ASVAB Mathematics Knowledge Practice Test

Answer: D

Correct answer: 720 degrees. Use

with n = 6. Then S = 4 times 180 = 720 degrees.

• A: This is the total of the exterior angles of any convex polygon, not the interior sum of a hexagon.
• B: This multiplies 6 by 180 without first subtracting 2 from the number of sides.
• C: This subtracts 3 instead of 2 from the number of sides; 540 is the interior sum of a pentagon.
• D (correct): A hexagon has 6 sides, so the sum is (6 - 2) times 180 = 720.

Answer: A

Correct answer: −5. The signs differ, so subtract the absolute values:

The number with the larger absolute value, −9, is negative, so the sum is −5.

• A (correct): 9 − 4 = 5, and the answer takes the sign of −9, the number with the larger absolute value.
• B: This adds the absolute values as if both numbers were negative.
• C: This adds the absolute values and ignores both signs.
• D: The size is right, but the sum takes the sign of −9, which is negative.

Answer: B

Correct answer: 13. Simplify inside the bars first: |6 − 15| = |−9| = 9 and |−4| = 4. Then

• A: This ignores the bars on the first term, using −9 + 4 instead of 9 + 4.
• B (correct): Inside first gives |−9| = 9, and adding |−4| = 4 gives 13.
• C: This subtracts 4 instead of adding the absolute value |−4| = 4.
• D: This drops all the signs before simplifying, adding 6 + 15 + 4.

Answer: C

Correct answer: 36π square inches. Change the diameter to a radius: 12 divided by 2 is 6.

• A: This is the circumference, pi times the diameter, which is a length, not an area.
• B: This squares the diameter instead of the radius.
• C (correct): The radius is half of 12, or 6, and pi times 6 squared is 36 pi.
• D: This multiplies pi by the radius without squaring it.

Answer: A

Correct answer: 66°. Let the complement be c, so the angle is 2c + 18. Together they make 90°:

so 3c = 72 and c = 24. The angle is

°.

• A (correct): With the complement c = 24°, the angle is 2(24) + 18 = 66°, and 66 + 24 = 90.
• B: 24° is the complement; the question asks for the angle itself.
• C: This sets the total at 180° (3c = 162, c = 54), which describes supplements, not complements.
• D: 114° is the supplement of 66°; the question asks for the angle.

Answer: C

Correct answer: (-5, 8). Symmetry about the origin matches (x, y) with (-x, -y). Changing both signs of (5, -8) gives (-5, 8).

• A: This changes only the x sign, which is symmetry about the y-axis.
• B: This changes only the y sign, which is symmetry about the x-axis.
• C (correct): Symmetry about the origin pairs (x, y) with (-x, -y), so both signs change.
• D: This swaps the coordinates and changes a sign, which is a turn, not origin symmetry.

Answer: A

Correct answer: (2a - 9)(2a + 9). Both parts are perfect squares:

A difference of squares factors as a difference times a sum: $(2a-9)(2a+9)$. Multiplying back, the middle terms cancel.

• A (correct): 4a^2 is (2a)^2 and 81 is 9^2, so the difference of squares gives (2a - 9)(2a + 9).
• B: This squares a difference, which gives 4a^2 - 36a + 81, adding a middle term.
• C: This squares a sum, which gives 4a^2 + 36a + 81, and the constant would be positive.
• D: This splits 4a^2 into 4a times a, which gives a middle term of 27a.

Answer: D

Correct answer: x = 16. Subtract 5 from both sides: −(3/4)

Multiply both sides by the reciprocal −4/3:

Check: −(3/4)

• A: This multiplies by 4/3 instead of −4/3, dropping the sign of the coefficient.
• B: This multiplies −12 by −3/4, the coefficient itself, instead of by its reciprocal.
• C: This multiplies −12 by 3/4 instead of by the reciprocal −4/3.
• D (correct): Subtracting 5 gives −(3/4)x = −12, and multiplying by −4/3 gives x = 16.

