Standardized Test Practice - Cumulative, Chapter 1-5
Read each question. Then fill in the correct answer on the answer document provided by
your teacher or on a sheet of paper.
1. Miguel received a $100 gift certificate for a
graduation gift. He wants to buy a CD player that costs $38 and CDs that cost $12 each. Which of the
following inequalities represents how many CDs
Miguel can buy?
A B C D SOLUTION: CD player + (cost of one CD number of CDs) gift certificate.
Let n = number of CDs purchased.
Round 5.16666667 to 5 so
This means that the correct choice is D.
2. Craig is paid time-and-a-half for any additional hours
over 40 that he works. Craig’s goal is to earn at least $600 next week, what
is the minimum number of hours he needs to work?
F 43 hours
G 44 hours
H 45 hours
J 46 hours
SOLUTION: If Wilson works 40 hours, he will earn 40(12.80) =
$512. So he needs to work more than 40 hours. Let h
represent the number of hours more than 40 hours he
needs to work.
Round 5.16666667 to 5 so
This means that the correct choice is D.
2. Craig is paid time-and-a-half for any additional hours
over 40 that he works. So he needs to work at least 4.58333 more hours, for
a total of 44.58333 hours. Since 44 hours would not
quite be enough to work to earn $600, 45 hours is the
first choice given that would be over $600. Therefore, the correct choice is H.
3. Which equation has a slope of
Craig’s goal is to earn at least $600 next week, what
is the minimum number of hours he needs to work?
F 43 hours
G 44 hours
H 45 hours
J 46 hours
SOLUTION: If Wilson works 40 hours, he will earn 40(12.80) =
$512. So he needs to work more than 40 hours. Let h
represent the number of hours more than 40 hours he
needs to work.
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and a y-intercept
of 6?
A B C D SOLUTION: Slope intercept form is
where m is the
slope and b is the y-intercept. Substituting in the
given slope and y-intercept into the slope-intercept
form,
.
Therefore, the correct choice is C.
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So he needs to work at least 4.58333 more hours, for
a total of 44.58333 hours. Since 44 hours would not
quite be enough to work to earn $600, 45 hours is the
Standardized
Test Practice - Cumulative, Chapter 1-5
first choice given that would be over $600. Therefore, the correct choice is H.
3. Which equation has a slope of
and a y-intercept
of 6?
A with < must be used. The equal to must also be used
to include both the lowest and highest score since
they are also part of the range. Therefore is the correct inequality and J is the
correct answer.
5. The current temperature is 82°. If the temperature rises more than 4 degrees, there will be a new
record high for the date. Which number line
represents the temperatures that would set a new
record high?
B C D SOLUTION: Slope intercept form is
where m is the
slope and b is the y-intercept. Substituting in the
given slope and y-intercept into the slope-intercept
form,
.
Therefore, the correct choice is C.
4. The highest score that is on record on a video game
is 10,219 points. The lowest score on record is 257 points. Which of the following inequalities best shows the range of scores recorded on the game?
F G H J SOLUTION: The range of scores for the video game has both a
lowest and highest score so a compound inequality
with < must be used. The equal to must also be used
to include both the lowest and highest score since
they are also part of the range. Therefore is the correct inequality and J is the
correct answer.
5. The current temperature is 82°. If the temperature rises more than 4 degrees, there will be a new
record high for the date. Which number line
represents the temperatures that would set a new
record high?
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SOLUTION: SOLUTION: If the current temperature rises more than 4 degrees,
a new record high h will be set. The current
temperature is 82 degrees. Therefore the inequality
that can be used to represent the temperatures at
which a new record high will be set is h > 82 + 4, or
h > 86. The number line that corresponds to this
inequality has an open circle at 86 and an arrow that
includes all of the values greater than 86. This is
shown in choice B.
6. The girls’ volleyball team is selling T-shirts and
pennants to raise money for new uniforms. The team hopes to raise more than $250.
Which of the following combinations of items sold
would meet this goal?
F 16 T-shirts and 20 pennants
G 20 T-shirts and 12 pennants
H 18 T-shirts and 18 pennants
J 15 T-shirts and 20 pennants
SOLUTION: Let x = the number of T-shirts and y = the number
of pennants. Write an inequality. $10 times the number of T-shirts plus $4 times the number of
pennants is at least $250. Find the slope by rearranging the inequality similar to slopeintercept form.
