ASVAB Mathematics Knowledge Test
2022
Vision a box...
Side box 5cm
bottom right long side 4 cm
front bottom short side 3cm
The volume of this box is
A. 12 cm 3
B. 15 cm 3
C. 20 cm 3
D. 60 cm3
The correct answer is (D) 60 cm3.
The volume of a cubic rectangle is length x width x height:
3 x 4 x 5 = 60
If n is a positive integer divisible by 7, and if n < 70, what is the greatest possible value of n?
A. 49
B. 56
C. 63
D. 69
The correct answer is (C) 63. If you know one multiple of a number, you can find the other
multiples by adding and subtracting that number. The number 70 is divisible by 7. The
greatest multiple that is less than 70 will be 70 − 7 = 63.
Blair's average (arithmetic mean) on two physics tests is 7. What should Blair's score be on
the next test to have an overall average of 8 for all the tests?
A. 7
B. 8
C. 9
D. 10
The correct answer is (D) 10. The arithmetic mean is defined as the sum of the terms divided
by the number of terms.
7 = sum / 2
14 = sum
Adding the next test's score will change the average to an 8, and the total terms to 3.
8 = (14 + new score) / 3
24 = 14 + new score
10 = new score
(4x + 2) (x + 1) =
, A. 5x + 3
B. 4x2 + 6x + 2
C. 4x + 2x + 2
D. 4x2 + 2
The correct answer is (B) 4x2 + 6x + 2
This is a multiplying binomials problem. Multiply the first term in the first binomial by both
terms in the second binomial:
4x2 + 4x
Then multiply the second term in the first binomial by each term in the second binomial:
2x + 2
Adding them all together you get:
4x2 + 4x + 2x + 2
4x2 + 6x + 2
2 − 8 ÷ (24 ÷ 2) =
A. -6
B. -¾
C. 1
D. 2
The correct answer is (C) 1. Remember your order of operations:
Complete operations within parentheses first.
Calculate exponents.
Then multiply and divide in order from left to right.
Then add and subtract in order from left to right.
2 − 8 ÷ (24 ÷ 2) =
2 − 8 ÷ (16 ÷ 2) =
2−8÷8=
2−1=
1
3(x − 4) = 18, what is the value of x?
A. 3/2
B. 22/3
C. 6
D. 10
The correct answer is (D) 10. Begin by dividing both sides by 3 to open the parenthesis:
x−4=6
Add 4 to both sides to find x:
x = 10
A scoutmaster is preparing his troop for their annual fishing expedition. He surveys each of
his scouts to find out how many fishing poles they own.
2022
Vision a box...
Side box 5cm
bottom right long side 4 cm
front bottom short side 3cm
The volume of this box is
A. 12 cm 3
B. 15 cm 3
C. 20 cm 3
D. 60 cm3
The correct answer is (D) 60 cm3.
The volume of a cubic rectangle is length x width x height:
3 x 4 x 5 = 60
If n is a positive integer divisible by 7, and if n < 70, what is the greatest possible value of n?
A. 49
B. 56
C. 63
D. 69
The correct answer is (C) 63. If you know one multiple of a number, you can find the other
multiples by adding and subtracting that number. The number 70 is divisible by 7. The
greatest multiple that is less than 70 will be 70 − 7 = 63.
Blair's average (arithmetic mean) on two physics tests is 7. What should Blair's score be on
the next test to have an overall average of 8 for all the tests?
A. 7
B. 8
C. 9
D. 10
The correct answer is (D) 10. The arithmetic mean is defined as the sum of the terms divided
by the number of terms.
7 = sum / 2
14 = sum
Adding the next test's score will change the average to an 8, and the total terms to 3.
8 = (14 + new score) / 3
24 = 14 + new score
10 = new score
(4x + 2) (x + 1) =
, A. 5x + 3
B. 4x2 + 6x + 2
C. 4x + 2x + 2
D. 4x2 + 2
The correct answer is (B) 4x2 + 6x + 2
This is a multiplying binomials problem. Multiply the first term in the first binomial by both
terms in the second binomial:
4x2 + 4x
Then multiply the second term in the first binomial by each term in the second binomial:
2x + 2
Adding them all together you get:
4x2 + 4x + 2x + 2
4x2 + 6x + 2
2 − 8 ÷ (24 ÷ 2) =
A. -6
B. -¾
C. 1
D. 2
The correct answer is (C) 1. Remember your order of operations:
Complete operations within parentheses first.
Calculate exponents.
Then multiply and divide in order from left to right.
Then add and subtract in order from left to right.
2 − 8 ÷ (24 ÷ 2) =
2 − 8 ÷ (16 ÷ 2) =
2−8÷8=
2−1=
1
3(x − 4) = 18, what is the value of x?
A. 3/2
B. 22/3
C. 6
D. 10
The correct answer is (D) 10. Begin by dividing both sides by 3 to open the parenthesis:
x−4=6
Add 4 to both sides to find x:
x = 10
A scoutmaster is preparing his troop for their annual fishing expedition. He surveys each of
his scouts to find out how many fishing poles they own.