Answer: A

Correct answer: 5. The x-coefficients match, so subtract the second equation from the first, every term:

That gives 4y = 20, so y = 5. Then

so x = 4.

• A (correct): Subtracting gives 3y − (−y) = 4y and 31 − 11 = 20, so y = 5.
• B: This treats 3y − (−y) as 2y; subtracting a negative adds, giving 4y.
• C: This is the value of x, not y.
• D: This adds the constants (31 + 11 = 42) while subtracting the variable terms; every term must be subtracted.

Answer: A

Correct answer: 51 feet. The pole, the ground and the wire form a right triangle with legs 24 and 45, which are 3 times the 8-15-17 triple. So the wire is

Check:

• A (correct): The legs 24 and 45 are 3 times 8 and 15, so the hypotenuse is 3 × 17 = 51 feet.
• B: This adds the legs; the Pythagorean theorem adds their squares.
• C: This subtracts the squares, which finds a leg, but the wire is the hypotenuse.
• D: 2,601 is $c^2$; the square root still has to be taken.

Answer: C

Correct answer: The 20th term. Set up

Subtract 7:

and n = 20. Check:

• A: This stops at n − 1 = 19 and forgets to add 1 to get the term number.
• B: This adds one step too many; the 21st term is 7 + 20(6) = 127.
• C (correct): Solving 7 + 6(n − 1) = 121 gives n − 1 = 19, so n = 20.
• D: This divides 121 by the first term 7 instead of using the common difference.

Answer: A

Correct answer:

·x + 7. Solve

for y:

x - 2, so the slope is 3/4 and the perpendicular slope is -4/3.

Point-slope form:

x + 8, so

x + 7. Check: (-4/3)

• A (correct): The given slope is 3/4, the perpendicular slope is -4/3, and y + 1 = (-4/3)(x - 6) simplifies to this line.
• B: This uses y - 1 instead of y + 1 for the point (6, -1), so the 1 is added instead of subtracted.
• C: This keeps the original slope 3/4, which gives a parallel line instead of a perpendicular one.
• D: This takes the reciprocal but forgets to make the perpendicular slope negative.

Answer: C

Correct answer: 100π square cm. The hypotenuse is

Because the right angle is inscribed, the hypotenuse is a diameter, so r = 10 and the area is

square centimeters.

• A: This adds the legs to get 28 as the diameter, but the diameter is the hypotenuse found with the Pythagorean theorem.
• B: This uses the 20 cm hypotenuse as the radius, but the hypotenuse is a diameter, so the radius is 10.
• C (correct): The right angle stands on a diameter, so the 20 cm hypotenuse is the diameter, the radius is 10 and the area is 100 pi.
• D: This is the circumference, pi times the 20 cm diameter, not the area.

Answer: B

Correct answer: (3a²)/b². Apply the outside power to every factor:

Divide:

• A: This adds exponents for $(a^2{)}^3$, getting $a^5$ instead of $a^6$.
• B (correct): The numerator becomes $27a^6{b}^3$; dividing gives 3, $a^2$ and $b^{-2}$.
• C: This leaves the 3 uncubed, so the coefficient becomes 3 ÷ 9 = 1/3.
• D: This subtracts the b exponents backward; $b^{3-5}=b^{-2}$ puts $b^2$ in the denominator.

Answer: B

Correct answer: 7 or 8 vans. Seating:

so v is at least 6.5; round up to 7. Budget:

so v is at most about 8.57; round down to 8. Both conditions hold for 7 or 8 vans.

• A: Eight vans also work: they seat 64 people and cost $560, within the budget.
• B (correct): Seating requires v ≥ 6.5, so at least 7; the budget requires v ≤ about 8.57, so at most 8.
• C: Nine vans cost $630, over the budget; a maximum count must be rounded down.
• D: Six vans seat only 48 people; a minimum count must be rounded up, not down.