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of pennants. Write an inequality. $10 times the number of T-shirts plus $4 times the number of
pennants is at least $250. Find the slope
by
rearranging
the
inequality
similar
to
slope- 1-5
Standardized Test Practice - Cumulative, Chapter
intercept form.
Horizontal lines have a zero slope. Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes. Vertical lines are the only
lines with an undefined slope.
The correct choice is D
8. Which expression below illustrates the Associative
Property?
F G H J Next, test each possibility in the inequality.
16 T-shirts and 20 pennants
20 T-shirts and 12 pennants
18 T-shirts and 18 pennants
SOLUTION: The Associative Property states that the way you
group three or numbers when adding or multiplying
does not change their sum or product. Grouping is accomplished by ( )s. Choice H is the only answer that changes the order of the numbers added but
does not change the sum. In choice F, the order of
the factors changes (Commutative Property).
Choice G distributes the factor of 2 (Distributive
Property). Choice J is the Additive Inverse.
The correct choice is H.
Record your answers on the answer sheet provided
by your teacher or on a sheet of paper.
.
9. Solve
SOLUTION: First, express
solve each inequality.
using and. Then 15 T-shirts and 20 pennants
Choice C is the only choice that produces a correct
statement.
7. What type of line does not have a defined slope?
A horizontal
B parallel
C perpendicular
D vertical
SOLUTION: Horizontal lines have a zero slope. Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes. Vertical lines are the only
lines with an undefined slope.
The correct choice is D
8. Which expression below illustrates the Associative
Property?
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F G H and
The solution is
.
10. GRIDDED RESPONSE Tien is saving money for
a new television. She needs to save at least $720 to pay for her expenses. Each week Tien saves $50 toward her new television. How many weeks will it
take so she can pay for the television?
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SOLUTION: $50 per week number of weeks at least $720 .
that the inequality will also be equal to. The line is
shaded below, which means that the inequality is less
than or equal to. Therefore, the inequality is
Standardized
Test
The solution
is Practice -. Cumulative, Chapter 1-5
10. GRIDDED RESPONSE Tien is saving money for
a new television. She needs to save at least $720 to pay for her expenses. Each week Tien saves $50 toward her new television. How many weeks will it
take so she can pay for the television?
SOLUTION: $50 per week number of weeks at least $720 .
Let w = number of weeks of saving.
.
12. Solve
.
SOLUTION: Rewrite
for Case 1 and Case 2.
Case 1 is positive.
Case 2 is negative.
Round 14.4 to the next whole week of 15 to have
enough money to pay for the television. It will take
her 15 weeks.
11. Write an inequality that best represents the graph.
The answer is
SOLUTION: Use the slope- intercept form,
, where m
= the slope and b = the y-intercept. From the graph,
the y-intercept is 1. A second point can be located by
moving down 2 units and left 3 units, so the slope is
.
Substituting these values into
,
13. GRIDDED RESPONSE Daniel wants to ship a set
of golf clubs and several boxes of golf balls in box that can hold up to 20 pounds. If the set of clubs weighs 9 pounds and each box of golf balls weighs
12 ounces, how many boxes of golf balls can Daniel
ship?
SOLUTION: Golf clubs + (cost of one box of golf balls number of boxes of golf balls) 20 pounds .
Let b = number of boxes of golf balls. Before writing an inequality, convert all weights to the same
type of units. . The line is a solid line, which means that the inequality will also be equal to. The line is
shaded below, which means that the inequality is less
than or equal to. Therefore, the inequality is
.
.
12. Solve
.
SOLUTION: Rewrite
for Case 1 and Case 2.
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Case 1 is positive.
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Standardized
Test Practice - Cumulative, Chapter 1-5
The answer is
.
13. GRIDDED RESPONSE Daniel wants to ship a set
of golf clubs and several boxes of golf balls in box that can hold up to 20 pounds. If the set of clubs weighs 9 pounds and each box of golf balls weighs
12 ounces, how many boxes of golf balls can Daniel
ship?
SOLUTION: Golf clubs + (cost of one box of golf balls number of boxes of golf balls) 20 pounds .
Let b = number of boxes of golf balls. Before writing an inequality, convert all weights to the same
type of units. The largest whole number (since partial boxes cannot
be shipped) is 14.
He can ship 14 boxes of golf balls.
