ASVAB Math Knowledge Practice Test 707217 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.98
Score	0%	60%

Review

Simplify (y + 6)(y - 3)

63% Answer Correctly

	y² - 9y + 18
	y² + 9y + 18
	y² + 3y - 18
	y² - 3y - 18

Solution

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 6)(y - 3)
(y x y) + (y x -3) + (6 x y) + (6 x -3)
y² - 3y + 6y - 18
y² + 3y - 18

The endpoints of this line segment are at (-2, -9) and (2, 1). What is the slope-intercept equation for this line?

41% Answer Correctly

	y = -1\(\frac{1}{2}\)x + 4
	y = 2\(\frac{1}{2}\)x - 4
	y = -x + 2
	y = 2\(\frac{1}{2}\)x - 2

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 -4. 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, -9) and (2, 1) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (-9.0)}{(2) - (-2)} \) = \( \frac{10}{4} \)
m = 2\(\frac{1}{2}\)

Plugging these values into the slope-intercept equation:

y = 2\(\frac{1}{2}\)x - 4

For this diagram, the Pythagorean theorem states that b² = ?

47% Answer Correctly

	c - a
	c² - a²
	a² - c²
	c² + a²

Solution

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c²= a² + b² or, solved for c, \(c = \sqrt{a + b}\)

If AD = 30 and BD = 29, AB = ?

76% Answer Correctly

	11
	20
	12
	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 = 30 - 29
AB = 1

Which of the following statements about math operations is incorrect?

70% Answer Correctly

	you can multiply monomials that have different variables and different exponents
	you can add monomials that have the same variable and the same exponent
	you can subtract monomials that have the same variable and the same exponent
	all of these statements are correct

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.