# Full-Length 8th Grade ACT Aspire Math Practice Test Taking a Full-length 8th Grade ACT Aspire Math practice test is the best way to help you get familiar with the test format and feel more confident. Not only will this help you measure your exam readiness and solidify the concepts you’ve learned, but it is the best way to simulate test day.
To help you get the best out of this complete and realistic 8th Grade ACT Aspire Math practice test and prepare your mind and body for the actual test, we recommend that you treat this practice test as a real test. Prepare scratch papers, a pencil, a timer, and a calculator and take the test in one sitting and follow the time limits to the minute.
Take the following full-length 8th Grade ACT Aspire Math practice test to simulate the test day experience. After you’ve finished, score your tests using the answer keys.
Good luck!

## The Absolute Best Book to Ace the 8th Grade ACT AspireMath Test

Time to refine your Math skill with a practice test

Take a REAL 8th Grade ACT Aspire Mathematics test to simulate the test day experience. After you’ve finished, score your test using the answer key.

Before You Start

• You’ll need a pencil, a calculator, and a timer to take the test.
• It’s okay to guess. You won’t lose any points if you’re wrong. So be sure to answer every question.
• After you’ve finished the test, review the answer key to see where you went wrong.
• Calculators are permitted for the 8th Grade ACT Aspire Math Test.
• The 8th Grade ACT Aspire Mathematics test contains a formula sheet, which displays formulas relating to geometric measurement and certain algebra concepts. Formulas are provided to test-takers so that they may focus on the application, rather than the memorization, of formulas.
• For each multiple-choice question, there are five possible answers. Choose which one is best.

Good Luck!

## 8th Grade ACT Aspire Math Practice Test

53 questions: 33 multiple choice questions and 20 grid-ins questions
Total time for this test: 60 Minutes
You may use a calculator for this test.

1- A rope weighs 600 grams per meter of length. What is the weight in kilograms of 12.2 meters of this rope? (1 kilograms = 1000 grams)

A. 0.0732

B. 0.732

C. 7.32

D. 7,320

2- In a school, the ratio of number of boys to girls is 3:7. If the number of boys is 180, what is the total number of students in the school?

3- In two successive years, the population of a town is increased by $$15\%$$ and $$20\%$$. What percent of its population is increased after two years?

A. 32

B. 35

C. 38

D. 68

4- A football team had $40,000 to spend on supplies. The team spent$22,000 on new balls. New sport shoes cost $240 each. Which of the following inequalities represent how many new shoes the team can purchase. A. $$240x+22,000 ≤40,000$$ B. $$240x+22,000 ≥40,000$$ C. $$22,000x+240 ≤40,000$$ D. $$22,000x+240 ≥40,000$$ 5- Which graph shows a non–proportional linear relationship between $$x$$ and $$y$$? A. B. C. D. 6- In the rectangle below if $$y>5$$ cm and the area of rectangle is 50 $$cm^2$$ and the perimeter of the rectangle is 30 cm, what is the value of $$x$$ and $$y$$ respectively? A. 4, 11 B. 5, 11 C. 5, 10 D. 4, 10 7- Right triangle ABC has two legs of lengths 6 cm (AB) and 8 cm (AC). What is the length of the third side (BC)? 8- If $$3x-5=8.5$$, What is the value of $$5x+3$$? A. 13 B. 15.5 C. 20.5 D. 25.5 9- A bank is offering $$4.5\%$$ simple interest on a savings account. If you deposit$8,000, how much interest will you earn in five years?

10- In a party, 10 soft drinks are required for every 12 guests. If there are 252 guests, how many soft drink is required?

A. 21

B. 105

C. 210

D. 2,510

11- A chemical solution contains $$4\%$$ alcohol. If there is 24 ml of alcohol, what is the volume of the solution?

A. 240 ml

B. 480 ml

C. 600 ml

D. 1,200 ml

12- What is the area of the shaded region?

13- A $40 shirt now selling for$28 is discounted by what percent?