14. Graph the solution set for the inequality
.
SOLUTION: First, express
Then solve each inequality.
using and. and
The solution is
.
The graph will be the numbers in-between
and 5 with the circles filled in to include both
and 5.
15. Write an equation that represents the data in the
table.
The largest whole number (since partial boxes cannot
be shipped) is 14.
He can ship 14 boxes of golf balls.
14. Graph the solution set for the inequality
.
SOLUTION: First, express
Then solve each inequality.
using and. SOLUTION: First determine if there is a constant rate of change
by finding the change in the x values and y values. Each x value increases by 1 and each value increases by 1 and each y value increases by 3.5. The slope of a line is determined by
and
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Use the slope-intercept form, y = mx + b, and Page 5
substitute in the rate of change for m and the point (3,
12.5) for (x, y).
The solution is
.
The graph will be the numbers in-between
and 5 with the circles filled in to include both
and 5.
Standardized Test Practice - Cumulative, Chapter 1-5
Substitute 2 for b and 3.5 for m to get: y = 3.5x + 2.
15. Write an equation that represents the data in the
table.
16. A sporting goods company near the beach rents
bicycles for $10 plus $5 per hour. Write an equation in slope-intercept form that shows the total cost, y, of
renting a bicycle for x hours. How much would it cost Emily to rent a bicycle for 6 hours?
SOLUTION: Total cost equals (cost per hour number of hours) + initial bike cost .
Let y = total cost and x = renting a bicycle for x
hours.
SOLUTION: First determine if there is a constant rate of change
by finding the change in the x values and y values. Each x value increases by 1 and each value increases by 1 and each y value increases by 3.5. The slope of a line is determined by
Use the slope-intercept form, y = mx + b, and
substitute in the rate of change for m and the point (3,
12.5) for (x, y).
Substitute 2 for b and 3.5 for m to get: y = 3.5x + 2.
16. A sporting goods company near the beach rents
bicycles for $10 plus $5 per hour. Write an equation in slope-intercept form that shows the total cost, y, of
renting a bicycle for x hours. How much would it cost Emily to rent a bicycle for 6 hours?
SOLUTION: Total cost equals (cost per hour number of hours) + initial bike cost .
Let y = total cost and x = renting a bicycle for x
hours.
To calculate Emily’s cost for 6 hours, let x = 6.
It will cost Emily $40 to rent the bike for 6 hours.
Record your answers on a sheet of paper. Show
your work.
17. Theresa is saving money for a vacation. She needs to save at least $640 to pay for her expenses. Each week, she puts $35 towards her vacation savings.
Let w represent the number of weeks Theresa saves
money. a. Write an inequality to model the situation.
b. Solve the inequality from part a. What is the minimum number of weeks Theresa must save
money in order to reach her goal?
c. If Theresa were to save $45 each week instead, by how many weeks would the minimum savings
time be decreased?
SOLUTION: a. $35 per week number of weeks is at least $640 .
Let w = number of weeks of saving.
b.
To calculate Emily’s cost for 6 hours, let x = 6.
Round
to the next whole week of 19 to
have enough money to pay for the television. It will take her 19 weeks.
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It will cost Emily $40 to rent the bike for 6 hours.
c. $45 per week number of weeks is at least Page 6
$640 .
Let w = number of weeks of saving.
Standardized
Test Practice - Cumulative, Chapter 1-5
It will cost Emily $40 to rent the bike for 6 hours.
Record your answers on a sheet of paper. Show
your work.
17. Theresa is saving money for a vacation. She needs to save at least $640 to pay for her expenses. Each week, she puts $35 towards her vacation savings.
Let w represent the number of weeks Theresa saves
money. a. Write an inequality to model the situation.
b. Solve the inequality from part a. What is the minimum number of weeks Theresa must save
money in order to reach her goal?
c. If Theresa were to save $45 each week instead, by how many weeks would the minimum savings
time be decreased?
SOLUTION: a. $35 per week number of weeks is at least $640 .
Let w = number of weeks of saving.
b.
Round
to the next whole week of 19 to
have enough money to pay for the television. It will take her 19 weeks.
c. $45 per week number of weeks is at least $640 .
Let w = number of weeks of saving.
Round
to the next whole week of 15 to
have enough money to pay for the television. It will take her 15 weeks. Calculate the decrease. The minimum savings time would decrease by 4
weeks.
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