Did you take the SBAC 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.

## SBAC 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 \(9,000(\frac{1}{5} × 45,000=9,000)\).

\(36,000(45,000-9,000=36,000)\) 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:

\( 375-305=70\)

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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.