This page shows questions in the Math 7 2024 public release module at MSDE. 7th Grade Math
"Math 7 2024"

Which graph represents a proportional relationship from $y$ to $x$ with a constant of proportionality of $\frac{1}{2}\text{?}$

The freezing temperatures, in degrees Celsius, of two substances are shown in the table.

The freezing temperature of chloroform is how many degrees Celsius greater than the freezing temperature of ethanol?

Enter your answer in the space provided.

$°\text{C}$

Miguel eats a meal at a restaurant and leaves a $15$ % tip for the server. The cost of the meal without the tip is $p$ dollars.

Which expressions represent the total cost, in dollars, of the meal and the tip?

Select all that apply.

The graph shows the relationship between the number of cans of tuna bought and the total cost of the cans of tuna.

Cost of Tuna

For which point on the graph does the $y$ -coordinate represent the unit rate for the cost of the cans of tuna?

A certain three-dimensional figure has one base and $3$ faces.

• The area of each face is the same.

• The area of the base is $5$ square centimeters.

• The total surface area of the figure, including the base, is $26$ square centimeters.

What is the area of one face of the three-dimensional figure?

Enter your answer in the space provided.

square centimeters

The graph of a proportional relationship passes through the point with coordinates 10, 5 \( (10, 5) \) on the xy‑coordinate plane.

Which equation represents the given relationship?

Select one answer.

What is the value of the following expression?

$$(-\frac{1}{2})÷\left(\frac{3}{5}\right)$$

Enter your answer as a fraction in the spaces provided.

fraction bar

$$ \rule[0.4cm]{3.5cm}{0.5mm} $$

Consider the following expression.

$$-2(w-3)+5(6w+4)$$

Create an equivalent expression with exactly two terms.

Move a number into each box.

$w+$

The following table shows the low temperatures and the high temperatures, in degrees Fahrenheit, in four different cities on the same day.

In which city was there the greatest difference in low and high temperatures? In which city was there the least difference in low and high temperatures?

Select from the lists of choices to complete each statement.

The graph shows a proportional relationship from $y$ to $x$ that passes through the points located at $(2,6)$ and $(3,9)\text{.}$

What is the constant of proportionality?

Enter your answer in the space provided.

The location of point $k$ is plotted on the number line. Plot a point on the number line to represent the value of the expression $k+4\text{.}$

Select a place on the number line to plot the point that represents the value of the expression.

A volunteer is planning to hold tutoring sessions next year to tutor students in math and science.

• The volunteer will provide $4$ tutoring sessions each month.

• The number of hours the volunteer will tutor in each session is the same.

• The volunteer will spend $1$ hour of each session tutoring science.

• The volunteer wants to spend at least $120$ hours tutoring next year.

The inequality $48(x+1)\ge 120$ can be used to represent this situation.

What is the meaning of the possible solutions for $x$ in the inequality?

At the end of the year 2010, a business had 140 stores in the United States. By the end of the year 2016, the number of stores in the United States had increased by 60%, and $\frac{1}{14}$ of the total number of stores were located in California.

How many stores were located in California at the end of the year $2016$ ?

Select one answer.

A copy machine prints $10$ copies per $\frac{1}{4}$ minute.

At what rate, in copies per minute, does the copy machine print?

Enter your answer in the space provided.

copies per minute

A student correctly used division to find the decimal equivalent of $\frac{1}{12}$ using the work shown.

The student claims that the decimal equivalent of $\frac{1}{12}$ is 0.083 with a repeat bar above the digits 0 8 3 \( 0.\overline{083} \)

Complete the statement to explain why the student’s claim is incorrect.

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

A student will buy packs of AA batteries, packs of AAA batteries, and $1$ pack of C batteries.

• The student will buy the same number of packs of AA and AAA batteries.

• Each pack of AA batteries costs $\$10\text{.}$

• Each pack of AAA batteries costs $\$5\text{.}$

• The pack of C batteries costs $\$18\text{.}$

• The student will spend a total of $\$108\text{.}$

Which equations can be used to determine $x\text{,}$ the number of packs of each of AA batteries and AAA batteries the student will buy?

Select all that apply.

A hotel wants to buy a pump to fill a hot tub with water. The lines graphed on the coordinate grid represent the rates at which three pumps can fill the hot tub with water.

The hotel determined that the slowest of the three pumps can fill the hot tub with water in $90$ minutes. Using this information, explain how to determine the number of minutes it will take for the fastest of the three pumps to fill the hot tub with water.

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

Drawing Box

The floor of a room is going to be covered with ceramic tiles.

• The length of the room is $12$ feet.

• The width of the room is $\frac{2}{3}$ of the length of the room.

• The ceramic tiles are squares with $1\frac{1}{2}$ inches per side.

Which expression represents the number of ceramic tiles that will be needed?

A spinner has $12$ sections of equal size. The sections are numbered from $1$ to $12$ , as shown in the following figure.

The arrow on the spinner will be spun once. Consider the following events.

• J is the event that the arrow stops in a section with an even number.

• K is the event that the arrow stops in a section with a number greater than $2$ .

• L is the event that the arrow stops in the section with the number $10$ .

Place the name of each event under the heading that best describes its probability of occurrence.

Move each event into the appropriate box.

The cube shown in the following figure will be sliced by a plane. The plane will intersect exactly four faces of the cube and will not contain any point where three faces meet.

Which polygons could represent the shape of the region where the plane intersects the cube?

Select all that apply.

Three linear relationships are shown in the following tables, where $x$ is the independent variable and $y$ is the dependent variable.

For each table, determine whether the relationship represented is proportional or not proportional.

Select one cell per row.

A farmer’s horses drink from a rectangular water tank with dimensions shown.

