ASVAB Math Knowledge Practice Test 86865 Results

Your Results Global Average
Questions 5 5
Correct 0 2.86
Score 0% 57%

Review

1

Which of the following is not true about both rectangles and squares?

63% Answer Correctly

the area is length x width

the lengths of all sides are equal

all interior angles are right angles

the perimeter is the sum of the lengths of all four sides


Solution

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).


2

Simplify 8a x 2b.

86% Answer Correctly
16ab
16\( \frac{a}{b} \)
10ab
16\( \frac{b}{a} \)

Solution

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

8a x 2b = (8 x 2) (a x b) = 16ab


3

The formula for the area of a circle is which of the following?

24% Answer Correctly

c = π r

c = π d2

c = π d

c = π r2


Solution

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.


4

If a = c = 8, b = d = 9, and the blue angle = 71°, what is the area of this parallelogram?

66% Answer Correctly
72
20
42
24

Solution

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 8 x 9
a = 72


5

Solve for c:
c2 - 4c - 1 = -4c + 3

48% Answer Correctly
9 or -9
4 or -1
-2 or -7
2 or -2

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:

c2 - 4c - 1 = -4c + 3
c2 - 4c - 1 - 3 = -4c
c2 - 4c + 4c - 4 = 0
c2 - 4 = 0

Next, factor the quadratic equation:

c2 - 4 = 0
(c - 2)(c + 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 2) must equal zero:

If (c - 2) = 0, c must equal 2
If (c + 2) = 0, c must equal -2

So the solution is that c = 2 or -2