Did you take the ACT Aspire 8 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.

## ACT Aspire 8 Math Practice Test Answers and Explanations

**1- Choice C is correct**The weight of 12.2 meters of this rope is: 12.2 × 600 g = 7320 g

1kg = 1000 g, therefore, 7320 g ÷ 1000 = 7.32 kg

**2- The correct answer is 600.**The ratio of boys to girls is 3 : 7. Therefore, there are 3 boys out of 10 students. To find the answer, first divide the number of boys by 3, then multiply the result by 10.

180 ÷ 3 = 60 ⇒ 60 × 10 = 600

**3- Choice C is correct.**the population is increased by \(15\%\) and \(20\%\). \(15\%\) increase changes the population to \(115\%\) of original population.

For the second increase, multiply the result by \(120\%\).

\((1.15) × (1.20) = 1.38 = 138\%\)

38 percent of the population is increased after two years.

**4- Choice A is correct.**Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase 240 \(x\).

The team had $40,000 and spent $22,000. Now the team can spend on new shoes $18,000 at most.

Now, write the inequality: \(120x+22.000 ≤40.000\)

**5- Choice B is correct.**A linear equation is a relationship between two variables, \(x\) and \(y\), that can be put in the form \(y = mx + b\).

A non-proportional linear relationship takes on the form \(y = mx + b\), where b ≠ 0 and its graph is a line that does not cross through the origin.

**6- Choice C is correct**The perimeter of the rectangle is: \(2x+2y=30→x+y=15→x=15-y\)

The area of the rectangle is: \(x×y=50→(15-y)(y)=50→y^2-15y+50=0\)

Solve the quadratic equation by factoring method.

\((y-5)(y-10)=0→y=5\) (Unacceptable, because y must be greater than 5) or \(y=10\)

If \(y=10 →x×y=50→x×10=50→x=5\)

**7- The correct answer is 10.**Use the information provided in the question to draw the shape.

Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)

\(6^2 + 8^2 = c^2 ⇒ 100 = c^2 ⇒ c = 10\)

**8- Choice D is correct**\(3x-5=8.5→3x=8.5+5=13.5→x=\frac{13.5}{3}=4.5\)

Then; \(5x+3=5 (4.5)+3=22.5+3=25.5\)

**9- The correct answer is 1,800.**Use simple interest formula: I=prt (I = interest, p = principal, r = rate, t = time)

\(I=(8000)(0.045)(5)=1800\)

**10- Choice C is correct.**Let \(x\) be the number of soft drinks for 252 guests. Write the proportion and solve for \(x\).

\(\frac{10 \space soft \space drinks}{12 \space guests}=\frac{x}{252 \space guests}\)

\(x =\frac{252×10}{12} ⇒x=210\)

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**11- Choice C is correct**\(4\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution.

Then: \(4\%\) of \(x = 24\) ml ⇒ \(0.04 x = 24 ⇒ x = 24 ÷ 0.04 = 600\)

**12- The correct answer is 40.**Use the area of rectangle formula \((s = a × b)\).

To find area of the shaded region subtract smaller rectangle from bigger rectangle.

\(S_1 – S_2 = (10 \space ft × 8 \space ft) – (5 \space ft × 8 \space ft) ⇒ S_1 – S_2 = 40 \space ft\)

**13- Choice B is correct**Use the formula for Percent of Change

\(\frac{New \space Value-Old \space Value}{Old \space Value}

× 100\%\)

\(\frac{28-40}{40} × 100 \% = –30 \%\) (negative sign here means that the new price is less than old price).

