8th Grade Math "Math 8 2024" - Public Release

Which expression is equivalent to $8^{- 4} \cdot 8^{3}$ ?

Select one answer.

To determine the equivalent expression, the student may have represented 8^(–4) as 1/(8^4). The student then may have rewritten the given expression as 1/(8^4) × 8^3 which simplified to (8^3)/(8^4) which could be interpreted as 8×8×8/8×8×8×8 or 1/8.i1

Multiplied 8 by the difference of the exponents.i2

Used the difference of the exponents as the coefficient of the expression.i4

May have simplified the expression as (8^4)/(8^3).

Which sets of ordered pairs represent functions?

Select all that apply.

Correcti3

Correcti5

Correcti2

Not a functioni4

Not a function

Consider the following equation.

$x^{2} = \frac{49}{16}$

Which values are the solutions to the equation?

Select one answer.

To determine the solution, the student could have taken the square root of both sides of the equation. The square root of 49 is 7 and the square root of 16 is 4, resulting in the fraction 7/4.i1

Divided the denominator by 2 instead of taking the square root.i3

Interpreted the exponent as a divisor and only divided the even number in the fraction.i4

Applied the square root to the denominator only.

The following figure shows three lines. Lines $m$ and $p$ are parallel. Angle $1$ is labeled. Some of the other seven angles that are labeled in the figure are congruent to angle $1$ .

Which angles are congruent to angle $1$ ?

Select all the correct angles.

Which fraction is the best estimate for the value of $\frac{\sqrt{65}}{\sqrt{122}} ?$

Correcti1

Used only the leading numbers from the numerator (6) and denominator (12) to create a fractioni2

Divided the numerator by 2 (and rounded) and divided the denominator by 2, instead of taking the square root of eachi3

For the numerator, took the square root of 64, but for the denominator took the square root of 144, resulting in $\frac{8}{12}$ or $\frac{2}{3}$

What value of $x$ satisfies the equation $5 (x - 6) - 2 (x + 3) = 12 ?$

Enter your answer in the space provided.

$x =$

Which of the following numbers are rational?

Select all that apply.

The equation x plus 3 y equals negative 3 represents a linear function.

Select two points on the coordinate plane to represent the function. A line will be drawn between the two points, and you can then move the points on the line to correct locations.

The population of the world is estimated to be $8 \times 10^{9} .$ The population of a country is estimated to be $2 \times 10^{8} .$

The world population is about how many times as large as the population of the country?

Enter your answer in the space provided.

Line segment $P Q$ is the result of reflecting line segment $A B$ across the $x$ ‑axis. $P$ has coordinates of $2 comma negative 2$ and $Q$ has coordinates $8 comma negative 2$

What is the length of line segment $A B ?$

A.

$4$
B.

$6$
C.

$8$
D.

$10$

Correcti1

May have divided 8 by 2i3

May have used the value 8 directly from the coordinatei4

May have added 2 and 8

The graph of the system of equations ${\begin{matrix} y = 2 x + 3 \\ y = x + 5 \end{matrix}$ is shown on the coordinate plane.

What is the solution to the system of equations?

Select from the drop-down menus to correctly complete the statement.

The solution is because the solution to the system must .

The following scatter plot shows the dollar amount of sales at an ice cream shop for $12$ days and the average daily temperature for each of the days.

Which graph shows the scatter plot with the linear model that best predicts sales for a given temperature?

Select one answer.

Determine the number of solutions for each equation shown in the following table.

Select one cell per row.

To determine the number of solutions in the first equation, the student solved the equation for x by first subtracting 7 from both sides resulting in 9x = 8x. Then, the student may have subtracted 8x from both sides, got x = 0, and concluded that the first equation had exactly one solution. For the second equation, the student also subtracted the 7’s, resulting in 8x = 8x. This time, the student may have divided both sides by 8, got x = x which is always true, and concluded that the second equation had infinitely many solutions. For the third equation, the student may have subtracted 9x from both sides, got 5 = 7 which is never true, and concluded that there was no solution.

The graph of a function is shown in the following coordinate plane.

Over which interval does the graph show a constant rate of change?

Select one answer.

Correcti2

Nonlineari3

Nonlineari4

Nonlinear

The amounts that two plumbers charge for their services are described.

The first plumber charges a fixed fee of $$40$ for house calls and $$15$ per hour of work.

The second plumber charges a fixed fee of $$30$ for house calls and $$19$ per hour of work.

For what number of hours of work do the first plumber and the second plumber charge the same total amount?

Enter your answer in the space provided.

hours

Consider the function defined by $y = 2 x - 5 .$

Which statements can be used to justify that the function is linear?

Select all that apply.

