# Full-Length Common Core 7 Math Practice Test-Answers and Explanations

Did you take the Common Core 7 Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## Common Core 7 Math Practice Test Answers and Explanations

1- Choice C is correct.
If the score of Mia was 90, then the score of Ava is 30. Since, the score of Emma was one and a half as that of Ava, therefore, the score of Emma is 1.5 × 30 = 45.

2- Choice A is correct
Write the ratio and solve for $$x$$.
$$\frac{60}{50}=\frac{5x+2}{10}⇒ 12=5x+2 ⇒12-2=5x⇒ x=\frac{10}{5}=2$$

3- Choice B is correct
Let $$x$$ be the number of students in the class. $$40\%$$ of $$x$$ = girls, $$25\%$$ of girls = tennis player,
Find $$25\%$$ of $$40\%$$. Then: $$25\%$$ of $$40\%=0.25×0.40=0.1=10\%$$ or $$\frac{10}{100}=\frac{1}{10}$$

4- Choice C is correct
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $$a^2+b^2=c^2$$

$$30^2+40^2=c^2⇒ 900+1600= c^2⇒2500= c^2⇒c=50$$

5- Choice A is correct
Write a proportion and solve for $$x$$.
$$\frac{12 \space Cans}{ 7.40}=\frac{30 \space Cans}{x }, x= \frac{7.40×30}{12} ⇒x=18.5$$

6- Choice D is correct
Use the volume of square pyramid formula.
$$V= \frac{1}{3} a^2 h ⇒V=\frac{1}{3} (12 \space m)^2×20 \space m ⇒ V=960 \space m^3$$

7- Choice C is correct
Let $$x$$ be the number of soft drinks for 240 guests. Write a proportional ratio to find $$x$$. $$\frac{6 \space soft \space drinks}{8 \space guests}=\frac{x}{240 \space guests}, x=\frac{240×6}{8}⇒x=180$$

8- Choice B is correct
Use the formula for Percent of Change: $$\frac{New \space Value-Old \space Value}{Old \space Value}×100\%, \frac{1.75-1.4}{1.4}×100\%=25\%$$

9- The answer is: $$-99$$
Use PEMDAS (order of operation):
$$[8×(-14)+15]-(10)+[4×6]÷3=[-122+15]-(10)+8=-97-10+8=-99$$

10- Choice D is correct
Simplify. $$5x^2 y(2xy^3)^4=5x^2 y(16x^4 y^{12} )=80x^6 y^{13}$$

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11- Choice C is correct
The distance between Jason and Joe is 14 miles. Jason running at 6 miles per hour and Joe is running at the speed of 8 miles per hour. Therefore, every hour the distance is 2 miles less.
14 ÷ 2 = 7

12- Choice A is correct.
Let x be the integer. Then: $$5x-9=101$$, Add 9 both sides: $$5x=110$$, Divide both sides by 5: $$x=22$$

13- Choice D is correct
Two and half times of 18,000 is 45,000. One fifth of them cancelled their tickets.
One sixth of $$45,000$$ equals $$9,000(\frac{1}{5} × 45000=9000)$$.
$$36,000(45000-9000=36000)$$ fans are attending this week

14- Choice C is correct
Write the numbers in order: $$25,12,13,18,22,36,22$$
Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 22.

15- Choice D is correct.
The question is: 615 is what percent of 820?
Use percent formula: $$part=\frac{percent}{100}×whole$$
$$615=\frac{percent}{100}×820 ⇒ 615=\frac{percent ×820}{100}⇒61,500=percent×820$$ ⇒
$$percent=\frac{61,500}{820}=75$$, $$615$$ is $$75\%$$ of $$820$$. Therefore, the discount is: $$100\%-75\%=25\%$$

16- The answer is $$22 \frac{1}{3}$$ miles.
Robert runs $$4 \frac{1}{3}$$ miles on Saturday and $$2(4 \frac{1}{3})$$ miles on Monday and Wednesday.
Robert wants to run a total of 35 miles this week. Therefore, subtract 4 $$\frac{1}{3}+2(4 \frac{1}{3})$$ from 35.
$$35-(4 \frac{1}{3}+2(4 \frac{1}{3} ))=35-12 \frac{2}{3}=22 \frac{1}{3}$$ miles

17- Choice B is correct
To find the area of the shaded region, find the difference of the area of two circles. $$S_1$$: the area of bigger circle. $$S_2$$: the area of the smaller circle). Use the area of circle formula. $$S=πr^2$$
$$S_1- S_2=π(6 \space cm)^2- π(4 \space cm)^2⇒S_1- S_2=36π \space cm^2-16π \space cm^2 ⇒ S_1- S_2 =20π \space cm^2$$

18- Choice A is correct
Use Pythagorean Theorem: $$a^2+b^2=c^2$$,
$$12^2+5^2=c^2⇒ 144+25= c^2 ⇒ c^2=169 ⇒c=13$$

19- Choice A is correct
Let L be the price of laptop and C be the price of computer. 4(L) =7(C) and L = $240 + C Therefore, 4($240 + C) =7C ⇒ $960 + 4C = 7C ⇒ C=$320

Jason needs an $$75\%$$ average to pass for five exams. Therefore, the sum of 5 exams must be at least $$5×75=375$$, The sum of 4 exams is: $$62+73+82+88=305$$.
The minimum score Jason can earn on his fifth and final test to pass is:
$$375-305=70$$

