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Benchmark 3 Review

Total questions: 64

Worksheet time: 32mins

Name
Class
Date
1.

What is the approximate volume of a sphere with a diameter of 2 inches? (Use 3.14 as an approximation of pi.)

a)

4.2 cubic inches

b)

12.6 cubic inches

c)

25.1 cubic inches

d)

33.5 cubic inches

2.

A community leader records the total number of pickleball players in the community each year for 10 years, starting in 2010. Which scatter plot has the best linear model to represent the community leader’s data?

a)

Plot A

b)

Plot B

c)

Plot C

d)

Plot D

3.

Consider the three relations. Which statement is true?

a)

Relation 1 and Relation 2 are not functions.

b)

Relation 1 and Relation 3 are not functions.

c)

Relation 1, Relation 2, and Relation 3 are all functions.

d)

Relation 2 and Relation 3 are the only functions.

4.

Consider the number line. Which point best represents the location of √52?

a)

point Q

b)

point R

c)

point S

d)

point T

5.

For which list of ordered pairs is y a function of x ?

a)

(5, 2), (6, 3), (7, 2), (5, 1)

b)

(3, 2), (3, 4), (5, 4), (6, 5)

c)

(1, 2), (3, 4), (5, 6), (7, 8)

d)

(1, 1), (2, 3), (1, 4), (4, 5)

6.

In 2022, the population of New York City was approximately 8.622×1068.622 \times 10^6 people, and the population of Los Angeles was approximately 4.085×1064.085 \times 10^6 people. What is the difference between the two populations?

a)


1.26 x 1061.26\ x\ 10^6 people

b)


1.26 x 10131.26\ x\ 10^{13} people

c)


4.537 x 1064.537\ x\ 10^6 people

d)


4.537 x 10124.537\ x\ 10^{12} people

7.

Which fraction is equivalent to 0.450.\overline{45} ?

a)

4/9

b)

5/11

c)

5/9

d)

6/11

8.

There are approximately 50,000,000 students enrolled in kindergarten through grade 12 in the United States. What is this amount written in scientific notation?

a)

5 × 10810^8 students

b)

5 × 10710^7 students

c)

5 × 10710^{-7} students

d)

5 × 10810^{-8} students

9.

Consider the two lines graphed on the coordinate plane, where each line represents an equation. Which ordered pair represents the solution to the system of equations?

a)

(−3, 4)

b)

(0, 2)

c)

(0, 5)

d)

(4, −3)

10.

Consider the linear function represented by the table. Based on the table, what is the rate of change of the linear function?

a)

2-2

b)


23\frac{2}{3}

c)

32\frac{3}{2}

d)

44

11.

The scatter plot shows the relationship between two variables, x and y . Which best describes the relationship shown by the scatter plot?

a)

A. linear association

b)

B. negative association

c)

C. no association

d)

D. positive association

12.

Consider the equation -9(4x + 1) = 18(-2x - 9). A student’s final two steps when correctly solving the equation are shown in the picture. Which statement correctly interprets the student’s solution?

a)

A. There is no solution to the equation since -9 = -162 is a false statement.

b)

B. There are infinitely many solutions to the equation since -9 = -162 is a false statement.

c)

C. The only solution to the equation is $ x = -9 $.

d)

D. The only solution to the equation is the ordered pair (-9, -162).

13.

Rectangle JKLM is rotated 90° counterclockwise about the origin to form rectangle J'K'L'M'. Which statement is true?

a)

Line segment J'K' is 2 units long, and line segment J'M' is 2 units long.

b)

Line segment J'K' is 2 units long, and line segment J'M' is 7 units long.

c)

Line segment J'K' is 7 units long, and line segment J'M' is 2 units long.

d)

Line segment J'K' is 7 units long, and line segment J'M' is 7 units long.

14.

Which statement must be true if angle PQR is a right angle?

a)

The sum of the areas of squares X and Z is equal to the area of square Y.

b)

The sum of the areas of squares Y and Z is equal to the area of square X.

c)

The sum of the perimeters of squares X and Z is equal to the perimeter of square Y.

d)

The sum of the perimeters of squares Y and Z is equal to the perimeter of square X.

15.

Parallel lines m and n are intersected by transversal t . What is the value of x?

a)

73

b)

97

c)

102

d)

107

16.

For which equation is x = 6 a solution?

a)

x2=12x^2=12

b)

x2=216x^2=216

c)

x3=18x^3=18

d)

x3=216x^3=216

17.

