MATHEMATICS
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Yasmine is raising money for a charity.
To get her started, her parents pay her
$25 to clean the house. She earns $8 an
hour for babysitting. The expression
8x + 25 represents the total Yasmine
raises.
A salesperson sells x premium plans
per week and y discount plans per
week. To earn a bonus, he must sell
more than 30 plans within the week
and at least twice as many premium
plans as discount plans.
What does the coefficient represent?
Which number of premium plans and
discount plans will not earn the
salesperson his bonus?
A amount of money raised
B rate per hour for babysitting
A 20 premium plans; 10 discount plans
C number of hours babysitting
B 30 premium plans; 15 discount plans
D payment for cleaning the house
C 40 premium plans; 20 discount plans
D 46 premium plans; 20 discount plans
2
Consider the graph that represents the
number of adults, in thousands, who
participate in a city’s recycling program
each year.
4
Oil enters a pipeline at a rate of 60
barrels/hour. There are 42
gallons/barrel of oil and 50 gallons/foot
of oil.
One mile equals 5,280 feet.
About how long, in hours, will it take
to fill one mile of the pipeline?
If this trend continues, how many
thousand adults would be participating in
the city’s recycling program after 15
years?
A 24
B 50
A 200
C 105
B 300
D 151
C 280
D 440
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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A folder on a computer has a capacity
of 7.5 gigabytes (GB) of data space. A
movie that uses 3.27 gigabytes (GB) of
data space is downloaded into the
folder.
What number of gigabytes most
accurately represents the available
data space the folder now contains?
Kenneth has worked out a study
program to prepare for end-of-year
exams. His program includes x
minutes of algebra and y minutes of
English studies per week. He wants to
spend at least 240 minutes studying
these subjects per week, with more
than three times as many minutes
studying algebra as minutes studying
English.
A 4 GB
Which pair of inequalities represents
the constraints?
B 4.2 GB
C 4.23 GB
A y – 240 ≥ x ; x < 3y
D 4.233 GB
B x – 240 ≥ y ; 3x < y
C x + y ≤ 240 ; x > 3y
D x + y ≥ 240 ; x > 3y
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This formula shows the area, A, of a
trapezoid with base lengths b1 and b2
and height h.
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A = h(b1 + b2)
2
If the area, the height, and base b1 of
the trapezoid are given, which equation
can be used to determine the length of
base b2?
A b2 =
Consider this equation.
Ax – 17 = 2x + 3
Solve for x in terms of A.
A x=
2𝐴
- b1
ℎ
B x=
B b2 =
C b2 =
D b2 =
2𝑏1
ℎ
-A
C x=
2𝐴− 𝑏1
D x=
ℎ
20
𝐴−2
20
2−𝐴
2−𝐴
20
𝐴− 2
20
2𝐴
ℎ𝑏1
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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10
Tameka works for Organic Farmers of
Oregon and is preparing for an
upcoming conference. She translates
the information from the table into a
line graph. She forgets to add the
vertical scale for the number of acres.
Consider the equation.
2x – 12 = 7x + 5
-2
3
What is the solution to the equation?
A
B
C
D
11
−12
5
17
20
13
10
13
4
The flow rate of a river can be
determined by Q = WDV, where Q is
the flow rate, W is the width, D is the
depth, and V is the velocity.
If the flow rate is 427.5 cubic feet per
second and the velocity is 10 feet per
second, which equation represents
depth, D, of the river?
Which list contains the values of the
vertical scale, in thousands of acres,
Tameka should use?
A
A 20; 30; 40; 50; 70; 80; 90
427.5
10𝑊
=𝐷
B 20; 30; 40; 50; 60; 70; 80
B
C 30; 40; 50; 70; 80; 100
D
427.5𝑊
10
=𝐷
30; 50; 70; 90; 110; 130
C 10W(427.5) = D
D 427.5 – 10W = D
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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12
Natalia has two credit cards. One
charges 12% annual interest, and the
other charges 18% annual interest.
She paid $650 in interest this year.
Manuel joins a car share service. He
will be charged $120 for an application
fee and car rental. He must also pay
$0.35 per mile for each mile driven
over 150 miles.
Which equation can be used to find the
possible amounts of money that were
charged to each of Natalia’s credit
card?
Which inequality shows the total
number of miles Manuel can drive
without the charges exceeding $200?
