Benchmark: Keystone Benchmark 1 (analysis)

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Question #1

A compound inequality is shown below.

4 3x - 8 13


What is the solution of the compound inequality?

A. / 1 x 4
B. / 4 < x < 7
C. / 1 < x < 4
D. / 4 x 7

Question #2

Simplify: 9|(-5)-3|

A. /
B. /
C. /
D. /

Question #3

When the expression 2x2 - 2x - 12 is factored completely, which is one of its factors?

A. / (x + 3)
B. / (x + 2)
C. / (x - 4)
D. / (x - 6)

Question #4

The number of students enrolled at Carter High School for the first 5 years the school was open are listed below.

1,674 1,702 1,730 1,758 1,786


The enrollment numbers follow a pattern. Which expression can be used to determine the enrollment in the nth year the school is open?

A. / 28(n + 1,646)
B. / 1,646n + 28
C. / 28n + 1,646
D. / 1,674n

Question #5

Ariel purchased x student tickets for $7 each and y adult tickets for $9 each at the movie theater. She spent a total of $120 and bought 16 tickets in all. The system of equations shown below can be used to determine how many of each type of ticket Ariel purchased.


What is the value of x, the number of student tickets Ariel purchased?

A. / 17
B. / 13
C. / 12
D. / 4

Question #6

Rory earns $12 per hour mowing lawns plus $9 for each yard (r) he rakes the leaves. Rory mowed lawns for 6 hours and earned a total of $108 last week. Which equation could be used to find r, the number of yards Rory raked?

A. / 108 = 12(6) + 9r
B. / 108 = 12 + 6 + 9r
C. / 108 = 12(6) + 9 + r
D. / 108 = 12r + 9(6)

Question #7

Ben and Clay purchased art supplies. Ben purchased 6 tubes of paint for x dollars each and 8 paintbrushes for y dollars each and spent $34 in all. Clay purchased 7 tubes of paint for x dollars each and 4 paintbrushes for y dollars each and spent $29 in all. The system of equations shown below represents this situation.


Which statement is true?

A. / A tube of paint costs $1 more than a paintbrush.
B. / A paintbrush costs $2 more than a tube of paint.
C. / Clay spent $3 on each paintbrush.
D. / Ben spent more on paintbrushes than he did on tubes of paint.

Question #8

A clothing store has everything on sale for between 10% and 40% off. This can be represented by the system of inequalities shown below, where y is the amount of discount and x is the cost of the clothing item.


Which of the following is a true statement?

A. / When the cost of the clothing item (x) is $20, the amount of the discount (y) must be between $2 and $8.
B. / When the amount of the discount (y) is $4, the cost of the clothing item (x) must be between $0.40 and $1.60.
C. / When the cost of the clothing item (x) is $15, the amount of the discount (y) must be between $1 and $4.
D. / When the amount of the discount (y) is $5, the cost of the clothing item (x) must be between $10 and $40.

Question #9

Two monomials are shown below.

275xy3 / 75x3y


What is the greatest common factor (GCF) of these monomials?

A. / 75xy3
B. / 25xy3
C. / 75xy
D. / 25xy

Question #10

Nikki recorded the height of a plant every day as shown in the scatter plot below.


Based on the line of best fit, about how tall will the plant be on day 18?

A. / 6 cm
B. / 8 cm
C. / 18 cm
D. / 7 cm

Question #11

Travis bought x CDs and y DVDs at the mall. He spent a total of $105. The equation below describes the relationship between the number of CDs and the number of DVDs he bought.

15x + 25y = 105


The ordered pair (2, 3) is a solution of the equation. What does the solution (2, 3) represent?

A. / Travis bought 2 CDs and 3 DVDs.
B. / Travis spent $2 on CDs and $3 on DVDs.
C. / CDs cost $2 each and DVDs $3 each.
D. / DVDs cost 1.5 times as much as CDs.

Question #12

The following stem-and-leaf plot shows the scores for the class from the last math exam.

6 / / 4 6 7 7 9
7 / 5 8
8 / 2 5 6 8
9 / 4 4 5 8


What is the median score?

A. / 78
B. / 82
C. / 67
D. / 86

Question #13

If one card is drawn from a standard deck of 52 cards, what is the probability it is a red king card?

A. /
B. /
C. /
D. /

Question #14

The solution set of an inequality is graphed on the number line below.


The graph shows the solution set of which inequality?

A. / 4x - 6 -2
B. / 4x - 6 < -2
C. / 4x - 6 -2
D. / 4x - 6 > -2

Question #15

A graph of a linear equation is shown below.


Which equation describes the graph?

A. / y = 0.25x + 1
B. / y = 4x + 1
C. / y = 4x - 4
D. / y = 0.25x - 4

Question #16

A personal trainer charges a fee for a package of weight training sessions plus a charge for each bottle of supplements. The price (p), in dollars, to order b bottles of supplements and a weight training package is described by the function p = 9b + 300. Which statement is true?

