FREE 8th Grade Common Core Math Practice Test

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Common Core Math Exercise Book for Grade 8 Student Workbook and Two Realistic Common Core Math Tests

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10 Sample 8th Grade Common Core Math Practice Questions

1- What is the slope of a line that is perpendicular to the line
\(4x-2y=12\)?

A. 2

B. 1

C. \(-2\)

D. \(-\frac{1}{2}\)

2- The diagonal of a rectangle is 10 inches long and the height of the rectangle is 8 inches. What is the perimeter of the rectangle in inches?

3- You can buy 5 cans of green beans at a supermarket for $3.40. How much does it cost to buy 35 cans of green beans?

A. $17

B. $23.80

C. $34.00

D. $119

4- Which of the following is the solution of the following inequality?
\(2x+4>11x-12.5-3.5x\)

A. \(x<3\)

B. \(x>3\)

C. \(x≤4\)

D. \(x≥4\)

5- What is the perimeter of a square that has an area of 595.36 feet?

6- A tree 32 feet tall casts a shadow 12 feet long. Jack is 6 feet tall. How long is Jack’s shadow?

A. 2.25 ft

B. 4 ft

C. 4.25 ft

D. 8 ft

7- The perimeter of the trapezoid below is 54 cm. What is its area?

8- Which graph does not represent \(y\) as a function of \(x\)?

A.

B.

C.

D.

9- Which of the following is equivalent to \(13<-3x-2<22\)?

A. \( -8 < x < -5\)

B. \( 5 < x < 8\)

C. \(\frac{11}{3} < x < \frac{20}{3}\)

D. \(\frac{-20}{3} < x < \frac{-11}{3}\)

10- In a certain bookshelf of a library, there are 35 biology books, 95 history books, and 80 language books. What is the ratio of the number of biology books to the total number of books in this bookshelf?

A. \(\frac{1}{4}\)

B. \(\frac{1}{6}\)

C. \(\frac{2}{7}\)

D. \(\frac{3}{8}\)

11- A bank is offering \(3.5\%\) simple interest on a savings account. If you deposit $12,000, how much interest will you earn in two years?

A. $420

B. $840

C. $4200

D. $8400

12- The area of a circle is \(64 π\). What is the circumference of the circle?

A. \(8 π\)

B. \(16 π\)

C. \(32 π\)

D. \(64 π\)

13- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. \((200) (0.70)\)

B. \((200) – 200 (0.30)\)

C. \((200) (0.15) – (200) (0.15)\)

D. \((200) (0.85) (0.85)\)

14- Joe scored 20 out of 25 marks in Algebra, 30 out of 40 marks in science and 68 out of 80 marks in mathematics. In which subject his percentage of marks is best?

A. Algebra

B. Science

C. Mathematics

D. Algebra and Science

15- What is the volume of the following triangular prism?

16- The marked price of a computer is D dollar. Its price decreased by \(20\%\) in January and later increased by \(10\%\) in February. What is the final price of the computer in D dollar?

A. 0.80 D

B. 0.88 D

C. 0.90 D

D. 1.20 D

17- Triangle ABC is graphed on a coordinate grid with vertices at A \((–3, –2)\), B \((–1, 4)\) and C \((7, 9)\). Triangle ABC is reflected over\( x\) axes to create triangle A’ B’ C’.
Which order pair represents the coordinate of C’?

A. \((7, 9)\)

B. \((–7, –9)\)

C. \((–7, 9)\)

D. \((7, –9)\)

18-

What’s the maximum ratio of woman to man in the four cities?

A. 0.98

B. 0.97

C. 0.96

D. 0.95

19-

What’s the ratio of percentage of men in city A to percentage of women in city C?

A. 0.9

B. 0.95

C. 1

D. 1.05

20-

A container holds 3.5 gallons of water when it is \(\frac{7}{24}\) full. How many gallons of water does the container hold when it’s full?

A. 8

B. 12

C. 16

D. 20

Best 8th Grade Common Core Math Prep Resource for 2026

Answers:

2- 28

Let\( x\) be the width of the rectangle. Use Pythagorean Theorem:
\(a^2 + b^2 = c^2\)
\(x^2 + 8^2 = 10^2 {\Rightarrow} x^2 + 64 = 100 {\Rightarrow} x^2 = 100 – 64 = 36 ⇒ x = 6\)
Perimeter of the rectangle =\( 2 (length + width) = 2 (8 + 6) = 2 (14) = 28\)

3- B
Let \(x\) be the number of cans. Write the proportion and solve for \(x\).
\(\frac{5 \space cans}{$ 3.40}=\frac{35 \space cans}{x}\)
\(x =\frac{3.40×35}{5}⇒x=$23.8\)

4- A
\(2x+4>11x-12.5-3.5x\)→ Combine like terms:
\(2x+4>7.5x-12.5→\) Subtract \(2x\) from both sides: \(4>5.5x-12.5\)
Add 12.5 both sides of the inequality.
\(16.5>5.5x, \)
Divide both sides by 5.5.
\(\frac{16.5}{5}>x→x<3\)

5- 97.6
Area of a square: \(S = a^2 ⇒ 595.36 = a^2 ⇒ a = 24.4\)
Perimeter of a square: \(P = 4a ⇒ P = 4 × 24.4 ⇒ P = 97.6\)

6- A
Write the proportion and solve for the missing number.
\(\frac{32}{12}=\frac{6}{x}→ 32x=6×12=72 \)
\(32x=72→x=\frac{72}{32}=2.25\)

7- 130
The perimeter of the trapezoid is 54 cm.
Therefore, the missing side (high) is \( 54 – 18 – 12 – 14 = 10\)
Area of a trapezoid: \(A = \frac{1}{2} h (b_1 + b_2) = \frac{1}{2} (10) (12 + 14) = 130\)

8- C
A graph represents \(y\) as a function of \(x\) if
\(x_1=x_2→y_1=y_2 \)
In choice C, for each \(x\), we have two different values for \(y\).

