AFOQT Math Knowledge

AFOQT Math Knowledge In this figure, angle POS measures 90°. What is the measure of angle ROQ? a. 45° b. 90° c. 180° d. 270° e. 360° - ANS b. PQ and RS are intersecting lines. The fact that angle POS is a 90-degree angle means that PQ and RS are perpendicular, indicating that all the angles formed by their intersection, including ROQ, measure 90 degrees. 4 1/5 + 1 2/5 + 3 3/10 a. 8 9/10 b. 9 1/10 c. 8 4/5 d. 8 6/15 e. 9 5/10 - ANS a. Incorrect answers include adding both the numerator and the denominator and not converting fifths to tenths properly. 3/4 is equal to a. 0.25 b. 0.30 c. 0.34 d. 0.50 e. 0.75 - ANS e. To convert a fraction to a decimal, divide the numerator, 3, by the denominator, 4. 3 ÷ 4 = 0.75. 76 1/2 + 11 5/6 = a. 87 1/2 b. 88 1/3 c. 88 2/3 d. 88 5/6 e. 89 - ANS b. The correct answer is 88 1/3. What is the decimal equivalent of 1/6 rounded to the nearest thousandth? a. 0.165 b. 0.666 c. 0.123 d. 0.167 e. 0.176 - ANS d. Divide the numerator by the denominator: 1 ÷ 6 = 0.166667. Round the answer to the thousandths place (three decimal places) to get the answer 0.167. 1/6 + 7/12 + 2/3 = a. 10/24 b. 2 1/6 c. 1 5/6 d. 1 5/12 e. 2 5/6 - ANS d. You have to convert all three fractions to twelfths before adding them. Which of the following is equivalent to 202,436? a. 20,000 + 2,000 + 400 + 30 + 6 b. 2,000 + 40 + 300 + 6 c. 200,000 + 2,000 + 400 + 30 + 6 d. 200,000 + 2,000 + 4,000 + 300 + 6 e. 200,000 + 12,000 + 4,000 + 300 + 6 - ANS c. Choice a totals 22,436; choice b totals 2,346; choice d totals 206,306, and choice e totals 216,306. What are the missing integers on this number line? a. -4 and 1 b. -6 and 1 c. -6 and -1 d. 4 and 9 e. 5 and 8 - ANS a. The first box is one greater than -5; the second is one greater than 0. 1 1/2 is equal to a. 0.50 b. 1.25 c. 2.50 d. 1.50 e. .150 - ANS d. 1 1/2 is a mixed number. To convert this into a decimal, first take the whole number (in this case, 1) and place it to the left of the decimal point. Then, take the fraction (in this case, 1/2) and convert it to a decimal by dividing the numerator by the denominator, yielding .50. If x/54 = 2/9, then x is a. 12 b. 14 c. 18 d. 108 e. 118 - ANS a. Raise the fraction 2/9 to 54ths by multiplying both numerator and denominator by 6. Which of the following is divisible by both 7 and by 8? a. 63 b. 106 c. 114 d. 112 e. 78 - ANS d. 7(8)(2) = 112. What is 3/8 equal to? a. 0.25 b. 0.333 c. 0.60 d. 0.375 e. 3.80 - ANS d. Divide 3 by 8 in order to convert the fraction into a decimal. 3 ÷ 8 = 0.375. What is another way to write 4 × 4 × 4? a. 3 × 4 b. 8 × 4 c. 4^3 d. 3^4 e. 8^3 - ANS c. The meaning of 43 is 4 times itself 3 times. Which of the following choices completes this number sentence? 5_____ = (10 × 2) + (5 × 3) a. × (5 + 2) b. + (5 + 2) c. × (5 × 2) d. + (5 × 2) e. + (5 × 3) - ANS a. The total on the right is 35. On the left, you need an operation you can do on 5 to get 35. Multiplying by (5 + 2) does the trick. Which of these is equivalent to 20°C? (F = (9/5)C + 32) a. 68°F b. 95°F c. 45°F d. 19°F e. 70°F - ANS a. Using 20 for C: F = ((9/5) × 20) + 32. Therefore F = 36 + 32, or 68. What is the volume of a pyramid that has a rectangular base 5 feet by 3 feet and a height of 8 feet? (V = (1/3)l * w * h) a. 16 feet^3 b. 30 feet^3 c. 40 feet^3 d. 120 feet^3 e. 220 feet^3 - ANS c. 5(3)(8) = 120; 120 ÷ 3 = 40. What is another way to write 7.25 × 10^3? a. 72.5 b. 725 c. 7,250 d. 72,500 e. 720,500 - ANS c. 10(10)(10) = 1,000; 1,000(7.25) = 7,250. How many inches are there in 3 1/3 yards? a. 126 b. 120 c. 160 d. 168 e. 313 - ANS b. To solve this problem, you must first convert yards to inches. There are 36 inches in a yard; and 1/3 of a yard is 12 inches; 36 × 3 = 108 + 12 = 120. 3/5 = a. 0.60 b. 0.20 c. 0.50 d. 0.80 e. 0.90 - ANS a. Divide 3 by 5 to convert from a fraction into a decimal: 3 ÷ 5 = 0.60. 0.97 is equal to a. 97% b. 9.7% c. 0.97% d. 0.097% e. 0.0097% - ANS a. 0.97 multiplied by 100 is 97. In a triangle, angle A is 70 degrees and angle B is 30 degrees. What is the measure of angle C? a. 90 degrees b. 70 degrees c. 80 degrees d. 100 degrees e. 120 degrees - ANS c. The sum of the measure of the angles in a triangle is 180°; 70° + 30° = 100°; 180° - 100° = 80°. Which value of x will make the number sentence x + 32 ≤ 14 true? a. -16 b. -21 c. 12 d. 38 e. none of the above - ANS b. Since the solution to the problem x + 32 = 14, x = -18. Choices a, c, and d are all too large to be correct. What is the length of a rectangle if its width is 6 feet and its area is 108 square feet? a. 1.8 feet b. 10.5 feet c. 18 feet d. 16 feet e. 68 feet - ANS c. Use the formula A = lw. or 108 = l × 6. Since the area is the length × the width of the rectangle, then dividing the area (108) by the width (6) will give you the length, 18 feet. 37.5 percent is equal to a. 3/8 b. 5/8 c. 4 3/4 d. 6 3/4 e. 3 7/5 - ANS a. 37.5% is the same as 37.5/100 . Multiply both the numerator and the denominator by 10 to move the decimal point, resulting in 375/1,000. Next, factor both the numerator and denominator to find out how far you can reduce the fraction: (5 * 5 * 5 * 3)/(5 * 5 * 5 * 8). If you cancel the three 5s that are in both the numerator and the denominator, you get 3/8. 0.15 is equal to a. 2/5 b. 3/20 c. 2/10 d. 1/20 e. 1.5/20 - ANS b. In the decimal, 0.15, the 5 falls in the hundredths place (two places to the right of the decimal). To convert this to a fraction, the 15 is placed over 100. Reduce, which gives you 3/20.