Full-Length ACT Aspire 6 Math Practice Test

Taking a Full-length ACT Aspire 6 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 ACT Aspire 6 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, 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 ACT Aspire 6 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 ACT Aspire 6Math Test

Time to refine your Math skill with a practice test

Take a REAL ACT Aspire 6 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 ACT Aspire 6 Math Test.
• The ACT Aspire 6 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 application, rather than the memorization, of formulas.
• For each multiple-choice question, there are five possible answers. Choose which one is best.

Good Luck!

ACT Aspire 6 Math Practice Test

46 questions: 30 multiple choice questions and 16 grid-ins questions
Total time for this test: 60 Minutes
You may use a calculator for this test.

1- What is the value of the expression $$5(4x-3y)-7(y)^2$$, when $$x=2$$ and $$y=-3$$ ?

☐A. 15

☐B. 22

☐C. 36

☐D. 42

2- Martin earns $18 an hour. Which of the following inequalities represents the amount of time Martin needs to work per day to earn at least$78 per day?

☐A. $$18-t≥78$$

☐B. $$18+t≤78$$

☐C. $$18t≥78$$

☐D. $$18t≤78$$

3- $$(108-(3×9))÷9$$ is equivalent to …

☐A. $$(\frac{2}{5}+\frac{7}{8}) ×3$$

☐B. $$9^3÷81$$

☐C. $$(5×5×5) ÷ \frac{9}{2}$$

☐D. $$(2×2×5)÷(3×4)$$

4- The ratio of boys to girls in a school is 3 ∶ 5. If there are 240 students in the school, how many boys are in the school?

☐A. 60

☐B. 90

☐C. 120

☐D. 150

5- Anita’s trick–or–treat bag contains 9 pieces of chocolate, 15 suckers, 14 pieces of gum, 16 pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of chocolate?

☐A. $$\frac{1}{6}$$

☐B. $$\frac{5}{7}$$

☐C. $$\frac{3}{4}$$

☐D. $$\frac{5}{6}$$

6- Which of the following lists shows the fractions in order from greatest to least?
$$\frac{3}{4},\frac{2}{3}, \frac{4}{5}, \frac{7}{9}$$

☐A. $$\frac{4}{5},\frac{7}{9},\frac{3}{4},\frac{2}{3}$$

☐B. $$\frac{3}{4},\frac{7}{9},\frac{4}{5},\frac{2}{3}$$

☐C. $$\frac{7}{9},\frac{3}{4},\frac{2}{3},\frac{4}{5}$$

☐D. $$\frac{2}{3},\frac{3}{4},\frac{7}{9},\frac{4}{5}$$

7- The area of a rectangular yard is 84 square meters. What is its width if its length is 14 meters?

☐A. 5 meters

☐B. 6 meters

☐C. 7 meters

☐D. 8 meters

8- Which statement about 4 multiplied by $$\frac{5}{16}$$ must be true?

☐A. The product is greater than $$2$$

☐B. The product is between 1 and $$2$$

☐C. The product is equal to $$\frac{3}{8}$$

☐D. The product is equal to $$2^2$$

9- In the following rectangle, which statement is false?

☐A. AD is parallel to BC

☐B. The measure of the sum of all the angles equals $$180^\circ$$.

☐C. Length of AB equal to length DC.

☐D. AB is perpendicular to AD.

10- Round $$\frac{824}{17}$$ to the nearest tenth.

☐A. 48

☐B. 48.4

☐C. 48.5

☐D. 49

11- If the area of the following trapezoid is equal to A, which equation represent $$x$$?

☐A. $$x=\frac{11}{A}$$

☐B. $$x=\frac{A}{11}$$

☐C. $$x=A-11$$

☐D. $$x=A+11$$

12- By what factor did the number below change from first to fourth number?
$$8 ,72, 648, 5832$$

☐A. 6

☐B. 9

☐C. 12

☐D. 16

13- 234 is equal to …

☐A. $$13-(3×6)+(7×(-6))$$

☐B. $$(\frac{25}{400})+(\frac{7}{50})$$

☐C. $$((22×\frac{30}{6})-(7×\frac{144}{12}))×\frac{18}{2}$$

☐D. $$\frac{6}{24}+\frac{12}{36}-50$$

14- A car costing $240 is discounted $$16\%$$. Which of the following expressions can be used to find the selling price of the car? ☐A. $$(450)(0.16)$$ ☐B. $$450-(450×0.84)$$ ☐C. $$(450)(0.16)$$ ☐D. $$450-(450×0.16)$$ 15- Mr. Jones saves$1,400 out of his monthly family income of \$11,900. What fractional part of his income does Mr. Jones save?

