Full-Length AFOQT Math Practice Test

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 a length of 8 feet. The area of the square is:

A. 16 square feet

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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. \(7x^4\)

Answers and Explanations

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How to use Full-Length AFOQT Math Practice Test as real practice

Full-Length AFOQT Math Practice Test works best when it is used as a short, focused study session rather than a quick click-through activity. The goal is not simply to finish the questions. The goal is to notice which skills feel automatic, which skills still need review, and which mistakes happen when you rush.

Start with a clean piece of scratch paper. For each item, answer the questions under realistic conditions, then review every missed problem before retaking a similar set. If you get something wrong, do not immediately move on. Write the correct step, circle the part that caused the mistake, and try one similar item before continuing. That small correction habit is what turns an online practice test into lasting math improvement.

A three-round study routine

This routine is simple, but it solves a common problem: students often practice only until an answer looks familiar. Real readiness means you can solve a fresh problem without hints, explain the first step, and check whether the final answer is reasonable.

What to write down while you practice

Keep a tiny mistake log next to the activity. You only need three columns: the topic, the mistake, and the correction. For example, a student might write “fractions,” “forgot common denominator,” and “rewrite both fractions before adding.” A log like that is more useful than a long list of scores because it tells you exactly what to review next.

• If the mistake is a fact or formula, review it before the next round.
• If the mistake is a setup error, copy one worked example and label each step.
• If the mistake is from rushing, slow down and require written work for the next five items.
• If the same mistake appears twice, stop and review that topic before continuing.

When you are ready to move on

You are ready for the next topic when you can get several items correct in a row and explain why the method works. A score by itself is helpful, but it is not the whole story. You should also be able to describe the rule, formula, or pattern that the activity is testing.

For test preparation, come back to Full-Length AFOQT Math Practice Test after a day or two and try a fresh round. If the skill still feels easy after a short break, it is much more likely to stay with you during a quiz, unit test, or standardized test. If it feels shaky, that is useful information too: it tells you exactly where to spend your next study session.

Study tips for parents and teachers

When using this page with a student, ask for the reasoning before the answer. Questions such as “What is the first step?”, “Why did you choose that operation?”, and “How can you check it?” help students build mathematical language. That matters because many test questions measure more than calculation; they also measure whether the student can read the problem, choose a method, and explain a result.

Short sessions are usually best. Ten to fifteen minutes of careful practice can be more productive than a long session full of guessing. End by naming one skill that improved and one skill to review next time. That keeps practice positive, specific, and easy to continue.