ASVAB Math Knowledge Practice Test 640431 Results

Your Results Global Average
Questions 5 5
Correct 0 3.20
Score 0% 64%

Review

1

If side a = 2, side b = 8, what is the length of the hypotenuse of this right triangle?

64% Answer Correctly
\( \sqrt{98} \)
\( \sqrt{26} \)
\( \sqrt{18} \)
\( \sqrt{68} \)
Solution

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

c2 = a2 + b2
c2 = 22 + 82
c2 = 4 + 64
c2 = 68
c = \( \sqrt{68} \)

2

The dimensions of this cylinder are height (h) = 3 and radius (r) = 5. What is the surface area?

48% Answer Correctly
16π
182π
96π
80π
Solution

The surface area of a cylinder is 2πr2 + 2πrh:

sa = 2πr2 + 2πrh
sa = 2π(52) + 2π(5 x 3)
sa = 2π(25) + 2π(15)
sa = (2 x 25)π + (2 x 15)π
sa = 50π + 30π
sa = 80π

3

The dimensions of this cylinder are height (h) = 1 and radius (r) = 5. What is the volume?

63% Answer Correctly
448π
324π
25π
4π
Solution

The volume of a cylinder is πr2h:

v = πr2h
v = π(52 x 1)
v = 25π

4

Which of the following statements about math operations is incorrect?

71% Answer Correctly

you can add monomials that have the same variable and the same exponent

all of these statements are correct

you can multiply monomials that have different variables and different exponents

you can subtract monomials that have the same variable and the same exponent
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.

5

This diagram represents two parallel lines with a transversal. If d° = 166, what is the value of c°?

73% Answer Correctly
150
170
14
161
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 d° = 166, the value of c° is 14.