A. $$20\%$$

B. $$30\%$$

C. $$40\%$$

D. $$60\%$$

14- How much interest is earned on a principal of $5000 invested at an interest rate of $$5\%$$ for four years? 15- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool? 16- The price of a car was$20,000 in 2014, $16,000 in 2015 and$12,800 in 2016. What is the rate of depreciation of the price of car per year?

A. $$15\%$$

B. $$20\%$$

C. $$25\%$$

D. $$30\%$$

17- What is the area of the shaded region if the diameter of the bigger circle is 12 inches and the diameter of the smaller circle is 8 inches.

18- What is the area of an isosceles right triangle that has one leg that measures 6 cm?

19- A taxi driver earns $9 per 1-hour work. If he works 10 hours a day and in 1 hour he uses 2-liters petrol with price$1 for 1-liter. How much money does he earn in one day?

A. $90 B.$88

C. $70 D.$60

20- Five years ago, Amy was three times as old as Mike was. If Mike is 10 years old now, how old is Amy?

21- What is the solution of the following system of equations?
$$\begin{cases}\frac{-x}{2}+\frac{y}{4}=1\\\frac{-5y}{6}+2x=4\end{cases}$$

A. $$x=48,y=22$$

B. $$x=50,y=20$$

C. $$x=20,y=50$$

D. $$x=22,y=48$$

22- What is the length of AB in the following figure if AE = 4, CD = 6 and AC = 12?

23- If a gas tank can hold 25 gallons, how many gallons does it contain when it is $$\frac{2}{5}$$ full?

A. 50

B. 125

C. 62.5

D. 10

24- In the $$𝑥𝑦$$-plane, the point (4, 3) and (3, 2) are on line A. Which of the following equations of lines is parallel to line A?

A. $$y=3x$$

B. $$y=\frac{x}{2}$$

C. $$y=2x$$

D. $$y=x$$

25- If $$x$$ is directly proportional to the square of $$y$$, and $$y=2$$ when $$x=12$$, then when $$x=75$$, $$y=$$ ?

26- Jack earns $616 for his first 44 hours of work in a week and is then paid 1.5 times his regular hourly rate for any additional hours. This week, Jack needs$826 to pay his rent, bills and other expenses. How many hours must he work to make enough money in this week?

Questions 27, 28 and 29 are based on the following data

27- If a is the mean (average) of the number of cities in each pollution type category, b is the mode, and c is the median of the number of cities in each pollution type category, then which of the following must be true?

A. $$a<b<c$$

B. $$b<a<c$$

C. $$a=c$$

D. $$b<c=a$$

28- What percent of cities are in the type of pollution A, C, and E respectively?

A. $$60\%, 40\%, 90\%$$

B. $$30\%, 40\%, 90\%$$

C. $$30\%, 40\%, 60\%$$

D. $$40\%, 60\%, 90\%$$

29- How many cities should be added to type of pollution’s B until the ratio of cities in type of pollution B to cities in type of pollution E will be 0.625?

30- In the following right triangle, if the sides AB and AC become twice longer, what will be the ratio of the perimeter of the triangle to its area?

A. $$\frac{1}{2}$$

B. $$2$$

C. $$\frac{1}{3}$$

D. $$3$$

31- The capacity of a red box is $$20\%$$ bigger than the capacity of a blue box. If the red box can hold 30 equal sized books, how many of the same books can the blue box hold?

32- The sum of six different negative integers is $$-70$$. If the smallest of these integers is $$-15$$, what is the largest possible value of one of the other five integers?

A. $$-14$$

B. $$-10$$

C. $$-5$$

D. $$-1$$

33- In the figure below, what is the value of $$x$$?

34- The following table represents the value of $$x$$ and function $$f(x)$$. Which of the following could be the equation of the function $$f(x)$$?