Which equation represents a nonlinear function?

a)

y=4x8y=-4x-8

b)

y=18y=\frac{1}{8}

c)

y=x54+3y = \frac{x - 5}{4} + 3

d)

y=3x6x2y=3x-6x^2

18.

Consider the table. Which numbers complete the table correctly?

a)

q = 3, r = 12, s = 36

b)

q = 3, r = 48, s = 216

c)

q = 9, r = 72, s = 12

d)

q = 81, r = 288, s = 12

19.

Consider the values five students write. Which two students write a value that is irrational?

a)

Student 1

b)

Student 2

c)

Student 3

d)

Student 4

e)

Student 5

20.

A hardware store sells drywall screws by the pound. If 1 drywall screw weighs 4.4×1034.4 \times 10^{-3} pound, how many pounds do 5,000 drywall screws weigh?

a)

1.1×1041.1\times10^4 pounds

b)

2.2×1012.2 \times 10^{1} pounds

c)

2.2×1042.2\times10^4 pounds

d)

22×10322\times10^{-3} pound

21.

Polygon 1 and polygon 2 are in different quadrants on the coordinate plane. If polygon 1 is congruent to polygon 2, which statement is true?

a)

Polygon 1 can always be mapped onto polygon 2 by a series of reflections, rotations, and/or translations.

b)

Polygon 1 can always be mapped onto polygon 2 by a series of rotations and translations only.

c)

Polygon 1 can always be mapped onto polygon 2 by a single reflection only.

d)

Polygon 1 can always be mapped onto polygon 2 by a single rotation only.

22.

Consider the graph of the equation y = -5x that intercepts the y-axis at the origin. If a student creates a new line with the same slope as the original graph, and the new line intercepts the y-axis at (0, 4), which statement is true?

a)

The new line’s equation should be written as y = -9x .

b)

The new line’s equation should be written as y = -5x - 4 .

c)

The new line’s equation should be written as y = -5x + 4 .

d)

The new line’s equation should be written as y = -x .

23.

What is the approximate shortest distance between Defy Gravity and Loop-de-Loop?

a)

4 meters

b)

5.8 meters

c)

8 meters

d)

8.3 meters

24.

What is the approximate shortest distance between Defy Gravity and Speed Demon?

a)

7.7 meters

b)

8.2 meters

c)

10 meters

d)

12 meters

25.

Consider the graph of a function. Which two statements about the function are true?

a)

A. When x is between -8 and -6, the function is increasing.

b)

B. When x is between -6 and -4, the function is decreasing.

c)

C. When x is between -4 and -1, the function is linear.

d)

D. When x is between 3 and 6, the function is nonlinear.

e)

E. When x is between 6 and 8, the function is decreasing.

26.

A wildlife biologist studies the population of a newly formed ant colony in the wild. The linear model y = 25x + 30 represents the data the wildlife biologist collects, where x represents the number of days since the wildlife biologist first began studying the colony, and y represents the total number of ants in the colony. Based on the linear model, how many ants are expected to be in the colony after 6 days?

a)

A. 55 ants

b)

B. 80 ants

c)

C. 155 ants

d)

D. 180 ants

27.

Which sequence of transformations maps triangle QRS onto triangle Q'R'S'?

a)

A dilation of triangle QRS by a scale factor of 1/2 about the origin followed by a translation left 2 units

b)

A dilation of triangle QRS by a scale factor of 1/2 about the origin followed by a translation left 5 units

c)

A dilation of triangle QRS by a scale factor of 2 about the origin followed by a reflection across the x-axis

d)

A dilation of triangle QRS by a scale factor of 2 about the origin followed by a reflection across the y-axis

28.

Two families buy large tubs of popcorn and bags of chips at a concession stand. Family 1 buys 3 large tubs of popcorn and 3 bags of chips for $11.25. Family 2 buys 4 large tubs of popcorn and 2 bags of chips for $12.00. What is the cost of 1 bag of chips?

a)

$0.75

b)

$1.50

c)

$2.25

d)

$3.00

29.

The equation T=13.75hT=13.75h represents the total cost, T , in dollars, of hiring Lawn Care Pro for h hours. Which statement is true?

a)

The Lawn Doctor charges more than Lawn Care Pro by a rate of $4.65 per hour.

b)

The Lawn Doctor charges more than Lawn Care Pro by a rate of $4.45 per hour.

c)

Lawn Care Pro charges more than The Lawn Doctor by a rate of $4.65 per hour.

d)

Lawn Care Pro charges more than The Lawn Doctor by a rate of $4.45 per hour.

30.

