FREE AFOQT Math Practice Test

1- An athletic team has a $20,000 budget and has already spent $14,000 on uniforms. New athletic shoes cost $120 per pair. Which inequality represents the maximum number of pairs of shoes \(x\) the team can purchase without exceeding the budget?

A. \(120x + 14{,}000 \le 20{,}000\)

B. \(120x + 14{,}000 \ge 20{,}000\)

C. \(120x – 14{,}000 \le 20{,}000\)

D. \(20{,}000 – 14{,}000 \le 120x\)

2- A trapezoid has a perimeter of \(36\) cm. Three of its sides measure \(8\) cm, \(12\) cm, and \(6\) cm; the fourth side is the height. What is the area of the trapezoid?

A. \(35 cm^2\)

B. \(70 cm^2\)

C. \(48 cm^2\)

D. \(24 cm^2\)

3- A bank is offering \(3.5\%\) simple interest on a savings account. If you deposit $12,000, how much interest will you earn in two years?

A. \($420\)

B. \($840\)

C. \($4200\)

D.\($8400\)

4- Which of the following graphs represents the compound inequality \(-2{\leq}2x-4<8\)?

A.

B.

C.

D.

5- Last week \(24,000\) fans attended a football match. This week three times as many bought tickets, but one-sixth of them canceled their tickets. How many are attending this week?

A.\(48,000\)

B. \(54,000\)

C.\(60,000\)

D. \(72,000\)

6- In the \(xy\)-plane, the point \(4,3\) and \(3,2\) are on line A. Which of the following points could also be on line A?

A. (-1, 2)

B. (5, 7)

C. (3, 4)

D. (-1, -2)

7- What is the equivalent temperature of \(104^{\circ}\) F in Celsius?
C = \(\frac{5}{9}\) F \(- 32\)

A. 32

B. 40

C. 48

D. 52

8- If \(150\%\) of a number is 75, then what is the \(90\%\) of that number?

A. 45

B. 50

C. 70

D. 85

9- Simplify the expression:
\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 )\)

A. \(4x^3-12x^2\)

B. \(4x^4+4x^3-12x^2\)

C. \(8x^3-12x^2\)

D. \(x^4+4x^3-12x^2\)

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

A. \(32\%\)

B. \(35\%\)

C. \(38\%\)

D. \(68\%\)

11- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. (200) (0.70)

B. (200) – 200 (0.30)

C. (200) (0.15) – (200) (0.15)

D. (200) (0.85) (0.85)

12- In a stadium, the ratio of home fans to visiting fans in a crowd is 5:7. Which of the following could be the total number of fans in the stadium?

A. 12,324

B. 42,326

C. 44,566

D. 66,812

13- In a classroom of 60 students, 42 are female. What percentage of the class is male?

A. \(34\%\)

B. \(22\%\)

C. \(30\%\)

D.  \(26\%\)

14- Which of the following points lies on the line \(x+2y=4\)?

A. (-2, 3)

B. (1, 2)

C. (–1, 3)

D.  (-3, 4)

15- During the last week of track training, Emma achieves the following times in seconds: 66, 57, 54, 64, 57, and 59. Her three best times this week (least times) are averaged for her final score on the course. What is her final score?

A. 56 seconds

B. 57 seconds

C. 59 seconds

D. 61 seconds

16- 5 less than twice a positive integer is 83. What is the integer?

A. 39

B. 41

C. 42

D. 44

17- How many square feet of tile is needed for a 15 feet \(x\) 15 feet room?

A. 225 square feet

B. 118.5 square feet

C. 112 square feet

D. 60 square feet

18- 11 yards 6 feet and 4 inches equal to how many inches?

A. 388

B. 468

C. 472

D. 476

19- Mr. Carlos’s family is choosing a menu for their reception. They have 3 choices of appetizers, 5 choices of entrees, 4 choices of cake. How many different menu combinations are possible for them to choose from?

A. 12

B. 32

C. 60

D. 120

20- The average of five consecutive numbers is 38. What is the smallest number?

