Full-Length MCAS 7 Math Practice Test-Answers and Explanations

Full-Length MCAS 7 Math Practice Test-Answers and Explanations

Did you take the MCAS 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.

MCAS 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

20- The answer is 70.
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:
\( 375-305=70\)

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 \(D\)

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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: \( 0.50x=6.2 ⇒x=6.2÷0.50=12.4\)

34-The answer is 56
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 \(\frac{6}{36}=\frac{1}{6}\)

39-The answer is 168.
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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