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

Select from the list to explore. Read any associated passages and then interact with the questions here.

Expand All Official Practice Test

This is a multiple choice question that allows you to select only one option.

Which expression is equivalent to 8−4⋅83 ?

Select one answer.

  1. A.
    −8
  2. B.
    −18
  3. C.
    18
  4. D.
    8
i3

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).

This is a multiple choice question that allows you to select only one option.

Consider the following equation.

x2=4916

Which values are the solutions to the equation?

Select one answer.

  1. A.
    ±78
  2. B.
    ±74
  3. C.
    ±498
  4. D.
    ±494
i2

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.

This is a fill in the blank question that allows you to enter only numbers.

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

Enter your answer in the space provided.

x=

This is a fill in the blank question that allows you to enter only numbers.

The population of the world is estimated to be 8×109. The population of a country is estimated to be 2×108.

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

Enter your answer in the space provided.

This is a question with 2 parts, including a question with drop-down menus from which you must select an option to fill in the blank.

The graph of the system of equations {y=2x+3y=x+50 is shown on the coordinate plane.

The figure shows the graph of two intersecting lines in the coordinate plane. The numbers negative 8, through 8, are indicated on the x and y axes. Both lines move upward, and to the right, through quadrants 3, 2, and 1. One line has an x intercept of negative 5, and a y intercept of 5. The other line has an x intercept of negative 1.5, and a y intercept of 3. The lines intersect at the point with coordinates 2, comma, 7.

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  
  .

This is a matching question that allows you to match elements from one list with those on another list.

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

Select one cell per row.

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

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.

This is a fill in the blank question that allows you to enter only numbers.

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

This is a multiple choice question that allows you to select only one option.

Triangle PRT and triangle QRS 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.

The figure shows triangle P, R, T, and triangle Q, R, S, in the coordinate plane. The horizontal axis is labeled, x, and the numbers negative 9, through 4, are indicated on it. The vertical axis is labeled, y, and the numbers negative 4, through 9, are indicated on it. The vertices of triangle P R T, are at the following coordinates. Vertex P is at negative 6, comma, negative 2. Vertex R is at 0, comma, 8. Vertex T is at 0, comma, negative 2. Point Q is graphed on segment P R, at the coordinates negative 3, comma, 3, and point S is graphed on segment R T, at the coordinates 0, comma 3, and line segment Q S, is drawn to form triangle Q R S.

Which statement about the slopes is true?

  1. A.
    The slopes of segment P R and segment Q R are equal because PTQS=SRTR.
  2. B.
    The slopes of segment P R and segment Q R are equal because TRTP=SRSQ.
  3. C.
    The slope of segment P R is less than the slope of segment Q R because PTQS<SRTR.
  4. D.
    The slope of segment P R is greater than the slope of segment Q R because TRTP>SRSQ.
i2

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

This is a question with 2 parts, including a fill in the blank question that allows you to enter only numbers.

Consider the following system of two equations. { 3 x − 4 y = − 24 3 x + 2 y = − 6

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

Enter the coordinates in the spaces provided.

( , )

This is a question with 2 parts, including a question with drop-down menus from which you must select an option to fill in the blank.

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

In the equation y=2.75x , 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.