A. 38

B. 36

C. 34

D. 12

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Answers:

2- B
The perimeter of the trapezoid is \(36 cm\).
Therefore, the missing side (height) is =\( 36 – 8 – 12 – 6 = 10\)
Area of a trapezoid: \(A = \frac{1}{2} h ({b_{1} + b_{2}}) = \frac{1}{2} (10) (6 + 8) = 70\)

3- B
Use simple interest formula:
\(I=prt\)
\((I = interest, p = principal, r = rate, t = time)\)
\(=(12000)(0.035)(2)=840\)

4- D
Solve for \(x\).
\(-2 {\leq} 2x-4 < 8 ⇒\) (add 4 all sides) \(-2+4 {\leq} 2x-4+4 < 8+4 {\Rightarrow}\)
\(2{\leq}2x<12 {\Rightarrow}\) (divide all sides by 2) \(1 {\leq}x < 6\)
\(x\) is between \(1\) and \(6\).

5- C
Three times of \(24,000\) is \(72,000\). One-sixth of them canceled their tickets.
One sixth of \972,000\) equals \(12,000\) \((\frac{1}{6}\) \(\times\) \(72000\) = \(12000)\).
\(60,000\) \((72000 – 12000 = 60000)\) fans are attending this week

6- D
The equation of a line is in the form of \(y=mx+b\), where m is the slope of the line and b is the y-intercept of the line.
Two points \(4,3\) and \(3,2\) are on line A. Therefore, the slope of the line A is:
slope of line \(A=\frac{(y_2- y_1)}{(x_2 – x_1) } =\frac{2-3}{3-4} = \frac{-1}{-1}\)
The slope of line A is 1. Thus, the formula of the line A is:
\(y=mx+b=x+b\), choose a point and plug in the values of x and y in the equation to solve for b. Let’s choose point \(4, 3\). Then:
\(y=x+b\)\(\rightarrow\)\(3=4+b\)\(\rightarrow\)\(b=3-4=-1\)
The equation of line A is: \(y=x-1\)
Now, let’s review the choices provided:
A. \((-1,2)\) \(y=x-1\)\(\rightarrow\)\(2=-1-1=-2\) (This is not true.)
B. \((5,7)\) \(y=x-1\)\(\rightarrow\)\(7=5-1=4\) (This is not true.)
C. \((3,4)\) \(y=x-1\)\(\rightarrow\)\(4=3-1=2\) (This is not true.)
D. \((-1,-2)\) \(y=x-1\)\(\rightarrow\)\(-2=-1-1=-2\) (This is true!)

7- B
Plug in 104 for F and then solve for C.
\(C = \frac{5}{6} (F – 32) {\Rightarrow} C = \frac{5}{9} (104 – 32) {\Rightarrow} C = \frac{5}{9} (72) = 40\)

8- A
First, find the number.
Let \(x\) be the number. Write the equation and solve for \(x\).
\(150\%\) of a number is 75, then:
\(1.5{\times}x=75 {\Rightarrow} x=75{\div}1.5=50\)
\(90\%\) of 50 is:
\(0.9 {\times} 50 = 45\)

9- B
Simplify and combine like terms.
\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 ) {\Rightarrow} (6x^3-8x^2+2x^4 )-4x^2+2x^4-2x^3 {\Rightarrow}
4x^4+4x^3-12x^2\)

10- C
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 \(120\%\).
\((1.15)\) \(\times\) \((1.20)\) = \(1.38\) = \(138\%\)
38 percent of the population is increased after two years.

11- C
To find the discount, multiply the number by \(100{%} -\) rate of discount.
Therefore, for the first discount we get: \(200\) \(100{%} – 15{%}\) = \(200\) \(0.85\) = \(170\)
For the next 15{%} discount: \(200\) \(0.85\) \(0.85\)

12- A
In the stadium, the ratio of home fans to visiting fans in a crowd is 5:7. Therefore, total number of fans must be divisible by \(12: 5 + 7 = 12\).
Let’s review the choices:
A. \(12,324: 12,324 (\div ) 12 = 1027\)
B. \(42,326 42,326 (\div ) 12 = 3,527.166\)
C. \(44,566 44,566 (\div ) 12 = 3,713.833\)
D. \(66,812 66,812 (\div ) 12 = 5,567.666\)
Only choice A when divided by 12 results a whole number.