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21- Choice B is correct.
Let $$x$$ be the original price. If the price of a laptop is decreased by $$15\%$$ to \$425, then:
$$85\%$$ of $$x=425 ⇒ 0.85x=425 ⇒ x=425÷0.85=500$$

22- Choice C is correct.
The weight of 12 meters of this rope is: $$12×450 \space g=5,400 \space g$$
$$1 \space kg=1,000 \space g$$, therefore, $$5,400 \space g÷1,000=5.4 \space kg$$

23- Choice D is correct.
Only option D is correct. Other options don’t work in the equation.
$$(4x-2)x=42$$

24- Choice C is correct
Compare each score: In Algebra Joe scored 24 out of 32 in Algebra that it means $$75\%$$ of total mark. $$\frac{24}{32}= \frac{x}{100}⇒x=75$$
Joe scored 28 out of 40 in science that it means $$70\%$$ of total mark. $$\frac{28}{40}=\frac{x}{100} ⇒x=70$$
Joe scored 72 out of 90 in mathematics that it means $$80\%$$ of total mark. $$\frac{72}{90}=\frac{x}{100} ⇒x=80$$
Therefore, his score in mathematics is higher than his other scores.

25- Choice B is correct
To find the discount, multiply the number by ($$100\%$$-rate of discount).
Therefore, for the first discount we get: $$(D)(100\%-25\%)=(D)(0.75)=0.75$$
For increase of $$15\%$$: $$(0.75D)(100\%+15\%)=(0.75D)(1.15)=0.8625 D=86.25\%$$ of $$D$$

26- Choice B is correct
Write the numbers in order: $$42,21,15,28,43,34,26$$
Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 28.

27- Choice C is correct
The average speed of John is: $$210÷7=30$$ km, The average speed of Alice is: $$160÷5=32$$ km, Write the ratio and simplify. $$30∶ 32 ⇒ 15∶16$$

28- Choice D is correct
Use the formula for Percent of Change: $$\frac{New \space Value-Old \space Value}{Old \space Value)}×100\%$$
$$\frac{42-56}{56}×100\%=-25\%$$ (negative sign here means that the new price is less than old price).

29- Choice C is correct
Use the formula of areas of circles.
Area $$=πr^2 ⇒ 121π= πr^2 ⇒ 121= r^2⇒ r=11$$
Radius of the circle is 11. Now, use the circumference formula:
Circumference $$=2πr=2π(11)=22π$$

30- Choice B is correct.
Let $$x$$ be the number of balls. Then: $$\frac{1}{2} x+\frac{1}{5} x+\frac{1}{10} x+12=x$$
$$(\frac{1}{2}+\frac{1}{5}+\frac{1}{10})x+12=x, (\frac{8}{10})x+12=x,x=60$$, In the bag of small balls $$\frac{1}{5}$$ are white, then: $$\frac{60}{5}=12$$, There are 12 white balls in the bag.

31-Choice A is correct
William ate $$\frac{4}{5}$$ of $$10$$ parts of his pizza that it means $$8$$ parts out of $$10$$ parts $$(\frac{4}{5}$$ of 10 parts $$=x ⇒ x=8)$$ and left $$2$$ parts. Ella ate $$\frac{1}{2}$$ of 10 parts of her pizza that it means $$5$$ parts out of 10 parts $$(\frac{1}{2}$$ of 10 parts $$= x ⇒ x=5)$$ and left $$5$$ parts. Therefore, they ate $$(5+2)$$ parts out of $$(10+10)$$ parts of their pizza and left $$(5+2)$$ parts out of $$(10 + 10)$$ parts of their pizza. It means: $$\frac{7}{20}$$, After simplification we have: $$\frac{7}{20}$$

32-Choices D is correct.
The failing rate is $$14$$ out of $$50=\frac{14}{50}$$, Change the fraction to percent: $$\frac{14}{50} ×100\%=28\%$$
$$28$$ percent of students failed. Therefore, $$72$$ percent of students passed the exam.

33-Choice C is correct
$$x\%$$ of $$50$$ is $$6.2$$, then: $$0.50x=6.2 ⇒x=6.2÷0.50=12.4$$

Use the area of square formula. $$S=a^2 ⇒ 196= a^2 ⇒ a=14$$ One side of the square is 14 feet. Use the perimeter of square formula. $$P=4a ⇒ P=4(14) ⇒ P=56$$

35-Choice B is correct.
Input the points instead of $$x$$ and $$y$$ in the formula. Only option B works in the equation.$$6x-14=4y, 4(2)-14=4(-\frac{1}{2})⇒-2=-2$$

36-Choice B is correct.
The sum of supplement angles is 180. Let $$x$$ be that angle.
Therefore, $$x+4x=180$$
$$5x=180$$, divide both sides by 5: $$x=36$$

37-Choice B is correct.
Use simple interest formula: $$I=prt (I=interest,p=principal,r= rate,t=time) I=(16,000)(0.035)(3)=1,680$$

38-Choice B is correct.
Total number of way is $$6×6=36$$.favorable cases is $$(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$$. Thus probability that sum of two tice get $$7$$ is $$\frac{6}{36}=\frac{1}{6}$$

To find the number of possible outfit combinations, multiply number of options for each factor: $$3×8×7=168$$

40-Choice B is correct.
$$7\%$$ of the volume of the solution is alcohol. Let $$x$$ be the volume of the solution. Then: $$7\%$$ of $$x=35 \space ml ⇒ 0.07 x=35 ⇒ x=35 ÷ 0.07=500$$

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