ASVAB Math Knowledge Practice Test 109769 Results

Your Results Global Average
Questions 5 5
Correct 0 3.14
Score 0% 63%

Review

1

Solve for a:
a - 3 = \( \frac{a}{5} \)

46% Answer Correctly
3\(\frac{3}{4}\)
\(\frac{1}{2}\)
1\(\frac{9}{31}\)
-1\(\frac{1}{9}\)

Solution

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

a - 3 = \( \frac{a}{5} \)
5 x (a - 3) = a
(5 x a) + (5 x -3) = a
5a - 15 = a
5a - 15 - a = 0
5a - a = 15
4a = 15
a = \( \frac{15}{4} \)
a = 3\(\frac{3}{4}\)


2

What is the circumference of a circle with a diameter of 5?

71% Answer Correctly
14π
10π
12π

Solution

The formula for circumference is circle diameter x π:

c = πd
c = 5π


3

Which of the following statements about math operations is incorrect?

71% Answer Correctly

you can multiply monomials that have different variables and different exponents

you can subtract monomials that have the same variable and the same exponent

all of these statements are correct

you can add monomials that have the same variable and the same exponent


Solution

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.


4

If AD = 30 and BD = 23, AB = ?

76% Answer Correctly
8
17
4
7

Solution

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

Solving for AB:

AB = AD - BD
AB = 30 - 23
AB = 7


5

Solve for x:
x2 + 9x + 11 = -x + 2

49% Answer Correctly
4 or 1
9 or 2
-1 or -9
4 or -8

Solution

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

x2 + 9x + 11 = -x + 2
x2 + 9x + 11 - 2 = -x
x2 + 9x + x + 9 = 0
x2 + 10x + 9 = 0

Next, factor the quadratic equation:

x2 + 10x + 9 = 0
(x + 1)(x + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x + 9) must equal zero:

If (x + 1) = 0, x must equal -1
If (x + 9) = 0, x must equal -9

So the solution is that x = -1 or -9