Mathematics Knowledge Overview for ASVAB Power Practice Problems

These mathematics knowledge practice questions are based on the actual ASVAB. Take this quiz to see how you would do if you took the exam today and to determine your strengths and weaknesses as you plan your study schedule.

Time: 24 minutes

1. Which of the following is equivalent to (x – 3)(x + 7)?
   1. x² – 3x – 21
   2. x² – 4x – 21
   3. x² + 4x – 21
   4. x² – 21
2. Which of the following represents a composite number?
   1. 11
   2. 29
   3. 41
   4. 91
3. Choose the answer to the following problem:



4. Find the median of the following group of numbers: 14 12 20 22 14 16
   1. 12
   2. 14
   3. 15
   4. 16
5. What is the value of X in the following figure?



1. 3
2. 4
3. 5
4. 9
6. In which of the following are the diagonals of the figure always congruent and perpendicular?
   1. isosceles trapezoid
   2. square
   3. isosceles triangle
   4. rhombus
7. In the following diagram, a circle of area 100π square inches is inscribed in a square. What is the length of side AB?



1. 10 inches
2. 20 inches
3. 100 inches
4. 400 inches
8. Which of the following expressions is equal to 40,503?
   1. 400 + 50 + 3
   2. 4,000 + 500 + 3
   3. 40,000 + 50 + 3
   4. 40,000 + 500 + 3
9. If the perimeter of a rectangle is 40 centimeters and the shorter sides are 4 centimeters, what is the length of the longer sides?
   1. 12 centimeters
   2. 10 centimeters
   3. 18 centimeters
   4. 16 centimeters
10. A straight angle is
    1. exactly 180°.
    2. between 90° and 180°.
    3. 90°.
    4. less than 90°.
11. 
    1. 3
    2. 3.5
    3. 4
    4. 5
12. Which value of x will make the following inequality true: 12x – 1 < 35
    1. 2
    2. 3
    3. 4
    4. 5
13. Which of the following could describe a quadrilateral with two pairs of parallel sides and two interior angles that measure 65°?
    1. square
    2. triangle
    3. rectangle
    4. rhombus
14. Simplify the radical completely:.



15. Write ten thousand, four hundred forty-seven in numerals.
    1. 10,499,047
    2. 104,447
    3. 10,447
    4. 1,047
16. Which of the following numbers is represented by the prime factors 2 × 3 × 7?
    1. 21
    2. 42
    3. 84
    4. 237
17. olve the equation for a: .
    1. 2
    2. 17
    3. 23
    4. 47
18. Find the sum of 4x – 7y and 7x + 7y.
    1. 11x
    2. 14y
    3. 11x + 14y
    4. 11x – 14y
19. 3 hours 20 minutes – 1 hour 48 minutes =
    1. 5 hours 8 minutes
    2. 4 hours 8 minutes
    3. 2 hours 28 minutes
    4. 1 hour 32 minutes
20. 20. Name the fraction that indicates the shaded part of the following figure.



21. Which expression best describes the sum of three numbers multiplied by the sum of their reciprocals?



22. Find three consecutive odd integers whose sum is 117.
    1. 39, 39, 39
    2. 38, 39, 40
    3. 37, 39, 41
    4. 39, 41, 43
23. Which of the following points is the solution to the system of equations?

y = –x + 10

y = x – 2

1. (2,10)
2. (2,0)
3. (3,6)
4. (6,4)
24. Find the sum: .



