Mathematics Knowledge Practice Test 5 (ASVAB)

Answer: B

Correct answer:

The filled circle shows the boundary −2 is part of the solution, so the sign is ≤ or ≥. Shading to the left means all smaller numbers, so the inequality is

• A: Greater-than values lie to the right of −2, but the shading goes left.
• B (correct): A closed circle means −2 is included, and shading to the left means smaller values, so x ≤ −2.
• C: This would need an open circle and shading to the right, the opposite of the graph.
• D: A strict sign would be drawn with an open circle, not a filled one.

Answer: D

Correct answer: Exactly two. Two lines in a plane can cross once (one solution), be parallel (no solution) or be the same line (infinitely many). Straight lines cannot cross in exactly two places, so exactly two solutions is impossible.

• A: Lines with different slopes cross at one point, giving exactly one solution.
• B: Parallel lines never meet, so a system can have no solution.
• C: If both equations describe the same line, every point on it is a solution.
• D (correct): Two straight lines either cross once, never meet or coincide, so two crossing points are impossible.

Answer: C

Correct answer: 75°. Angles around a point total 360°. The known angles add to

so the fourth angle is

°.

• A: This comes from adding the known angles as 295° instead of 285°.
• B: This comes from adding the known angles as 275° instead of 285°.
• C (correct): The known angles total 285°, and 360 - 285 = 75.
• D: This leaves the 60° angle out of the total and subtracts only 225° from 360°.

Answer: A

Correct answer: A circle centered at the origin. A graph is a function only if no vertical line touches it more than once. A vertical line through the center of a circle hits the top and the bottom, so the circle fails.

• A (correct): A vertical line through the middle of a circle crosses it twice, so one input has two outputs.
• B: Each vertical line meets an upward parabola only once, so it passes the test.
• C: Every input has the single output 3; a vertical line touches it once, so it passes.
• D: Any vertical line meets a slanted line exactly once, so it passes the test.

Answer: B

Correct answer: 7,392. Alternately subtract and add the digits from the left. For 7,392:

a multiple of 11, so 7,392 is divisible by 11. Check:

• A: 4 − 5 + 7 − 3 = 3, which is not 0 or a multiple of 11.
• B (correct): 7 − 3 + 9 − 2 = 11, a multiple of 11, and 7,392 ÷ 11 = 672.
• C: 5 − 2 + 8 − 1 = 10, which is not 0 or a multiple of 11.
• D: 9 − 1 + 4 − 6 = 6, which is not 0 or a multiple of 11.

Answer: B

Correct answer: 80 + 20π meters. The straight sides add

The two semicircular ends together make one full circle with diameter 20 m, whose circumference is

The perimeter is $80+20\pi$ meters; the diameters are inside the shape and are not counted.

• A: This adds the two 20-meter diameters, but those are interior edges where the ends meet the straight part, so they are not on the outside.
• B (correct): The two straight sides give 80 m, and the two semicircles together form one circle of diameter 20, adding 20 pi m.
• C: This treats each semicircular end as a full circle of diameter 20, doubling the curved length.
• D: This counts only one of the two straight sides.

Answer: C

Correct answer: (8, -5). Double the midpoint and subtract the known endpoint, one coordinate at a time.

Check: the average of (-4, 3) and (8, -5) is (2, -1).

• A: This adds P to 2M instead of subtracting it.
• B: This is the midpoint of P and M, not the far endpoint.
• C (correct): Q = 2M - P: x = 2(2) - (-4) = 8 and y = 2(-1) - 3 = -5.
• D: This is M - P, the step from P to M, but it was not added on to M.

Answer: D

Correct answer: 50 feet below sea level. Write below sea level and descents as negatives: −42 + 17 + (−25). Then

so she is 50 feet below sea level.

• A: The size is right, but the result is negative, so she is below sea level.
• B: This treats the 17-foot rise as another descent, giving −42 − 17 − 25.
• C: This reverses the moves, subtracting the 17-foot rise and adding the 25-foot descent.
• D (correct): −42 + 17 − 25 = −50, which is 50 feet below sea level.

