ASVAB Math Knowledge Practice Test 387902 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.64
Score	0%	53%

Review

If BD = 21 and AD = 22, AB = ?

76% Answer Correctly

	1
	4
	10
	14

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 = 22 - 21
AB = 1

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

24% Answer Correctly

	c = π d
	c = π d²
	c = π r²
	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.

If side a = 3, side b = 6, what is the length of the hypotenuse of this right triangle?

64% Answer Correctly

	\( \sqrt{50} \)
	\( \sqrt{52} \)
	\( \sqrt{80} \)
	\( \sqrt{45} \)

Solution

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 3² + 6²
c² = 9 + 36
c² = 45
c = \( \sqrt{45} \)

Solve for a:
a - 7 < \( \frac{a}{9} \)

45% Answer Correctly

	a < 2\(\frac{2}{5}\)
	a < -\(\frac{18}{47}\)
	a < -\(\frac{8}{23}\)
	a < 7\(\frac{7}{8}\)

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 < sign and the answer on the other.

a - 7 < \( \frac{a}{9} \)
9 x (a - 7) < a
(9 x a) + (9 x -7) < a
9a - 63 < a
9a - 63 - a < 0
9a - a < 63
8a < 63
a < \( \frac{63}{8} \)
a < 7\(\frac{7}{8}\)

Factor y² + 3y - 4

54% Answer Correctly

	(y - 1)(y - 4)
	(y - 1)(y + 4)
	(y + 1)(y + 4)
	(y + 1)(y - 4)

Solution

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -4 as well and sum (Inside, Outside) to equal 3. For this problem, those two numbers are -1 and 4. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 3y - 4
y² + (-1 + 4)y + (-1 x 4)
(y - 1)(y + 4)