13- C
\(60 – 42 = 18\) male students
\(\frac{18}{60} = 0.3 \)
Change 0.3 to percent ⇒\(0.3 × 100\) =\(30\%\)

14- A
\((x+2y=4)\). Plug in the values of x and y from choices provided. Then:
A. \(-2,3\) \(x+2y=4\)\(\rightarrow \)\(-2+2(3)=4\)\(\rightarrow \)\(-2+6=4\) (This is true!)
B. \((1,2)\) \(x+2y=4\)\(\rightarrow\)\(1+2(2)=4\)\(\rightarrow\)\(1+4=4\) (This is NOT true!)
C. \((-1,3)\) \(x+2y=4\)\(\rightarrow \)\(-1+2(3)=4\)\(\rightarrow\)\(-1+6=4\) (This is NOT true!)
D. \((-3,4)\) \(x+2y=4\)\(\rightarrow\)\(-3+2(4)=4\)\(\rightarrow\)\(-3+8=4\) (This is NOT true!)

15- A
Emma’s three best times are 54, 57, and 57.
The average of these numbers is:
average \(=\frac{sum}{total}\)
Sum \(= 54 + 57 + 57 = 168\)
Total number of numbers = 3
average \(=\frac{168}{3}=56\)

16- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add 5 both sides: \(2x = 88\)
Divide both sides by 2:\( x = 44\)

17- A
The area of a 15 feet\(x\) 15 feet room is 225 square feet.
\(15 × 15 = 225\)

18- C
\(11 \times 36 + 6 \times 12 + 4 = 47\)

19- C
To find the number of possible outfit combinations, multiply number of options for each factor:
\(3\) \(\times\) \(5\) \(\times\) \(4 = 60\)

20- B
Let \(x\) be the smallest number. Then, these are the numbers:
\( x, x+1, x+2, x+3, x+4 \)
average =\(\frac{sum of terms}{number of terms} \Rightarrow 38 = \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5} \Rightarrow 38= \frac{5x+10}{5} \Rightarrow 190 = 5x+10 \Rightarrow 180 = 5x \Rightarrow x=36\)

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Frequently Asked Questions

How many math subtests are on the AFOQT?

Two: Arithmetic Reasoning (AR) and Math Knowledge (MK). AR is 25 questions in 29 minutes, focused on applied math word problems. MK is 25 questions in 22 minutes, focused on algebra, geometry, and number theory.

Is a calculator allowed on the AFOQT?

No. The AFOQT is administered without a calculator on every subtest. Practice mental arithmetic, fraction work, and quick estimation strategies before test day.

Is there a formula sheet on the AFOQT?

No. The AFOQT does not provide a formula reference. Walk in with area, perimeter, volume, slope, the Pythagorean theorem, the quadratic formula, and exponent rules memorized cold.

What’s the minimum Quantitative score to qualify?

The minimum AFOQT score to be considered for most Air Force officer training programs is 15 in the Quantitative composite and 15 in the Verbal composite. Pilot candidates need higher in the Pilot composite (usually 25+). Most competitive applicants score in the 70s or higher.

What math topics are on the AFOQT?

AR covers arithmetic word problems: fractions, decimals, percentages, ratios, work/rate problems, mixture problems, and basic probability. MK covers algebra (equations, exponents, factoring, radicals), geometry (area, volume, angles, triangles), and number properties.

How long is the AFOQT test in total?

About 3.5 hours of testing time across 11 subtests on AFOQT Form T, plus around an hour of administrative time. The two math sections together take 51 minutes (29 + 22).

How is the AFOQT scored?

Raw scores convert to percentile scores from 1 to 99 in six composite areas: Pilot, Combat Systems Officer (CSO), Air Battle Manager (ABM), Academic Aptitude, Verbal, and Quantitative. Each composite uses a different weighted combination of subtests.

Can I retake the AFOQT?

Yes, but only once. You must wait 150 days between attempts, and the most recent score replaces the prior score (not the higher of the two). Don’t retake unless you’ve changed something substantial in your prep.

How long should I study for the AFOQT?

Most successful candidates put in 8 to 12 weeks of dedicated study at 60-90 minutes per day, with about half that time on math. Prioritize the topics where you can move from weak to strong fastest — algebra fundamentals and geometry formulas usually give the biggest score lift per study hour.

What’s the difference between AFOQT and ASVAB math?

The AFOQT math is harder and more compressed. AR on the AFOQT has the same general format as ASVAB AR but with more multi-step word problems. MK on the AFOQT runs heavier on algebra and includes more advanced topics. The AFOQT is officer-track only; the ASVAB is for enlisted entry.

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