Consider the equation −9(4x + 1) = 18(−2x − 9). A student's final two steps when correctly solving the equation are shown. −36x − 9 = −36x − 162 and −9 = −162. Which statement correctly interprets the student's solution?

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

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

The only solution to the equation is x = −9.

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

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

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

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

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

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

Right triangle PQR is formed by arranging three squares along its sides, as shown.

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

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

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

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

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?

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

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

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

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

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?

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

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

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

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

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?

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

The triangle will be a right triangle if c is equal to (2a − 2b) feet.

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

The triangle will be a right triangle if c is equal to (√(a 2 − b 2 )) feet.

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

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

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

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

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

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

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

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

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

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

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

Triangle QRS is similar to triangle Q'R'S'. Which sequence of transformations maps triangle QRS onto triangle Q'R'S'?

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

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

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

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

A building manager considers hiring a lawn service to do lawn maintenance for various properties. The Lawn Doctor's rates are shown in the table. The equation T = 13.75h represents the total cost, T, in dollars, of hiring Lawn Care Pro for h hours. Which statement is true?

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

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

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

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

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?

There is a negative, linear association.

There is a negative, nonlinear association.

There is not enough information to determine the association.

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?

The measure of angle W is 90°.

The measure of angle Z is 90°.

The measure of angle W is 117°.

The measure of angle X is 63°.

The measure of angle X is 90°.

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

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

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

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

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'?

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

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

R'(−4, 6), S'(−2, 6), and T'(−2, 2)

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

Which expressions are equivalent to 5 9 · 5 -3 ?

Expression 1 and Expression 4 only

Expression 1, Expression 2, and Expression 4 only

Expression 2 and Expression 3 only

Expression 3 and Expression 4 only

Consider the two parallelograms. Which statement is true?

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.

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.

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.

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.

After conducting an experiment in science class, students write the linear model $ w = -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?

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.

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.

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

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.

Two rain barrels are used to water a school garden. Which statement is true?

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

Barrel 1 initially contains more water than Barrel 2.

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

Barrel 1 and Barrel 2 drain water at the same rate.

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. According to the table, which statement is true?

The fixed shipping cost is $11.00.

The cost per pound of candy is $2.50.

The cost per pound of candy is $10.00.

The fixed shipping cost is $13.50.

A teacher asks four students to write a number that has a decimal expansion. The numbers written by the students are as follows: Student 1 wrote 4π, Student 2 wrote 5/6, Student 3 wrote 2.3, and Student 4 wrote √25. Which statement is true?

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

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

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

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

Two students each track how much money they deposit into already existing savings accounts one summer. The table and graph represent the students’ total savings, y, after x weeks of summer. The table shows data for Student 1 with weeks x and total savings y, and the graph shows a line representing the savings for Student 2 over weeks x. Which two statements are true?

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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?

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

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

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

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

8th Math Benchmark Review

Authored by Allen Price

Mathematics

8th Grade

CCSS covered

Used 5+ times

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58 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

4.2 cubic inches

12.6 cubic inches

25.1 cubic inches

33.5 cubic inches

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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?

Scatter plot A

Scatter plot B

Scatter plot C

Scatter plot D

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Consider the three relations.

Relation 1 and Relation 2 are not functions.

Relation 1 and Relation 3 are not functions.

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

Relation 2 and Relation 3 are the only functions.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which point best represents the location of √52?

point Q

point R

point S

point T

Tags

CCSS.8.NS.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

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

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

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

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

Tags

CCSS.8.F.A.1

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

1.26 x 10^6 people

1.26 x 10^13 people

4.537 x 10^6 people

4.537 x 10^12 people

Tags

CCSS.8.EE.A.4

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which fraction is equivalent to 0.45?

4/9

5/11

5/9

6/11

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8th Math Benchmark Review

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

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?

Consider the three relations.

Which point best represents the location of √52?

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

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

Which fraction is equivalent to 0.45?

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?

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?

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

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