**14- The correct answer is 1,000.**Use simple interest formula: I=prt (I = interest, p = principal, r = rate, t = time)

\(I=(5000)(0.05)(4)=1,000\)

**15- The answer is 8.**Use formula of rectangle prism volume. V = (length) (width) (height) ⇒ 2000 = (25) (10) (height) ⇒ height = 2000 ÷ 250 = 8

**16- Choice B is correct.**Use this formula: Percent of Change

\(\frac{New \space Value-Old \space Value}{Old \space Value}

× 100\%\)

\(\frac{16,000-20,000}{20,000} × 100\% = 20\% \space and \space \frac{12,800-16,000}{16000} × 100\% = 20\%\)

**17- The correct answer is 62.8.**To find the area of the shaded region subtract smaller circle from bigger circle.

\(S_ {bigger} – S_ {smaller} = π (r _{bigger} )^2 – π (r _{smaller} )^2 ⇒ S _{bigger} – S _{smaller} = π (6)^2 – π (4)^2\)

\(⇒ 36 π – 16π = 20 π = 20 × 3.14 = 62.8\)

**18- The answer is 18.**\(a=6\)⇒ area of the triangle is \(=\frac{1}{2}(6×6)=\frac{36}{2}=18 \space cm^2\)

**19- Choice C is correct**\($9×10=$90\)

Petrol use: \(10×2=20\) liters

Petrol cost: \(20×$1=$20\)

Money earned: \($90-$20=$70\)

**20- The answer is 20.**Five years ago, Amy was three times as old as Mike. Mike is 10 years now. Therefore, 5 years ago Mike was 5 years.

Five years ago, Amy was: \(A=3×5=15\)

Now Amy is 20 years old: \(15 + 5 = 20\)

**21- Choice D is correct**\(\begin{cases}\frac{-x}{2}+\frac{y}{4}=1\\\frac{-5y}{6}+2x=4\end{cases}\)

Multiply the top equation by 4. Then,

\(\begin{cases}-2x+y=4\\\frac{-5y}{6}+2x=4\end{cases}\)

→ Add two equations.

\(\frac{1}{6}y=8→y=48\) , plug in the value of y into the first equation →\(x=22\)

**22- The answer is 4.8.**Two triangles ∆BAE and ∆BCD are similar. Then:

\(\frac{AE}{CD}=\frac{AB}{BC}→\frac{4}{6}=\frac{x}{12}→48-4x=6x→10x=48→x=4.8\)

**23- Choice D is correct**\(\frac{2}{5}×25=\frac{50}{5}=10\)

**24- Choice D is correct**The slop of line A is: \(m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{4-3}=1\)

Parallel lines have the same slope and only choice D \((y=x)\) has slope of 1.

**25- The answer is 5.**\(x\) is directly proportional to the square of \(y\). Then:

\(x=cy^2\)

\(12=c(2)^2→12=4c→c=\frac{12}{4}=3\)

The relationship between \(x\) and \(y\) is: \(x=3y^2, x=75\), \(75=3y^2→y^2=\frac{75}{3}=25→y=5\)

**26- The answer is 54.**The amount of money that jack earns for one hour: \(\frac{$616}{44}=$14\)

Number of additional hours that he work to make enough money is: \(\frac{$826-$616}{1.5×$14}=10\)

Number of total hours is: \(44+10=54\)

**27- Choice C is correct**Let’s find the mean (average), mode and median of the number of cities for each type of pollution.

Number of cities for each type of pollution: 6, 3, 4, 9, 8

𝑎𝑣𝑒𝑟𝑎𝑔𝑒 (𝑚𝑒𝑎𝑛) \(=\frac{sum \space of \space terms}{number \space of \space terms}= \frac{6+3+4+9+8}{5}=\frac{30}{5}=6\)

Median is the number in the middle. To find median, first list numbers in order from smallest to largest.

3, 4, 6, 8, 9

Median of the data is 6.

Mode is the number which appears most often in a set of numbers. Therefore, there is no mode in the set of numbers.

Median = Mean, then, 𝑎 = 𝑐

**28- Choice A is correct**Percent of cities in the type of pollution A: \(\frac{6}{10}×100=60\%\)

Percent of cities in the type of pollution C: \(\frac{4}{10}0×100=40\%\)

Percent of cities in the type of pollution E: \(\frac{9}{10}×100=90\%\)

**29- The answer is 2.**Let the number of cities should be added to type of pollution’s B be \(x\). Then: \(\frac{x+3}{8}=0.625→x+3=8×0.625→x+3=5→x=2\)

**30- Choice A is correct**AB = 12 and AC = 5

\(BC=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\)

Perimeter \(=5+12+13=30\)

Area \(=\frac{5×12}{2}=5×6=30\)

