# Full-Length AFOQT Math Practice Test

Taking a Full-length AFOQT 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 AFOQT 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 AFOQT 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 AFOQT Math Test

Time to refine your Math skill with a practice test

Take AFOQT Arithmetic Reasoning and Mathematics Knowledge tests to simulate the test day experience. After you’ve finished, score your tests using the answer keys.

Before You Start

• You’ll need a pencil and a timer to take the test.
• For each question, there are five possible answers. Choose which one is best.
• It’s okay to guess. There is no penalty for wrong answers.
• After you’ve finished the test, review the answer key to see where you went wrong.

Calculators are NOT permitted for the AFOQT Test

Good Luck!

## AFOQT Math Test 1Arithmetic Reasoning

• 25 questions
• Total time for this section: 29 Minutes
• Calculators are not allowed at the test.

1- A writer finishes 198 pages of his manuscript in 18 hours. How many pages is his average per hour?

☐A. 9

☐B. 10

☐C. 11

☐D. 12

2- If a rectangle is 12 feet by 27 feet, what is its area?

☐A. 324

☐B. 452

☐C. 678

☐D. 750

3- Aria was hired to teach four identical math courses, which entailed being present in the classroom 44 hours altogether. At $36 per class hour, how much did Aria earn for teaching one course? ☐A.$144

☐B. $176 ☐C.$396

☐D. $1,584 4- A family owns 8 dozen of magazines. After donating 32 magazines to the public library, how many magazines are still with the family? ☐A. 64 ☐B. 96 ☐C. 118 ☐D. 124 5- Karen is 6 years older than her sister Michelle, and Michelle is 3 years younger than her brother David. If the sum of their ages is 45, how old is Michelle? ☐A. 12 ☐B. 23 ☐C. 29 ☐D. 36 6- John is driving to visit his mother, who lives 450 miles away. How long will the drive be, round−trip, if John drives at an average speed of 60 mph? ☐A. 75 Minutes ☐B. 450 Minutes ☐C. 750 Minutes ☐D. 900 Minutes 7- If one acre of forest contains 124 pine trees, how many pine trees are contained in 19 acres? ☐A. 2,356 ☐B. 3,207 ☐C. 4,415 ☐D. 4,712 8- You are asked to chart the temperature during an 8-hour period to give the average. These are your results: 7 am: 4 degrees 8 am: 7 degrees 9 am: 14 degrees 10 am: 19 degrees 11 am: 24 degrees 12 pm: 36 degrees 1 pm: 39 degrees 2 pm: 41 degrees What is the average temperature? ☐A. 23 ☐B. 25 ☐C. 32 ☐D. 44 9- A woman owns a dog walking business. If 5 workers can walk 15 dogs, how many dogs can 8 workers walk? ☐A. 15 ☐B. 18 ☐C. 24 ☐D. 75 10- Each year, a cyber café charges its customers a base rate of$12, with an additional $0.15 per visit for the first 30 visits, and$0.10 for every visit after that. How much does the cyber café charge a customer for a year in which 45 visits are made?

☐A. $12 ☐B.$18

☐C. $23 ☐D.$45

11- If a vehicle is driven 45 miles on Monday, 33 miles on Tuesday, and 27 miles on Wednesday, what is the average number of miles driven each day?

☐A. 25 Miles

☐B. 31 Miles

☐C. 35 Miles

☐D. 39 Miles

12- Three co−workers contributed $9.85,$15.45, and $12.75 respectively to purchase a retirement gift for their boss. What is the maximum amount they can spend on a gift? ☐A.$38.05

☐B. $39.85 ☐C.$40.25

☐D. $42.95 13- While at work, Emma checks her email once every 40 minutes. In 8−hour, how many times does she check her email? ☐A. 6 Times ☐B. 8 Times ☐C. 10 Times ☐D. 12 Times 14- Julie gives 6 pieces of candy to each of her friends. If Julie gives all her candy away, which amount of candy could have been the amount she distributed? ☐A. 98 ☐B. 128 ☐C. 210 ☐D. 385 15- In the deck of cards, there are 5 spades, 3 hearts, 10 clubs, and 7 diamonds. What is the probability that William will pick out a spade? ☐A. $$\frac{1}{9}$$ ☐B. $$\frac{1}{7}$$ ☐C. $$\frac{1}{6}$$ ☐D. $$\frac{1}{5}$$ 16- William is driving a truck that can hold 10 tons maximum. He has a shipment of food weighing 27,000 pounds. How many trips will he need to make to deliver all of the food? ☐A. 1 Trip ☐B. 3 Trip ☐C. 4 Trip ☐D. 5 Trip 17- A man goes to a casino with$145. He loses $30 on blackjack, then loses another$40 on roulette. How much money does he have left?

☐A. $75 ☐B.$105

☐C. $115 ☐D.$120

18- Will has been working on a report for 5 hours each day, 7 days a week for 3 weeks. How many minutes has will worked on his report?

☐A. 4,700 Minutes

☐B. 6,300 Minutes

☐C. 6,854 Minutes

☐D. 7,560 Minutes

19- What is the prime factorization of 378?

☐A. $$2 × 2 × 3 × 7$$

☐B. $$2 × 3 × 3 × 3 × 7$$

☐C. $$2 × 3 × 5 × 5 × 7$$

☐D. $$3 × 3 × 5 × 7 × 7$$

20- Camille uses a $$25\%$$ off coupon when buying a sweater that costs $80. If she also pays $$9\%$$ sales tax on the purchase, how much does she pay? ☐A.$20

☐B. $24.8 ☐C.$36.75

☐D. \$65.4

21- I’ve got 28 quarts of milk and my family drinks 2 gallons of milk per week. How many weeks will that last us?

