Asvab Mathematical knowledge test fully solved 2023.

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: 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. 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 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. 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 (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. 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. (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. 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: 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. What's the mode of the following group of numbers? 4 4 8 8 8 (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. 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: 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 (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. . 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 (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. 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. . 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