A 0.12a + 0.18b = 650
A 120 + 0.35x ≤ 200
B 0.12a – 0.18b = 650
B 120 + 0.35 + x ≤ 200
C 120 + 0.35x – 150 ≤ 200
C 650(0.12a) = 650(0.18b)
D 120 + 0.35(x – 150) ≤ 200
D (0.12 + 0.18)(a + b) = 650
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Consider the expression used to
convert degrees Fahrenheit to degrees
Celsius, where F is degrees Fahrenheit.
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𝟓
(𝑭 − 𝟑𝟐)
𝟗
Which statement accurately interprets
the impact of adding k to the value of
F?
Kim plans to spend between $10 and
$12 to purchase songs from an online
music store. The music store sells
downloaded songs for $1.25 each and
offers a $2.00 discount.
The compound inequality describes the
number of songs, s, Kim can purchase.
10 < 1.25s – 2 < 12
A adds k to the value of the expression
5
B adds 9 𝑘 to the value of the expression
How many songs can Kim purchase?
C subtracts k from the value of the
expression
A 8 or 9
B 9 or 10
5
C 10 or 11
D subtracts 9 𝑘 from the value of the
expression
LPS Algebra 1 Benchmark #1
D 11 or 12
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MATHEMATICS
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A student simplifies the equation
3x + 16 = 7x to the equivalent equation
shown.
A construction company has designed
an elevator to carry cement mix from
the ground to the roof. The elevator
has a maximum capacity of 3,170
pounds. It takes 2 construction
workers to operate, load, and unload
the elevator. The first worker weighs
225 pounds and the second worker
weighs 245 pounds.
16 = 4x
Which statement explains how the
student simplifies the equation?
A divides both sides by x
Which inequality represents the
number of bags of cement mix that can
be taken on any one trip if a bag of
cement mix weighs 45 pounds?
B multiplies both sides by 4
C adds 4x to the right side
D subtracts 3x from both sides
A 225 + 245 + 45x ≥ 3170
B 225 + 245 + 45x ≤ 3170
C 225 + 245 – 45x ≥ 3170
D 225 + 245 – 45x ≤ 3170
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Duane buys five movie tickets from a
theater’s website. He pays a $6 service
charge for using the website. His total
cost can be expressed as 5x + 6.
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The distance (d) an airplane travels is
given by the equation d = vt, where v
represents the velocity of the airplane
and t represents the time the airplane
travels.
What does the variable represent?
A total cost
If the distance is given in kilometers
(km) and the time is given in minutes
(min), what is the unit for the velocity?
B number of tickets
C cost of one ticket
D amount of service charge
A km
B min
C min/km
D km/min
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Consider the function f(x) = 3x + 2.
What is the value of f(-4)?
Mark is playing a computer game,
Jungle, which requires him to rescue
endangered animals. Rescuing an
endangered animal earns r points,
while being unable to save an
endangered animal costs d points.
Players earn 10 bonus points for
completing each level. At a certain
point in time, Mark’s score is given by
the expression shown.
A -1
B 1
C 14
D -10
(9r – 4d) + 10
Which scenario explains Mark’s score?
A Mark rescued 5 endangered animals and
completed ten levels.
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B Mark rescued 19 endangered animals and
was unable to save 6 endangered animals.
Timothy has completed 4 assignments
for math class. After his next
assignment he wants his mean grade to
be 85. The mean value of a set of 5
numbers is calculated using this
formula.
85 =
C Mark rescued 9 endangered animals, was
unable to save 4 endangered animals,
and completed one level.
D Mark rescued 9 endangered animals, was
unable to save 4 endangered animals,
and completed ten levels.
𝒏𝟏 + 𝒏𝟐 +𝒏𝟑 + 𝒏𝟒 + 𝒏𝟓
𝟓
Which formula should Timothy use to
calculate the grade he needs to earn on his
fifth assignment?
A n5 =
23
(5)(85)
𝑛1 + 𝑛2 +𝑛3 + 𝑛4
B n5 = 85 -
𝑛1 + 𝑛2 +𝑛3 + 𝑛4
5
Let x equal the cost to purchase from
Company B. Which equation can be
used to find the cost to purchase the
telescope from Company B?
C n5 = 5(85) – n1 – n2 – n3 – n4
D n5 = 5(85) – n1 + n2 + n3 + n4
LPS Algebra 1 Benchmark #1
The cost to purchase a certain model
telescope from Company A is $60 more
than half the cost to purchase the same
telescope from Company B. The cost
to purchase the telescope from
Company A is $170.
