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)
(Answers provided at the bottom of the page)
Practice Questions
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
16
Three consecutive even integers have a sum of 102. If x represents the least number in the set, what equation can be used to determine the value of the sum of the integers?
A
x + (x + 2) + (x + 4) = 102
B
x + (x + 1) + (x + 3) = 102
C
x + (x + 1) + (x + 2) = 102
D
x + 2x + 4x = 102
E
x + x + x = 102
17
Allison drove from her house to a friend’s house 420 kilometers away. She left at 10:30 a.m. and arrived at 3:50 p.m., making one stop along the way for a snack. If Allison’s average speed for the trip whilst driving was 90 kilometers per hour, how long was her snack break?
A
10 minutes
B
20 minutes
C
40 minutes
D
1 hour
E
1 hour and 20 minutes
18
Each person in a room is a freshman or a sophomore. The number of freshman in the room is 7 times the number of sophomores. Which of the following could be the number of people in the room? Indicate ALL such numbers.
A
14
B
26
C
35
D
48
E
49
19
Lauren bought a new cell phone, cell phone case and an external battery charger. The cell phone cost $149.99, the case cost $24.99 and the charger was $29.99. If the tax on each item was 9.5%, which of the following is closest to the amount Lauren spent?
A
$175
B
$200
C
$210
D
$224
E
$250
20
The exterior angle of triangle XYZ at vertex X is 130° and the exterior angle at vertex Y is 110°. What is the interior angle at vertex Z?
A
40°
B
60°
C
70°
D
110°
E
120°
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)
- A
- C
- D (If the number of sophomores in the room is x, then the number of freshman is 7x. The total number of people in the room is 7x + x = 8x. The number of people in the room (8x) must be a multiple of 8.)
- D
- B (The sum of the exterior angles of any polygon is 360°, so the exterior angle at vertex Z is 360°-130°-110° = 120°. However, this is not the value of the question asked. Since the sum of the interior angle of a polygon and its exterior angle is 180°, the interior angle at vertex Z is 180°-120° = 60°)