Answer: D

Correct answer: x = 13. Cross-multiply, keeping the numerators in parentheses:

Then

Subtract 5x and add 21:

Check: both sides equal 2.

• A: This drops the parentheses, multiplying only the x terms by 7 and 5.
• B: This pairs each numerator with its own denominator instead of the opposite one.
• C: This subtracts 21 from 5 instead of adding 21 to both sides, giving 2x = −16.
• D (correct): Cross-multiplying gives 7(x − 3) = 5(x + 1), so 7x − 21 = 5x + 5 and x = 13.

Answer: D

Correct answer: Obtuse. Compare the squares with c = 14 as the longest side. Here

Because 185 < 196, the triangle is obtuse.

• A: Equal angles would require equal sides, and these three sides are all different.
• B: A right triangle would need 64 + 121 to equal exactly 196, and it does not.
• C: An acute triangle would need the sum of the smaller squares to exceed 196, but 185 falls short.
• D (correct): Since 64 + 121 = 185 is less than 14 squared, 196, the angle across from the longest side is greater than 90 degrees.

Answer: D

Correct answer: 5√3. Split 75 into a perfect square times what remains:

• A: This uses 75 = 5 × 15 and pulls out 5 even though 5 is not a perfect square.
• B: This places the factors backward; $3\sqrt{5}$ equals $\sqrt{45}$, not $\sqrt{75}$.
• C: The 25 was pulled out without taking its square root.
• D (correct): 75 = 25 × 3, and $\sqrt{25}=5$ comes out of the radical.

Answer: B

Correct answer: 120 seconds. Use the LCM. With

take each prime at its highest power:

• A: This multiplies 6 × 8 × 10; it is a common multiple but counts the shared factors of 2 too many times.
• B (correct): $2^3\times 3\times 5=120$ is the smallest number that 6, 8 and 10 all divide.
• C: This multiplies the LCM of 6 and 8, which is 24, by 10 without removing the shared factor of 2.
• D: This is the greatest common factor; a repeating schedule calls for the LCM.

Answer: A

Correct answer: 4.8 liters. The stone pushes the water up by its own volume. The rise is 32 minus 30, or 2 cm.

cubic centimeters, and since 1 liter is 1000 cubic centimeters, that is 4.8 liters.

• A (correct): The water rises 2 cm, so the stone is 60 times 40 times 2, or 4800 cubic centimeters, which is 4.8 liters.
• B: This finds 4800 cubic centimeters but divides by 100 instead of 1000 to get liters.
• C: This is the volume of the water before the stone was added, not the stone itself.
• D: This is the volume of everything below the new 32 cm level, water plus stone.

Answer: B

Correct answer: 128 degrees. A pentagon's angles total (5 - 2) times 180 = 540 degrees. Adding the expressions gives

so 5x = 440 and x = 88. The largest angle is

the angles 88, 98, 108, 118, and 128 sum to 540.

• A: This is one angle of a regular pentagon, but these angles are not equal.
• B (correct): Setting 5x + 100 = 540 gives x = 88, so the largest angle is 88 + 40 = 128.
• C: This is x, the smallest angle, not the largest.
• D: This uses 360 as the angle sum, which applies to a quadrilateral, not a pentagon.

Answer: A

Correct answer: 2y(y - 5)(y + 5). The GCF of both terms is 2y:

Since

it factors as $(y-5)(y+5)$. The complete factorization is $2y(y-5)(y+5)$.

• A (correct): Pulling out 2y leaves $y^2-25$, a difference of squares that factors as $(y-5)(y+5)$.
• B: A difference of squares factors as a sum times a difference, not as a squared binomial.
• C: This uses 25 itself instead of its square root 5 in each factor.
• D: This loses the common factor y; multiplying back gives $2y^2-50$, not the original.