ASVAB Math Knowledge Practice Test 555766 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.91
Score	0%	58%

Review

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

36% Answer Correctly

	same-side interior angles are complementary and equal each other
	all acute angles equal each other
	all of the angles formed by a transversal are called interior angles
	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°).

If BD = 27 and AD = 28, AB = ?

75% Answer Correctly

	2
	5
	6
	1

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 = 28 - 27
AB = 1

Simplify (3a)(5ab) + (2a²)(7b).

65% Answer Correctly

	-a²b
	29a²b
	a²b
	72a²b

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.

(3a)(5ab) + (2a²)(7b)
(3 x 5)(a x a x b) + (2 x 7)(a² x b)
(15)(a¹⁺¹ x b) + (14)(a²b)
15a²b + 14a²b
29a²b

This diagram represents two parallel lines with a transversal. If b° = 162, what is the value of x°?

72% Answer Correctly

	27
	162
	161
	20

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 b° = 162, the value of x° is 162.

The endpoints of this line segment are at (-2, 0) and (2, 2). What is the slope-intercept equation for this line?

41% Answer Correctly

	y = x + 1
	y = \(\frac{1}{2}\)x + 1
	y = -1\(\frac{1}{2}\)x + 1
	y = -1\(\frac{1}{2}\)x + 3

Solution

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 0) and (2, 2) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(2.0) - (0.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)
m = \(\frac{1}{2}\)

Plugging these values into the slope-intercept equation:

y = \(\frac{1}{2}\)x + 1