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ASVAB Section 6 : Mathematics Knowledge
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Question: 223
What’s the mode of the following series of numbers? 4, 4, 8, 8, 8, 10, 10, 12, 12
Answer: B
The mode of a series of numbers is the number that appears in the series the most frequently. In this case, it’s 8.
Question: 224
If a = 4, then a3 ÷ a = .
Answer: D
(4 × 4 × 4) ÷ 4 = 64 ÷ 4 = 16
Question: 225
Which of the following is a prime number?
Answer: B
A prime number is a number that can be divided evenly by itself or by one, but not by any other number. Choices 27, 8 and 4 can all be divided evenly by other numbers.
Question: 226
(x + 4)(x + 2) =
.
Answer: D
Multiply the first variable in the first set of parentheses with the first variable in the second set of parentheses (x × x = x2).
Next, multiply the first variable in the first set of parentheses with the second number in the second set of parentheses (x × 2 = 2x). So far, the results are x2+ 2x.
Now, multiply the second number in the first set of parentheses to the first variable in the second set of parentheses (4 × x = 4x).
Next, multiply the second variable in the first set of parentheses to the second number in the second set of parentheses (4 × 2 = 8). The solution is x2+ 2x + 4x + 8. Combining the like terms results in x2+ 6x + 8.
Question: 227
1.5 × 103= .
Answer: C
1.5 × 103= 1.5 × (10 × 10 × 10) = 1.5 × 1,000 = 1,500.
Question: 228
(12 yards + 14 feet) ÷ 5 =
.
Answer: C
Convert 12 yards and 14 feet to feet:
(12 yards × 3 feet per yard) + 14 feet = 36 feet + 14 feet = 50 feet. Divide by 5 as instructed: 50 feet ÷ 5 = 10 feet.
Question: 229
x3 × x4 = .
Answer: D
If two powers have the same base, they can be multiplied by keeping the base and adding the powers together.
Question: 230
The fourth root of 16 is .
Answer: D
24 = 16; the fourth root of 16 is 2.
Question: 231
What’s the equation of a line that passes through points (0, – 1) and (2, 3)?
Answer: A
The slope of the line is equal to the change in y values divided by the change in x values. The change in y values is 4(3 – -1). The change in x values is 2 (2 – 0). 4/2 = 2.
To find the intercept, substitute 0 for x in the equation y = 2x + b – 1 = 2(0) + b. Therefore, b = -1, so the equation is y = 2x – 1.
Question: 232
The cube of 5 is .
Answer: A
The cube of 5 = 5 × 5 × 5 = 125.
Question: 233
2.5 × 33 = .
Answer: C
2.5 × 33= 2.5 (3 × 3 × 3) = 2.5 × 27 = 67.50.
Question: 234
If x = 8, what’s the value of y in the equation: y = (x2 ÷ 4) – 2?
4
6
8
0
Answer: A
– 2 y = (82 ÷ 4) – 2 y = (64
÷ 4) – 2 y = 16 – 2 = 14