Correcti4

Correcti5

Correcti1

Student may have thought a positive coefficient was pertinent to determining if the function is lineari3

Student may have thought a negative $y -$ intercept was pertinent to determining if the function is linear

A person purchased $10$ items to donate to a school, backpacks that cost $$25.75$ each and notebooks that cost $$4.25$ each. The total cost of the items is $$150.$ This situation can be represented by a system of equations with a unique solution.

What does the solution to the system of equations represent in this context?

Correcti1

Student may have thought the solution represents total cost of only one of the itemsi2

Student may have thought the solution represents total cost of only one of the itemsi3

Student may have thought the solution represents total cost the items

On the following coordinate grid, points $N, P, R,$ and $T$ are collinear. The coordinates of each point are integers. The dashed lines shown on the coordinate grid form triangles $M N P$ and $Q R T$ .

Part A

Linda claimed that the slope of line segment P R is $\frac{6}{4}$ because point $P$ is $6$ units to the left of point $R$ and $4$ units up from point $R$ .

Explain the error in Linda’s claim and calculate the correct slope of line segment P R. Show all of your work.

Enter your work and explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Part B

Use triangles $M N P$ and $Q R T$ to show that the slope of the line is the same from point $N$ to point $P$ and from point $R$ to point $T$ .

Enter your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

The figure shows the front side of a store sign and its dimensions, in feet. The store owner will paint the entire front side of the sign.

What is the area, in square feet, of the front side of the sign?

Enter your answer in the space provided.

square feet

Certain values of linear function J are shown in the following table, where $x$ is the input variable and $y$ is the output variable.

$x$	$y$
$0$	$2$
$1$	$7$
$2$	$12$

Linear function K is represented by the equation $y = 3 x + 8$ .

Complete the statements about the slopes and the $y$ -intercepts of the graphs of the functions.

Select from the lists of choices to complete the statements.

The slope of the graph of function J is the slope of the graph of function K.

The

y

‑intercept of the graph of function J is the

y

‑intercept of the graph of function K.

Triangle $P R T$ and triangle $Q R S$ are shown on the coordinate plane. Points $P, Q,$ and $R$ all lie on the same line, and points $T, S,$ and $R$ all lie on the $y$ -axis. The vertices of both triangles have integer coordinates.

Which statement about the slopes is true?

Correcti1

Compared a ratio using the 'runs' to a ratio using the 'rises'i3

Did not realize the slopes would be equal and compared a ratio using the 'runs' to a ratio using the 'rises'i4

Did not realize the slopes would be equal

The following figure shows triangle XYZ. The length of line segment x y is $19$ units, and the length of line segment Y Z is $181$ units.

What is the value of $\frac{X Z}{Y Z}$ ?

Enter your answer as a fraction in the spaces provided.

fraction bar

A school had 380 sweatshirts in stock for students to buy. Two colors, green and purple, and two styles, hood and no hood, were available. Of all the sweatshirts, 210 had no hood and 180 were green. Of the sweatshirts that were purple, 70 had a hood.

Complete the following two‑way table to show the number of sweatshirts in each classification.

Move a number into each box.

70 80 100 130 170 180 200 210 380

	Green	Purple	Total
Hood
No Hood
Total

Student J and Student K are both reading the same book for a class assignment. Student J reads $20$ pages of the book each day. Student K starts reading $2$ days after Student J starts reading, and Student K reads $30$ pages of the book each day.

Define one variable and write an equation that represents the information given.

Determine the number of days after Student J starts reading when both students will have read the same number of pages of the book. Show your work or explain how you found your answer.

Enter your answers and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

Holistic Rubric for 3-Point Modeling Constructed Response Items
Points	Sample Characteristics
3 Points	A three-point response provides full and complete evidence of the modeling process used to solve a real-world problem. The response may: identify the problem that needs to be solved. determine information that is needed to solve the problem. communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and precise representations. contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding. evaluate or validate a partial or complete solution and show how to improve or refine the solution.
2 Points	A two-point response provides partial evidence of the modeling process used to solve a real-world problem. The response may: partially identify the problem that needs to be solved. determine some of the information that is needed to solve the problem. include a partial solution path that may be incomplete. contain some errors in identifying the mathematics that is needed to solve the problem. evaluate or validate a partial or complete solution and attempt to improve or refine the solution.
1 Point	A one-point response provides limited evidence of the modeling process used to solve a real-world problem. The response may: partially or incorrectly identify the problem that needs to be solved. determine a minimal amount of the information that is needed to solve the problem. include an incomplete or unorganized solution path. contain errors in identifying the mathematics that is needed to solve the problem. contain the correct solution, but work is limited or missing. evaluate or validate a partial or complete solution but does not show how to improve or refine the solution.
0 Point	A zero-point response is completely incorrect, incoherent or irrelevant.

A grocery store sells pumpkin seeds and sunflower seeds by the pound.

The equation $y equals 6 x$ models the relationship between $y,$ the cost, in dollars, and $x,$ the weight, in pounds, of the pumpkin seeds.

