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Grade 8 Mathematics Diagnostic

NC EOG-Aligned Readiness Assessment

📚 Mathematics 🎓 Grade 8 ⏱️ 65 minutes

Learning Objectives

  • Work with irrational numbers, exponents, roots, scientific notation, and linear equations and systems.

  • Define, compare, and model linear functions, interpreting rate of change and initial value.

  • Apply transformations, similarity, angle relationships, the Pythagorean Theorem, and volume formulas.

  • Construct and interpret scatter plots, linear models, and two-way tables.

Progress 5 sections
1

Directions

~3 minutes

This diagnostic screens all four reporting areas for Grade 8 math. Item counts follow the NC End-of-Grade weighting, so functions and geometry carry the most items, followed by the combined number-system-and-equations area and statistics. Read each question carefully and use scratch paper.

2

Number System & Expressions/Equations

~16 minutes
Question 1

Which of these numbers is irrational?

Question 2

Between which two whole numbers does the square root of 50 lie?

Question 3

Which expression is equivalent to $3^{2}$ multiplied by $3^{4}$?

Question 4

What is the positive solution of $x^{2} = 49$?

Question 5

Express 0.00045 in scientific notation.

Question 6

Solve $3x + 4 = x + 12$.

Question 7

How many solutions does the equation $2x + 3 = 2x + 5$ have?

Question 8

The solution to a system of two linear equations on a graph is found at which location?

3

Functions

~18 minutes
Graph of y = 2x minus 3
A coordinate graph of a straight line that crosses the y-axis at -3 and rises 2 units for every 1 unit to the right, passing through (0,-3) and (3,3)....

Function table.

xy
01
14
27
| 3 | 10 |

Question 9

Which set of ordered pairs represents a function?

Question 10

A function assigns to each input how many outputs?

Question 11

Which equation represents a linear function?

Question 12

Use the graph of $y = 2x - 3$ shown. What are the slope and the y-intercept?

Question 13

Use the function table shown. What is the rate of change?

Question 14

A taxi charges $C = 3d + 5$ dollars for a trip of d miles. What does the 5 represent?

Question 15

In the taxi equation $C = 3d + 5$, what does the 3 represent?

Question 16

Linear function A is $y = 4x + 1$. Linear function B has a slope of 2. Which has the greater rate of change?

Question 17

What is the slope of the line passing through the points (2, 3) and (4, 7)?

Question 18

A line goes downward from left to right. Its slope is which of the following?

4

Geometry

~16 minutes
Translation of a triangle
A coordinate grid showing a pre-image triangle with vertices (1,1), (3,1), and (1,4), and its image after sliding 4 units right and 2 units up to (5,3), (7,3), and (5,6)....
Right triangle with legs 6 and 8 cm
A right triangle with a vertical leg of 6 centimeters, a horizontal leg of 8 centimeters, a right angle between them, and an unknown hypotenuse labeled c....
Parallel lines cut by a transversal
Two parallel lines m and n cut by a slanted transversal. The marked angle at the upper intersection is 110 degrees, and the corresponding angle at the lower intersection is labeled x degrees....
Cylinder with radius 3 cm and height 10 cm
A cylinder drawn with a top ellipse, vertical sides, and a curved base. The radius is labeled 3 and the height is labeled 10....
Question 19

Use the figure shown. Triangle ABC has vertex A at (1, 1). After the translation $(x + 4, y + 2)$, what are the coordinates of the image of A?

Question 20

Two figures are similar with a scale factor of 3. A side that is 4 cm on the smaller figure corresponds to what length on the larger figure?

Question 21

Two angles of a triangle measure 40 degrees and 75 degrees. What is the measure of the third angle?

Question 22

Use the parallel lines cut by a transversal shown. If one angle is 110 degrees, what is the measure of its corresponding angle x?

Question 23

Use the right triangle shown with legs of 6 cm and 8 cm. What is the length of the hypotenuse?

Question 24

A ladder leans against a wall. Its base is 5 ft from the wall and it reaches 12 ft up the wall. How long is the ladder?

Question 25

Use the cylinder shown with radius 3 cm and height 10 cm. What is its volume? Use 3.14 for $\pi$.

Question 26

Match each solid with its volume formula.

Cylinder
Cone
Sphere
Rectangular prism
5

Statistics & Probability

~12 minutes
Scatter plot with positive association
A scatter plot of eight points that rise from lower left to upper right, showing a positive linear association, with a line of best fit drawn through them....

Two-way frequency table: students and sports.

Likes sportsDoes notTotal
Boys18624
Girls121426
| Total | 30 | 20 | 50 |

Question 27

Use the scatter plot shown. What type of association do the data show?

Question 28

In a scatter plot, a point that lies far away from the overall pattern is called a(n):

Question 29

What is the purpose of a line of best fit on a scatter plot?

Question 30

A linear model for a plant's height is $h = 2d + 5$, where d is the number of days. What does the slope of 2 mean?

Question 31

Use the two-way table shown. How many girls like sports?

Question 32

Use the two-way table shown. What fraction of the boys like sports?