ASVAB Study GuideMathematics Knowledge Practice Test 9
Tap an answer to check it instantly and read the explanation. 9 questions: 2 easy, 4 medium and 3 hard.
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Question 1 easy
What is the area of a rectangle with a length of 12 inches and a width of 7 inches?
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Correct answer: C — 84 in²
The area of a rectangle is calculated by multiplying its length by its width (Area = length × width). Multiplying 12 inches by 7 inches gives 84 in².
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Question 2 easy
What is the measurement of the angle formed by the hour and minute hands on a clock at 6:00 p.m.?
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Correct answer: B — 180 degrees
At 6:00 p.m., the hour hand points directly at the 6 and the minute hand points directly at the 12, forming a straight line across the clock face. A straight line represents a straight angle, which measures 180 degrees.
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Question 3 medium
What is the total number of degrees when you add up all the interior angles of any quadrilateral (four-sided polygon)?
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Correct answer: C — 360 degrees
The sum of the interior angles of any convex polygon can be found using the formula $$(n - 2) \times 180^\circ$$, where n is the number of sides. For a quadrilateral $$(n = 4)$$: $$(4 - 2) \times 180^\circ = 2 \times 180^\circ = 360$$ degrees.
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Question 4 medium
An L-shaped polygon has a bottom base of 10 ft, a left height of 5 ft, a top width of 4 ft, and an inner vertical drop of 2 ft. What is the total perimeter of this polygon?
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Correct answer: C — 30 ft
To find the perimeter, sum all outer side lengths. Bottom = 10 ft, Left = 5 ft, Top = 4 ft, Inner drop = 2 ft. The remaining horizontal top-step is $$10 - 4 = 6$$ ft, and the remaining vertical right-side is $$5 - 2 = 3$$ ft. Adding all sides together: $$10 + 5 + 4 + 2 + 6 + 3 = 30$$ ft.
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Question 5 medium
What is the total number of degrees when you add up all the interior angles of a regular hexagon (six-sided polygon)?
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Correct answer: B — 720 degrees
The sum of the interior angles of any convex polygon is given by the formula $$(n - 2) \times 180^\circ$$, where n is the number of sides. For a hexagon, $$n = 6$$. Substituting this into the formula: $$(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720$$ degrees.
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Question 6 medium
Calculate the perimeter of a regular octagon (eight-sided polygon) where each side measures 11.5 centimeters.
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Correct answer: C — 92 cm
The perimeter of a regular polygon is found by multiplying the number of sides by the length of one side. An octagon has 8 sides. Multiplying 8 by 11.5 cm gives $$8 \times 11.5 = 92$$ cm.
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Question 7 hard
Which of the following geometric formulas correctly represents the circumference of a circle?
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Correct answer: B — $$C = 2\pi r$$
The circumference (distance around the outer edge of a circle) is calculated using the formula $$C = 2\pi r$$ (or $$C = \pi d$$, where d is the diameter). Note that $$C = \pi r^2$$ represents the area of a circle, not its circumference.
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Question 8 hard
What term describes two lines in the same plane that intersect to form right angles (90 degrees)?
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Correct answer: B — Perpendicular lines
Perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°). Parallel lines never intersect, and skew lines are in different planes and do not intersect.
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Question 9 hard
If the area of a circle is $$64\pi$$ square centimeters, what is the length of its diameter?
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Correct answer: C — 16 cm
The area of a circle is given by the formula $$A = \pi r^2$$. Set this equal to $$64\pi$$: $$\pi r^2 = 64\pi$$. Divide both sides by $$\pi$$: $$r^2 = 64$$, which means the radius $$r = 8$$ cm. The diameter is twice the radius $$(d = 2r)$$, so $$d = 2 \times 8 = 16$$ cm.