In this case, the ratio of the perimeter of the triangle to its area is: \(\frac{30}{30}=1\)

If the sides AB and AC become twice longer, then:

AB = 24 and AC = 10

BC \(=\sqrt{24^2+10^2}=\sqrt{576+100}=\sqrt{676}=26\)

Perimeter \(=26+24+10=60\)

Area \(=\frac{10×24}{2}=10×12=120\)

In this case the ratio of the perimeter of the triangle to its area is: \(\frac{60}{120}=\frac{1}{2}\)

## Best *ACT Aspire 8* *Math** *Prep Resource for 2020

*ACT Aspire 8*

*Math*

**31- The answer is 25.**The capacity of a red box is \(20\%\) bigger than the capacity of a blue box and it can hold 30 books. Therefore, we want to find a number that \(20\%\) bigger than that number is 30. Let \(x\) be that number. Then:

\(1.20×x=30\), Divide both sides of the equation by 1.2. Then:

\(x=\frac{30}{1.20}=25\)

**32- Choice C is correct**The smallest number is \(-15\). To find the largest possible value of one of the other five integers, we need to choose the smallest possible integers for four of them. Let x be the largest number. Then:

\(-70=(-15)+(-14)+(-13)+(-12)+(-11)+x→-70=-65+x →x=-70+65=-5\)

**33- The answer is 67.**\(α=180\circ -112\circ=68\circ\)

\(β=180\circ-135\circ=45\circ\)

\(x+α+β=180\circ→x=180\circ-68\circ-45\circ=67\circ\)

**34- Choice D is correct**A. \(f(x)=x^2-5\) →if \(x=1→f(1)=(1)^2-5=1-5=-4≠5\)

B. \(f(x)=x^2-1\) →if \(x=1→f(1)=(1)^2-1=1-1=0≠5\)

C. \(f(x)=\sqrt{x+2}\)→ if \(x=1→f(1)=\sqrt{1+2}=\sqrt{3}≠5\)

D. f(x)=\sqrt{x}+4 \) →if \(x=1→f(1)=\sqrt{1}+4=5\)

**35- The answer is $810.**Let \(x\) be all expenses, then \(\frac{22}{100} x=$660 →x=\frac{100×$660}{22}=$3000\)

He spent for his rent: \(\frac{27}{100}×$3000=$810\)

**36- Choice C is correct**The amount of money for \(x\) bookshelf is: \(100x\)

Then, the total cost of all bookshelves is equal to: \(100x+800\)

The total cost, in dollar, per bookshelf is: \(\frac{Total \space cost}{number \space of \space items}=\frac{100x+800}{x}\)

**37- The answer is 0.**\(\sqrt{x}=4→x=16\)

then; \(\sqrt{x}-7=\sqrt{16}-7=4-7=-3\) and \(\sqrt{x-7}=\sqrt{16-7}=\sqrt{9}=3\)

Then: \((\sqrt{x-7})+(\sqrt{x}-7)=3+(-3)=0\)

**38- Choice B is correct**The angles on a straight line add up to 180 degrees. Then: \(x+25+y+2x+y=180\)

Then, \(3x+2y=180-25→3(35)+2y=155\)

\(→2y=155-105=50→y=25\)

**39- Choice C is correct**Square root of 16 is \(\sqrt{16}=4<6\) Square root of 25 is \(\sqrt{25}=5<6 \) Square root of 37 is \(\sqrt{37}=\sqrt{36+1}>\sqrt{36}=6\)

Square root of 49 is \(\sqrt{49}=7>6\)

Since, \(\sqrt{37}<\sqrt{49}\), then the answer is C.

**40- The answer is 11.**\(|-12-5|-|-8+2|=|-17|-|-6|=17-6=11\)

**41- Choice C is correct**A probability is the likelihood of a successful event occurring divided by the total number of events possible. In this case, a successful event is selecting either a red or a yellow marble and the total number of events possible is the total number of marbles. Combine the number of red and yellow marbles: 8 + 5 = 13, and divide this by the total number of marbles: 6 + 8 + 5 = 19. The probability is 13 out of 19.

