ASVAB Math Knowledge Practice Test
- Algebra, Exponents and Geometry
- 12 questions
- 12 minutes
Math Knowledge tests algebra, exponents, roots and geometry facts rather than word problems. Work without a calculator, as on the real ASVAB, and make sure you know basic formulas such as area, circumference and angle sums by heart.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the value of (23)2 × 2−4?
Correct answer: C
A power of a power multiplies the exponents: (23)2 = 26. Then 26 × 2−4 = 26 + (−4) = 22 = 4. The answer 2 comes from adding 3 + 2 instead of multiplying the exponents.
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Question 2
Which expression is equal to 72?
Correct answer: C
Find the largest perfect square factor: 72 = 36 × 2, so 72 = 36 × 2 = 62. Check the others by squaring: 92 equals 162, and 36 equals 54.
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Question 3
If a = −3 and b = 4, what is the value of a2 − 2ab?
Correct answer: D
Substitute: (−3)2 − 2(−3)(4) = 9 − (−24) = 9 + 24 = 33. The answer −15 comes from ignoring the negative sign of a, which turns +24 into −24.
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Question 4
Which inequality is the solution of −3x + 7 > 22?
Correct answer: A
Subtract 7: −3x > 15. Dividing both sides by −3 gives x < −5, because dividing by a negative number reverses the inequality sign. Option B forgets to reverse the sign.
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Question 5
Which expression is equal to (2x − 3)(x + 4)?
Correct answer: B
Multiply each pair of terms: 2x · x = 2x2, 2x · 4 = 8x, −3 · x = −3x and −3 · 4 = −12. Combining 8x − 3x gives 2x2 + 5x − 12. Option A multiplies only the first terms and the last terms.
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Question 6
Which is the correct factored form of x2 − 5x − 14?
Correct answer: A
You need two numbers that multiply to −14 and add to −5: those are −7 and 2. Option B gives a middle term of +5x, and option C gives +14 as the constant.
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Question 7
What is the slope of the line 4x − 2y = 6?
Correct answer: C
Solve for y: −2y = −4x + 6, so y = 2x − 3. The slope is the coefficient of x, which is 2. The value −3 is the y-intercept, and 4 is the coefficient of x before solving for y.
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Question 8
What is (3 × 104)(2 × 10−2) written in scientific notation?
Correct answer: A
Multiply the numbers (3 × 2 = 6) and add the exponents of 10 (4 + (−2) = 2), giving 6 × 102, or 600. Option B multiplies the exponents instead of adding them.
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Question 9
What is the sum of the interior angles of a hexagon?
Correct answer: D
The sum of the interior angles of a polygon with n sides is (n − 2) × 180°. A hexagon has 6 sides, so the sum is 4 × 180° = 720°. The value 540° is the sum for a pentagon.
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Question 10
The angles of a triangle are in the ratio 2 : 3 : 4. What is the measure of the largest angle?
Correct answer: D
Write the angles as 2x, 3x and 4x. Their sum is 9x = 180°, so x = 20° and the largest angle is 4 × 20° = 80°. The answer 20° is just the value of x.
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Question 11
A circle has a radius of 7 inches. Using 227 for π, what is the circumference of the circle?
Correct answer: B
Circumference = 2πr = 2 × 22/7 × 7 = 44 inches. The value 154 is the area (πr2), which would be measured in square inches.
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Question 12
A trapezoid has parallel sides of 8 cm and 14 cm, and its height is 5 cm. What is its area?
Correct answer: B
Area of a trapezoid = ½ × (base1 + base2) × height = ½ × (8 + 14) × 5 = 55 cm2. The answer 110 forgets to multiply by ½.
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