8th grade math placement test

21 questions, one for each 8th grade math topic, with an answer key and worked steps. Mark the answers on this page to see which topics to practice. Free, with no sign-up.

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8th Grade Math Placement Test

21 questions, one for each 8th grade topic

Answer each question. Show your work in the space under it. If you don’t know how to do one, skip it and go on.

1.
Order from least to greatest: 3.2, √12, 2.9, π
2.
Simplify. Write the answer as a single power, then as a number when it is small enough.
x⁵ ÷ x²
3.
Write in scientific notation or standard form, or calculate.
(7 × 10⁴)(7 × 10⁸)
4.
Evaluate the root or solve the equation.
√169
5.
Solve the equation. If it has no solution or infinitely many, say so.
3(x + 4) − 2x = 16
6.
Solve the equation. Show your work.
8x + 11 = 6x + 5
7.
Solve the system. Write the solution as an ordered pair (x, y).
4x − 3y = 31 and x + 3y = −11
8.
Does the table show y as a function of x? Explain.
x 1 2 2 3
y 5 6 9 7
9.
For this pair, which function has the greater rate of change? Which has the greater initial value?
Function A: y = x + 5. Function B:
x 0 1 2 3
y 6 10 14 18
10.
Find the slope, or write the equation of the line.
Find the slope of the line through (1, −2) and (5, −4).
11.
Find the rate of change and the initial value, then write y = mx + b.
A line goes through (4, −9) and (5, −12).
12.
Is the function linear or nonlinear? Explain.
2x + y = 5
13.
Find the coordinates of the image point.
Translate (1, 4) 3 units right and 3 units down.
14.
A 5-foot pole casts a 8-foot shadow. At the same time, a tree casts a 48-foot shadow. How tall is the tree?
15.
Two parallel lines are cut by a transversal. Find the angle or the value of x.
Corresponding angles measure (6x + 3)° and 75°. Find x.
16.
Find the missing angle or the value of x.
The angles of a triangle measure 3x°, 4x° and 5x°. Find x and each angle.
17.
Use the Pythagorean theorem. Round to the nearest tenth if needed.
The legs of a right triangle are 6 ft and 8 ft. How long is the hypotenuse?
18.
Find the distance between the pair of points. Round to the nearest tenth if needed.
(2, −1) and (10, −16)
19.
Find the volume. Use 3.14 for π and round to the nearest tenth, or leave the answer in terms of π when asked.
A cylinder has a radius of 7 in and a height of 2 in.
20.
Use the scatter plot or trend line to answer the questions.
Describe the association between age of the tree (years) and height (feet).
21.
Use the two-way table to answer the question. Round percents to the nearest whole percent.
Fill in the missing numbers (?) in the table.
Soccer Basketball Total
Grade 7 37 ? 50
Grade 8 ? 36 47
Total 48 49 ?

x	1	2	2	3
y	5	6	9	7

x	0	1	2	3
y	6	10	14	18

	Soccer	Basketball	Total
Grade 7	37	?	50
Grade 8	?	36	47
Total	48	49	?

Check the answers

When your kid has finished, open the answers and mark each one. You’ll see the score and which topics to practice. Your marks stay on this page: nothing is sent to StudyWiz or saved.

Answer key: 8th grade math placement test

Each answer shows the topic it checks. Any question your kid missed points to a topic worth practicing.

1. 2.9, π, 3.2, √12
Rational and irrational numbers (8.NS.A.1)
π ≈ 3.14, √12 ≈ 3.46
2. x³
Exponent rules (8.EE.A.1)
Subtract the exponents: 5 − 2
3. 4.9 × 10¹³
Scientific notation (8.EE.A.4)
7 × 7 = 4910⁴ × 10⁸ = 10¹²49 × 10¹² = 4.9 × 10¹³
4. 13
Square and cube roots (8.EE.A.2)
13² = 169
5. x = 4
Linear equations (8.EE.C.7)
3x + 12 − 2x = 16x + 12 = 16x = 4
6. x = −3
Equations with variables on both sides (8.EE.C.7b)
2x + 11 = 52x = −6x = −3
7. (4, −5)
Systems of equations (8.EE.C.8)
Check: 4(4) − 3(−5) = 31and 4 + 3(−5) = −11
8. No. x = 2 has two y-values, 6 and 9.
Functions (8.F.A.1)
9. Greater rate of change: B (4 vs 1). Greater initial value: B (6 vs 5).
Comparing functions (8.F.A.2)
B: y goes up by 4 for each 1 of x, and y = 6 when x = 0
10. −12
Slope and linear functions (8.EE.B.6)
(−4 − (−2)) ÷ (5 − 1) = −2 ÷ 4= −12
11. Rate −3, initial value 3: y = −3x + 3
Rate of change and initial value (8.F.B.4)
Rate: (−12 − (−9)) ÷ (5 − 4) = −3b = −9 − (−3)(4) = 3
12. Linear. It can be written y = −2x + 5.
Linear and nonlinear functions (8.F.A.3)
13. (4, 1)
Transformations (8.G.A.3)
(1 + 3, 4 − 3)
14. 30 feet
Congruence and similarity (8.G.A.4)
The triangles are similar: 58 = t48t = 5 × 6 = 30
15. x = 12
Angles and parallel lines (8.G.A.5)
6x + 3 = 75x = 12
16. x = 15; 45°, 60° and 75°
Triangle angle sum (8.G.A.5)
12x = 180x = 15
17. 10 ft
Pythagorean theorem (8.G.B.7)
6² + 8² = 36 + 64 = 100√100 = 10
18. 17 units
Distance on the coordinate plane (8.G.B.8)
Horizontal 8, vertical 15√(8² + 15²) = √289 = 17
19. ≈ 307.7 in³
Volume of cylinders, cones and spheres (8.G.C.9)
V = 3.14 × 7² × 2 = 3.14 × 98
20. Positive linear association: as age of the tree (years) goes up, height (feet) tends to go up.
Scatter plots and trend lines (8.SP.A.3)
21. Grade 7 and Basketball: 13. Grade 8 and Soccer: 11. Grand total: 97
Two-way tables (8.SP.A.4)
50 − 37 = 1348 − 37 = 1150 + 47 = 97

How to give the test

Print it, or put it on a screen and have your kid write the answers on paper.
Let them work on their own. Skipping a question is fine: it simply counts as not yet.
Allow up to an hour. Two shorter sittings work too.
Then open the answers above and mark each one. The checker lists the topics to practice.

What the score means

One question per topic makes this a quick check, not a final grade. A missed question means a topic is worth a look, not that your kid can’t do it. As a rough guide:

80% or more: ready for high school math. Review any topics they missed.
50% to 79%: nearly there. Practice the missed topics, then take a new version of the test.
Under 50%: a lot to review. Try the 7th grade test first, to see which earlier skills need work.

What the test covers

One question from each 8th grade math topic, grouped the way schools teach them. Each topic has its own free worksheet for practice.

The number system (8.NS)

Rational and irrational numbers

Expressions and equations (8.EE)

Functions (8.F)

Geometry (8.G)

Statistics and probability (8.SP)

Practice what the test finds

Every topic has a free printable worksheet with an answer key, and you can make new problems any time. The free 8th grade math formula sheet has every formula from the grade, each with an example. On StudyWiz, your kid can also take 5-question online quizzes on any topic, checked as they go, and get a hint for each step of a homework problem instead of the answer.

Other grades

6th grade placement test and 7th grade placement test. Or see which test to start with.

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