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

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Updated on Aug 12, 2011

1. a.   To solve this problem, you must first convert all the fractions to the lowest common denominator, which is 24; The fraction with the largest numerator, has the greatest value.
2. b.   This is a special expression called a perfect square. The x terms cancel each other out, leaving just two terms in the expression; therefore, (x + 5)(x – 5) is the correct factoring of the expression.
3. d.   Square each side of the equal sign to eliminate the radical: becomes b – 4 = 25. Add 4 to both sides of the equation: b = 29.
4. c.   The perimeter is the sum of the triangle's two legs plus the hypotenuse. Knowing two of the sides, you can find the third side, or hypotenuse (h), using the Pythagorean theorem: a2 + a2 = h2, which simplifies to 2a2 = h2. So h = . This means the perimeter is 2a+ .
5. a.   The formula for finding the area of triangle is ×the base ×the height; therefore, if you divide the given area, 60, by the height, 15, it will give half the base, 4. The base is 8 centimeters.
6. b.   To solve this division problem, subtract the exponents only: 5 – 2 = 3, so the answer is 103.
7. d.   Divide the numerator by the denominator to get the correct answer of 0.4.
8. c.   To find the perimeter, you can double each of the sides and add the sums: 2(834) + 2(1,288) = 1,668 + 2,576 = 4,244 feet.
9. b.   There are 60 minutes in one hour. Multiply 60 ×by multiplying 60 ×7 = 420 and 60 × = 10. Then add 420 +10 to get 430 minutes.
10. d.   First, the radius needs to be found, which is of the diameter: r = 47 centimeters; then, to find the area, square the radius and multiply by π. The correct answer is 2,209π.
11. d.   Since both dimensions are tripled, there are two additional factors of 3. Therefore, the new are is 3 × 3 = 9 times as large as the original.
12. a.   The distance between Plattville and Quincy is the hypotenuse of a right triangle with sides of length 80 and 60. The length of the hypotenuse equals , which equals , which equals , which equals 100 miles.
13. c.   In order for a number to be divisible by six, it must be able to be divided by six without a remainder. A shortcut to check divisibility by six is to see if the number is divisible by both two and three. Since 546 is even (ends in 6), the number is divisible by two. Since the sum of the digits is 5 + 4 + 6 = 15 and 15 is divisible by three, 546 is also divisible by three. Since 546 is divisible by both two and three, it is also divisible by six.
14. a.   A triangle with two congruent sides could either be isosceles or equilateral. However, because one angle is 40°, it cannot be equilateral (the angles would be 60°).
15. c.   Use the FOIL method to find the answer. This stands for the order by which the terms are multiplied: First + Outside + Inside + Last: (3x ×x) + (3x ×–6) + (4x) + (4 ×–6); 3x2 – 18x + 4x – 24. The correct answer is 3x2 – 14x – 24.
16. d.   An acute angle is less than 90°.
17. b.   The vertical bars on either side of the expression tell you to find the absolute value of 4 – 15. To complete the question, find 4 – 15 to get –11. Then find the absolute value (the distance the number is away from zero on a number line) of –11, which is 11.
18. a.   Since 4 and 6 are factors of 24, and 4 is a perfect square, or .
19. d.   The hundredth is the second digit to the right of the decimal point. Because the third decimal is 6, the second is rounded up to 4.
20. b.   The correct answer is 1.
21. d.   Factor the left side of the equation and set each factor equal to zero: x2 – 25 = (x – 5)(x + 5); x – 5 = 0 or x + 5 = 0. Therefore, x = 5 or –5.
22. c.   This is a division problem with mixed numbers. First, convert the mixed numbers to fractions: Next, invert the second fraction and multiply: Reduce to a mixed number: With this result, you know that only six glasses can be completely filled.