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

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

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

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

Rectangle JKLM 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.

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

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 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 reflection 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 .

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

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

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

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

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

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

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

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 $$5^9\cdot5^{-3}$$ ?

Expression 3 and Expression 4 only

Expression 1 and Expression 4 only

Expression 1, Expression 2, and Expression 4 only

Expression 2 and Expression 3 only

Consider the two parallelograms.

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 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 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 140 days 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.

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

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 number has a decimal expansion because it is the only decimal number.

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. Which two statements are true?

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

Student 1 saves $20 less 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.

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?

Both programs cost $45 at visit 5.

Both programs cost $50 at visit 5.

Both programs cost $55 at visit 6.

Both programs cost $65 at visit 7.

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

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

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

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

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

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

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

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

C. The system has infinitely many solutions.

Benchmark 3 Review

Authored by Courtney Davies

Mathematics

8th Grade

Used 4+ times

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64 questions

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MULTIPLE CHOICE QUESTION

30 sec • 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

MULTIPLE CHOICE QUESTION

30 sec • 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?

Plot A

Plot B

Plot C

Plot D

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Consider the three relations. Which statement is true?

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

30 sec • 1 pt

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

point Q

point R

point S

point T

MULTIPLE CHOICE QUESTION

30 sec • 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)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

4/9

5/11

5/9

6/11

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Benchmark 3 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 statement is true?

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

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

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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