MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
1
4
Nisha attempted 50 free throws during the
basketball season. She scored on 39 of the
free throws.
Which of these represents the ratio of free
throws Nisha made?
Paula has two valuable coins: a gold dollar
and a silver half-dollar. The value of the
gold dollar is changing according to the
equation V = 20t + 350, where V = value in
dollars and t = time in years. The value of
the silver half-dollar is changing as shown
in this graph.
A 0.39
B 0.22
C 0.28
D 0.78
8.NS.1
2
Which of these equations is correct?
A (35)3 = 38
B 43 + 43 = 46
C (5 × 5 × 5)4 = 57
D 25 × 22 × 24 = 211
8.EE.1
3
If the equation for the value of the gold
dollar were graphed on the same
coordinate grid, which statement would
best compare the two graphs?
Look at these numbers.
A The graphs would have the same slope
and same y-intercept.
Which of these shows the numbers in order
from greatest to least?
A 𝜋, 2.4,
7
3
B The graphs would have different slopes
and different y-intercepts.
, 5
7
C The graphs would have the same slope,
but different y-intercepts.
C 5 , 3 , 2.4, 𝜋
D The graphs would have different slopes,
but the same y-intercept.
B 𝜋, 5 , 2.4, 3
7
7
D 3 , 2.4, 5 , 𝜋
8.F.2
8.NS.2
LPS 8th Grade Math Benchmark 1
1
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
5
This table shows the gallons of gasoline used by a power generator over time.
Which graph represents the data in the table?
A
C
B
D
8.F.1
LPS 8th Grade Math Benchmark 1
2
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
6
9
Light travels at a speed of approximately
2.9 x 108 meters per second. There are
approximately 3.2 x 107 seconds in one
year.
The following system of equations will
result in how many solutions?
2𝑥 − 6𝑦 = 8 and 𝑥 − 3𝑦 = 4
About how far does light travel in one year?
A One solution
A 6.1 x 1015 meters
B 6.1 x 1056 meters
C 9.28 x 1015 meters
D 9.28 x 1056 meters
B Infinitely solutions
C No solutions
D Cannot be determined
8.EE.4
8.EE.7a
7
What is the slope of a line that passes
through points (4, 8) and (6, 3)?
A
B
10
2
James took a taxi ride from his hotel to the
airport. He is charged an initial fee of $2.50.
The distance the taxi traveled, x, can be
determined using this equation.
2
9.5 = 0.4(5x) + 2.5
5
5
C
−
D
−
What distance did James travel in the taxi?
5
A 0.35 miles
B 2.25 miles
C 5.00 miles
D 3.50 miles
2
2
5
8.F.4
8
8.EE.7b
Carmen worked more than 40 hours last
week and earned $352.95. Her regular
hourly pay rate is $7.80. After 40 hours, she
is paid an extra $3.90 for each hour she
works. How many hours did Carmen work
last week?
A 43.50
B 44.85
C 40.95
D 45.25
8.EE.7b
LPS 8th Grade Math Benchmark 1
3
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
12
11
A computer programmer was conducting
probability experiments. The programmer
used this expression to determine the
probability of an event occurring.
What is the value of the expression the
programmer used?
A
B
C
D
1
2
1
64
1
4
1
32
8.EE.1
Which statement about the table and graph
is correct?
13
A The table has the same x-intercept as
the graph.
Kevin buys bicycle inner tubes for $4.50
each. He uses a coupon for $8.00 off his
purchase.
Which equation can be used to determine
Kevin's total cost, c, for t inner tubes?
B The table shows a greater x-intercept
than the graph.
A 𝑐 = 4.5𝑡 – 8
C The table shows the same rate of
change as the graph.
B 𝑐 = 4.5𝑡 + 8
C 𝑐=
D The table shows a greater rate of change
than the graph.
D 𝑐=
8.F.2
𝑡
4.5
𝑡
4.5
−8
+8
8.F.4
LPS 8th Grade Math Benchmark 1
4
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
14
17
Look at this set of real numbers.
Which of these is the subset of all irrational
numbers in the given set?
