ASVAB Math Knowledge Practice Test 2

Distribute first: 4x + 12 − 2x = 20, so 2x + 12 = 20, 2x = 8 and x = 4. The answer 8.5 comes from multiplying only the x by 4 (4x + 3 − 2x = 20).

Simplify each root: 50 = 25 × 2 = 52 and 18 = 9 × 2 = 32. Like radicals add like terms: 52 + 32 = 82. Adding the numbers under one root (68) is not allowed, and 152 multiplies 5 × 3 instead of adding.

Absolute value is the distance from zero, so |−7| = 7 and |3 − 10| = |−7| = 7. Then 7 − 7 = 0. The answer −14 ignores both absolute value signs.

Add the two equations: 2x = 14, so x = 7. Then y = 10 − 7 = 3. Check: 7 − 3 = 4. The answer 7 is the value of x, not y.

A negative exponent means the reciprocal: x⁻² = 1 ÷ x² = 1 ÷ 14 = 4. A negative exponent does not make the result negative, so −4 and −14 are wrong.

Both 7 × 7 and (−7) × (−7) equal 49, so the equation has two solutions. Writing only x = 7 misses the negative root, and 24.5 comes from dividing 49 by 2.

Raise each factor to the third power: 3³ = 27, (a²)³ = a⁶ and b³. The coefficient 9 comes from multiplying 3 × 3 instead of cubing it, and a⁵ comes from adding the exponents 2 + 3 instead of multiplying them.

Complementary angles add up to 90°, so the complement is 90° − 37° = 53°. The answer 143° is the supplement (180° − 37°).

The radius is half the diameter, 5 cm, so the area is πr² = π × 5² = 25π square centimeters. The answer 100π uses the diameter in place of the radius, and 10π is the circumference.

By the Pythagorean theorem, c² = 8² + 15² = 64 + 225 = 289, so c = 17 inches. The answer 23 simply adds the legs, which is always too long.

A cube has 6 equal square faces, so each face has an area of 54 ÷ 6 = 9 square inches and each edge is 3 inches. The volume is 3³ = 27 cubic inches. The answer 9 is the area of one face.

Average the coordinates: x = (−2 + 8) ÷ 2 = 3 and y = (6 + (−4)) ÷ 2 = 1, so the midpoint is (3, 1). The point (6, 2) adds the coordinates but forgets to divide by 2.

Same-side interior angles formed by parallel lines are supplementary, so the other angle is 180° − 115° = 65°. An angle equal to 115° would be an alternate interior or corresponding angle, not the same-side interior one.

The numerator is a difference of squares: x² − 9 = (x + 3)(x − 3). Cancelling the common factor x + 3 leaves x − 3. You cannot cancel terms that are only added or subtracted, which is the mistake behind x² − 3.

Cross-multiply: 12x = 3 × 20 = 60, so x = 5. Check: 35 = 0.6 and 1220 = 0.6. The answer 1.8 comes from cross-multiplying the wrong pair (3 × 12 ÷ 20).