The graph shows the relationship between the cost, in dollars, and the weight, in pounds, of the sunflower seeds.

Sunflower Seeds

A customer purchased seeds and paid $$12$ for the pumpkin seeds and $$20$ for the sunflower seeds.

Which statement is true?

Correct i1

Confused the difference in unit rates for the difference in the number of pounds the customer purchased i3

Confused the difference in unit rates for the difference in the number of pounds the customer purchased i4

Found the difference between the number of pounds of seeds but, incorrectly concluded that more pumpkin seeds were purchased

The vertices of triangle P Q R are $P (6, 1), Q (3, 5),$ and $R with the coordinates 11 comma 11.$ The length of segment $P R$ is $the square root of 125$ units.

Use the coordinates and geometric reasoning to show that triangle P Q R is a right triangle. Explain your reasoning and show your work.

Enter your explanation and your work in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

Holistic Rubric for 3-Point Reasoning Constructed Response Items
Points	Sample Characteristics
3 Points	A three-point response for reasoning items provides evidence of correct, complete, and appropriate mathematical reasoning. The response may: be clear and well developed with logical reasoning communicated by the use of precise and appropriate representations, symbols, drawings, or mathematical vocabulary. contain minor flaws that do not detract from the correct reasoning or demonstration of a thorough understanding.
2 Points	A two-point response for reasoning items provides evidence of partially correct mathematical reasoning. The response may: display an incomplete reasoning process. contain minor flaws that detract from the correct reasoning or demonstration of a thorough understanding.
1 Point	A one-point response for reasoning items provides limited evidence of correct mathematical reasoning. The response may: demonstrate the beginning of a valid chain of reasoning. reflect a lack of essential understanding of the underlying mathematical concepts. contain the correct solution, but work is limited or missing. contain errors in the fundamental mathematical procedures or reasoning. contain omissions or irregularities that lead to an inadequate solution.
0 Point	A zero-point response is completely incorrect, incoherent or irrelevant.

A drama club is selling tickets to a play. The cost of each adult ticket is $$8$ and the cost of each student ticket is $$4.$ One customer purchased $8$ tickets and spent a total of $$56$

The system of equations shown can be used to model this situation. ${\begin{matrix} y = 8 - x \\ 8 x + 4 y = 56 \end{matrix}$

Which equation can be used to find $x,$ the number of adult tickets the customer purchased?

Correcti2

Substituted the first equation into the incorrect variable in the second equationi3

Set the equations equal to each other instead of substituting the first equation into the second equationi4

Added the first equation to the right side of the second equation instead of substituting the first equation into the second equation

Consider the following system of two equations. ${\begin{matrix} 3 x - 4 y = - 24 \\ 3 x + 2 y = - 6 \end{matrix}$

What are the coordinates $(x, y)$ of the solution to the system of equations?

Enter the coordinates in the spaces provided.

$($ $,$ $)$

The dimensions of a circular cylinder are described.

The diameter of the cylinder is $6$ meters.

The height of the cylinder is $12$ meters.

What is the volume, in cubic meters , of the cylinder?

Select one answer.

A.

$18 pi$
B.

$36 pi$
C.

$54 pi$
D.

$108 pi$

Correcti1

Determined the volume by multiplying the radius times the height times pi.i2

Determined the volume by multiplying the radius times the square of the height times pi.i3

Determined the volume by multiplying the radius times the height times 2 times pi.

A group raised money by selling key chains and coffee cups.

In the equation $y equals 2.75 x$ , the variable $y$ represents the amount, in dollars, that the group raised from selling $x$ key chains.

The following table shows the amount, in dollars, that the group raised from selling coffee cups, based on the number of cups sold each of four days.

Coffee Cup Sale

Day	Number of Coffee Cups Sold	Amount Raised (dollars)
Monday	$5$	$14$
Tuesday	$10$	$28$
Wednesday	$15$	$42$
Thursday	$25$	$70$

On Friday, the group sells $40$ key chains and $40$ coffee cups.

How does the total amount raised from selling $40$ key chains compare to the total amount raised from selling $40$ coffee cups ?

Select from the lists of choices to complete the statement.

The total amount raised from selling

40

key chains is than the total amount raised from selling

40

coffee cups by dollars.

The figure shows parallel lines $h$ and $k$ intersected by two transversals.

A student claims that the measure of angle R equals 80 degrees.

Which statement about the claim is true?

Correcti1

Used an incorrect method to calculate the measure of angle S and incorrectly concluded that angle R and angle S are corresponding anglesi2

Used an incorrect method to calculate the measure of angle S but correctly concluded that angle R and S are alternate interior anglesi3

Used an incorrect method to calculate the measure of angle S and incorrectly concluded that angle R and angle S are corresponding angles

A teacher has a cube. Each face of the cube has an area of $1 over 36$ square foot.

