (spread out)? Give reasons for your
answer.
Part B. Which set appears to be somewhat skewed? Which direction is it
skewed?
Part C. What would be the best display to draw, using the information in the
tale, to compare the two sets more closely?
8. Simplify:
a. 8
b. 10
c. 12
4 + 3(10 − 23 )
d. 14
e. 16
9. The triangles shown below are similar. Find the length of MV.
f.
2
g.
3
h.
7
j.
9
k.
11
10.Which diagram shows angle 1 and angle 2 as vertical angles?
a.
b.
c.
d.
e.
figure A
figure B
figure C
figure D
figure B and C
11. Angle x is (2n + 12)° and angle y is (3n + 18)°. Find the measure of angle x.
f.
24°
g.
30°
h.
72°
j.
108°
k.
40°
12. A city population was 67,255 on January 1, 2000, and its population has
been increasing by 2935 people each year since then. Which linear model
would represent the population P, where t is in years after 2000?
a. P(t) = 2935t
b. P(t) = 67255t
c. P(t) = 67255t + 2935
d. P(t) = 2935t + 67255
e. P(t) = 2935t – 67255
13. Given the number, two-fifths, generate its equivalent forms as a fraction, a
decimal, and a percent. In addition, give a real world example in which each
form might be used.
14. Evaluate:
f.
−1
g.
−
h.
1
j.
k.
1
4
5
8
1
4
5
8
1
5
15.Chris just found a new job that pays $600 a week. This is 4 times what his
old job paid. What was Chris’s weekly salary at his old job?
a. $50 a week
b. $100 a week
c. $125 a week
d. $150 a week
e. $200 a week
6(3𝑥 − 5) + 2(3𝑥 − 5) − 8(3𝑥 − 5)
16. Simplify:
f.
0
g.
24x – 40
h.
36x – 60
j.
48x – 80
k.
36x + 60
5
6
7
7
17. Sherie says, “There is no rational number between and .” Tim replies,
“Yes there is, because
11
14
is between them.” Is Tim right?
a. No, because the denominators are different.
b. No, since there is no number between 5 and 6.
5
10
7
14
c. Yes, since =
5
6
and =
6
d. Yes, because + =
7
7
12
.
7
14
11
14
.
e. No, because the numbers between 5 and 6 are not whole numbers.
18. Which equation describes the relationship expressed in the table?
f.
y=x
g.
y = 3x
h.
y = 2x
j.
y=
1
6
𝑥
k.
1
y= 𝑠
3
19. Isabelle, who is 62 inches tall is standing beside a tree and casts a 93 inch
shadow on the ground. The shadow of the tree she is standing next to is
279 inches long, what is the height of the tree based upon the information
given. Use a model in your explanation to solve the problem.
20. When you multiply a number by ¼, the result is
a. 50% of the original number
b. 400% of the original number
c. Four times the original number
d. One-fourth the original number
e. 20% of the original number
21. A children’s birthday party at an indoor play center costs $50 to rent the
space and $6.25 per child. Gina wants to spend no more than $100 on her
son’s fourth birthday party. Write and solve an inequality to determine the
number of children who can attend the birthday party.
f.
50 + 6.25x ≤ 100; x ≤ 8
g.
50 + 6.25x ≥ 100; x ≥ 8
h.
50 + 6.25x < 100; x < 8
j.
50 + 6.25x > 100; x > 8
k.
6.25x – 50 ≤ 100; x ≤ 24
22.If Christopher consumed 600 calories by drinking x number of sodas, which
expression represents the number of calories in each soda?
a. 600x
b. 600 + x
c. 600 – x
600
d.
𝑥
𝑥
e.
600
23. A card is chosen at random from a standard deck of 52 playing cards. What
is the probability that the card chosen is a queen?
f.4
g.1
h.
j.
k.
1
13
1
52
3
52
24. Kasi is making a scrapbook of her trip to Europe. If she creates 7 pages in 2
hours, which is a reasonable estimate of the amount of time it will take her
to create a 50-page scrapbook.
a. between 14 and 15 hours
b. between 15 and 16 hours
c. between 16 and 17 hours
d. between 13 and 14 hours
e. between 17 and 18 hours
25. A plane intersects a rectangular pyramid horizontally. Describe the crosssection.
f.
circle
g.
rectangle
h.
trapezoid
j.
square
k.
triangle
26. If you know the diameter of a circle, which statement describes how to
find the area?
a. Double the diameter and multiply by π
b. Multiply the diameter by π
c. Square the diameter and multiply by π
d. Divide the diameter in half and multiply by π
e. Divide the diameter in half, square the diameter, and multiply by π
27. Target sells 24 bottles of water for $3 and 36 bottles of water for $4.
Which is a better but and by how much?
f.
24 bottles for $3 by 1.5₵ per bottle
g.