**42- Choice C is correct**A factor must divide evenly into its multiple. 14 cannot be a factor of 80 because 80 divided by 16 = 5.71

**43- The answer is 16.**The total cost of the phone call can be represented by the equation:

\(TC = $4.00 + $0.4x\), where \(x\) is the duration of the call after the first five minutes. In this case, \(x = 30\). Substitute the known values into the equation and solve: \(TC = $4.00 + $0.4 × 30\)

\(TC = $4.00 + $12.00 , TC = $16.00\)

**44- Choice C is correct**Find the difference of the two expression: \((5x+8)-(5x-3)=5x+8-5x+3=11\)

**45- The answer is 45.**First, find the number. Let \(x\) be the number. Write the equation and solve for \(x\). \(150\%\) of a number is 75, then:

\(1.5×x=75→x=75÷1.5=50, 90\%\) of 50 is: \(0.9×50=45\)

**46- Choice A is correct**The length of MN is equal to: \(3x+5x=8x, Then: 8x=40→x=\frac{40}{8}=5\)

The length of ON is equal to: \(5x=5×5=25\) cm

**47- Choice A is correct**The general slope-intercept form of the equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. By substitution of the given point and given slope, we have:

\(-2 = (2)(7) + b\), So, \(b = –2 – 14 = -6\), and the required equation is \(y = 2x – 16\).

**48- Choice D is correct**Multiplying each side of \(-3x-y=6\) by \(2\) gives \(-6x -2y = 12\). Adding each side of \(-6x – 2y = 12\) to the corresponding side of \(6x+4y=10\) gives \(2y=22\) or \(y=11\). Finally, substituting \(11\) for \(y\) in \(6x+4y=10\) gives \(6x+4(11)=10\) or \(x=-\frac{17}{3}\).

**49- Choice B is correct**\(x_{1,2} =\frac{-b ± \sqrt{b^2-4ac}}{2a}\) ,

\( ax^2 + bx + c = 0, 4x^2 + 14x + 6 = 0 \) ⇒ then: \(a = 4\), \(b = 14\) and \(c = 6\),

\(x = \frac{-14 +\sqrt{14^2 – 4 .4 .6}}{2.4} = – \frac{1}{2}, x =\frac{-14 – \sqrt{14^2 – 4 .4 .6}}{2.4} = – 3\)

**50- Choice A is correct**Use Pythagorean theorem: \(a^2+b^2=c^2→s^2+h^2=(5s)^2→s^2+h^2=25s^2\)

Subtracting s^2 from both sides gives: \(h^2=24s^2\)

Square roots of both sides: \(h=\sqrt{24s^2}=\sqrt{4×6×s^2} =\sqrt{4}×\sqrt{6}×\sqrt{s^2 }=2×s×\sqrt{6}=2s\sqrt{6}\)

**51- Choice D is correct**Let \(x\) be the number of purple marbles. Let’s review the choices provided:

A. \(\frac{1}{10}\), if the probability of choosing a purple marble is one out of ten, then:

Probability \(=\frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{x}{20+30+40+x}=\frac{1}{10}\)

Use cross multiplication and solve for \(x\).

\(10x=90+x→9x=90→x=9\)

Since, number of purple marbles can be 9, then, choice be the probability of randomly selecting a purple marble from the bag.

Use same method for other choices.

B. \(\frac{1}{4}\)

\(\frac{x}{20+30+40+x}=\frac{1}{4}→4x=90+x→3x=90→x=30\)

C. \(\frac{2}{5}\)

\(\frac{x}{20+30+40+x}=\frac{2}{5}→5x=180+2x→3x=180→x=60\)

D. \(\frac{7}{15}\)

\(\frac{x}{20+30+40+x}=\frac{7}{15}→15x=630+7x→8x=630→x=78.75\)

Number of purple marbles cannot be a decimal.

**52- Choice C is correct**Area = w × h

Area = 138 × 83 = 11,454

**53- Choice D is correct**\(4x^2y^3 + 5x^3y^5 – (5x^2y^3 – 2x^3y^5) = 4x^2y^3 + 5x^3y^5 – 5x^2y^3 + 2x^3y^5 = – x^2y^3 + 7x^3y^5\)