Full-Length 7th Grade FSA Math Practice Test-Answers and Explanations
Did you take the 7th Grade FSA 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.
7th Grade FSA 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 a 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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ac{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 between the areas of the two circles. \(S_1\): the area of the bigger circle. \(S_2\): the area of the smaller circle). Use the area of a 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 the laptop and C be the price of the 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 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, which means \(75\%\) of the total mark. \(\frac{24}{32}= \frac{x}{100}⇒x=75\)
Joe scored 28 out of 40 in science that it means \(70\%\) of the total mark. \(\frac{28}{40}=\frac{x}{100} ⇒x=70\)
Joe scored 72 out of 90 in mathematics that it means \(80\%\) of the 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 for the area of a circle.
Area \(=πr^2 ⇒ 121π= πr^2 ⇒ 121= r^2⇒ r=11\)
The 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.
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