# 8th Grade Common Core Math FREE Sample Practice Questions

Preparing your student for the 8th Grade Common Core Math test? To succeed on the Common Core Math test, students need to practice as many real Common Core Math questions as possible.  There’s nothing like working on Common Core Math sample questions to measure your student’s exam readiness and put him/her more at ease when taking the Common Core Math test. The sample math questions you’ll find here are brief samples designed to give students the insights they need to be as prepared as possible for their Common Core Math test.

Check out our sample Common Core Math practice questions to find out what areas your student needs to practice more before taking the Common Core Math test!

Start preparing your student for the 2021 Common Core Math test with our free sample practice questions. Also, make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions students need to practice.

## 10 Sample 8th Grade Common Core Math Practice Questions

1- Five years ago, Amy was three times as old as Mike was. If Mike is 10 years old now, how old is Amy?

A. 4

B. 8

C. 12

D. 20

2- What is the length of AB in the following figure if AE$$=4$$, CD$$=6$$ and AC$$=12$$?
$$\img {https://appmanager.effortlessmath.com/public/images/questions/test2121212121212.JPG }$$

A. 3.8

B. 4.8

C. 7.2

D. 24

3- If a gas tank can hold 25 gallons, how many gallons does it contain when it is $$\frac{2}{5}$$ full?

A. 50

B. 125

C. 62.5

D. 10

4- In the xy-plane, the points (4,3) and (3,2) are on line A. Which of the following equations of lines is parallel to line A?

A. $$y=3x$$

B. $$y=\frac{x}{2}$$

C. $$y=2x$$

D. $$y=x$$

5- If $$x$$ is directly proportional to the square of $$y$$, and $$y=2$$ when $$x=12$$, then when $$x=75 y=$$ ?

A. $$\frac{1}{5}$$

B. 1

C. 5

D. 12

6- Jack earns $616 for his first 44 hours of work in a week and is then paid 1.5 times his regular hourly rate for any additional hours. This week, Jack needs$826 to pay his rent, bills and other expenses. How many hours must he work to make enough money in this week?

A. 40

B. 48

C. 53

D. 54

7-
$$\img {https://appmanager.effortlessmath.com/public/images/questions/test252525252525252525252525.JPG }$$
If a is the mean (average) of the number of cities in each pollution type category, b is the mode, and c is the median of the number of cities in each pollution type category, then which of the following must be true?

A. $$a<b<c$$

B. $$b<a<c$$

C. $$a=c$$

D. $$b<c=a$$

8-
$$\img {https://appmanager.effortlessmath.com/public/images/questions/test252525252525252525252525.JPG }$$
What percent of cities are in the type of pollution A, C, and E respectively?

A. $$60\%, 40\%, 90\%$$

B. $$30\%, 40\%, 90\%$$

C. $$30\%, 40\%, 60\%$$

D. $$40\%, 60\%, 90\%$$

9-
$$\img {https://appmanager.effortlessmath.com/public/images/questions/test252525252525252525252525.JPG }$$
How many cities should be added to type of pollutions B until the ratio of cities in type of pollution B to cities in type of pollution E will be 0.625?

A. 2

B. 3

C. 4

D. 5

10- In the following right triangle, if the sides AB and AC become twice longer, what will be the ratio of the perimeter of the triangle to its area?
$$\img {https://appmanager.effortlessmath.com/public/images/questions/test3030303030303030.JPG }$$

A. $$\frac{1}{2}$$

B. 2

C. $$\frac{1}{3}$$

D. 3

## Answers:

1- D
Five years ago, Amy was three times as old as Mike. Mike is 10 years now. Therefore, 5 years ago Mike was 5 years.
Five years ago, Amy was:
$$A=3×5=15$$
Now Amy is 20 years old:
$$15 + 5 = 20$$

2- B
Two triangles $$∆$$BAE and $$∆$$BCD are similar. Then:
$$\frac{AE}{CD}=\frac{AB}{BC}=\frac{4}{6}=\frac{x}{12}$$
$$→48-4x=6x→10x=48→x=4.8$$

3- D
$$\frac{2}{5}×25=\frac{50}{5}=10$$

4- D
The slop of line A is:
m $$= \frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{4-3}=1$$
Parallel lines have the same slope and only choice D $$(y=x)$$ has slope of 1.

5- C
$$x$$ is directly proportional to the square of $$y$$. Then:
$$x=cy^2$$
$$12=c(2)^2→12=4c→c=\frac{12}{4}=3$$
The relationship between $$x$$ and $$y$$ is:
$$x=3y^2$$
$$x=75$$
$$75=3y^2→y^2=\frac{75}{3}=25→y=5$$

6- D
he amount of money that jack earns for one hour: $$\frac{616}{44}=14$$
Number of additional hours that he work to make enough money is: $$\frac{826-616}{1.5×14}=10$$
Number of total hours is: $$44+10=54$$

7- C
Let’s find the mean (average), mode and median of the number of cities for each type of pollution.
Number of cities for each type of pollution: $$6, 3, 4, 9, 8$$
Mean $$= \frac{sum \space of \space terms}{number \space of \space terms}=\frac{6+3+4+9+8}{5}=6$$
Median is the number in the middle. To find median, first list numbers in order from smallest to largest.
$$3, 4, 6, 8, 9$$
Median of the data is 6.
Mode is the number which appears most often in a set of numbers. Therefore, there is no mode in the set of numbers.
Median $$=$$ Mean, then, $$a=c$$

8- A
Percent of cities in the type of pollution A:
$$\frac{6}{10} × 100=60\%$$
Percent of cities in the type of pollution C:
$$\frac{4}{10} × 100 = 40\%$$
Percent of cities in the type of pollution E:
$$\frac{9}{10}× 100 = 90\%$$

9- A
Let the number of cities should be added to type of pollutions B be $$x$$. Then:
$$\frac{x + 3}{8}=0.625→x+3=8×0.625→x+3=5→x=2$$

10- A
AB$$=12$$ And AC$$=5$$
BC$$=\sqrt{(12^2+5^2 )} = \sqrt{(144+25)} = \sqrt{169}=13$$
Perimeter $$=5+12+13=30$$
Area $$=\frac{5×12}{2}=5×6=30$$
In this case, the ratio of the perimeter of the triangle to its area is:
$$\frac{30}{30}= 1$$
If the sides AB and AC become twice longer, then:
AB$$=24$$ And AC$$=10$$
BC$$=\sqrt{(24^2+10^2 )} = \sqrt{(576+100)} = \sqrt{676} = 26$$
Perimeter $$=26+24+10=60$$
Area $$=\frac{10×24}{2}=10×12=120$$
In this case the ratio of the perimeter of the triangle to its area is:
$$\frac{60}{120}=\frac{1}{2}$$

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