ASVAB Math Knowledge Practice Test 106404 Results

Your Results Global Average
Questions 5 5
Correct 0 2.23
Score 0% 45%

Review

1

Solve for a:
a2 - 16a + 35 = -4a + 3

48% Answer Correctly
4 or 8
-1 or -2
3 or -2
6 or -5
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:

a2 - 16a + 35 = -4a + 3
a2 - 16a + 35 - 3 = -4a
a2 - 16a + 4a + 32 = 0
a2 - 12a + 32 = 0

Next, factor the quadratic equation:

a2 - 12a + 32 = 0
(a - 4)(a - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 4) or (a - 8) must equal zero:

If (a - 4) = 0, a must equal 4
If (a - 8) = 0, a must equal 8

So the solution is that a = 4 or 8

2

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

24% Answer Correctly

c = π r2

c = π d2

c = π d

c = π r
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.

3

Which of the following statements about parallel lines with a transversal is not correct?

36% Answer Correctly

all acute angles equal each other

all of the angles formed by a transversal are called interior angles

same-side interior angles are complementary and equal each other

angles in the same position on different parallel lines are called corresponding angles
Solution

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

4

Find the value of c:
6c + x = -2
9c - 3x = -1

42% Answer Correctly
2\(\frac{3}{4}\)
1\(\frac{1}{4}\)
-1\(\frac{19}{42}\)
-\(\frac{7}{27}\)
Solution

You need to find the value of c so solve the first equation in terms of x:

6c + x = -2
x = -2 - 6c

then substitute the result (-2 - 6c) into the second equation:

9c - 3(-2 - 6c) = -1
9c + (-3 x -2) + (-3 x -6c) = -1
9c + 6 + 18c = -1
9c + 18c = -1 - 6
27c = -7
c = \( \frac{-7}{27} \)
c = -\(\frac{7}{27}\)

5

This diagram represents two parallel lines with a transversal. If x° = 164, what is the value of w°?

73% Answer Correctly
16
160
157
39
Solution

For parallel lines with a transversal, the following relationships apply:

  • angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
  • alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
  • all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
  • same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with x° = 164, the value of w° is 16.