When the farmer refills the tank, it takes the horses $4$ days to drink all the water. The farmer wants to build a new, larger tank and plans to increase each measurement of the tank by $25\%\text{.}$

• By what percentage will the amount of water the farmer can put in the tank increase when the larger tank is built?

• How many days will it take the horses to drink all the water in the larger tank?

Explain how you found your answers.

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

Drawing Box

The regular price of $\$28$ for dog food is discounted by $25\%\text{.}$ The sales tax is $8\%$ of the discounted price. The steps used to determine the price of the dog food after the discount is applied including sales tax are shown.

• Step $1\text{:}$ $28\left(\frac{3}{4}\right)(1+0.08)$

• Step $2\text{:}$ $21\left(1\text{.}08\right)$

• Step $3\text{:}$ $22\text{.}68$

Which statement is true about the work?

Two expressions are given.

• $3\text{.}5n+4(5\frac{1}{4}n-1\text{.}5)$

• $-21(\frac{2}{7}-\frac{7}{6}n)$

Apply the properties of operations to show why $3\text{.}5n+4(5\frac{1}{4}n-1\text{.}5)$ is equivalent to $-21(\frac{2}{7}-\frac{7}{6}n)\text{.}$

Show your work or explain your reasoning.

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

Each day, a salesperson earns $\$25$ plus $5\%$ of their total sales for the day. The salesperson’s goal is to earn more than $\$50$ on Thursday.

Which statements are true?

Select all that apply.

A sports organization collected data about the shoe sizes of soccer players and hockey players. The dot plots show the data that was collected.

How do the medians of the data sets compare in terms of the mean absolute deviations of the data sets?

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

The following figure shows a solid. At each vertex, three line segments intersect at right angles.

What is the surface area, in square feet, of the solid?

Select one answer.

Jackson is using bricks to make a patio. He completed $\frac{1}{8}$ of the patio in $\frac{2}{5}$ hour. If Jackson continues to work at this constant rate, what fraction of the patio will he complete each hour?

Enter your answer as a fraction in the spaces provided.

fraction bar

$$ \rule[0.4cm]{3.5cm}{0.5mm} $$

A worker will create a circular concrete patio around a square planter. The shaded region in the figure shown represents the patio and the unshaded region represents the planter.

• The side length of the square planter is 4 feet.

• The cost of the concrete is $0.90 per square foot.

The worker needs to calculate the cost of the concrete needed for the patio based on r, the radius, in feet, of the patio.

Write an expression that represents the total cost, in dollars, of the concrete the gardener needs to create the patio in terms of r.

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

A flat, rectangular garden has a perimeter of $24$ meters, and the ratio of the length of the garden to the width is $2$ to $1\text{.}$ The steps to determine the length, in meters, of the garden are shown.

At least one mistake was made.

• Step $1\text{:}$ $2l+2w=24$

• Step $2\text{:}$ $2l+2\left(2l\right)=24$

• Step $3\text{:}$ $2l+4l=24$

• Step $4\text{:}$ $6l=24$

• Step $5\text{:}$ $l=4$

In which step was the first mistake made, and what is the correct length of the garden?

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

A game has two players. On each turn, a player spins two spinners to determine how far to move a game piece.

• Each spinner is divided into $4$ equal sections.

• A different integer from $1$ to $4$ is written on each section of one spinner.

• A different integer from $-1$ to $2$ is written on each section of the other spinner.

• The player finds the sum of the integers shown and moves the game piece that number of spaces.

• The first player to land on or pass the “Win” space wins the game.

The figure shows the position of each player’s game pieces. Player A needs to move $6$ spaces or more to win and Player B needs to move $3$ spaces or more to win.

• If Player A has the next turn, what is the probability that Player A wins the game? Show or explain how you determined your answer.

• If Player B has the next turn, what is the probability that Player B wins the game? Show or explain how you determined your answer.

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

Drawing Box

Two students both solved the equation $-4(x-0.5)=6$ incorrectly. The work of each student is shown.

Student A’s Work:

$\begin{array}{cc}\phantom{0}& -4(x-0.5)=6\\ \mathrm{S}\mathrm{t}\mathrm{e}\mathrm{p}1\text{:}& -4x-2=6\phantom{000}\\ \mathrm{S}\mathrm{t}\mathrm{e}\mathrm{p}2\text{:}& -4x=8\phantom{000000}\\ \mathrm{S}\mathrm{t}\mathrm{e}\mathrm{p}3\text{:}& x=-2\phantom{000000}\end{array}$

Student B’s Work:

$\begin{array}{cc}\phantom{0}& -4(x-0.5)=6\\ \mathrm{S}\mathrm{t}\mathrm{e}\mathrm{p}1\text{:}& -4x+2=6\phantom{000}\\ \mathrm{S}\mathrm{t}\mathrm{e}\mathrm{p}2\text{:}& -4x=8\phantom{000000}\\ \mathrm{S}\mathrm{t}\mathrm{e}\mathrm{p}3\text{:}& x=-2\phantom{000000}\end{array}$

In which step of their work did Student A and Student B make their first mistake?

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

A company produces $25\text{,000}$ cans of soup per day that should each contain $8$ ounces of soup. A quality control employee selects a random sample of $50$ cans of soup each day and determines if those cans contain $8$ ounces of soup. On a certain day, $2$ cans in the sample contained less than $8$ ounces of soup.

Based on this sample, which value is the best estimate for the number of cans of soup produced on this day that will contain less than $8$ ounces of soup?

A person waxed $\frac{1}{40}$ of a floor every $\frac{1}{2}$ hour. The area of the floor was $\text{2,}000$ square feet.

At what unit rate, in square feet per hour, did the person wax the floor?

Enter your answer in the space provided.

square feet per hour