Mathematics Knowledge Practice Set 1

  1. Select the best answer for each question. This practice set contains 16 practice questions, which is the number of Mathematics Knowledge questions you will see if you take the CAT-ASVAB.

  1. What is the height of a rectangular box with volume of 140, length of 10, and width of 7?
    1. 2
    2. 17
    3. 70
    4. 9,800
  2. If x = , y = 2, and z = , then x2 − 5yz + y2 =
    1. 1
    2. 2
    3. 4
    4. 7
  3. Solve for a:
    1. a < –240
    2. a > 240
    3. a > 180
    4. a > 40
  4. (3d − 7) − (5 − 2d) =
    1. d − 12
    2. 5d − 2
    3. 5d + 12
    4. 5d − 12
  5. Which of the following are possible values of x, if x2 − x − 20 = 0?
    1. −5, 4
    2. −4, 5
    3. −2, 10
    4. 5, 4
  6. The following two points lie on a line on the coordinate grid: (−2, 0) and (4, 6). Which of the following is the equation of the line?
    1. x = y + 2
    2. y = 3x + 6
    3. y = 2x + 1
    4. y = x + 2
  7. image
    If the perimeter of the above square is 36, what is the circumference of the circle?
    1. 6π
    2. 9π
    3. 12π
    4. 18π
  8. image
    What is the area of the frame in the above diagram if the picture inside has a length of 8 and a width of 4?
    1. 16
    2. 24
    3. 48
    4. 56
  9. image
    In the figure above, what is the distance from the midpoint of to the midpoint of ?
    1. 12
    2. 14
    3. 16
    4. 18
  10. If s − t = 5, what is the value of 3s − 3t + 3?
    1. 11
    2. 12
    3. 15
    4. 18

  11. Manuel is 4 years older than Grace. The total of their ages in years is 30. How old will Manuel be 3 years from now?

    1. 13
    2. 17
    3. 20
    4. 23
  12. Given the equation  , if y = 3, what is the value of x?

    2. 1
    3. 2
    4. 4

  13. At what point do the lines described by the equations y = 3x – 8 and y = –x + 4 intersect?

    1. (–1, –3)
    2. (–3, –1)
    3. (1, 3)
    4. (3, 1)

  14. Given the equation , what is r in terms of w and k?




  15. If b < 0 and  , which of the following is always true?

    3. ad > bc
    4. a < bcd
  16. image

    In the parallelogram above, if x = 4y, what is the value of z?

    1. 36°
    2. 108°
    3. 135°
    4. 144°

Mathematics Knowledge Practice Set 2

  1. Select the best answer for each question. This practice set contains 16 practice questions, which is the number of Mathematics Knowledge questions you will see if you take the CAT-ASVAB.

  2. Which of the following statements cannot be true under any circumstances?

    1. Triangle ABC is an equilateral right triangle.
    2. Triangle ABC is an isosceles right triangle.
    3. Triangle ABC has three acute interior angles.
    4. Triangle ABC has an interior angle greater than 170°.
  3. image

    In the figure above, what is the area of the semicircle that is on top of the square if the area of the square is 400 cm2?

    1.  

  4. If 7x + 2y = x – 4y and both sides of the equation equal 15, what is the value of x?

    1. –3
    2. 1
    3. 3
    4. 6

  5. The fuel gauge in Earl's car has been calibrated to ensure it is accurate. The gauge showed that his tank was one-quarter full before Earl added $15 worth of fuel. After he added that fuel, the gauge showed that the tank was five-eighths full. If the type of fuel that Earl purchased cost $2.50 per gallon, what is the capacity of his fuel tank?

    1. 12 gallons
    2. 16 gallons
    3. 20 gallons
    4. 24 gallons
  6. image

    If the area of the triangle above is 6, what is the perimeter?

    1. 9
    2. 12
    3. 15
    4. 18

  7. If the perimeter of an equilateral triangle is 24 cm, what is its area?



    3. 24

  8. Solve  for x.

    1. 2
    2. 5
    3. 10
    4. 20
  9. image

    If the straight line in the graph were extended to a point where y = 100, what would be the value of x at that point?

    1. 100
    2. 102
    3. 200
    4. 202

  10. The Greek letter delta, Δ, represents the sensitivity of the price of stock options to price movements of the stock upon which the derivative option is based. If an option has Δ = 0.50, then a $1.00 increase in the underlying stock should result in a $0.50 increase in the value of that option. Joseph owns an option on 200 shares of XYZ Corporation. That stock is currently priced at $45.00 per share. If the price of the stock of XYZ were to decrease by 2%, what would be the expected change in the value of Joseph's option if its Δ = 0.40?

    1. –$72
    2. –$36
    3. $36
    4. $72
  11. image

    In the figure above, ED = 3 cm, CD = 5 cm, and BA = 4 cm. What is the perimeter of triangle ABC?

    1. 12 cm
    2. 15 cm
    3. 16 cm
    4. 18 cm

  12. A teacher accompanied her students on a trip to the museum. She wanted to be certain that she kept track of all the students during the trip, so she counted the students by the color of the coats they were wearing. One-half of the students wore black coats, one-sixth wore red, one-fourth wore blue, and the remaining two students wore green. How many students went on the trip?

    1. 12
    2. 24
    3. 36
    4. 48

  13. Which of the following equations describes a straight line on a standard coordinate plane?

    1. x = 3

    3. z = 2x + y
    4. y = x2 + 3
  14. image

    Quadrilateral ABCD is a parallelogram. Vertex A is located at (–5, –2), vertex B has coordinates (–3, 3), and the position of vertex D is (5, –2). What is the length of diagonal AC?

    1. 10
    2. 13
    3. 15
    4. 20
    1. If x + y = 2 and x2 – xy – 10 – 2y2 = 0, what does x – 2y equal?
    1. 0
    2. 1
    3. 2
    4. 5

  16. If each side of a regular hexagon is 6 cm long, what is the area of the hexagon?

    1. If a is an integer and 2a2 + a = 28, what is the value of a?
    1. –4
    2. 0
    3. 4
    4. 7