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# Additional Mathematics Knowledge for ASVAB Power Practice Problems (page 2)

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Updated on Aug 12, 2011

1. a.   Area = (b × h). To get the height of the triangle, use the Pythagorean theorem: 32 + height2 = 52, so height = 4.When this is plugged into the area equation, you'll get an area of 6 square units for half of the triangle. Double this, and the answer is 12 square units.
2. b.   Break the statement down into smaller parts. The first part, "the sum of two numbers, a and b," can be translated (a + b). This part needs to be in parentheses to ensure that the correct order of operations is executed. The second part, "divided by a third number, c," takes the first part and divides it by c. This now becomes (a + b) ÷ c.
3. b.   The line right, or 90°, angle is split into two complementary angles. The given angle is 32°; therefore, 90 – 32 = 58°.
4. d.   Divide the top number by the bottom number: 160 ÷ 40 = 4.
5. d.   The farther to the right the nonzero digits are, the smaller the number. Forty-three thousandths is greater than 43 ten-thousandths.
6. b.   Add the four numbers together for a sum of 244. Then, divide by 4 to get a quotient of 61.
7. c.   A ratio is a comparison of two numbers.
8. c.   This equation is a proportion, expressing the equivalence of two ratios.
9. a.   Forty-six goes into 184 four times. The other choices cannot be divided evenly into 184.
10. a.   The area of a triangle is A = (b × h). Since b = 2h, you have 16 = (2h)(h) or h2 = 16; h = 4 inches.
11. b.   Subtract both 6 and 9 from 49. The correct answer is 34.
12. a.   Only like terms can be added: 4x – 7y + 7x + 7y; 4x + 7x and –7y + 7y. The y terms cancel each other out, leaving 11x as the correct answer.
13. c.   The sum of the measures of the exterior angles of any convex polygon is 360°.
14. b.   To solve this problem, you must first convert yards to inches. There are 36 inches in one yard; .
15. c.   Add the hours first, and then the minutes: 1 hour + 3 hours = 4 hours. 20 minutes + 30 minutes = 50 minutes. Combine: 4 hours 50 minutes.
16. a.   The correct answer is x(x2 + 6).
17. d.   This is a mixed decimal, which included a whole number placed to the left of the decimal point. The zero is in the tenths place and the 4 is in the hundredths place: 5.04.
18. c.   First, find the product of the given values, which is 12. Then, square that number. Twelve squared equals 144. The correct answer is 144.
19. a.   Divide the circumference by 3.14 to find the diameter; therefore, the correct answer is 42 inches.
20. a.   The correct answer is 126.24.
21. b.   Substitute 8 for y in the expression and perform the operations: x = 4 + 6(8); x = 52.
22. a.   Simply set up the equation in the manner in which the problem is written. Since x% = the equation is = . Cross multiply: 1.40x = (0.35)(100). Simplify: x = . Thus, x = 25, which means \$0.35 is 25% of \$1.40.
23. c.   A regular octagon has eight equal sides; therefore, the perimeter equals 8 × 13. The correct answer is 104 centimeters.
24. a.   The greatest value to the right of the decimal point can be determined by the tenths place. Choices a, c, and d all have a two in the tenths place. Choice a is correct because its values in the hundredths and thousandths places are greater than the other two possible answers.
25. d.   When the given values are plugged into the expression, it reads: (–3)(6) – 6(–5); –18 + 30 = 12.