Mel is comparing the costs per kilowatthour of electricity for two different
companies. Transit Electricity uses the
equation y = 0.15x to calculate y, the cost
for their electricity based on x kilowatt-hours
used. Maximum Electricity uses this graph
to describe the cost for their electricity.
2
A {2.6667, }
3
B {𝜋, 15 , e}
C {2.6667, 𝜋, e}
D { 15}
8.NS.1
15
A blue whale that weighs 3.2 x 105 pounds
can eat 8.0 x 103 pounds of krill in a day.
How many days does it take for the whale
to eat an amount of krill equivalent to its
body weight?
Based on the information, which statement
is a valid conclusion about the electric
costs?
A 2.5 x 102
B 4.0 x 109
C 1.12 x 103
D 4.0 x 101
A Maximum Electricity charges 7 cents for
500 kilowatt-hours used.
8.EE.4
16
B Mel will use less electricity if he
purchases kilowatt-hours from Transit
Electricity.
Which equation represents a linear
function?
C The cost per kilowatt-hour for Maximum
Electricity is less than the cost per kilowatthour for Transit Electricity.
A 𝑦 = 4𝑥
B 𝑦 = 𝑥2 − 1
D The costs for the same number of
kilowatt-hours used are equal for both
Transit Electricity and Maximum Electricity.
C 𝑦 = 6𝑥 + 15
D −𝑥 2 + 5𝑥 + 6
8.EE.5/8.EE.6
8.F.3
LPS 8th Grade Math Benchmark 1
5
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
18
20
Bree wants to find the square root of 5, but
her calculator does not have a square root
key. She uses her calculator to approximate
5, as shown in this table.
An architect wants to determine the value
of the number 5 to use it as a
measurement on a diagram. Which point on
the number line is closest in value to 5?
A point P
B point Q
C point R
D point S
8.NS.2
Which of these would be the most
reasonable calculation Bree should try
next?
21
A 2.2 × 2.3
B 2.3 × 2.4
C 2.25 × 2.25
D 2.35 × 2.35
The length of an E. Coli bacterium is
approximately 3 × 10 −6 meters, as shown
in this figure.
8.NS.2
19
Jim's car has 20 gallons of gas in its tank.
After driving 200 miles, the car has 15
gallons of gas remaining. Which of these
equations represents the car's gasoline
consumption if g represents gallons of gas
and m represents the miles traveled?
1
A 𝑔 = 200 −
B 𝑔 = 20 −
C 𝑔 = 20 −
4
3
40
𝑚
A human hair is approximately 1 × 10−4
meters in thickness. About how many times
greater is the thickness of a human hair
than the length of an E. Coli bacterium?
𝑚
1
40
𝑚
A 3 times greater
B 33 times greater
C 333 times greater
D 3,333 times greater
3
D 𝑔 = 200 − 𝑚
4
8.F.4
LPS 8th Grade Math Benchmark 1
8.EE.4
6
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
22
23
Mr. Ferrill drew trapezoid JLMO and KN on
a coordinate plane to help his students
derive the slope-intercept equation.
In the diagram, ΔRQU is similar to ΔSQT.
Which proportion shows that the slope of
QR is the same as the slope of QS?
Which proportion shows that the slope of JL
is the same between any two points?
A
B
C
D
3−0
6−4
6−4
3−0
3−0
6−4
6−4
3−0
=
10−4
A
9−0
9−0
= 10−4
=
=
This diagram shows the side view of a
section of a highway being built through a
mountain pass. The highway is represented
by line L, which passes through points
Q, R, and S.
B
9−0
C
10−4
10−4
D
9−0
8.EE.6
LPS 8th Grade Math Benchmark 1
3000
1500
750
10
=
1500
3000
10
750
=
20
2250
30
=
=
40
20
40
30
2250
8.EE.6
7
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
24
27
A scientist began a bacteria culture with 4
cells. She used this exponential expression
to determine the number of cells in the
culture after 3 hours.
The size of a skin cell is about 3 × 10 - 4
meters. The size of an antibody is about
1 × 10 - 8 meters. What is the relationship
between the size of a skin cell and the size
of an antibody?
