# Full-Length ACT Aspire 8 Math Practice Test-Answers and Explanations 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 $$x$$. $$\frac{10 \space soft \space drinks}{12 \space guests}=\frac{x}{252 \space guests}$$ $$x =\frac{252×10}{12} ⇒x=210$$ ## The Absolute Best Book to Ace the ACT Aspire 8Math Test 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 8MathPrep Resource for 2020 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: $$\frac{Total \space cost}{number \space of \space items}=\frac{100x+800}{x}$$

$$\sqrt{x}=4→x=16$$
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.

$$|-12-5|-|-8+2|=|-17|-|-6|=17-6=11$$

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

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: $$(5x+8)-(5x-3)=5x+8-5x+3=11$$

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
$$4x^2y^3 + 5x^3y^5 – (5x^2y^3 – 2x^3y^5) = 4x^2y^3 + 5x^3y^5 – 5x^2y^3 + 2x^3y^5 = – x^2y^3 + 7x^3y^5$$

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