8th Grade ACT Aspire Like
Summative Assessment
Time – 65 minutes
Student Name ____________________
Date ____________________________
1
1. In which set are the numbers equivalent?
A.
B.
C.
D.
E.
⅓, ³⁄₂₇, 33%
0.090, 90%, 0.90
0.15, 15%, ⅕
0.66%, ⅔, 66.7%
88%, ⁸⁸⁄₁₀₀, ²²⁄₂₅
2. The average distance from Jupiter to the Sun is about 5 x 10⁸ miles. The average distance
from Venus to the Sun is about 7 x 10⁷ miles.
The average distance from Jupiter to the Sun is about how many times as great as the
average distance from Venus to the Sun? Round your answer to the nearest hundredths
place.
F.
G.
H.
J.
K.
7
7.1
7.14
7.15
71.4
3. What is the distance between (0,0) and (8,15) on the coordinate plane?
A.
B.
C.
D.
E.
6 units
7 units
8 units
17 units
23 units
4. A triangle has 0 diagonals, a quadrilateral has 2 diagonals, a pentagon has 5 diagonals, and a
hexagon has 9 diagonals. If the pattern continues, how many diagonals will an octagon
have?
Sides
Diagonals
F.
G.
J.
K.
L.
3
0
4
2
5
5
6
9
22
20
18
14
11
2
5. The school newspaper conducted a survey about which ingredient was most preferred as a
pizza topping. This graph appeared in the newspaper article.
What information would best help you determine the number of people surveyed who
preferred sausage?
A.
B.
C.
D.
E.
number of people surveyed and type of survey used
type of survey used and ages of people surveyed
percent values shown on chart and number of people surveyed
ages of people surveyed and percent values shown on chart
type of survey used and gender (male or female) of people surveyed
6. Antonio and Maria have different methods for finding square roots.
Antonio's Method To find the square root of x, find a number so that the product of the number and itself
is x. For example, 2 x 2 = 4, so the square root of 4 is 2.
Maria's Method To find the square root of x, multiply x by ½. For example, 4 x ½ = 2, so the square root
of 4 is 2.
Which student's method is not correct? In your answer document using words, numbers,
and/or pictures, explain why that student's method is not correct.
7. Secretariat and Affirmed were famous racehorses. At his top speed, Secretariat ran ⅞ mile.
At his top speed, Affirmed ran 1½ miles. How much farther, in furlongs, did Affirmed run
than Secretariat? (Note: 1 mile = 8 furlongs)
A.
B.
C.
D.
E.
5
6
7
8
9
3
8. Which decimal is the equivalent of ⁶⁄₁₁ ?
F.
G.
H.
J.
K. 0.54
9. Look at the drawing. The numbers alongside each column and row are the total of the
values of the symbols within each column and row. What should replace the question
mark?
A.
B.
C.
D.
E.
23
25
28
30
32
10. The graph of a non linear function is shown on the coordinate plane. In the graph, y
is a function of x.
When the input of the function is -4, what is the output of the function?
F.
G.
H.
J.
K.
0
-5
-1
1
5
4
11. A scatterplot is shown on the coordinate plane.
Which of these most closely approximates a line of best fit for the data in the scatter plot?
E. None of the above
5
12. Ryan and Tomas walked to school and then to the park, as described below.
Ryan walked 2.3 miles from his home to meet Tomas at school.
Tomas walked 2.7 miles from his home to meet Ryan at school.
Once they were at school, the boys walked x miles to the park and then x miles back to the
school.
The sum of the distance Ryan walked and the distance Tomas walked was at least 15 miles
but not more than 21 miles. One of the following is the graph of the possible value of x.
Which one?
F.
G.
H.
J.
K.
6
13. The total cost of an order of shirts from a company consists of the cost of each shirt plus
a one-time design fee. The cost of each shirt is the same regardless of how many shirts
are ordered.
The company provides the following examples to customers to help them estimate the
total cost of an order of shirts:


50 shirts cost $349.50
500 shirts cost $2370
In your answer document, completely answer Parts A and B.
Part A - Based on the examples, what is the cost of each shirt, not including the one-time
design fee? Explain how you found your answer using words, numbers, and/or pictures.
Part B - What is the cost of the one-time design fee? Explain how you found your answer
using words, numbers, and/or pictures.
14. Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures
20° and angle BCA measures 30°.
What are the values of x and y?
F.
G.
H.
J.
K.
x = 20° , y = 30°
x = 40° , y = 40°
x = 40° , y = 50°
x = 50° , y = 50°
x = 50° , y = 60°
7
Use the following information to answer questions 15-17.