25. Divide:

Answers

1. c.   Multiply the two binomials using the distributive property so that each term from the first set of parentheses gets multiplied by each term of the second set of parentheses: (x – 3)(x + 7) = x(x + 7) + –3(x + 7). Simplify the multiplication next: x² + 7x –3x – 21. Combine like terms: x² + 4x – 21.
2. d.   A composite number is a whole number greater than one that has other factors besides one and itself; in other words, it is not prime. Each of the answer choices is a prime number except 91, which has factors of 1, 7, 13, and 91.
3. c.   Multiply across:. Then reduce to lowest terms to get the answer:.
4. c.   The median of a group of numbers is found by arranging the numbers in ascending or descending order, and then finding the number in the middle of the set. First, arrange the numbers in order: 12, 14, 14, 16, 20, 22. Since there is an even number of numbers in the list, find the average of the two numbers that share the middle. In this case, the numbers in the middle are 14 and 16, and the average between them is 15.
5. a.   The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, so you know that the following equation applies: 12 + x2 = 10, so x2 = 10 – 1 = 9, so x = 3.
6. b.   Both the isosceles trapezoid and the square have congruent diagonals, but only the square has diagonals that are both congruent and perpendicular.
7. b.   If the circle is 100π square inches, its radius must be 10 inches, using the formula A = πr². Side AB is twice the radius, so it is 20 inches.
8. d.   Use the place value of each of the nonzero numbers. The four is in the ten thousands place, so it is equal to 40,000, the five is in the hundreds place, so it is equal to 500, and the three is in the ones place, so it is equal to 3; 40,000 + 500 + 3 = 40,503.
9. d.   If the shorter sides are each 4 centimeters, then the longer sides must each equal 40 – 8 ÷ 2; therefore, the length of each of the longer sides is 16 centimeters.
10. a.   A straight angle is exactly 180°.
11. c.   In order to find an equivalent fraction, you need to perform the same action on both the numerator and the denominator. One way to solve for x is to ask the question, "What is multiplied by 19 (the denominator) to get a product of 76?" Divide: 76 ÷ 19 = 4. Then, multiply the numerator by 4 in order to find the value of x: 4 × 1 = 4.
12. a.   To solve the inequality 12x – 1 < 35, first solve the equation 12x – 1 = 35. In this case, the solution is x = 3. Replace the equal sign with the less than symbol (<): x < 3. Since values of x less than 3 satisfy this inequality, 2 is the only answer choice that would make the inequality true.
13. d.   Squares, rectangles, and rhombuses are quadrilateral (have four sides), and each has two pairs of parallel sides. However, all angles in both squares and rectangles are 90°. Therefore, only a rhombus could contain two angles that measure 65°.
14. a.   To simplify the radical, first find the square root of 64, which is 8. Then divide each exponent on the variables by 2 to find the square root of the variables. If the exponent is odd, the remainder stays inside the radical: and . Thus, the result is 8x²y² .
15. c.   The correct answer is 10,447. It helps, if you are in a place where you can do so, to read the answer aloud; that way, you will likely catch any mistake. When writing numbers with four or more digits, begin at the right and separate the digits into groups of three with commas.
16. b.   A prime number is a whole number whose only factors are one and itself. Two, three, and seven are all prime numbers. The prime factors of a number are the prime numbers that multiply to equal that number: 2 ×3 × 7 = 42.
17. d.   First, add 4 to both sides of the equation: – 4 + 4 = 6 + 4. The equation simplifies to = 10. Square each side to eliminate the radical sign: ()² = 10². The equation becomes 2a + 6 = 100. Subtract 6 from each side of the equal sign and simplify: 2a + 6 – 6 = 100 – 6; 2a = 94. Divide each side by . Therefore, a = 47.
18. a.   Only like terms can be added: 4x – 7y + 7x + 7y; 4x + 7x and –7y + 7y. The y terms cancel each other out, leaving 11x as the correct answer.
19. d.   You must "borrow" 60 minutes from the three hours in order to be able to subtract.
20. b.   Since there are three sections shaded out of a total of five sections, the part shaded is .
21. a.   The sum of three numbers means (a + b + c), the sum of their reciprocals means . Combine terms: (a + b + c) . Thus, choice a is the correct answer.
22. c.   Consecutive odd integers are positive or negative whole numbers in a row that are two apart, such as 1, 3, 5 or –23, –21, –19. To find three consecutive odd integers whose sum is 117, divide 117 by 3 to get 39; 39 – 2 = 37 and 39 + 2 = 41. To check, add the three integers: 37 + 39 + 41 = 117.
23. d.   By adding the two equations vertically, you end up with 2y = 8, so y must equal 4. Substitute 4 for y in either original equation to get x = 6. Therefore, the point of intersection where the two lines are equal is (6,4).
24. c.   Since there is a common denominator, add the numerators and keep the denominator: .
25. b.   Take the reciprocal of the fraction being divided by, change the operation to multiplication, and cancel common factors between the numerators and denominators: .