ASVAB Mathematics Knowledge Test
(4x + 2) (x + 1) =
A. 5x + 3
B. 4x2 + 6x + 2
C. 4x + 2x + 2
D. 4x2 + 2 - ANS-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 - ANS-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 - ANS-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 rectangle is cut in half to create two squares that each have an area of 25. What is the
perimeter of the original rectangle?
A. 20
B. 25
C. 30
D. 35 - ANS-Question 11 Explanation: The correct answer is (C) 30. The formula to find the area
of a square is side x side. If each square has an area of 25, then the dimensions of the
rectangle are 5 x 10. The perimeter is the sum of all the sides, and would therefore be 5 + 10 +
5 + 10 = 30.
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.
fishing pole owned
What is the mode of this data set?
A. 0
B. 1
C. 2
D. 3 - ANS-The correct answer is (A) 0. The mode of the data is the number that appears the
most often. In this case the largest number of scouts (7) own 0 fishing poles.
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 - ANS-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
If (3.2 + 3.3 + 3.5)w = w, then what is the value of w?
(4x + 2) (x + 1) =
A. 5x + 3
B. 4x2 + 6x + 2
C. 4x + 2x + 2
D. 4x2 + 2 - ANS-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 - ANS-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 - ANS-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 rectangle is cut in half to create two squares that each have an area of 25. What is the
perimeter of the original rectangle?
A. 20
B. 25
C. 30
D. 35 - ANS-Question 11 Explanation: The correct answer is (C) 30. The formula to find the area
of a square is side x side. If each square has an area of 25, then the dimensions of the
rectangle are 5 x 10. The perimeter is the sum of all the sides, and would therefore be 5 + 10 +
5 + 10 = 30.
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.
fishing pole owned
What is the mode of this data set?
A. 0
B. 1
C. 2
D. 3 - ANS-The correct answer is (A) 0. The mode of the data is the number that appears the
most often. In this case the largest number of scouts (7) own 0 fishing poles.
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 - ANS-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
If (3.2 + 3.3 + 3.5)w = w, then what is the value of w?
