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

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Expand All Official Practice Test

This is a multiple choice question that allows you to select several options.

Consider the function defined by y=2x−5.

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

Select all that apply.

  1. A.
    The coefficient of x is greater than 1.
  2. B.
    The function has a constant slope of 2.
  3. C.
    The function has a negative y –intercept.
  4. D.
    The graph of the function is a straight line.
  5. E.
    The equation is written in the form y=mx+b.
i2

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

This is a question with 2 parts, including a test question that allows you to enter extended text in your response.

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 MNP and QRT .

The figure presents a line, triangle M N P, and triangle Q R T, in the x y plane, with the origin labeled, O. The numbers negative 8 through 8, in increments of 2 are indicated on both axes. The line passes through the points with coordinates negative 9, comma, 7, and 9, comma, negative 5. The two triangles are on the left side of the line, with the line forming one side of each triangle. In triangle M N P, vertex M has coordinates negative 6, comma, 3; vertex N, has coordinates negative 6, comma 5; and vertex P, has coordinates negative 3, comma 3. Side N P, lies on the line. In triangle Q R T, vertex Q has coordinates 3, comma, negative 5; vertex are, has coordinates 3, comma, negative 1; and vertex T, has coordinates 9, comma, negative 5. Side R T, lies on the line.

Part A

Linda claimed that the slope of line segment P R is 64 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 MNP and QRT 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

There is no alt-text. (37 files were searched.)

This is a test question that allows you to enter extended text in your response.

The vertices of triangle P Q R are P(6,1),Q(3,5), and R(11,11). The length of segment PR is 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

There is no alt-text. (37 files were searched.)

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.

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

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. { y=8−x 000 8x+4y=56

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

  1. A.
    8x+4(8−x)=56
  2. B.
    8(8−x)+4y=56
  3. C.
    8x+4y−56=8−x
  4. D.
    8x+4y=56+8−x
i1

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

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

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

The figure shows parallel horizontal lines, h and k, with line h being above line k. Two transversals are drawn, intersecting lines h and k. One transversal moves upward, and to the right, from line k to line h. The angle formed with line k to the right of the transversal, is labeled angle R, and the angle formed with line h, to the left of the transversal, is labeled angle S. The other transversal moves upward, and to the left, from line k to the same point where the first transversal intersects line h. The angle formed with line h, to the right of this transversal, is labeled 60 degrees, and the angle formed between the two transversals at the intersection with line h, is labeled, 40 degrees.

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

Which statement about the claim is true?

  1. A.
    The claim is incorrect because the measure of angle S equals 180 degrees, divided by 3 equals 60 degrees, and since angle R and angle S are corresponding angles, the measure of angle R equals 60 degrees.
  2. B.
    The claim is incorrect because the measure of angle S equals 60 degrees plus 40 degrees, which equals 100 degrees, and since angle R and angle S are alternate interior angles, the measure of angle R equals 100 degrees
  3. C.
    The claim is correct because the measure of angle S equals open parenthesis 360 degrees divided by 3 close parenthesis minus 40 degrees equals 80 degrees, and since angle R and angle S are corresponding angles, the measure of angle R equals 80 degrees.
  4. D.
    The claim is correct because the measure of angle S equals 180 degrees minus open parenthesis 40 degrees plus 60 degrees close parenthesis equals 80 degrees. and since angle R and angle S are alternate interior angles, the measure of angle R equals 80 degrees.
i4

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

This is a question with 4 parts, including a question with drop-down menus from which you must select an option to fill in the blank.

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

The figure shows the graph of a line on the coordinate plane. The numbers negative 9, through 9, are indicated on the x and y axes. The line moves downward, and to the right, through quadrants 2, 1, and 4. The line passes through the point with coordinates 0, comma, 7, and the point with coordinates 2, comma, 0.

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.