A. $$f(x)=x^2-5$$

B. $$f(x)=x^2-1$$

C. $$f(x)=\sqrt{x+2}$$

D. $$f(x)=\sqrt{x}+4$$

35- The circle graph below shows all Mr. Green’s expenses for last month. If he spent $660 on his car, how much did he spend for his rent? 36- The Jackson Library is ordering some bookshelves. If x is the number of bookshelves the library wants to order, which each costs$100 and there is a one-time delivery charge of $800, which of the following represents the total cost, in dollar, per bookshelf? A. $$100x+800$$ B. $$100+800x$$ C. $$\frac{100x+800}{100}$$ D. $$\frac{100x+800}{x}$$ 37- What is the sum of $$\sqrt{x-7}$$ and $$\sqrt{x}-7$$ when $$\sqrt{x}=4$$ ? 38- In the following figure, point $$Q$$ lies on line n, what is the value of $$y$$ if $$x = 35$$? A. 15 B. 25 C. 35 D. 45 39- What is the smallest integer whose square root is greater than 6? A. 16 B. 25 C. 37 D. 49 40- What is the value of $$|-12-5|-|-8+2|$$? 41- There are 6 blue marbles, 8 red marbles, and 5 yellow marbles in a box. If Ava randomly selects a marble from the box, what is the probability of selecting a red or yellow marble? A. $$\frac{1}{6}$$ B. $$\frac{1}{5}$$ C. $$\frac{13}{19}$$ D. $$\frac{5}{8}$$ 42- Which of the following is NOT a factor of 80? A. 8 B. 10 C. 14 D. 16 43- A phone company charges$4 for the first six minutes of a phone call and 40 cents per minute thereafter. If Sofia makes a phone call that lasts 36 minutes, what will be the total cost of the phone call?

44-On a map, the length of the road from City A to City B is measured to be 20 inches. On this map, \frac{1}{3} inch represents an actual distance of 12 miles. What is the actual distance, in miles, from City A to City B along this road?

A. 580

B. 720

C. 960

D. 1,140

45- If $$150 \%$$ of a number is $$75$$, then what is the $$90 \%$$ of that number?

46- In the figure, MN is 40 cm. How long is ON?

A. 25 cm

B. 20 cm

C. 15 cm

D. 10 cm

47- What is the equation of the line that passes through $$(2, –2)$$ and has a slope of $$7$$?

A. $$y = 2x – 16$$

B. $$y = 2x – 12$$

C. $$y = 2x+ 16$$

D. $$y = 2x+ 12$$

48- Find the solution $$(x,y)$$ to the following system of equations?
$$-3x-y=6$$
$$6x+4y=10$$

A. $$(14,5)$$

B. $$(6,8)$$

C. $$(11,17)$$

D. $$(-\frac{17}{3},11)$$

49- Find all values of $$x$$ for which $$4 x^2 + 14 x + 6 = 0$$

A. $$–\frac{3}{2}, – \frac{1}{2}$$

B. $$– \frac{1}{2}, – 3$$

C. $$–2, – \frac{1}{3}$$

D. $$– \frac{2}{3}, \frac{1}{2}$$

50- Use the diagram below to answer the question.
Given the lengths of the base and diagonal of the rectangle below, what is the length of height $$h$$, in terms of $$s$$?

A. $$2s\sqrt{6}$$

B. $$s\sqrt{7}$$

C. $$5s$$

D. $$5s^2$$

Use the chart below to answer the question.

51- There are also purple marbles in the bag. Which of the following can NOT be the probability of randomly selecting a purple marble from the bag?

A. $$\frac{1}{10}$$

B. $$\frac{1}{4}$$

C. $$\frac{2}{5}$$

D. $$\frac{7}{15}$$

52- Find the area of a rectangle with a length of 138 feet and a width of 83 feet.

A. 11, 504 sq. ft

B. 11, 404 sq. ft

C. 11,454 sq. ft

D. 11, 204 sq. ft

53- $$4x^2y^3 + 5x^3y^5 – (5x^2y^3 – 2x^3y^5) =$$

A. $$–x^2y^3$$

B. $$6x^2y^3 – x^3y^5$$

C. $$7x^2y^3$$

D. $$7x^3y^5 – x^2y^3$$

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