ASVAB Study GuideMathematics Knowledge Practice Test 10
Tap an answer to check it instantly and read the explanation. 10 questions: 3 easy, 4 medium and 3 hard.
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Question 1 easy
A circle has a radius of 3 inches. What is its approximate circumference?
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Correct answer: A — 18.85 inches
The circumference of a circle is calculated using the formula $$C = 2\pi r$$. Given a radius of 3 inches: $$C = 2 \times 3.14159 \times 3 \approx 18.85$$ inches.
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Question 2 easy
In a right triangle, one leg measures 6 units and the hypotenuse measures 10 units. What is the length of the other leg?
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Correct answer: B — 8 units
Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$. Here, one leg $$a = 6$$ and the hypotenuse $$c = 10$$. So, $$6^2 + b^2 = 10^2 \Rightarrow 36 + b^2 = 100 \Rightarrow b^2 = 64 \Rightarrow b = 8$$ units.
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Question 3 easy
What is the area of a trapezoid with a top base of 6 cm, a bottom base of 12 cm, and a height of 8 cm?
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Correct answer: C — 72 cm²
The area of a trapezoid is given by the formula $$A = \frac{1}{2} (b_1 + b_2)h$$. Plugging in the values: $$A = \frac{1}{2} (6 + 12) \times 8 = \frac{1}{2} (18) \times 8 = 9 \times 8 = 72$$ cm².
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Question 4 medium
If a circle has a radius measuring 12 feet, what is its approximate circumference?
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Correct answer: B — 75.4 feet
The circumference of a circle is calculated using the formula $$C = 2\pi r$$ (or $$C = \pi d$$). Given a radius of 12 feet, the diameter is 24 feet. $$C = 24 \times 3.14159 \approx 75.4$$ feet.
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Question 5 medium
What is the area of a circle that has a radius measuring 6 cm?
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Correct answer: C — 113.1 cm²
The area of a circle is calculated using the formula $$A = \pi r^2$$. Given a radius of 6 cm: $$A = 3.14159 \times 6^2 = 3.14159 \times 36 \approx 113.1$$ cm².
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Question 6 medium
If one of two complementary angles measures 53 degrees, what is the measure of the other angle?
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Correct answer: A — 37 degrees
Complementary angles are two angles whose sum equals 90 degrees. To find the measure of the other angle, subtract the given angle from 90 degrees: $$90^\circ - 53^\circ = 37$$ degrees.
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Question 7 medium
In which quadrant of the Cartesian coordinate system does the point $$(-5, 6)$$ lie?
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Correct answer: B — Quadrant II
In the Cartesian coordinate system, the quadrants are defined by the signs of the coordinates (x, y): Quadrant $$I (+, +)$$, Quadrant II $$(-, +)$$, Quadrant III $$(-, -)$$, and Quadrant IV $$(+, -)$$. Since the x-coordinate is negative $$(-5)$$ and the y-coordinate is positive (6), the point lies in Quadrant II.
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Question 8 hard
Find the area of a triangle with a base of 12 inches and a perpendicular height of 9 inches.
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Correct answer: B — 54 in²
The area of a triangle is calculated using the formula Area = ½ × base × height. Plugging in the given values: Area = $$\frac{1}{2} \times 12 \times 9 = 6 \times 9 = 54$$ in².
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Question 9 hard
If a circle has a radius measuring 8 feet, what is its approximate circumference?
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Correct answer: B — 50.27 feet
The circumference of a circle is calculated using the formula $$C = 2\pi r$$. Given a radius of 8 feet: $$C = 2 \times 3.14159 \times 8 \approx 50.27$$ feet.
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Question 10 hard
What is the measurement of Angle D if the remaining portion of the full circle measures 290 degrees?
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Correct answer: C — 70°
A full circle or complete rotation around a point equals 360 degrees. To find the measurement of Angle D when the outer angle is 290 degrees, subtract from 360 degrees: $$360^\circ - 290^\circ = 70^\circ$$