# Full-Length 6th Grade PSSA Math Practice Test-Answers and Explanations

Did you take the 6th Grade PSSA 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.

## 6th Grade PSSA Math Practice Test Answers and Explanations

**1- Choice B is correct**Plug in the value of \(x\) and \(y\) and use order of operations rule. \(x=2\) and \(y=-3\)

\(5(4x-3y)-7y^2=5(4(2)-3(-3))-7(-3)^2=5(8+9)-7(9)=5(17)-63=85-63=22\)

**2- Choice C is correct**For one hour he earns $18, then for t hours he earns $18t. If he wants to earn at least $78, therefore, the number of working hours multiplied by 18 must be equal to 78 or more than 78.

\(18t≥78\)

**3- Choice B is correct**\((108-(3×9))÷9=9^3÷81=9\)

**4- Choice B is correct**The ratio of boys to girls is 3 ∶ 5. Therefore, there are 3 boys out of 8 students. To find the answer, first, divide the total number of students by 8, then multiply the result by 3.

\(240÷8=30 ⇒ 30×3=90\)

**5- Choice A is correct**Probability\(=\frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{9}{9+15+14+16}=\frac{9}{54}\frac{1}{6}=0.16\)

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**6- Choice D is correct**Let’s compare each fraction: \(\frac{2}{3}<\frac{3}{4}<\frac{7}{9}<\frac{4}{5}\) Only choice D provides the right order.

**7- Choice B is correct **Let \(y\) be the width of the rectangle. Then; \(14×y=84→y=\frac{84}{16}=6\)

**8- Choice B is correct **\(4×\frac{5}{16}=\frac{20}{16}=1.25\)

A. \(1.25>2\)

B. \(1<1.25<2\) This is the answer!

C. \(\frac{3}{8}=1.25\)

D. \(1.25=2^2\)

**9- Choice B is correct**In any rectangle, The measure of the sum of all the angles equals \(180^\circ\).

**10- Choice C is correct**\(\frac{824}{17}=48.5\)

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**11- The answer is **\(7^2\).\(588=2^2×3^1×7^2\)

**12- Choice B is correct**The area of the trapezoid is: Area \(=\frac{base \space 1+base \space 2}{2}×height=\frac{12+10}{2}x=A→ 11x=A→x=\frac{A}{11}\)

**13- Choice B is correct**\(\frac{72}{8}=9, \frac{648}{72}=9, \frac{5,832}{648}=9\), Therefore, the factor is 9.

**14- Choice C is correct**Simplify each option provided.

A. \(13-(3×6)+(7×(-6))=13-18+(-42)=-5-42=-47\)

B. \((\frac{25}{400})+(\frac{7}{50})=\frac{25}{400}+\frac{56}{400}=\frac{81}{400}\)

C. \(((22×\frac{30}{6})-(7×\frac{144}{12}))×\frac{18}{2}=(110-84)×9=26×9=234\) (this is the answer)

D. \((\frac{6}{24}+\frac{12}{33})-50=(\frac{1}{4}+\frac{1}{3})-50=(\frac{3}{12}+\frac{4}{12})-50=\frac{7}{12}-50=\frac{-593}{15}\)

**15- Choice D is correct**To find the discount, multiply the number (\(100\%\)- rate of discount)

Therefore; \(450(100\%-16\%)=450(1-0.16)=450-(450×0.16)\)

**16- Choice A is correct**1,400 out of 11,900 equals to \(\frac{1,400}{11,900}=\frac{200}{1,700}=\frac{2}{17}\)

**17- Choice C is correct**The opposite of Nicolas’s integer is \(25\). So, the integer is \(-25\). The absolute value of \(25\) is also \(25\).

**18- Choice B is correct**Volume of a box = length × width × height = 7 × 4 × 12 = 336

**19- Choice C is correct**1 yard = 3 feet, Therefore, \(33,759 ft×\frac{1 \space yd}{3 \space ft}=11,253\) yd

**20- Choice B is correct**\(16\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution.

Then: \(16\%\) of \(x=38\) ml ⇒ \(0.16x=38 ⇒ x=38÷0.16=237.5\)

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