The total cost, y , in dollars, to hire Always Green Grass for x hours can be represented by the equation y=11.8xy=11.8x . How much more does Always Green Grass charge per hour than The Lawn Doctor?

a)

$1.30 per hour

b)

$2.70 per hour

c)

$3.20 per hour

d)

$6.40 per hour

31.

An author publishes a book in 2015 and begins selling copies of the book. The table shows the total number of copies the author sells each year since 2015. If a student correctly makes a scatter plot of the data, which statement is true?

a)

There is a negative, linear association.

b)

There is a negative, nonlinear association.

c)

There is no association.

d)

There is not enough information to determine the association.

32.

Consider the angle measures of trapezoid QRST. If trapezoid QRST is graphed on the coordinate plane and reflected across the y-axis to form trapezoid WXYZ, which two statements are true?

a)

The measure of angle W is 90°.

b)

The measure of angle W is 117°.

c)

The measure of angle X is 63°.

d)

The measure of angle X is 90°.

e)

The measure of angle Z is 90°.

33.

Consider trapezoid LMNP and trapezoid L'M'N'P'. Which sequence of transformations maps trapezoid LMNP onto trapezoid L'M'N'P' and proves the two trapezoids are congruent?

a)

A translation 10 units right and a reflection across the x-axis

b)

A translation 10 units down and a reflection across the y-axis

c)

A reflection across the y-axis followed by a reflection across the x-axis

d)

A 180° rotation about the origin followed by a translation 1 unit up

34.

The vertices of triangle RST are located at R(-6, 4), S(-6, 2), and T(-2, 2). The triangle is rotated 270° counterclockwise about the origin to create triangle R'S'T'. What are the coordinates of triangle R'S'T'?

a)

R'(6, 4), S'(6, 2), and T'(2, 2)

b)

R'(4, 6), S'(2, 6), and T'(2, 2)

c)

R'(-4, 6), S'(-2, 6), and T'(-2, 2)

d)

R'(-6, -4), S'(-6, -2), and T'(-2, -2)

35.

Which expressions are equivalent to 59535^9\cdot5^{-3} ?

a)

Expression 1 and Expression 4 only

b)

Expression 1, Expression 2, and Expression 4 only

c)

Expression 2 and Expression 3 only

d)

Expression 3 and Expression 4 only

36.

A student writes an expression that is equivalent to Expression 1. Which expression could the student write?

a)

52(52)4\frac{5^2}{(5^2)^4}

b)

5552530\frac{5^5 \cdot 5^{-2}}{5^{30}}

c)

51256\frac{5^{12}}{5^6}

d)

59(50)35^9\cdot\left(5^0\right)^{-3}

37.

On a particular day, 325 people attend an amusement park, and 130 souvenirs are sold. Which graph best represents the scenario if the number of souvenirs sold, y, is proportional to the number of people in attendance at the amusement park, x?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

38.

A tablet costs $550 plus 6% sales tax. A student already has $150 saved and earns $120 per week lifeguarding. If the student saves half of the earnings from lifeguarding each week, what is the minimum number of weeks the student must lifeguard to save enough money to buy the tablet?

a)

3 weeks

b)

4 weeks

c)

7 weeks

d)

8 weeks

39.

Consider the two parallelograms.

a)

The parallelograms are not similar because there is not a sequence of reflections, rotations, translations, and/or dilations that can form parallelogram MNPQ into parallelogram TUVW.

b)

The parallelograms are similar because parallelogram MNPQ can be dilated by a scale factor of 1/3 about the origin and translated 6 units left to form parallelogram TUVW.

c)

The parallelograms are similar because parallelogram MNPQ can be dilated by a scale factor of 1/3 about the origin and translated 7 units right to form parallelogram TUVW.

d)

The parallelograms are similar because parallelogram MNPQ can be dilated by a scale factor of 3 about the origin and translated 10 units left to form parallelogram TUVW.

40.

After conducting an experiment in science class, students write the linear model w=0.2d+140w=-0.2d+140 to represent the weight of an orange, w , in grams, after d days of the orange sitting on a counter. Based on the linear model, which statement is true?

a)

The orange’s weight is initially 0.2 gram, and the weight decreases by 140 grams for every 1 day that the orange sits on the counter.

b)

The orange’s weight is initially 1 gram, and the weight decreases by 0.2 gram for every 140 days that the orange sits on the counter.

c)

The orange’s weight is initially 140 grams, and the weight decreases by 0.2 gram for every 1 day that the orange sits on the counter.

d)

The orange’s weight is initially 140 grams, and the weight decreases by 1 gram for every 2 days that the orange sits on the counter.

41.