A
B
C
D
7
170 = 2x + 60
170 = 0.5x + 60
x = 170(0.5) + 60
x = (0.5)(170 + 60)
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MATHEMATICS
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A company is offering an incentive for
employees to join a gym. The gym
membership includes a monthly fee
and a $60 joining charge. The
company will pay $200, which is equal
to one-third of the yearly cost for
members. The incentive is represented
by this equation, where x is the
monthly fee.
200 =
𝟏
𝟑
(12x + 60)
The graph below describes a student’s
drive from home to school.
Four points are labeled on the graph.
Which statement describes the steps to
determine the monthly fee?
Which statement is an accurate
description of the indicated point on
the graph?
A subtract 60 from each side of the
equation, divide each side of the equation
by 12, and then multiply each side of the
equation by 3
A At point D, the student was 15 miles
from home.
B subtract 60 from each side of the
equation, multiply each side of the
equation by 12, and then divide each side
of the equation by 3
B At point A, the student turned around to
head back home.
C At point B, the student was stopped at a
stoplight for 1 minute.
C multiply each side of the equation by 3,
subtract 60 from each side of the
equation, and then divide each side of
the equation by 12.
D At point C, the student was driving at a
steady speed for 3 minutes.
D divide each side of the equation by 3,
subtract 60 from each side of the
equation, and then multiply each side of
the equation by 12
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Consider this inequality.
-4x ≤
Consider the following system of
equations.
𝒙 + 𝟏𝟖
2x – 3y = -2
y = -4x + 24
𝟐
What is the solution to the inequality?
What is the solution to the system?
A x≤2
A (5, -4)
B x≥2
B (5, 4)
C x ≤ -2
C (-5, -4)
D x ≥ -2
D (-5, 4)
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Consider the graph of these linear
equations.
Alida’s exercise program includes x
minutes of aerobic exercise and y
minutes of weight training per week.
She is supposed to have a minimum of
180 minutes of exercise per week, with
more than twice as many minutes of
aerobic exercise as minutes of weight
training.
-2y = -x
2x + 6y – 15 = 0
Which solution is reasonable with the
given constraints?
A (60, 120)
B (80, 170)
What is the solution to the system?
5
A (0, 2)
C (115, 55)
3
B (3,2)
C The system has no solution.
D The system has many solutions.
D (125, 60)
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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System B in the table below is created by
retaining the first equation from System
A and replacing the second equation.
The second equation is replaced with the
sum of the first equation from System A
and the product of 2 and the second
equation in System A.
Consider this set of inequalities.
y–x<1
y+x≥3
Which graph represents the solutions to
this set of inequalities?
A
B
C
D
What can be said about the graphs and
solutions for the two systems?
A The graphs of System A and System
B have the same lines, and the systems
have the same solution.
B The graph of System A has one line
that differs from the graph of System B,
so the systems have different solutions.
C The graph of System A has one line
that differs from the graph of System B,
but the systems have the same solution.
D The graph of System A has two lines
that differ from the graph of System B,
and the systems have different solutions.
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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What are the x-and y-intercepts of the
equation graphed below?
Which equation could be the line of best
fit for this scatter plot?
A x-intercept = 1; y-intercept = -1
B x-intercept = 2; y-intercept = -2
A y=
C x-intercept = -1; y-intercept = 1
1
19
B y=−
D x-intercept = -2; y-intercept = 2
C y=
5
9
x + 74
1
19
x + 74
x+8
5
D y=− 9x+8
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Consider the following system of
equations.
x – 2y = -9
x + 3y = 16
What is the solution to this system?
A (1, 5)
B (5, 1)
C (-5, 7)
D (7, -5)
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Mandee is testing the download speed on
her computer. She downloads 10
different files of various sizes from
different websites. She collects data on
the size of the download in megabytes
(MB) and the time the download takes in
seconds. (s). For the first 5 downloads, the
correlation coefficient is 0.78.
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The Carters are deciding whether to
install new insulation in their home and
want to calculate how cost effective it
would be and when they could expect a
payback on their investment. The graph
shows their expected costs (yearly fuel
bills plus the cost of any new insulation)
over a period of years.
Which set of data would product a
correlation for the remaining downloads
that is most similar to the first 5
downloads?
A
B
Which statement does not accurately
represent the information in the graph?
A The initial cost of installing the
insulation will be b dollars.
