Arithmetic Reasoning & Math Knowledge

The two quantitative sections of the AFOQT are designed to test your understanding of basic math terms and problem-solving methods taught in high school and lower level college courses. Much like the Graduate Record Examination (GRE), there are three content areas of which the bulk of your quantitative study should focus:

Arithmetic Reasoning Subtest Information: Time: 29 MinutesItems: 25

Math Knowledge Subtest Information: Time: 22 MinutesItems: 25

AFOQT Mathematical Concepts to Master:

I. Arithmetic

      • Properties/Types of Integers:
        • Divisibility
        • Factorization
        • Prime Numbers
        • Remainders
        • Odd & Even Integers
        • Arithmetic Operations
        • Exponents & Roots
      • Concepts You Should Be Familiar With:
        • Estimation
        • Percent
        • Ratio
        • Rate
        • Absolute Value
        • The Number Line
        • Decimal Representation
        • Number Sequences

II. Algebra

        • Operations with Exponents
        • Factoring & Simplifying Algebraic Expressions
        • Relations
        • Functions
        • Equations & Inequalities (Solving Simultaneous Equations & Inequalities)
        • Setting Up Equations to Solve Word Problems

III. Geometry

        • Parallel & Perpendicular Lines
        • Circles (Find Area: (3.14)(r^2))
        • Triangles (Area & Perimeter)
        • Isósceles, Equilateral
        • Pythagorean Theorem
        • Rectangles, Squares (Area & Perimeter)
        • Cylinders (Area, Volume)

Practice Questions:

(Answers provided at the bottom of the page)

1) Of 7,562 college students, 3,451 have taken part in some intramural sport program. What percentage of students have played intramural sports?

A. 56.7%

B. 65.2%

C45.6%

D.  57.2%

E. 34.6%

2) A shipping container has a length of 327 feet and a width of 15.3 feet. If the height is 12.6 feet, what is the volume of the container (rounded to the nearest whole number)?

A. 19,975 cubic feet

B.  82,357 cubic feet

C.  23,965 cubic feet

D.  63,039 cubic feet

E.  76,346 cubic feet

3)  If a pound of rice costs $4.20, how much does ¾ pound cost?

A. $4.00

B. $3.75

C. $3.35

D. $3.95

E.  $3.15

4) Of 4,906 participants surveyed by an energy company, 80% are in favor of increasing the solar energy program, while 9% are not. How many people are in favor of increasing the solar energy program?

A. 2,446

B. 3,451

C. 7,394

D. 4,276

E. 3,925

5) The temperature in Calgary is -1°C. Using the formula F° = C°x (9/5) + 32, what is the temperature in degrees Fahrenheit?

A. 30.2

B. 32

C. 29

D. 29.8

E. 33

6) Which of the following choices completes this equation: (_____) = (9 x 2) + (4 x 3)

A. (10 + 3)

B. (10 x 3)

C. (36 + 6)

D. (9 x 6)

E. (5 x 4)

7) A triangle has angles A (55°) and B (65°). What is the measure of angle C?

A. 60°

B.  65°

C.  70°

D.  75°

E.  80°

8) Which is another way to write 5.97 x 10^3?

A. 0.597

B. 5.97

C. 59,700

D. 597

E. 5,970

9) How many inches are there in 3 4/9 yards (rounded to nearest whole number)?

A. 36 in

B. 24 in

C. 82 in

D. 124 in

E. 187 in

10) Which value of ‘x’ will make the number sequence 4x + 27 ≤ 90 true?

A. 14

B. 19

C. 16

D. 17

E. 20

11) If x > 0, what is the median of the data set consisting of -3x, -6x, x, -9x, and 5x?

A. -3x

B. -6x

C. x

D. -9x

E. 5x

12) A game’s card set consists of 7 orange cards and 21 blue cards. If a player randomly selects one of these cards, what is the probability it will be orange?

A. 2/5

B. 3/8

C. 1/4

D. 1/3

E. 2/3

13) What is the value of x when 5x – 5 = 6x + 8?

A. 11

B. 30

C. -13

D. 3

E. -3

14) What is the value of a when 6a – 1 = 2(a + 1)?

A. 3/4

B. 3/8

C. 1/2

D. 0

E. 5/2

15) In square meters, what is the area of a rectangle with a diagonal of 25 meters and a width of 15 meters?

A. 250

B. 225

C. 275

D. 300

E. 350

Answers:

  1. C (3451/7562=.4563)
  2. D (V=LxWxH)
  3. E ($4.20/4 = $1.05; $4.20-$1.05=$3.15)
  4. E (3925/4906)
  5. A (-1×1.8+32=30.2)
  6. B (10×3) = 30 ; 12+18 = 30
  7. A (angles of a triangle add up to 180 deg)
  8. E
  9. D
  10. A
  11. A (-9x, -6x, -3x, x, 5x; Since we know x is positive, the terms can be placed in order from smallest to largest. By definition the median is the middle term in this list)
  12. C (There are a total of 28 cards – 7 orange; 21 blue. Therefore the probability of selecting an orange card is: 7/28 = 1/4)
  13. C (The goal here is to isolate the variable to one side with the constants on the other. By subtracting 5x from both sides, you can rewrite the equation as: -5 = x + 8. This simplifies to x = -13 when 8 is subtracted from both sides)
  14. A (After distributing the 2, the equation is equivalent to 6a -1 = 2a + 2. Simplifying, 4a = 3, so a = 3/4)
  15. D (The diagonal forms a right triangle with the width and the length acting as legs. Using the Pythagorean theorem, the length of the triangle will be √25^2 – 15^2 = √400 = 20, and the area will be 20 x 15 = 300)

Meet Tom

AFOQT Guide User #1

Hi there! I’m the guy who created AFOQTGuide.com. Upon completion of my Air Force enlistment, I decided it was time to pursue my college education. While attending the University of Michigan… More About Tom

Get The AFOQT Guide Newsletter

Have You Given Up On Your AFOQT Study Session?

Ensure You’re Ready When Test Day Arrives. Prep With A Full-Form ‘Form T’ Practice Test.