Asvab Mathematical knowledge

x^3 × x^4 = (A) x12 (B) 2x7 (C) 2x12 (D) x7

The answer is D. If two powers have the same base, you multiply them by keeping the base the same and adding the powers together: x3 × x4 = x3 + 4 = x7.

If (5 + 1)(6 ÷ 3)(8 - 5) = (3 + 3)x, then x = (A) 12 (B) 3 (C) 4 (D) 6

The answer is D. The problem asks you to solve (5 + 1)(6 ÷ 3)(8 - 5) = (3 + 3)x for x. Solve the first half of the equation, finding the values in parentheses first: (6)(2)(3) = 36 Therefore, the whole equation becomes 36 = (3 + 3)x, which turns into 36 = 6x. Isolate x: To check your answer, substitute 6 for x.

. If x = 2, then (x^x)x = (A) 8 (B) 2x^x (C) 4 (D) 6

Substitute 2 for all x's in the problem and then solve, starting with the powers: 2^2 × 2 = 4 × 2 = 8.

If a = 4, then a^3 ÷ a = (A) 4 (B) 12 (C) 64 (D) 16

Substitute 4 for all a's in the problem and then solve, doing the powers first:

the square root of 49 x the square root of 64= (A) 56 (B) 15 (C) 42 (D) 3,136

The answer is A. Find the square roots first: The square root of 49 is 7, and the square root of 64 is 8. Now multiply: 7 × 8 = 56.

If x = 8, what's the value of y in the equation y = (x^2 ÷ 4) - 2? (A) 14 (B) 16 (C) 18 (D) 20

The answer is A. Substitute 8 for x in the equation and then solve for y:

What's the equation of a line that passes through points (0, -1) and (2, 3)? (A) y = 2x - 1 (B) y = 2x + 1 (C) x = 2y - 1 (D) x = 2y + 1

The answer is A. The answer choices are in the form y = mx + b, so to get the equation of the line, you need to know the line's slope (m) and y-intercept (b). The slope of the line is equal to the change in y values divided by the change in x values. The change in y values is 3 - (-1) = 4. The change in x values is 2 - 0 4/2= 2. Thus, the slope m is . The y-intercept (b) is the y value when x = 0. The line passes through the point (0, -1), so b = -1. (Category: Mathematics Knowledg

The cube of 5 is (A) 125 (B) 25 (C) 15 (D) 50

The answer is A. The cube of 5 is 53, which is 5 × 5 × 5 = 125.

Which of the following is a prime number? (A) 27 (B) 11 (C) 8 (D) 4

The answer is B. A prime number is a number that can be divided evenly by itself and by 1 but not by any other whole number. Choices (A), (C), and (D) can all be divided evenly by other numbers.

. If 2 + x > 4, then x > (A) 6 (B) 2 (C) 4 (D) 1/2

The answer is B. Solve as you would solve for any unknown

What's the mode of the following group of numbers? 4 4 8 8 8 10 10 12 12 (A) 9 (B) 8 (C) 11 (D) 10

The answer is B. The mode of a group of numbers is the number that appears the most frequently. In this case, it's 8.

2.5 × 3^3 = (A) 22.5 (B) 75 (C) 67.5 (D) 675

The answer is C. Because of the order of operations, you need to find 33 first and then multiply by 2.5: 2.5 × 33 = 2.5 ( 3 × 3 × 3) = 2.5 × 27 = 67.5

If a circle has a radius of 12 feet, what's its circumference most nearly? (A) 24 feet (B) 72 feet (C) 75 feet (D) 36 feet

The answer is C. Circumference equals × diameter, and diameter is equal to two times the radius (or mathematically, C = d and d = 2r). For this problem, C = pie × 24. If you round to 3.14, the answer is about 75.36, or about 75 feet.

(12 yards + 14 feet) ÷ 5 = (A) 12 feet (B) feet (C) 10 feet (D) yards

The answer is C. Do what's in parentheses first. You need consistent units of measurement, so convert 12 yards to feet; then add 14 feet: The original problem asks for (12 yards + 14 feet) ÷ 5, so divide by 5 as instructed: 50 feet ÷ 5 = 10 feet.

Solve for the factorial of 5 (that is, 5!). (A) 25 (B) 125 (C) 120 (D) 15

The answer is C. The factorial (!) of a number is the number multiplied by the next-smallest whole number, then by the next-smallest whole number, and so on down to 1: 5! = 5 × 4 × 3 × 2 × 1 = 120

1.5 × 10^3 = (A) 45 (B) 150 (C) 1,500 (D) 15

The answer is C. You need to do powers (exponents) first, so find 103 and then multiply by 1.5:

The fourth root of 16 is (A) 4 (B) 1 (C) 3 (D) 2

The answer is D. Because 24 = 16, the fourth root of 16 is 2.

. Which of the following fractions is the largest? (A) 2/5 (B) 3/4 (C) 7/10 (D) 13/16

The answer is D. Find a common denominator for the fractions. In this case, 80 works for all the fractions. Convert all the fractions

(900 × 2) ÷ 6 = (A) 30 (B) 300 (C) 150 (D) 3,000

Do what's in parentheses first: (900 × 2) ÷ 6 = 1,800 ÷ 6 = 300.

(x + 4)(x + 2) = (A) x2 + 6x + 6 (B) x2 + 8x + 8 (C) x2 + 8x + 6 (D) x2 + 6x + 8

The answer is D. To find (x + 4)(x + 2), you need to multiply every term in the first set of parentheses by every term in the second and then add the results. The acronym FOIL (First, Outside, Inside, Last) can help you keep track of which terms you're multiplying: First: Multiply the first variable in the first set of parentheses by the first variable in the second set of parentheses: x(x) = x2. Outside: Multiply the first variable in the first set of parentheses by the second number in the second set of parentheses: x(2) = 2x. So far, the results are x2 + 2x. Inside: Multiply the second number in the first set of parentheses by the first variable in the second set of parentheses: 4(x) = 4x. Last: Multiply the second number in the first set of parentheses by the second number in the second set of parentheses: 4(2) = 8. The solution is x2 + 2x + 4x + 8. Combining the like terms results in x2 + 6x + 8.