24 bottles for $3 by 70₵ per bottle
h.
24 bottles for $3 by 75₵ per bottle
j.
36 bottles for $4 by 1.5₵ per bottle
k.
36 bottles for $4 by 70₵ per bottle
28. There are three properties involving multiplication that help make it easier
to solve problems. They are the commutative, associative, and distributive
properties. From the statement above complete each expression using the
commutative, associative, or distributive property and identify the property
used.
Part A. The sum of two numbers times a third number is equal to the sum
of each addend times the third number. Complete the expression and
identify the correct property: (4)(6 + 3)
Part B. when three or more numbers are multiplied, the product is the
same regardless of the grouping of the factors. Complete the expression
and identify the correct property: (2 x 3)(4)
Part C. When two or more numbers are multiplied together, the product is
the same regardless of the order of the multiplicands. Complete the
expression and identify the correct property: (4)(2)(3)
29. A cookie jar contains 6 chocolate cookies, 4 oatmeal cookies, 8 peanut
butter cookies, and 2 sugar cookies. If a cookie is pulled from the jar what is
the probability that it is oatmeal or peanut butter?
a.
b.
c.
d.
1
5
2
5
3
5
4
5
e. 1
30. Four data sets are shown in the box and whisker plots below, which set of
data has the largest 3rd quartile value?
f.
Data set A
g.
Data set B
h.
Data set C
j.
Data set D
k.
Data set A and C
31. Of these integers -65, -42, 65, and 90, which two are farthest a part on the
number line?
a. -65 and -42
b. -65 and 65
c. -65 and 90
d. -42 and 65
e. -42 and 90
32. Jamal has the following choices for his pizza: white sauce or red sauce,
white cheese or yellow cheese, mushrooms, pepperoni, or sausage. What is
the probability that he creates a pizza that has red sauce and white cheese?
f.
g.
h.
j.
k.
1
12
1
2
1
3
1
4
1
8
33. After making a deposit of $10 in the bank you went to the mall and made a
purchase of $45 with your check card. What is the least amount of money
that should have been in your account before making the deposit?
a. $15
b. $25
c. $35
d. $45
e. $55
34. Amy has $1,000 in a savings account at the beginning of the fall semester.
She wants to have at least $500 in the account by the end of the fall
semester. She withdraws $100 per week for living expenses. Write an
inequality for the number of weeks Amy can withdraw money, and solve.
f.
1000 – 100w ≤ 500; w ≥ 6
g.
1000 + 100w ≤ 500; w ≤ 5
h.
1000 + 100w ≥ 500; w ≥ 6
j.
1000 – 100w ≥ 500; w ≤ 5
k.
1000 – 100w ≤ 500; w ≥ 5
35. You are asked to draw a triangle using three of the following angles: 0°,
30°, 45°, 55°, 60°, 80°, 90°, 105°. Which triangle CANNOT exist?
a. 30°, 60°, 90°
b. 45°, 55°, 80°
c. 30°, 45°, 105°
d. 45°, 45°, 90°
e. 80°, 90°, 105°
36. Use the diagram to answer these questions. Note: The diagram is not
drawn to scale.
A. If m∠4 = 58° and m∠3 = 88°, find m∠2.
B. If m∠3 = 82° and m∠5 = 113°, find m∠2.
37. Jessica rented 1 video game and 3 movies for a total of $11.50. The video
game cost $4.75 to rent. The movies cost the same amount each to rent.
What amount did Jessica pay to rent each movie?
f.
$5.42
g.
$6.75
h.
$2.21
j.
$2.25
k.
$4.75
38. At the start of a month the value of an investment was $48.45. By the end
of the month the value of the investment changed by a loss of $13.80. The
next month the value of the investment changed by a growth of $16.80.
What was the value of the investment, in dollars, after the two months?
a. $51.45
b. $79.05
c. $45.45
d. $52.25
e. $46.25
39. A garden is 12-feet long and 4-feet wide. The length and width of the
garden will each be increased by the same number of feet. This expression
represents the perimeter of the larger garden:
(𝑥 + 12) + (𝑥 + 4) + (𝑥 + 12) + (𝑥 + 4)
Which expression is equivalent to the expression for the perimeter of the
larger garden?
f.
4x + 32
g.
4(x+12)(x+4)
h.
2(x+12)(x+4)
j.
4(x+16)
k.
X4 + 32
40. The spinner face shown is divided into 8 equal sections.
The arrow on this spinner is spun once. What is the probability that the
arrow will land on a section labeled with a number greater than 3?
a.
b.
c.
1
8
1
4
3
8
d.
e.
5
8
3
4
1
41. Which expression is equivalent to (8 − 6𝑥 + 12)?
f.
7
2
4
𝑥
g. −
13
2
𝑥
h. -6x + 14
3
i. − 𝑥 + 5
2
j. -2x + 5