B The savings from their investment in
insulation will show after a years.
C
C The slope of Line A represents the
amount they are now paying in fuel
bills each year.
D The graph shows that if they do not
install new insulation, the slope of their
yearly fuel bills will rise.
D
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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What does the scatter plot imply about
the relationship between coffee sales
and the average daily temperature?
An airplane can carry a maximum of
150 passengers. Each passenger
receives a meal and can choose either
vegetarian or beef. The airline’s policy
states that each airplane must carry 1
vegetarian meal for every 5 beef meals.
The airplane is supplied with x
vegetarian meals and y beef meals.
Given the system of inequalities and
equations x + y ≤ 150 and y = 5x, what
is the value of x, the number of
vegetarian meals?
A x ≤ 25
B x = 25
A There are fewer coffee sales when the
temperature is higher.
C x < 25
D x ≤ 30
B Higher temperatures will cause coffee
sales to rise.
C Coffee sales are going down.
D Coffee sales will never be less than
$150.
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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The equation y = 0.002x + 4.75 models the
total cost in dollars, y, of using a 20-watt
compact fluorescent light bulb for x
hours. The table models the cost of using
a 60-watt incandescent light bulb.
The scatter plot below displays the
distance someone traveled as a function of
time.
Which value is the best estimate of
the correlation coefficient?
Which solution represents the number of
hours of use when the costs of using the
two light bulbs are the same?
A -0.50
A 600 hours
B 0.50
B 688 hours
C -0.17
C 1000 hours
D 0.17
D 1148 hours
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Which of the following equations is
represented by this graph?
What system of inequalities defines the
shaded areas below?
A y=-¼x-1
A y > x + 1 and x < 2.5y
B y=¼x–1
B y ≥ x + 1 and x > 2.5
C y = - 4x – 1
C y ≤ x + 1 and x > 2.5
D y = 4x – 1
D y ≤ x + 1 and x < 2.5
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Based on the data in the scatter plot
below, what would be the value of a
three-year-old car?
George and Mario have been
publishing a weekly newspaper. They
sold copies at various prices: $0.25,
$0.75, and $1.00, as shown in the graph
below. They have made a business deal
with a printing company for 600 copies
per week. At what price per copy are
they likely to sell 600 copies?
.
A $12,000
B $9,000
C $5,000
A $0.30
D cannot be determined
B $0.40
C $0.50
D $0.60
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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Mary loves to drink espresso drinks in
the morning. She makes a table of how
many espresso drinks she is willing to
buy at each price. This table is
displayed below.
Which ordered pair is a solution to the
system of inequalities graphed below?
.
Which best describes the linear
correlation between the price of
espresso drinks and the number of
espresso drinks she is willing to buy?
A (-2, 0)
B (0, 2)
C (-3, -3)
D (2, 0)
A Strong negative correlation
B Strong positive correlation
C Weak negative correlation
D Weak positive correlation
LPS Algebra 1 Benchmark #1
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MATHEMATICS
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During the renovation of a house, a
contractor has a budget of $4500 for
installing new energy efficient
windows. Each window costs $225 and
there is a flat delivery rate of $60. The
installation cost per window is $80.
The total cost, c, of replacing x
windows is represented by this
equation.
Ohm’s law states that the current (in
amps I) through a resistor is directly
proportional to the voltage (in volts V)
and inversely proportional to the
𝑽
resistance (in ohms R): I =
𝑹
The graph shows the current through a
resistor as the voltage increases.
80x + 60 + 225x = c
Which solution shows the number of
windows that can be installed?
A 12 windows
B 14 windows
C 16 windows
D 15 windows
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After ordering the maximum number of
windows, the contractor discovers that an
additional 8 windows are required to
complete the installation. Explain how to
find the revised budget for completing the
installation?
What does the slope of the graph
represent?
The slope represents amps per volt or
There are now 22 windows needed.
amps/volts.
22 @ $225 each is $4,950 to purchase the
windows.
What is the resistance of the resistor in
ohms?
22 @ $80 each is $1,760 to install the windows.
The cost for the windows is $4,950 + $1,760 =
10 ohms
$6,710. Adding the $60 for delivery gives a
The resistance is I = V/R. Substituting I
for amps and V for volts, if we use
12 amps = 120 volts/R ohms, then R is 10
ohms.
total cost of $6,770.
What is the total cost for completing the
job?
___$6,770_______________
LPS Algebra 1 Benchmark #1
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