A teacher asks four students to write a number that has a decimal expansion. Which statement is true?

a)

All four students’ numbers have a decimal expansion because all rational and irrational numbers have a decimal expansion.

b)

Only Student 2’s and Student 3’s numbers have a decimal expansion because only fractions and decimals have a decimal expansion.

c)

Only Student 3’s number has a decimal expansion because it is the only decimal number.

d)

Only Student 3’s and Student 4’s numbers have a decimal expansion because only decimals and square roots have a decimal expansion.

42.

Two students each track how much money they deposit into already existing savings accounts one summer. Which two statements are true?

a)

Student 1 saves $5 less per week than Student 2 saves per week.

b)

Student 1 saves $5 more per week than Student 2 saves per week.

c)

Student 1 saves $20 less per week than Student 2 saves per week.

d)

Student 1’s initial amount is $10 less than Student 2’s initial amount.

e)

Student 1’s initial amount is $20 more than Student 2’s initial amount.

43.

Based on the table, what percentage of the tourists who are 1 – 8 years old prefer the elephant exhibit?

a)

4.7%

b)

12%

c)

19.7%

d)

61%

44.

Based on the results of the survey, which statement about the surveyed tourists is true?

a)

A tourist who prefers the penguin exhibit is most likely 1 – 8 years old.

b)

A tourist who prefers the tiger exhibit is most likely 9 – 16 years old.

c)

More than half of the tourists are 1 – 8 years old.

d)

More than half of the tourists who are 17 – 24 years old prefer the tiger exhibit.

45.

Points E, F, and G lie on the same line. Which statement is true?

a)

The slope between points E and F is equal to the slope between points E and G because the distance between points E and F is equal to the distance between points E and G.

b)

The slope between points E and F is equal to the slope between points E and G because the ratio of EX to XF is equivalent to the ratio of EZ to ZG.

c)

The slope between points E and F is less than the slope between points E and G because the distance between points E and F is less than the distance between points E and G.

d)

The slope between points E and F is less than the slope between points E and G because the ratio of EX to XF is less than the ratio of EZ to ZG.

46.

Two friends order cotton candy at the county fair. Friend 1 orders a large cylindrical cotton candy container, and Friend 2 orders a small conical container. Both containers have a radius of 3 inches and a height of 8 inches. What is the total volume of both containers of cotton candy? (Use 3.14 as an approximation of pi.)

a)

75.36 cubic inches

b)

226.08 cubic inches

c)

301.44 cubic inches

d)

1,205.76 cubic inches

47.

A city bus leaves the station for its normal morning route.

Which graph BEST describes the distance the bus is from the station?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

48.

A water park at the beach has two membership programs for admission. Program 1 charges a one-time fee of $30 in addition to $3 for every visit to the water park. Program 2 charges a one-time fee of $35 in addition to $2 for every visit to the water park. Which statement is true?

a)

Both programs cost $45 at visit 5.

b)

Both programs cost $50 at visit 5.

c)

Both programs cost $55 at visit 6.

d)

Both programs cost $65 at visit 7.

49.

Consider the list of values. 2π2\pi , 42\sqrt{42} , 30\sqrt{30} , 47\sqrt{47} , π+2.5\pi + 2.5 Which list orders the values from greatest to least on a horizontal number line?

a)

47\sqrt{47} , 42\sqrt{42} , 2π2\pi , π+2.5\pi + 2.5 , 30\sqrt{30}

b)

47\sqrt{47} , 42\sqrt{42} , 30\sqrt{30} , π+2.5\pi + 2.5 , 2π2\pi

c)

2π2\pi , π+2.5\pi + 2.5 , 30\sqrt{30} , 42\sqrt{42} , 47\sqrt{47}

d)

2π2\pi , π+2.5\pi + 2.5 , 47\sqrt{47} , 42\sqrt{42} , 30\sqrt{30}

50.

The points R(2, -3), S(6, -3), and T(6, -8) are the vertices of a triangle on the coordinate plane. What is the approximate length of side RT?

a)

4 units

b)

6 units

c)

8 units

d)

10 units

51.

Consider the figure. Which two statements must be true?

a)

k + m = p

b)

k + n = m

c)

k + n + p = 180

d)

m + n = j

e)

m + n + p = 180

52.

The Indian Ocean contains approximately 3×10203 \times 10^{20} liters of water. Lake Baikal contains approximately 2×10162 \times 10^{16} liters of water. Approximately how many times greater is the volume of the Indian Ocean than the volume of Lake Baikal?

a)

A. 66 times greater

b)

B. 1,500 times greater

c)

C. 15,000 times greater

d)

D. 66,000 times greater

53.