9- A
\(13<-3x-2<22\)→ Add 2 to all sides. \(13+2<-3x-2+2<22+2\)
\(→15<-3x<24\)→ Divide all sides by \(- 3\). (Remember that when you divide all sides of an inequality by a negative number, the inequality sing will be swapped. < becomes >)
\(\frac{15}{-3} > \frac{-3x}{3} >\frac{24}{-3} \)
\(-8 < x < -5\)

10- B
Number of biology book: 35
Total number of books; \(35+95+80=210\)
The ratio of the number of biology books to the total number of books is: \(\frac{35}{210}=\frac{1}{6}\)

11- B
Use simple interest formula:
I=prt
(I = interest, p = principal, r = rate, t = time)
\(I=(12000)(0.035)(2)=840\)

12- B
Use the formula for area of circles.
Area \(= πr^2 ⇒ 64 π = πr^2 ⇒ 64 = r^2 ⇒ r = 8\)
Radius of the circle is 8. Now, use the circumference formula:
Circumference\( = 2πr = 2π (8) = 16 π\)

13- D
To find the discount, multiply the number by (\(100\% -\) rate of discount).
Therefore, for the first discount we get: \((200) (100\% – 15\%) = (200) (0.85)\)
For the next \(15\%\) discount: \((200) (0.85) (0.85)\)

14- C
Compare each mark:
In Algebra Joe scored 20 out of 25 in Algebra. It means Joe scored \(80\%\) of the total mark.
\(\frac{20}{25}=\frac{x}{100}⇒x= 80%\)
Joe scored 30 out of 40 in science. It means Joe scored \(75\%\) of the total mark.
\(\frac{30}{40}=\frac{x}{100}⇒x= 75%\)
Joe scored 68 out of 80 in mathematic that it means \(85\%\) of total mark.
\(\frac{68}{80}=\frac{x}{100}⇒x= 85%\)
Therefore, his score in mathematic is higher than his other scores.

15- 12
Use the volume of the triangular prism formula.
\(V =\frac{1}{2} (length) (base) (high)\)
\(V = \frac{1}{2} × 4 × 3 × 2 ⇒ V = 12 \space m^3\)

16- B
To find the discount, multiply the price by (\(100\% -\) rate of discount).
Therefore, for the first discount we get: \((D) (100\% – 20\%) = (D) (0.80) = 0.80 D\)
To increase the \(10 \%: (0.80 D) (100\% + 10\%) = (0.85 D) (1.10) = 0.88 D = 88\%\) of \(D\)

17- D
When a point is reflected over \(x\) axes, the \((y)\) coordinate of that point changes to \((-y)\) while its \(x\) coordinate remains the same.
\(C (7, 9) → C’ (7, -9)\)

18- B
Ratio of women to men in city A: \(\frac{570}{600}=0.95\)
Ratio of women to men in city B: \(\frac{291}{300}=0.97 \)
Ratio of women to men in city C: \(\frac{665}{700}=0.95\)
Ratio of women to men in city D: \(\frac{528}{550}=0.96 \)

19- D
Percentage of men in city \(A = \frac{600}{1170}×100=51.28% \)
Percentage of women in city \(C = \frac{665}{1365}×100=48.72% \)
Percentage of men in city \(A\) to percentage of women in city \(C =\frac{51.28}{48.72}=1.05 \)

20- B
let \(x\) be the number of gallons of water the container holds when it is full.
Then;\(\frac{7}{24}x=3.5→x=\frac{24×3.5}{7}=12\)

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Frequently Asked Questions

Is 8th grade math hard?

8th grade math feels harder for many students because it moves from arithmetic toward algebra. New ideas such as functions, systems of equations, irrational numbers and the Pythagorean Theorem all arrive in one year. It gets easier with steady practice: master solving linear equations first, since most other 8th grade topics, including slope and systems, build on that skill.

What math is 8th grade?

Common Core 8th grade math covers five areas: the number system (rational and irrational numbers), expressions and equations (exponents, scientific notation, linear equations and systems), functions, geometry (transformations, the Pythagorean Theorem and volume of cylinders, cones and spheres) and statistics (scatter plots and lines of best fit). In many schools it serves as the bridge to Algebra 1.

Are there free grade 8 math exams for practice?

Yes, and a full practice test is a great way to check readiness. Take it under test-like conditions, then grade it the same day. For example, a line perpendicular to 4x − 2y = 12 has slope −1/2, because the original line is y = 2x − 6 with slope 2. Note which strand each missed question comes from and review that strand first.

Where can I find free grade 8 math worksheets?

Free grade 8 math worksheets are easy to find, and the most useful ones focus on one skill at a time, such as scientific notation or the Pythagorean Theorem. A good routine is to take a practice test first, then pick worksheets for the topics you missed. If a right triangle with legs 6 and 8 gives you trouble, practice until finding c = 10 feels automatic.

Related Lessons You May Like

• How to solve multi-step equations
• How to find the slope of a line
• How to graph linear equations
• How to use the Pythagorean Theorem
• How to find the volume of cylinders and spheres

If you want a workbook on this topic, Mastering Grade 8 Math (resource currently unavailable) covers every standard. Pre-Algebra for Beginners covers prerequisites.