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

Did you take the 6th Grade ACT Aspire 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 ACT Aspire 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\(=\frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{9}{9+15+14+16}=\frac{9}{54}\frac{1}{6}=0.16\)

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

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

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

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

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

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

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

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

**18- 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 ⇒ \(0.16x=38 ⇒ x=38÷0.16=237.5\)

**19- Choice C is correct**\((-2)(9x-8)=(-2)(9x)+(-2)(-8)=-18x+16\)

**20- Choice D is correct**1 pt = 16 fluid ounces. \(576÷16=36\)

Then: 576 fluid ounces = 36 pt

**21- Choice D is correct**1 kg = 1000 g and 1 g = 1000 mg,

120 kg = 120 × 1000 g = 120 × 1000 × 1000 = 120,000,000 mg

**22- Choice C is correct**The diameter of a circle is twice the radius. Radius of the circle is \(\frac{14}{2}=7\).

Area of a circle \(= πr^2=π(7)^2=49π=49×3.14=153.86≅153.9\)

**23- Choice B is correct**Average (mean) \(=\frac{sum \space of \space terms}{number \space of \space terms}=\frac{15+17+12+16+21+23}{6}=\frac{104}{6}=17.33\)

**24- Choice C is correct**Prime factorizing of \(18=2×3×3\), Prime factorizing of \(24=2×2×2×3\)

LCM \(= 2×2×2×3×3=72\)

**25- Choice B is correct**The coordinate plane has two axes. The vertical line is called the \(y\)-axis and the horizontal is called the \(x\)-axis. The points on the coordinate plane are addressed using the form \((x,y)\). Point A is one unit on the left side of the \(x\)-axis, therefore its \(x\) value is 4 and it is two units up, therefore its \(y\) axis is 2. The coordinate of the point is: (4, 2)

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**26- Choice B is correct**\(α\) and \(β\) are supplementary angles. The sum of supplementary angles is 180 degrees.

\(α+β=180^\circ→α=180^\circ-β=180^\circ-125^\circ=55^\circ,\) Then, \(\frac{α}{β}=\frac{55}{125}=\frac{11}{25}\)

**27- Choice C is correct**Opposite number of any number \(x\) is a number that if added to \(x\), the result is 0. Then:

\(7+(-7)=0\) and \(4+(-4)=0\)

**28- Choice D is correct**\(-5<2x+7≤3\)→ (add (\(-7\))all sides) \((-7)+(-5)<2x+7+(-7)≤3+(-7) \) →\(-12<2x≤-4\)→(divide all sides by 2),\(-6<x≤-2\)

In inequality \(-6<x≤-2\), \(x\) is fewer or equal to \(-2\) and more than \(-6\). Only choice D represents the same inequality on the number line.

**29- Choice B is correct**A. Number of books sold in April is: \(690\)

Number of books sold in July is: \(1,150→ \frac{690}{1,150}≠2\)

B. Number of books sold in July is: \(1,150\)

Half the number of books sold in May is: \(\frac{1,150}{2}=575→690>575\) (it’s correct)

C. Number of books sold in June is: \(375\)

Half the number of books sold in April is: \(\frac{690}{3}=230→240<375\)

D. \(690+375=1,065>1,150\)

**30- Choice B is correct**\(51∶18=17∶6, 17×3=51\) and \(8×3=18\)

**31- The answer is 175.**\(-60=115-x\); First, subtract 115 from both sides of the equation. Then:

\(-60-115=115-115-x→-175=-x\), Multiply both sides by (\(-1\)):

→\(x=175\)

**32- The answer is 340.**The ratio of boys to girls is \(4: 5\). Therefore, there are 4 boys out of 9 students. To find the answer, first, divide the total number of students by 9, then multiply the result by 4.

\(765 ÷ 9 = 85 ⇒ 85 × 4 = 340\)

**33- The answer is 43.**Plug in the value of \(x\) and \(y\) and use order of operations rule. \(x=2\) and \(y=-1\)

\(6(2x-3y)+(3-2x)^2=6(2(2)-3(-1))+(3-2(2))^2=6(4+3)+(-1)^2 = 42+1=43\)

**34- The answer is 30.7.**\(\frac{215}{7}≅30.71≅30.7\)

**35- The answer is 378.**Volume of a box \(= ength×width×height=6×7×9=378\)

**36- The answer is 6.**Let y be the width of the rectangle. Then; \(15×y=90→y=\frac{90}{15}=6\)

**37- The answer is 7.**\(420=2^2×3^1×5^1×7^1\)

**38- The answer is 13.**\(\frac{104}{8}=13, \frac{1,352}{104}=13, \frac{17,576}{1,352}=13\)

Therefore, the factor is 13

**39- The answer is 1,256.**1 yard = 3 feet

Therefore, \(3,768 ft.×\frac{1 \space yd}{3 \space ft}=1,256 \space yd\)

**40- The answer is 60.**Prime factorizing of \(20=2×2×5\)

Prime factorizing of \(12=2×2×3\)

LCM \(=2×2×3×5=60\)

**41- The answer is 491.**The diameter of a circle is twice the radius. Radius of the circle is \(\frac{25}{2}\).

Area of a circle \(= πr^2=π(\frac{25}{2})^2=156.25π=156.25×3.14=490.625≅491\)

**42- The answer is 13.5.**Average (mean) \(= \frac{sum \space of \space terms}{number \space of \space terms}=\frac{10+11+15+14+15+17+12.5}{7}=13.5\)

**43- The answer is 70.**Since E is the midpoint of AB, then the area of all triangles DAE, DEF, CFE, and CBE are equal.

Let x be the area of one of the triangles, then:

\(4x=140→x=35\)

The area of DEC \(=2x=2(35)=70\)

**44- The answer is 8.**The perimeter of a rectangle is: \(2×(4+7)=2×11=22\)

The perimeter of circle is: \(2πr=2×3×\frac{10}{2}=30\)

The difference in the perimeter is: \(30-22=8\)

**45- The answer is 30.**Find the difference of each pair of numbers:

2, 3, 5, 8, 12, 17, 23,

*_*, 38

The difference of 2 and 3 is 1, 3 and 5 is 2, 5 and 8 is 3, 8 and 12 is 4, 12 and 17 is 5, 17 and 23 is 6, 23 and next number should be 7. The number is 23 + 7 = 30

**46- The answer is** \(-122\).

Use PEMDAS (order of operation):

\([6 × (–24) + 8] – (–4) + [4 × 5] ÷ 2 = [–144 + 8] – (–4) + [20] ÷ 2 = [–144 + 8] – (–4) + 10 =

[–136] – (–4) + 10 = [–136] + 4 + 10 = –122\)

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