☐A. $$\frac{2}{17}$$

☐B. $$\frac{5}{17}$$

☐C. $$\frac{7}{17}$$

☐D. $$\frac{9}{17}$$

16- Nicolas wrote an integer. The opposite of Nicolas’s integer is $$-25$$. Which of the following statements about Nicolas’s integer must be true?
I . The integer is $$25$$.
I I . The absolute value of the integer is $$-25$$.
I I I . The integer is $$-25$$.
I V. The absolute value of the integer is $$25$$.

☐A. I and II

☐B. II and III

☐C. I and IV

☐D. III and IV

17- The distance between two cities is 33,759 feet. What is the distance of the two cities in yards?

☐A. 9,570 yd

☐B. 10,920 yd

☐C. 11,253 yd

☐D. 13,617 yd

18- A chemical solution contains $$16\%$$ alcohol. If there is 38 ml of alcohol, what is the volume of the solution?

☐A. 195 ml

☐B. 237.5 ml

☐C. 369 ml

☐D. 452.5 ml

19- Which expression is equivalent to $$(-2)(9x-8)$$?

☐A. $$-16x+18$$

☐B. $$16x-18$$

☐C. $$-18x+16$$

☐D. $$18x+16$$

20- A bottle contains 576 fluid ounces of special chemical solutions. How many pints of chemical solution does the bottle contain?

☐A. 18 pt

☐B. 22 pt

☐C. 30 pt

☐D. 36 pt

21- Solve: 120 kg= … ?

☐A. 1,200 mg

☐B. 120,000 mg

☐C. 1,200,000 mg

☐D. 120,000,000 mg

22- Calculate the approximate area of the following circle? (the diameter is 14)

☐A. 97.5

☐B. 114.8

☐C. 153.9

☐D. 216.2

23- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks?

☐A. 16.5

☐B. 17.3

☐C. 18.2

☐D. 19

24- What is the lowest common multiple of 18 and 24?

☐A. 18

☐B. 48

☐C. 72

☐D. 96

25- Which ordered pair describes point $$P$$ that is shown below?

☐A. $$(2,4)$$

☐B. $$(4,2)$$

☐C. $$(4, -2)$$

☐D. $$(-2,4)$$

26- What is the ratio between α and $$β(\frac{α}{β})$$ in the following shape?

☐A. $$\frac{5}{12}$$

☐B. \9\frac{11}{25}\)

☐C. $$\frac{5}{12}$$

☐D. $$\frac{25}{11}$$

27- Find the opposite of the numbers $$-4,7$$.

☐A. $$\frac{1}{4},-7$$

☐B. $$-4,\frac{1}{7}$$

☐C. $$4,-7$$

☐D. $$-4,-7$$

28- Which of the following graphs represents the following inequality?
$$-5<2x+7≤3$$

☐A.

☐B.

☐C.

☐D.

29- Which of the following statements is correct, according to the graph below?

☐A. The number of books sold in the April was twice the number of books sold in the July.

☐B. The number of books sold in the July was more than one third the number of books sold in the May.

☐C. The number of books sold in the June was less than one third the number of books sold in the April.

☐D.  The number of books sold in the July was equal to the number of books sold in April plus the number of books sold in the June

30- To produce a special concrete, for every 17 kg of cement, 6 liters of water is required. Which of the following ratios is the same as the ratio of cement to liters of water?

☐A. 78 ∶ 34

☐B. 51 ∶ 17

☐C. 49 ∶ 17

☐D. 63 ∶ 16

31- What is the value of $$x$$ in the following equation: $$-60=115-x$$

32- The ratio of boys to girls in a school is 4 : 5. If there are 765 students in the school, how many boys are in the school?

33- What is the value of the expression $$6(2x-3y)+(3-2x)^2$$, when $$x=2$$ and $$y=-1$$?

34- Round $$\frac{215}{7}$$ to the nearest tenth.

35- What is the volume of a box with the following dimensions?
Height = 6 cm, Width = 7 cm, Length = 9 cm

36- The area of a rectangular yard is 90 square meters. What is its width if its length is 15 meters?

37- What is the missing price factor of number 420?
$$420=2^2×3^1×…$$

38- By what factor did the number below change from first to fourth number?
8, 104, 1352, 17576

39- The distance between two cities is 3,768 feet. What is the distance of the two cities in yards?

40- What is the lowest common multiple of 12 and 20?

41- Calculate the approximate area of the following circle? (the diameter is 25)
(π=3.14)

42- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks?

43- If the area of the following rectangular ABCD is 140, and E is the midpoint of AB, what is the area of the shaded part?

44- What is the difference in perimeter between a 7 cm by 4 cm rectangle and a circle with diameter of 10 cm? (π = 3)

45- What is the missing term in the given numbers?
2, 3, 5, 8, 12, 17, 23, _, 38

46- [6 × (–24) + 8] – (–4) + [4 × 5] ÷ 2 = ?

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