Between which two whole numbers does √90 lie?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.NS.2
How many solutions does 4(x − 2) = 4x − 8 have?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.7
The lines y = 3x − 2 and y = −x + 10 cross at one point. What is that point?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.8
One town has about 6 × 10⁵ people. Another has about 3 × 10³. About how many times as many people does the first town have?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.3
Solve 3x + 5 = x + 17.North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.7
What are the solutions of x² = 144?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.2
What is (2 × 10³) × (4 × 10⁵)?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.4
Show all 50 questions (43 more)
The Number System, Expressions and Equations, continued
What is the cube root of 125?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.2
What is the value of 4⁻²?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.1
Which expression is equivalent to 7² × 7⁵?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.1
Which is 4,500,000 written in scientific notation?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.EE.3
Which is the best estimate of √30 to the nearest tenth?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.NS.2
Which of these four numbers is irrational?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.NS.1
Functions 15
A candle is 20 cm tall and burns down 2 cm each hour. What is the slope of the line for its height over time?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.4
A graph shows the distance of a bus from the depot over time. The line rises, then is flat, then rises again. What does the flat part show?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.5
A line has a slope of −3 and crosses the y-axis at 6. What is y when x = 4?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.4
A line passes through (0, 3) and (2, 11). What is its equation?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.4
A swim club charges a $40 joining fee plus $15 a month. Which equation gives the total cost y after x months?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.4
A table has x-values 1, 2, 3, 4 and y-values 3, 7, 11, 15. Is the relationship linear?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.3
A table pairs each input x with an output y. Which two rows would show that the table is NOT a function?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.1
Each student in a class is paired with his or her age in years. Is age a function of student?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.1
Function A is y = 3x + 1. Function B is a line through (0, 2) and (1, 7). Which has the greater rate of change?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.2
In y = 9x + 25, y is the cost in dollars of renting a bike for x hours. What does the 25 stand for?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.4
Plan A costs y = 6x dollars for x visits. Plan B costs $20 plus $2 a visit. For 4 visits, which plan costs less, and by how much?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.2
What is the slope of the line through (1, 2) and (4, 14)?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.4
Which equation is a linear function?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.3
Which of these lists of ordered pairs is a function?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.1
Which situation gives a graph that falls from left to right?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.F.5
Geometry 13
A 25-foot ladder leans on a wall with its base 7 feet from the wall. How high up the wall does it reach?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.7
A cone and a cylinder have the same base and the same height. The cylinder holds 60 cubic cm. How much does the cone hold?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.9
A cylinder has a radius of 5 cm and a height of 6 cm. What is its volume, in terms of π?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.9
A figure is dilated by a scale factor of 2 and then translated. How is the image related to the original?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.4
A figure is transformed, and its image is similar to it but NOT congruent. Which transformation was used?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.2
A triangle has a vertex at (2, 6). The triangle is dilated about the origin by a scale factor of 1/2. Where is that vertex now?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.3
An exterior angle of a triangle measures 120°. One of the two remote interior angles is 50°. What is the other?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.5
In triangle RST, angle R measures 41° and angle S measures 83°. What is the measure of angle T?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.5
The legs of a right triangle are 16 cm and 30 cm long. How long is the hypotenuse?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.7
Point (5, 2) is rotated 90° counterclockwise about the origin. Where is its image?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.3
Point (6, −5) is reflected across the x-axis. Where is its image?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.3
What is the distance between (2, 1) and (8, 9)?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.8
Which three side lengths form a right triangle?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.G.6
Statistics and Probability 9
A line of fit for a savings account is y = 25x + 100, where y is dollars saved after x months. What does the slope tell you?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.3
A line of fit for plant height is y = 2x + 5, where y is the height in cm after x weeks. What height does it predict at week 6?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.3
A line of fit for the cost of a taxi ride is y = 2.5x + 4, with y in dollars and x in miles. What does the 4 mean?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.3
A scatter plot compares hours of practice with free throws made. Most points rise together, but one point sits far below the rest. What is that point called?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.1
A two-way table shows 40 students who play a sport and 60 who do not. Of the 40 who play a sport, 30 also play an instrument. What is the relative frequency of instrument players among those who play a sport?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.4
In a survey, 80% of students who walk to school eat breakfast, and 78% of students who ride the bus eat breakfast. What does this suggest?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.4
Of 50 seventh graders, 20 have a pet. Of 50 eighth graders, 35 have a pet. How many of the 100 students have no pet?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.4
On a scatter plot, the points fall from the upper left to the lower right. What kind of association is this?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.1
Which line fits a scatter plot best?North Carolina Standard Course of Study for Mathematics (adopted June 2017), grade 8, standard NC.8.SP.2
Unofficial practice for North Carolina's 8th grade mathematics End-of-Grade (EOG) test. The questions are our own, written from the state's grade 8 standards, and none is from a released form. Not affiliated with the North Carolina Department of Public Instruction.
Read the full guide
What the 8th grade math EOG covers
The state's test specifications weight four domains. Functions is the largest, 28 to 32 percent: what makes a rule a function, slope, y = mx + b and reading graphs. Geometry is 24 to 28 percent: transformations, angle relationships, the Pythagorean Theorem and volume. The Number System with Expressions and Equations is also 24 to 28 percent: irrational numbers, exponents, scientific notation, multi-step equations and systems. Statistics and Probability is 16 to 20 percent: scatter plots, lines of fit and two-way tables.
Using it as an 8th grade math EOG study guide
Functions and geometry are more than half of the test: start there. Under every answer are the steps and the standard it practices, such as NC.8.G.7 for the Pythagorean Theorem. List the standards you miss.
Slope is the change in y divided by the change in x. Subtract in the same order on top and bottom.
Questions and answers
How many questions are on the 8th grade math EOG?
53 in all. 45 are operational items that count: 15 with the calculator inactive and 30 with it active. The other 8 are field test items that do not affect the score. Every item is worth one point.
What calculator can you use on the 8th grade math EOG?
For the calculator active section, the state requires a four-function calculator with square root, power and pi keys in grades 6 to 8. The online grade 8 test has a scientific and a graphing calculator built in.
How long does the 8th grade math EOG take?
The state estimates about two hours for most students and allows up to three. A student with a documented accommodation, such as scheduled extended time, may have more.
Is there a released 8th grade math EOG test?
Yes. North Carolina posts one released grade 8 mathematics form on its End-of-Grade page, and the box under the questions links to that page. The 50 questions here are separate and unofficial.