ASVAB MATHEMATICS ARITHMETIC & KNOWLEGE

ASVAB MATHEMATICS ARITHMETIC & KNOWLEGE Which of the following is the smallest prime number greater than 200? A. 201. B. 205. C. 211. D. 214. A prime number is a number larger than 1 that has only itself and 1 as factors. (It can be evenly divided only by itself and by 1.) 201 is divisible by 3; 205 is divisible by 5; 211, however, is a prime number If 40% is equal to the fraction x/30, what is the value of x? A. 0.4 B. 15 C. 1,200 D. 12 Change 40% to a decimal and write an equation to solve for x. 0.4 = x/30. Multiply both sides by 30. You are "undoing" the division. The expression "5 factorial" equals A. 125. B. 120. C. 25. D. 10. The product of all integers from 1 to x is called the x factorial. The product of all numbers from 1 to 5 is 5 factorials. Thus (5)(4)(3)(2)(1) = 20 (3)(2)(1) = 60 (2)(1) = 120 (1) = 120. The expression 5 factorial" is equal to 120 What is the result of subtracting 3x² - 5x - 1 from 8x² + 2x - 9? A. 5x² - 3x - 10 B. -5x² - 3x - 10 C. 5x² +7x - 8 D. -5x² - 7x + 8 To subtract one polynomial from another, you change the signs of the terms in the subtrahend. First write the example as a subtraction in arithmetic. (From) 8x² + 2x - 9 (Take) – (3x² - 5x – 1) Then change the signs of the terms in the bottom row (the subtrahend) and combine terms that are alike. 8x² + 2x - 9 -3x² + 5x + 1 5x² + 7x - 8 What is the meaning of the statement -30 < -5? A. 30 is greater than 5. B. 30 is less than minus 5. C. Negative 30 is less than negative 5. D. Negative 30 is greater than negative 5. On the number line above, -5 is to the left of 0 and is, therefore, less than 0, but -50 is to the left of -5. This makes -30 less than -5. The < sign is a symbol of inequality, meaning "less than". The statement (-30 < -5) means "negative 30 is less than negative 5." Solve for x: 8x - 2 - 5x = 8. A. x = 1.3 B. x = 2½ C. x = 3 and 1/3 D. x = -7 To solve for x, combine all similar terms, and set the equation equal to zero. (8x - 5x) + (-2 - 8) = 0 Do the operations inside the parenthesis. 3x - 10 = 0 Next, add 10 to each side. You are undoing the subtraction. 3x - 10 + 10 = 0 + 10 3x = 10 Finally, divide each side by 3 to find the value of x> You are undoing the multiplication. John is paid $26.00 for 8 hours of work. How much should he be paid for working 37 hours at the same hourly wage? We must find out how much John is being paid for each hour he works. To do this we divide the amount he had gained by the number of hours he worked. 26/8=3.25 $3.25perhour Then we multiply by 37 to get the amount he has earned in 37 hours 3.25⋅37=120.25 He should be paid $120.25 for 37 hours of work A woman has $500 in a bank account. Every week, she writes out a check for $50. If she doesn't make any new deposits, what will her bank account hold x weeks from now? A. $500 + $50x B. $500 - $50x C. $500 - x D. $500 + $50 + x In x weeks, she will make out check’s tor x times $50, or $50x. To find out how much she still has after writing these checks, she would subtract $50x from $500. Thus, her bank account will hold $500 - $50x. When the temperature is 20ºC, what is it the Fahrenheit (F) scale? (Use the following formula). F = (9/5 • C) +32 A. 93 and 3/5 degrees B. 78 degrees C. 62 and 7/5 degrees D. 68 degrees Use the formula F = (9/5 • C) + 32 Substitute 20 degrees for C. F = (9/5 • 20) + 32 F = 36 + 32 = 68 degrees. The perimeter of a rectangle is 38 inches. If the length is 3 inches more than the width, find the width. A. 17½ inches B. 8 inches C. 11 inches D. 14½ inches If Length = Width + 3, then l = w + 3 so, 2l + 2w =38 2(w + 3) + 2w =38 2w + 6 + 2w =38 4w + 6 =38 4w = 32 W= 8 The perimeter of a rectangle is the sum of its four sides. If x equals its width, then x + 3 equals the length. (The length is 3 inches more than the width.) From this, you can write an equation to find the perimeter. (Use the formula 2w + 2l = P.) x + x + (x + 3) + (x + 3) = 38 To solve for x, combine similar terms. 4x + 6 = 38 4x = 38 - 6 4x = 32 x = 8 (inches) Find the square root of 85 correct to the nearest tenth. A. 9.1 B. 9.2 C. 9.3 D. 9.4 One way to solve this is to square each of the suggested answers to see which is close to 85. Thus 9.1 • 9.1 = 82.81 9.2 • 9.2 = 84.64 9.3 • 9.3 = 86.49 9.4 • 9.4 = 88.36 To find squares of 9.2 and 9.3 are near 85. Find the difference between the square of each of these numbers and 85. (9.2) 85.00 - 84.64 = 0.36 (9.3) 86.49 - 85.00 = 1.49. The square 9.2 is closer to 85 than the square 9.3. Therefore, the square root of 85, to the nearest tenth, is 9.2. If 5x = 30, then x is equal to A. 150 B. 25 C. 6 D. 0.6 The statement 5x = 30 means "5 times a certain number is equal to 30." To find the number, divide each side by 5. This is to undo the multiplication. 5x/5 = 30/5 x = 6 What is the product of (a - 5) and (a + 3)? A. a² - 15 B. a² + 2a - 15 C. a² - 2a - 15 D. a² - 2 Set this up as a multiplication example in arithmetic. Remember that when you multiply terms with unlike signs, the product has minus sign. (a - 5) • (a + 3) =