☐A. 2 Weeks

☐B. 2.25 Weeks

☐C. 3.5 Weeks

☐D. 4.5 Weeks

22- A floppy disk shows 987,345 bytes free and 879,621 bytes used. If you delete a file of size 397,756 bytes and create a new file of size 487,236 bytes, how many free bytes will the floppy disk have?

☐A. 89,480

☐B. 745,874

☐C. 987,345

☐D. 1,076,825

23- Ten out of 50 students had to go to summer school. What is the ratio of students who did not have to go to summer school expressed, in its lowest terms?

☐A. $$\frac{1}{5}$$

☐B. $$\frac{1}{4}$$

☐C. $$\frac{4}{5}$$

☐D. $$\frac{5}{4}$$

24- If a circle has a diameter of 2 feet, what is its circumference?

☐A. $$2 π$$

☐B. $$4 π$$

☐C. $$8 π$$

☐D. $$12 π$$

25- Ava needs $$\frac{1}{4}$$ of an ounce of salt to make 1 cup of dip for fries. How many cups of dip will she be able to make if she has 60 ounces of salt?

☐A. 15

☐B. 60

☐C. 85

☐D. 240

26- In the following diagram what is the value of $$x$$?

☐A. $$30^\circ$$

☐B. $$45^\circ$$

☐C. $$60^\circ$$

☐D. $$90^\circ$$

27- What is the value of $$\sqrt{81} × \sqrt{49}$$ ?

☐A. 6

☐B. $$\sqrt{130}$$

☐C. 63

☐D. $$\sqrt{87}$$

28- If $$a = 5$$, what is the value of b in this equation? $$b = \frac{a^3}{5} -2$$

☐A. 5

☐B. 13

☐C. 15

☐D. 23

29- Which of the following is an obtuse angle?

☐A. $$35^\circ$$

☐B. $$105^\circ$$

☐C. $$145^\circ$$

☐D. $$175^\circ$$

30- Which of the following is not equal to $$3^2$$?

☐A. 3 squared

☐B. the square of 3

☐C. 3 to the second power

☐D. 3 cubed

31- The fourth root of 625 is:

☐A. 4

☐B. 5

☐C. 6

☐D. 8

32- A circle has a radius of 4 inches. What is its approximate area? $$(π = 3.14)$$

☐A. 31.41 square inches

☐B. 50.26 square inches

☐C. 78.87 square inches

☐D. 121.2 square inches

33- The volume of this box is:

☐A. 12 cm$$^3$$

☐B. 24 cm$$^3$$

☐C. 48 cm$$^3$$

☐D. 96 cm$$^3$$

34- If $$- 9a = 81$$, then $$a =$$ _______

☐A. $$-9$$

☐B. $$-8$$

☐C. 0

☐D. 9

35- A square has one side with length 8 feet. The area of the square is:

☐A. 16 square feet

☐B. 32 square feet

☐C. 64 square feet

☐D. 128 square feet

36- In the following right triangle, what is the value of $$x$$ rounded to the nearest hundredth?

☐A. 2.34

☐B. 6.70

☐C. 8.75

☐D. 9.85

37- $$(-3x +7) (3x-4) =$$ ?

☐A. $$-6x + 3$$

☐B. $$-9×2 + 33x – 28$$

☐C. $$-9×2 – 28$$

☐D. $$3x + 5$$

38- $$3(a –7)=34$$, what is the value of a?

☐A. 3.5

☐B. 7

☐C. 8.75

☐D. 15

39- If $$2^{18}=2^5× 2^x$$, what is the value of $$x$$?

☐A. 2

☐B. 8

☐C. 13

☐D. 16

40- Factor this expression: $$x^2 + 4x –21$$

☐A. $$x^2(4 – 21)$$

☐B. $$x(x + 4 – 21)$$

☐C. $$(x+7)(x-3)$$

☐D. $$(x-7)(x+3)$$

41- Find the slope of the line running through the points $$(4, 4)$$ and $$(7, 1)$$.

☐A. $$\frac{1}{3}$$

☐B. $$-1$$

☐C. 1

☐D. $$-\frac{1}{3}$$

42- The cube root of 4,197 is?

☐A. 7

☐B. 17

☐C. 70

☐D. 170

43- What is 87,456 in scientific notation?

☐A. 8.7456

☐B. $$0.087456 × 10^5$$

☐C. $$8.7456 × 10^4$$

☐D. $$87.456 × 10^4$$

44- What’s the area of the non-shaded part in the following figure?

☐A. 15

☐B. 20

☐C. 25

☐D. 35

45- A medium pizza has a diameter of 7 inches. What is its circumference?

☐A. $$3.5π$$

☐B. $$7π$$

☐C. $$14π$$

☐D. $$49π$$

46- A writer finishes 270 pages of his manuscript in 45 hours. How many pages is his average per hour?

☐A. 6

☐B. 8

☐C. 9

☐D. 12

47- Which of the following sets of factors do both 56 and 18 have in common?

☐A. {1, 2}

☐B. {6, 9, 14}

☐C. {0, 1, 2, 3}

☐D. {1, 3, 4, 18}

48- What is the circumference of a circle with center at point A if the distance from point $$X$$ to $$Y$$ is 10 feet? $$(π = 3.14)$$

☐A. 3.14 Feet

☐B. 15.7 Feet

☐C. 31.4 Feet

☐D. 314 Feet

49- In the following diagram, the straight line is divided by one angled line at 45$$^\circ$$. What is the value of a.

☐A. 45$$^\circ$$

☐B. 90$$^\circ$$

☐C. 135$$^\circ$$

☐D. 150$$^\circ$$

50- What’s the square root of $$49x^4$$?

☐A. $$7\sqrt{x}$$

☐B. $$7x$$

☐C. $$7x^2$$

☐D. $$7x^4$$

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