To earn money, Kellen started a lawn-mowing business in his neighborhood. All the lawns
that Kellen mows in his neighborhood are assumed to be the same size. Kellen spent
$250.00 for a new lawnmower, and the average cost for gasoline to mow each lawn in his
neighborhood is $1.55. He charges $25.00 for each lawn he mows in his neighborhood.
When Kellen mows n lawns in his neighborhood, the total cost, C, can be expressed by
C = $250.00 + $1.55n, and the total amount of money he charges, R, can be expressed by
R = $25.00n.
15. When the total amount of money Kellen has charged is $1,450.00, how many lawns has
Kellen mowed?
A.
B.
C.
D.
E.
38
45
48
58
65
16. Kellen was asked to mow a lawn outside his neighborhood that is 2⅓ times as large as the
assumed size of each lawn in his neighborhood. The cost of gasoline to mow a lawn is
proportional to the size of the lawn. Which of the following amounts is closest to the cost
of gasoline to mow this lawn?
F.
G.
H.
J.
K.
$1.75
$2.25
$2.65
$3.45
$3.62
17. Kellen wants to buy a $450.00 bike. What is the minimum number of lawns Kellen needs
to mow so that the difference between the total amount of money he charges and the
total cost of his expenses is enough to buy the bike?
A.
B.
C.
D.
E.
30
29
28
27
26
8
18. In the standard (x,y) coordinate plane, B(-2,3) is reflected over the x-axis. What will be the
coordinates of the image of B after the reflection?
F.
G.
H.
J.
K.
(2,3)
(2,-3)
(-2,-3)
(3,-2)
(-3,-2)
19. The table shows the results of a random survey of students in grade 7 and grade 8. Every
student surveyed gave a response. Each student was asked if he or she exercised less than
5 hours last week or 5 or more hours last weeks.
Based on the results of the survey, which statement is true?
A.
B.
C.
D.
E.
More grade 8 students were surveyed than grade 7 students.
A total of 321 students were surveyed.
A total of 107 grade 7 students were surveyed.
More than 50% of the students surveyed exercised less than 5 hours last week.
Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week.
20. In your answer document, completely answer Parts A and B.
Part A - Triangle STV has sides with lengths of 7, 11, and 14 units. Determine whether
this triangle is a right triangle. Show all work necessary using words, numbers, and/or
pictures to justify your answer.
Part B - A right triangle has a hypotenuse with a length of 15. The lengths of the legs
are whole numbers. What are the lengths of the legs? Show all work necessary using
words, numbers, and/or pictures.
9
21. What is the solution to the equation below?
2(x - 3) = 2x + 5
A.
B.
C.
D.
E.
x = 2¾
x = -2¾
There is no solution.
There are two solutions (x = 2¾ and x = -2¾).
There are infinitely many solutions.
22. All 720 students enrolled at Campbell Elementary School either walk to school or ride the
bus. Of these students, there are exactly 4 times as many who ride the bus as there are
who walk to school. How many Campbell Elementary School students walk to school?
F.
G.
H.
J.
K.
576
376
244
144
124
23. Evaluate (2.4 x 10⁴)(4.5 x 10³)
A.
B.
C.
D.
E.
1.08 x 10⁷
1.08 x 10⁸
1.08 x 10¹²
1.08 x 10¹³
1.08 x 10¹⁴
24. Which number is equivalent to
F.
G.
H.
J.
K.
2
4
9
81
729
10
25. Mr. Wallace surveyed 75 students at Poole Middle School to find out the students' favorite
place to eat lunch. The results are shown below.
Which table shows the approximate relative frequencies of Mr. Wallace's data?
E. None of the above
26. In the figure below, lines b and c are parallel and both cross line d. The measure of angle 1
is 120°. What is the measure of angle 2?
1
b
c
2
d
F.
G.
H.
J.
K.
60°
110°
120°
180°
360°
11
27. Jazmine surveyed 25 adults to ask whether they had at least one child under the age of 18
and whether they had at least one pet. This table show the results of the survey.
In your answer document, completely answer Parts A and B.
Part A - Use the results of the survey to complete the following table in your answer
document.
Part B - Jazmine made the conjecture that there is a possible association between
whether an adult has at least one child under the age of 18 and whether the adult has at
least one pet.
State whether the results of the survey provide evidence that adults who have at least
one child under the age of 18 also tend to have at least one pet. Explain your answer in the
answer document.
12
28. This cone and sphere have equal volumes (Formulas: Volume of a Cone = ⅓πr²h and the
Volume of a Cylinder = ⁴⁄₃πr³).
What is the radius of the sphere?
F.
G.
H.
J.
K.
12
13
14
15
16
29. The table below shows the cost of different numbers of goldfish at a pet store.
The cost is a linear function of the number of goldfish. Which statement describes the rate
of change of this function?
