ASVAB Mathematics Knowledge Practice Test 4

Answer: A

Correct answer: 10p + 8. Group like terms:

The result is $10p+8$.

• A (correct): Adding the p terms gives 10p and adding the constants −3 and 11 gives 8.
• B: This treats −3 as +3; the sign in front of the 3 belongs to that term.
• C: This adds the constants to the p terms, but a constant is not a like term with p.
• D: This subtracts 2p from 8p, but the 2p term is being added.

Answer: B

Correct answer: (2, 5). Set the right sides equal:

Then 3x = 6, so x = 2, and

The lines cross at (2, 5).

• A: The coordinates are swapped; x must be listed first.
• B (correct): Setting 2x + 1 = −x + 7 gives x = 2, and then y = 5; the point lies on both lines.
• C: This point lies on y = −x + 7, but on the first line x = 3 gives y = 7.
• D: This is only the y-intercept of the second line; the first line passes through (0, 1).

Answer: A

Correct answer: 12π cm. Use

With d = 12 cm, the circumference is $12\pi$ cm.

• A (correct): Circumference equals pi times the diameter, so it is 12 pi cm.
• B: This treats the 12 cm diameter as the radius in 2 pi r, doubling the answer.
• C: This is the area formula pi r squared with r = 6, which gives square units, not a length.
• D: This multiplies pi by the radius only; circumference needs 2 pi r, or pi d.

Answer: C

Correct answer: 40 square cm. Use

Here

square centimeters.

• A: This multiplies base by height but forgets the one-half in the area formula.
• B: This adds the base and height instead of multiplying them.
• C (correct): One-half of 16 times 5 is 40.
• D: This takes half of the sum of base and height rather than half of their product.

Answer: B

Correct answer: 3π + 12 feet. The curved part is one fourth of 2π(6) = 12π, which is 3π feet. Add the two straight radii,

The total is 3π + 12 feet.

• A: This is just the curved edge; the outline also includes the two straight radii.
• B (correct): The arc is one fourth of 12π, or 3π, plus two 6-foot radii.
• C: This uses the quarter-circle's area, 9π, in place of the arc length.
• D: This uses half the circumference, which is a semicircle's arc, not a quarter circle's.

Answer: D

Correct answer: 24. Add 5 to both sides:

Multiply by the reciprocal:

Check:

• A: This multiplies 18 by 3/4 instead of by the reciprocal 4/3.
• B: This multiplies 18 by 4 but never divides by 3.
• C: This divides 18 by 3 but never multiplies by 4.
• D (correct): Adding 5 gives (3/4)x = 18, and multiplying by 4/3 gives 24.

Answer: A

Correct answer: They are not parallel, because the two angles total 182° instead of 180°. If the lines were parallel, same-side interior angles would be supplementary. Here

°, not 180°, so the lines are not parallel.

• A (correct): Same-side interior angles of parallel lines must add to exactly 180°, and these add to 182°.
• B: Being close to 180° is not enough; the sum must be exactly 180° for the lines to be parallel.
• C: The conclusion is right, but the reason is wrong: same-side interior angles of parallel lines are supplementary, not equal.
• D: Linear pairs total 180° at any crossing, so this fact proves nothing about parallel lines.

Answer: B

Correct answer: x > 15. The LCD of 3 and 5 is 15. Multiply every term by 15:

Subtract 3x:

Add 30 and divide by 2: x > 15. Check x = 30:

which is greater than 6.

• A: This reverses the sign, but multiplying by 15 and dividing by 2 are both positive steps.
• B (correct): Multiplying by 15 gives 5x − 30 > 3x, so 2x > 30 and x > 15.
• C: This multiplies the fractions by 15 but not the constant 2, giving 5x − 2 > 3x.
• D: This is a sign slip when moving −30 to the other side; it should become +30.

Answer: C

Correct answer: a⁴. Power of a power first:

Then divide by subtracting exponents:

• A: This adds the exponents 10 and 6 instead of subtracting them when dividing.
• B: This adds 2 + 3 for the power of a power, making the denominator $a^5$.
• C (correct): The denominator is $a^6$, and 10 − 6 = 4.
• D: This subtracts the top exponent from the bottom one, 6 − 10, reversing the quotient rule.

Answer: C

Correct answer: x ≥ 10. 0.06 has two decimal places, so multiply every term by 100:

Subtract 6x and add 90: 240 ≤ 24x. Divide by 24: 10 ≤ x, which is x ≥ 10. The multiplier and divisor are positive, so the sign never flips.

• A: This reverses the sign, but the only division is by positive 24, so no reversal is needed.
• B: This subtracts 90 from 150 instead of adding 90 to both sides, giving 60 ≤ 24x.
• C (correct): Multiplying by 100 gives 6x + 150 ≤ 30x − 90, so 240 ≤ 24x and x ≥ 10.
• D: This multiplies the x terms by 100 but the constants only by 10, giving 6x + 15 ≤ 30x − 9.

Answer: B

Correct answer: 84 square feet. Use

with the perpendicular height: A = 14 times 6 = 84 square feet. The 9-foot slanted side is not needed.

• A: This is the perimeter, 2(14 + 9), a length rather than an area.
• B (correct): Area is base times perpendicular height, 14 times 6 = 84.
• C: This takes half of base times height, a rule for triangles, not parallelograms.
• D: This uses the slanted 9-foot side as the height; the height must be perpendicular to the base.

Answer: B

Correct answer: (-9, 2). Reflecting across the y-axis changes the sign of x: (4, -7) becomes (-4, -7). Moving 5 left subtracts 5 from x and moving 9 up adds 9 to y:

• A: This reflects across the x-axis, giving (4, 7), before applying the translation.
• B (correct): Reflecting gives (-4, -7); then (-4 - 5, -7 + 9) = (-9, 2).
• C: Moving left subtracts from x, but here 5 was added to -4.
• D: Moving up adds to y, but here 9 was subtracted from -7.

Answer: D

Correct answer: 3. The greatest number of identical kits is the GCF of 84 and 126. Since

the GCF is

kits. Each kit gets

snack bars.

• A: This uses 21 kits, a common factor but not the greatest one, so fewer kits than possible are made.
• B: This is the number of water bottles per kit (84 ÷ 42), not snack bars.
• C: This is the number of kits, not the number of snack bars in each kit.
• D (correct): With 42 kits, each kit holds 126 ÷ 42 = 3 snack bars.

Answer: C

Correct answer: 96π square feet. The radius is 4. An open-top cylinder has one base plus the curved side.

The answer is 96 pi square feet.

• A: This counts only the curved side and leaves out the bottom.
• B: This uses the diameter 8 as the radius in both the bottom and the side.
• C (correct): With radius 4, the bottom is 16 pi and the side is 80 pi, for 96 pi.
• D: This adds a top of 16 pi, but the barrel has no lid.

Answer: A

Correct answer: (-∞, -3) ∪ [4, ∞). First part:

divide by −2 and flip to get

Second part:

Or means combine the sets: $(-\infty ,-3)\cup [4,\infty )$.

• A (correct): The first part gives x < −3 (open at −3) and the second gives x ≥ 4 (closed at 4); or joins them with a union.
• B: This forgets to flip when dividing by −2, giving x > −3, which then swallows the second piece.
• C: The first inequality is strict, so −3 is not included and needs a parenthesis.
• D: Infinity always takes a parenthesis, never a bracket.