A. / The cost of 9 bottles of supplements is $9.
B. / Each bottle of supplements costs $9 and the weight training package is $300.
C. / Each bottle of supplements costs $300 and the weight training package is $9.
D. / The cost of 3 bottles of supplements is $24.

Question #17

Max asked 600 students at Walker High School their favorite pastime and then recorded the results in the circle graph below.


Max will ask another 100 students to select their favorite pastime. Based on the information in the circle graph, how many more students of the next 100 asked will select reading rather than fishing as their favorite pastime?

A. / 174
B. / 8
C. / 20
D. / 126

Question #18

A linear equation is shown below.


What is the slope of the linear equation?

A. /
B. /
C. /
D. /

Question #19

The math department has a budget of $5,000 this year. They need to spend $3,600 on new textbooks. New graphing calculators cost $40 each. The inequality 3,600 + 40c 5,000 can be used to determine the number of new graphing calculators (c) that the math department can purchase. Which statement about the number of new calculators that can be purchased is true?

A. / The maximum number of graphing calculators that the math department can purchase is 30.
B. / The math department can purchase 30 new graphing calculators, but this number is neither the minimum nor the maximum.
C. / The minimum number of graphing calculators that the math department can purchase is 30.
D. / The math department can purchase 40 new graphing calculators, but this number is neither the minimum nor the maximum.

Question #20

The table below shows values of y as a function of x.

x / y
12 / 55
22 / 98
32 / 141
42 / 184
52 / 227


Which linear equation best describes the relationship between x and y?

A. / y = 3.5x + 29
B. / y = 4.3x + 3.4
C. / y = 4.125x + 12.5
D. / y = 4x + 7

Question #21

(-4,13)
(2,1)
(6,33)
(9,78)


What is the domain of the set of ordered pairs above?

A. / {-4, 13}
B. / {-4, 2, 6, 9}
C. / {13, 1, 33, 78}
D. / {9, 78}

Question #22

The scatter plot below shows the cost (y) of purchasing collectible stamps, based on the age of the stamp (x).


Which equation best describes the line of best fit?

A. / y = 0.75x + 0.5
B. / y = 0.75x + 1.5
C. / y = 1.25x + 1.75
D. / y = 1.25x + 3.25

Question #23

Which of the following is ordered from least to greatest for all real values in which 0 < x < 1 is true?

A. / 2x3, 3x2, 2x-2, 3x-3
B. / 3x-3, 2x-2, 3x2, 2x3
C. / 2x3, 3x2, 3x-3, 2x-2
D. / 2x-2, 3x-3, 3x2, 2x3

Question #24

The bowling scores for a group of 10 friends are shown below.

97 91 116 78 104 84 95 88 121 103


Which statement correctly describes the data?

A. / The interquartile range is 16.
B. / The upper quartile value is 116.
C. / The median value is 94.
D. / The lower quartile value is 91.

Question #25

The amount a carpet cleaning company charges for service (c) is based on a base fee for coming out plus an additional charge for each room (r) as shown in the equation below.

c = 24.99r + 50


What does the number 24.99 represent in the equation?

A. / the base fee for coming out
B. / the number of rooms cleaned
C. / the additional cost for each room
D. / the total cost for service if 1 room is cleaned

Question #26

Which of the following relations is a function?

A. / (2,4), (-4, 2), (8, 1), (-8, 2)
B. / (2,0), (-4, 3), (8, 1), (-4, 5)
C. / (2,4), (-4, 6), (2, 3), (-8, 2)
D. / (8,1), (-4, 4), (2, 1), (8, 2)

Question #27

One of the steps Sarah used to solve an equation is shown below.


Which statements describe the procedure Sarah used in this step and identify the property that justifies this procedure?

A. / Sarah multiplied 3x and -8x to combine like terms. This procedure is justified by the associative property.
B. / Sarah added 3x and -8x to combine like terms. This procedure is justified by the distributive property.
C. / Sarah multiplied 3x and -8x to combine like terms. This procedure is justified by the distributive property.
D. / Sarah added 3x and -8x to combine like terms. This procedure is justified by the associative property.

Question #28

A ladder is leaning against a building with a slope of -2. The bottom of the ladder is 50 feet from the side of the building, as shown in the diagram below.


What is the vertical distance (y), in feet, from the ground to the top of the ladder?

A. / 100
B. / 12.5
C. / 200
D. / 25

Question #29

A system of inequalities is shown below.


Which graph shows the solution set of the system of inequalities?


W. /
X.

Y. /
Z.
A. / W
B. / X
C. / Z
D. / Y

Question #30

A tourist shop sells t-shirts for $19 each and sweatshirts for $39 each. Last week, the shop sold 717 t-shirts and 592 sweatshirts. Which is the closest estimate of the total amount of money the shop received for t-shirts and sweatshirts last week?

A. / $58,000
B. / $28,000
C. / $48,000
D. / $38,000