Which statement describes the solution(s) to the system of equations x+y=0x+y=0 and 3x3y=63x-3y=-6 ?

a)

A. The system has exactly one solution of (-1, 1).

b)

B. The system has exactly one solution of (0, 2)

c)

C. The system has infinitely many solutions.

d)

D. The system has no solution.

54.

Consider the right rectangular prism, where segment YZ is a diagonal connecting vertices Y and Z. What is the length of the diagonal?

a)

71.5 in.

b)

67.6 in.

c)

44.5 in.

d)

37.8 in.

55.

A florist makes floral arrangements for a wedding. The table shows the linear relationship between the number of flowers remaining in the florist's shop and the number of completed floral arrangements. Which function can be used to find y, the number of flowers remaining after x floral arrangements have been completed?

a)

y=11x+250y=11x+250

b)

y=11x+239y=11x+239

c)

y=11x+250y=-11x+250

d)

y=11x+239y=-11x+239

56.

Consider the equation 323m =(32)43^2\cdot3^{m\ }=\left(3^2\right)^4

What value of m makes the equation true?

a)

2

b)

4

c)

6

d)

8

57.

A landscaper builds a triangular garden with side lengths of a feet, b feet, and c feet, where c is greater than a and b. Which statement is true?

a)

The triangle will be a right triangle if c is equal to (2a2b) feet\left(2a-2b\right)\ feet

b)

The triangle will be a right triangle if c is equal to (2a+2b) feet\left(2a+2b\right)\ feet

c)

The triangle will be a right triangle if c is equal to (a2b2) feet\left(\sqrt[]{a^2-b^2}\right)\ feet

d)

The triangle will be a right triangle if c is equal to (a2+b2) feet\left(\sqrt[]{a^2+b^2}\right)\ feet

58.

Between which two numbers is 150\sqrt[]{150} located when plotted on a horizontal number line?

a)

11 and 11.5

b)

11.5 and 12

c)

12 and 12.5

d)

12.5 and 13

59.

Which statement about the equation y=x2y=-x-2 is true?

a)

The equation represents a linear function because when graphed on a coordinate plane, the graph will be a curve.

b)

The equation represents a linear function because when graphed on a coordinate plane, the graph will be a straight line.

c)

The equation represents a nonlinear function because when graphed on a coordinate plane, the graph will be a curve.

d)

The equation represents a nonlinear function because when graphed on a coordinate plane, the graph will be a straight line.

60.

From home, a student bikes 1 mile north, turns, and bikes 4 miles west. What is the shortest distance between the student and the student's home?

a)

3 miles3\ miles

b)

15 miles\sqrt[]{15}\ miles

c)

17 miles\sqrt[]{17}\ miles

d)

5 miles5\ miles

61.

Two rain barrels are used to water a school garden. The table and equation represent the amount of water remaining in each barrel, y, in gallons, x minutes since the students began watering the garden. Which statement is true?

a)

Barrel 1 initially contains more water than Barrel 2.

b)

Barrel 1 drains water at a faster rate than Barrel 2.

c)

Barrel 1 and Barrel 2 initially contain the same amount of water.

d)

Barrel 1 and Barrel 2 drain water at the same rate

62.

An online candy store calculates the total cost of an order as a function of the weight, in pounds, of the candy plus a fixed shipping cost. The table shows the total cost of three candy orders of different weights. According to the table, which statement is true?

a)

The cost per pound of candy is $2.50.

b)

The cost per pound of candy is $10.00.

c)

The fixed shipping cost is $11.00.

d)

The fixed shipping cost is $13.50.

63.

The hourly wage, in dollars, y, of an employee at The Burger Hut can be represented by the equation y=5.75x+7, where x is the number of years of employment. An employee at The Breakfast Diner makes $5 an hour the first year of employment, and the wage increases by $6.75 per hour for each additional year of employment. Which statement is true?

a)

For each additional year of employment, The Breakfast Diner increases a worker's wage $1 more per hour than The Burger Hut.

b)

For each additional year of employment, The Breakfast Diner increases a worker's wage $2 more per hour then The Burger Hut.

c)

For each additional year of employment, The Burger Hut increases a worker's wage $1 more per hour then The Breakfast Diner.

d)

For each additional year of employment, The Burger Hut increases a worker's wage $2 more per hour than The Breakfast Diner.

64.

Consider the list of numbers 125, π4, 3.12, 36-\frac{12}{5},\ \frac{\pi}{4},\ 3.1\overline{2},\ \sqrt[]{36} Which table categorizes the numbers correctly?

a)

Table A

b)

Table B

c)

Table C

d)

Table D