Arithmetic Reasoning & Math Knowledge
The two quantitative sections of the AFOQT are designed to test your understanding of basic math terms and problemsolving 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 Minutes; Items: 25
Math Knowledge Subtest Information: Time: 22 Minutes; Items: 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
 Properties/Types of Integers:

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%
C. 45.6%
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:
 C (3451/7562=.4563)
 D (V=LxWxH)
 E ($4.20/4 = $1.05; $4.20$1.05=$3.15)
 E (3925/4906)
 A (1×1.8+32=30.2)
 B (10×3) = 30 ; 12+18 = 30
 A (angles of a triangle add up to 180 deg)
 E
 D
 A
 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)
 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)
 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)
 A (After distributing the 2, the equation is equivalent to 6a 1 = 2a + 2. Simplifying, 4a = 3, so a = 3/4)
 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)
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