What this section covers: High school mathematics principles.
10 free practice questions
Click an answer: you see at once whether it is right, with the explanation.
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Question 1Which of these numbers is prime?
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Answer: A — 59.
59 has no factors other than 1 and itself. 51 = 3 × 17, 57 = 3 × 19 and 63 = 7 × 9.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 2What is the least common multiple of 12 and 18?
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Answer: B — 36.
Multiples of 18 are 18, 36, 54…; 36 is the first one that 12 also divides. 6 is the greatest common factor, and 216 is simply 12 × 18.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 3What is 2/3 + 3/4?
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Answer: D — 17/12.
Use the common denominator 12: 8/12 + 9/12 = 17/12 (or 1 5/12). Adding tops and bottoms (5/7) is a common error.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 4Which expression is equal to x³ multiplied by x to the 4th power?
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Answer: C — x to the 7th power.
When multiplying powers of the same base, add the exponents: 3 + 4 = 7. Multiplying the exponents (12) is the rule for a power of a power, not for a product.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 5Solve the inequality: -2x + 5 is greater than 11.
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Answer: C — x is less than -3.
Subtract 5: -2x is greater than 6. Divide by -2 and reverse the inequality sign: x is less than -3. Forgetting to reverse the sign gives x greater than -3.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 6Which is the factored form of x² - 5x + 6?
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Answer: D — (x - 2)(x - 3).
Find two numbers that multiply to 6 and add to -5: -2 and -3. So x² - 5x + 6 = (x - 2)(x - 3). (x + 2)(x + 3) would give +5x.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 7What is the supplement of a 65° angle?
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Answer: B — 115°.
Supplementary angles add up to 180°, so 180° - 65° = 115°. 25° is the complement (adds to 90°).
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 8Two angles of a triangle measure 40° and 75°. What is the measure of the third angle?
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Answer: A — 65°.
The angles of a triangle add up to 180°: 180 - 40 - 75 = 65°. 115° is the sum of the two given angles.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 9If x + y = 10 and x - y = 4, what is the value of x?
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Answer: A — 7.
Add the two equations: 2x = 14, so x = 7 (and y = 3). 14 is 2x, and 3 is y.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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Question 10A bag holds 4 red, 6 blue and 5 green marbles. One marble is drawn at random. What is the probability that it is red?
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Answer: B — 4/15.
There are 4 + 6 + 5 = 15 marbles and 4 are red, so the probability is 4/15. 4/11 compares red to the non-red marbles instead of to the total.
Checked against: Official ASVAB — Mathematics Knowledge (MK): knowledge of high school mathematics principles
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