A.
B.
C.
D.
E.
The cost increases $6.00 each time 5 goldfish is added.
The cost increases $3.00 each time 5 goldfish is added.
The cost increases $1.50 each time 1 goldfish is added.
The cost increases $0.30 each time 1 goldfish is added.
The cost increases $0.15 each time 1 goldfish is added.
13
30. The population growth of two towns over a period of five years is represented by the
system of equations below, both algebraically and graphically.
y=x+6
y = 2x + 2
Which ordered pair is the solution to the system of equations?
F.
G.
H.
J.
K.
(1,5)
(2,6)
(4,10)
(6,2)
(10,4)
31. In the figure shown below, the length of
A.
B.
C.
D.
E.
is 45 meters. What is the length, in meters, of
?
7
8
17
21
24
14
32. Stephen has 2 cans of soup. 1st can has a radius of 2 cm and a height of 10 cm and the 2nd
can has a radius of 4 cm and a height of 10 cm. The volume of the 2nd can of soup is how
many times the volume of the 1st can of soup?
(Volume of a right circular cylinder may be calculated by using the formula V=πr²h)
r = 2cm
h = 10cm
F.
G.
H.
J.
K.
r = 4cm
h = 10cm
2
3
4
5
6
33. Which of the following numbers is NOT rational?
A. -31
B. ⅓
C.
D.
E.
34. Two utility companies sell electricity in units of kilowatt-hours. The cost of electricity for
company P is shown in the table. The cost of electricity for company M can be found by
using the equation shown, where y represents the total cost in dollars for x kilowatt-hours
of electricity.


Use the information provided to find the unit rate, in dollars per kilowatt-hour, for each
company. In your answer document, show your work or explain your answers.
Find the total cost, in dollars, of buying 22,375 kilowatt-hours of electricity from the
least expensive company. In your answer document, show your work or explain your
answers.
15
Use the information provided below to answer questions 35-37.
35. What is the slope of line t?
A. 3
B. ⅓
C. -⅓
D. -3
E. -4
36. What is the y-intercept of line t?
F.
G.
H.
J.
K.
3
⅓
0
-⅓
-1
16
Continue to use the information provided below to answer question 37.
37. Line s (not shown) has the same slope and passes through the point (0,4). Which table
represents 4 points on line s?
E. None of the above
17
38. The erosion rate along a section of the coast is approximately 3 feet per year. Which of
these best approximates this rate of erosion?
F.
G.
H.
J.
K.
9.9 x 10¯²
9.9 x 10¯²
9.9 x 10¯²
9.9 x 10¯²
9.9 x 10¯²
inches per day
inches per month
inches per year
feet per day
feet per month
39. Manuel ran 7,800 meters per day for 5 days. How many kilometers did Manuel run in total?
(Note: 1,000 meters = 1 kilometer)
A.
B.
C.
D.
E.
0.039
3.9
39
3,900
39,000
40. The lengths, given in yards, in one of the following lists are the lengths of the sides of a
particular right triangle. Which one?
F.
G.
H.
J.
K.
1,2,3
2,2,5
2,3,4
4,5,6
6,8,10
41. Natasha went to the store to buy some snacks for a party. She left the store with 4 bags of
pretzels and 6 boxes of cupcakes. The bags of pretzels normally cost $4.50 for a bag, but
they were discounted 50% off. A box of cupcakes normally cost $6 for a box, but there was
a sale that allowed Natasha to get 1 box of cupcakes for free for every 2 boxes she bought.
How much did Natasha spend, not including tax?
A.
B.
C.
D.
E.
$54
$48
$38
$35
$33
18
42. Which of the following values of x is a solution to the equation X³ = 10?
F.
G.
H.
J.
K.
10
100
1000
10,000
43. The gasoline mileage for two cars can be compared by finding the distance each car
traveled and the amount of gasoline used. The table shows the distance that car M
traveled using x gallons of gasoline. The graph shows the distance, y, that car P traveled
using x gallons of gasoline.
Based on the information in the table and the graph, compare the approximate miles per
gallon of car M to car P. In your answer document, show your work or explain your
answers.
19
44. The mean is the same for both data sets below. What is the value of x?
Data set #1:
Data set #2:
F.
G.
H.
J.
K.
3, 11, 8, x, 5
5, 9, 6, 10, 4, 8
5
6
7
8
9
45. Which statement best describes the value of
A. The value of
is between 2 and 2.5.
B. The value of
is between 2.5 and 3.
C. The value of
is between 3 and 3.5.
D. The value of
is between 3.5 and 4.
E. The value of
is between 4 and 4.5.
?
20