4(3 − 1)·4(2·3)·4( −3)
A The antibody is about 33 times the size
of the skin cell.
The scientist needs to write the value of the
exponential expression in simplest form.
Which of these is equivalent to the
expression?
B The antibody is about 3,333 times the
size of the skin cell.
A 256−36
B 4−36
C 45
D 2565
C The skin cell is about 300 times the size
of the antibody.
D The skin cell is about 30,000 times the
size of the antibody.
8.EE.1
8.EE.3
25
Which fraction is equivalent to 0.18 ?
A
B
C
D
28
1
The graph shows the amount of money an
employee earns over an 8-hour period.
9
2
11
17
90
18
100
8.NS.1
26
What is the solution to x 3 = 27?
A 3
What does the slope of the graph
represent?
B 9
A The employee earns $8 per hour.
B The employee earns $10 per hour.
C The employee earns $15 per hour.
D The employee earns $20 per hour.
C 33
D 273
8.EE.2
LPS 8th Grade Math Benchmark 1
8.EE.5
8
Go On
MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
29
31
Which function has a greater rate of
change?
A microbiologist measured two bacteria.
Bacterium X measured 5.0 × 10−7 meters in
length, and bacterium Y measured
2.0 × 10−5 meters in length. Which
statement correctly compares these two
bacteria?
A Bacterium X is 25 times as long as
bacterium Y.
B Bacterium Y is 40 times as long as
bacterium X.
A Function #1
C Bacterium X is 250 times as long as
bacterium Y.
B Function #2
D Bacterium Y is 400 times as long as
bacterium X.
8.EE.3
C Function #1 and #2 have the same rate
of change.
D There is not enough given information to
determine the rate of change.
32
8.F.2
30
Evaluate the expression
.
A8
B 21
C4
D 32
DeShawn and Zsasia own a photo print
center. During DeShawn’s shift, he sold 10
black & white canvas photos and 12 color
canvas photos and made $380 in total.
During Zsasia’s shift, she sold 6 black &
white canvas photos and 8 color canvas
photos and made $244. How much do
color canvas photos cost?
8.EE.2
33
Which is a non-linear function?
2
A 𝑦 − = −3(𝑥 + 5)
3
A $20
B 𝑦 = 2(𝑥 + 3)
B $14
C 𝑦 = 𝑥2 + 4
C $6
D 𝑦 − 6 = 3𝑥 + 8
D $12
8.F.3
8.EE.8c
LPS 8th Grade Math Benchmark 1
9
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
34
37
Evaluate the following equation for x when
𝑥 2 = 729.
Describe the graph when x is between -4
and -8.
A x = 243
B x = 364.5
C x = 27
D x = 35
8.EE.2
35
Sean was comparing cell phone plans.
Plan A charges $20 a month and costs an
additional $0.15 per text message. Plan B
charges $30 a month and an additional
$0.10 per text message. How many texts
would Sean have to send so that the two
plans cost the same amount?
A
B
C
D
A The graph is increasing and linear.
B The graph is decreasing and linear.
C The graph is increasing and nonlinear.
D The graph is decreasing and nonlinear.
200 text messages
100 text messages
300 text messages
400 text messages
8.F.5
38
8.EE.8c
36
Which equation is represented by the
function table below?
The following system of equations will
result in how many solutions?
−𝑥 + 3𝑦 = 6 and −𝑥 + 3𝑦 = −15
1
A One solution
A 𝑓(𝑥) = 𝑥 + 3
2
B Infinitely many solutions
B 𝑓(𝑥) = 7𝑥 − 2
C No solutions
1
C 𝑓(𝑥) = 𝑥 + 2
3
D Cannot be determined
3
D 𝑓(𝑥) = 𝑥 + 4
8.EE.7a
2
8.F.1
LPS 8th Grade Math Benchmark 1
10
Go On
MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
39
41
Without evaluating the system of equations,
determine which of the sentences is true
about the following system of equations:
The distance between Sydney, Australia
and Los Angles, United States is
approximately 12,000 kilometers. How is
12,000 expressed in scientific notation?