Part A

Let $d$ represent the length, in feet, of each edge of the cube. Write and solve an equation that includes the use of exponents to determine the value of $d$ .

Enter your equation and solution in the space provided. You may also use the drawing tool to help explain or support your answer.

Part B

Let $v$ represent the volume, in cubic feet , of the cube. Write and solve an equation that includes the use of exponents to determine the value of $v$ .

Enter your answer and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

Holistic Rubric for 4-Point Modeling Constructed Response Items
Sample Top Score Response Part A $d^{2} = \frac{1}{36}$ $d = \sqrt{\frac{1}{36}}$ $d = \frac{1}{6}$ Part B $v = d^{3}$ $v = {(\frac{1}{6})}^{3}$ $v = \frac{1}{216}$
Points	Sample Characteristics
4 Points	A four-point response provides full and complete evidence of the modeling process used to solve a real-world problem. The response may: identify the problem that needs to be solved. determine information that is needed to solve the problem. communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and essentially precise representations. contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding. evaluate or validate a partial or complete solution and show how to improve or refine the solution.
3 Points	A three-point response provides evidence of the modeling process used to solve a real-world problem. The response may: identify most of the problem that needs to be solved. determine most of the information that is needed to solve the problem. communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and precise representations with minor flaws. evaluate or validate a partial or complete solution and show how to improve or refine the solution, but the improvement or refinement may include minor flaws.
2 Points	A two-point response provides partial evidence of the modeling process used to solve a real-world problem. The response may: partially identify the problem that needs to be solved. determine some of the information that is needed to solve the problem. include a partial solution path that may be incomplete. contain some errors in identifying the mathematics that is needed to solve the problem. evaluate or validate a partial or complete solution and attempt to improve or refine the solution.
1 Point	A one-point response provides limited evidence of the modeling process used to solve a real-world problem. The response may: partially or incorrectly identify the problem that needs to be solved. determine a minimal amount of the information that is needed to solve the problem. include an incomplete or unorganized solution path. contain errors in identifying the mathematics that is needed to solve the problem. contain the correct solution, but work is limited or missing. evaluate or validate a partial or complete solution but does not show how to improve or refine the solution.
0 Point	A zero-point response is completely incorrect, incoherent or irrelevant.

The graph of a line is shown on the coordinate plane.

Describe the equation of the line and explain what is true about the coordinates of the ordered pairs on the line.

Select from the drop-down menus to correctly complete each statement.

The equation of the line is because the slope of the line is , and the

y

-intercept is . The coordinates of the ordered pairs on the line satisfy the equation.

A school club ordered medium pizzas and large pizzas for a club meeting. Each medium pizza cost $10 and was shared by 3 students. Each large pizza cost $12 and was shared by 4 students. There are 26 students in the club, and the club spent $80 on the pizzas.

Write a system of equations to model this situation.

Enter your equations in the space provided. Enter only your equations.

Anton has some money saved for school. To increase the amount he has saved, he got a job and added all the money earned to the amount already saved.

Anton was paid a constant rate in dollars per hour at his job.

After working $10$ hours, the amount he had saved was $$450$ .

After working $20$ hours, the amount he had saved was $$600$ .

Anton did not save any other money or spend any of the money he had saved.

Which equation represents $y$ , the amount of money in dollars Anton would have saved after working $x$ hours?

Select one answer.

	No Solution	Exactly One Solution	Infinitely Many Solutions
$9 x + 7 = 8 x + 7$
$8 x + 7 = 8 x + 7$
$9 x + 5 = 9 x + 7$

This page shows questions in the Math 8 2024 public release module at MSDE. 8th Grade Math "Math 8 2024"

Icon representing a test question. 1. Math 8 2024 Release, Question 1 (8.EE.A.1) - No Calculator.

Icon representing a test question. 2. Math 8 2024 Release, Question 2 (8.F.A.1-1) - No Calculator.

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Icon representing a test question. 8. Math 8 2024 Release, Question 8 (8.F.A.3-1) - No Calculator.

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Icon representing a test question. 10. Math 8 2024 Release, Question 10 (8.G.A.1a) - No Calculator.

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Icon representing a test question. 12. Math 8 2024 Release, Question 12 (8.SP.A.2) - No Calculator.

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Icon representing a test question. 15. Math 8 2024 Release, Question 15 (8.EE.C.8c) - Calculator.

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Icon representing a test question. 17. Math 8 2024 Release, Question 17 (8.M.5, 8.EE.C.8a) - Calculator.

Icon representing a test question. 18. Math 8 2024 Release, Question 18 (8.R.1e, 8.EE.B.6-1) - Calculator - CR with Annotations.

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This page shows questions in the Math 8 2024 public release module at MSDE. 8th Grade Math
"Math 8 2024"