7𝑥 + 3𝑦 = −4 and 7𝑥 + 3𝑦 = 6.
A 1.2 x 104
A There will be infinitely many solutions
because the coefficients of the x and y
variables are the same.
B 12 x 104
C 1.2 x 10-4
B There will be one solution because each
equation represents a linear function, and
there will be a point of intersection.
D 12 x 10-4
8.EE.3
C There is not enough given information to
draw any conclusions.
42
D There will be no solution because
7𝑥 + 3𝑦 cannot equal -4 and 6 at the same
time.
This graph shows the relationship between
the number of hours a car repair takes and
the total cost at two different auto shops.
8.EE.8b
40
Using the graph, determine which of the
following ordered pairs is a solutions to the
given functions 𝑦 = −𝑥 + 5 and 𝑦 = 𝑥 + 3.
Which of these equations can be used to
determine the number of hours that the total
costs at the two auto shops are the same?
A 50 + 60h = 150 + 25h
B 50 − 150 = 60h − 25h
C 50 + 150 = 60h + 25h
D 50 − 60h = 150 − 25h
A (0, 5)
B (4, 1)
C (1, 4)
D (-1, 3)
8.EE.8.c
8.EE8a/8.EE.8b
LPS 8th Grade Math Benchmark 1
11
Go On
MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
43
46
Which set of ordered pairs represent a
linear relation?
A {(1, −2), (2, −4), (3, −6)}
Katie threw a bouncy ball into the air. The
ball bounced off the ground three times
before it rolled into the storm drain on the
side of the road. Which of the following
graphs best models the situation?
B {(−1, 3), (0, 0), (2, 12)}
C
A
1
(−1, −1), (1, 1), (5, )
5
D {(−1, −1), (0, 0), (2, 8)}
8.F.3
B
44
Is 𝑦 = −𝑥 + 2 a function?
A Yes, because it passes the vertical line
test.
B Yes, because it fails the horizontal line
test.
C
C No, because it passes the horizontal line
test.
D No, because it fails the vertical line test.
8.F.1
D
45
The sum of three times a number x and
nine is four times the sum of a number x
and two. Solve for x.
A There are infinitely many solutions.
B x= 2
C x=7
8.F.5
D x=1
8.EE.7a/8.EE.7b
LPS 8th Grade Math Benchmark 1
12
Go On
MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
47
48
In a catalog, Kealie found 2 different plans
for purchasing seeds. This graph shows the
relationship between the number of packets
of seeds and the total cost for each of the
two purchase plans.
4x + 2y = 8
3x + 3y = 9
For what number of seed packets are the
total costs of the two plans approximately
the same?
Using the graphed equations, what is the
solution to this system of equations?
A (0, 3)
B (1, 2)
C (1, –2)
D (0, 4)
A 2.5
B 4.3
C 5.5
D 9.8
8.EE.8a/8.EE.8b
8.EE.8a/8.EE.8b
LPS 8th Grade Math Benchmark 1
These equations are graphed on the
coordinate grid.
13
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MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
49
Look at this graph.
Describe the relationship shown in the graph.
Be sure to include the rate of change and initial depth.
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___________________________________________________________________________
8.F.5
LPS 8th Grade Math Benchmark 1
14
Go On
MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
50
The line in this graph shows the relationship between the number of fluid ounces for a certain type of
soda and the grams of sugar in the soda. For example, 24 ounces of soda has 80 grams of sugar.
Which statement about the slope of the line in the graph is correct?
A It represents the unit rate of grams of sugar per ounce of soda.
B It represents the unit rate of ounces of soda per gram of sugar.
C It represents the number of grams of sugar in 24 ounces of soda.
D It represents the number of ounces that contain 80 grams of sugar.
On the lines provided, explain the effects on the graph if a 24 ounce can of soda only had 70 grams of
sugar.
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8.EE.5/8.EE.6
END
LPS 8th Grade Math Benchmark 1
15
Go On
MATHEMATICS
DIRECTIONS: Read the question and choose the best answer.
LPS 8th Grade Math Benchmark 1
16
Go On