Free Compass Math Test Practice Questions
Solutions with Explanations - Sample 5

Solutions with detailed explanations to compass math test practice questions in sample 5.

  1. The solution of the equation - 3x + 7 = 4x - 12 falls bewteen what 2 numbers?

    A) 3 and 3.5
    B) 1 and 2.5
    C) 2.1 and 3
    D) 4 and 4.5
    E) 19 and 7

    Solution

    We first solve the given equation

    -3x + 7 = 4x - 12

    -3x - 4x = -12 - 7

    -7x = -19

    x = 19/7 ≈ 2.71

    The solution x = 19/7 is between 2.1 and 3. Answer C

  2. 35x2 -11x - 6 is the product of 5x - 3 and

    Solution

    We are given one factor 5x - 3 and we need to find the second factor of 35x2 -11x - 6 as follows

    35x2 -11x - 6 = (5x - 3)(7x + 2)

    So 35x2 -11x - 6 is the product of 5x - 3 and 7x + 2
  3. For all real numbers x, y and z, 3√(64 x3 y z2) =

    Solution

    Let us rewrite the given expression as follows

    3√(64 x3 y z2) = 641/3 (x3)1/3 y1/3 (z2)1/3

    then simplify

    = 4 x y1/3 z2/3

  4. For all x, 45 x4 - 115 x3 - 60 x2 =

    A) 45 x2(x + 4)(x - 3)
    B) 5 x2(9x + 4)(x - 3)
    C) 5 x2(9x - 4)(x + 3)
    D) 5 x2(9x - 4)(x - 3)
    E) 45 x2(x - 4)(x + 3)

    Solution

    Factor 5 x2 out

    45 x4 - 115 x3 - 60 x2 = 5x2 (9x2 -23x - 12)

    We now factor the trinominal

    = 5x2 (9x + 4)(x - 3)

  5. Which of the following is one of the factors of the polynomial -3x2 - 7x + 26?

    A) x + 2
    B) x + 1
    C) -3x + 7
    D) x - 2
    E) 3x - 2

    Solution

    Factor -3x2 - 7x + 26

    -3x2 - 7x + 26 = (-3x - 13)(x - 2)

    x - 2 is a factor of the given expressions

  6. What is the product of the solutions of the equation 2x2 + x - 15?

    Solution

    The product of the solutions of a quadratic equation of the form ax2 + bx + c = 0 is equal to c / a. Hence the product of the solutions of the solutions of the given equation is equal to

    -15/2

  7. If y = |x - 3|, what is the value of y2 when x = -2?

    Solution

    Evaluate y and then y2

    y = |-2 - 3| = 5

    y2 = 52 = 25

  8. The operation ||| is defined by x ||| y = x + y + xy. If -5 ||| y = -13, then y =

    Solution

    Use definition to express -5 ||| y in terms of y

    -5 ||| y = (-5) + y + (-5)y = -5 + y - 5y = -5 - 4y

    Use the fact that -5 ||| y = -13 to write an equation

    -5 - 4y = - 13

    Solve for y

    y = 2

  9. A car uses 15 gallons of gaz to travel 300 miles. How many gallons are needed for this car to travel a distance of 430 miles?

    Solution

    Let us first find how many gallons are used to travel 1 mile

    15 gallons / 300 miles = 1 /20 gallons per mile

    The number of gallons needed for 430 miles is given by

    (1 /20 gallons per mile)*(430 miles) = 21.5 gallons

  10. David has 200 books in his library. 30% of these books are about science. Of these books about science, 20% are about mathematics. How many math books does David have?

    Solution

    Number of science books is

    30% of 200 = 30% * 200 = 60 books

    Number of math books is

    20% of 60 = 20% * 60 = 12 bokks.

  11. √32 √2 =

    Solution

    Use 32 = 2 * 16 and simplify

    √32 √2 = √(2*16)√2

    = √2 √16 √2

    = 4 √2 √2 = 4 * 2 = 8

  12. If a = 3 and b = -1, then -3a2 - 2ab + b3

    Solution

    Substitute

    -3a2 - 2ab + b3 = -3(3)2 - 2(3)(-1) + (-1)3

    Simplify

    = -3(9) + 6 - 1 = -27 + 6 - 1 = -22

  13. (-3x2 - x - 10) - (- 3x + 8)?

    Solution

    Multiply, group like terms and simplify

    (-3x2 - x - 10) - (- 3x + 8) = -3x2 - x - 10 + 3x - 8)

    = -3x2 + 2x - 18

  14. (4 - √5)(4 + √5) =

    Solution

    Expand and simplify

    (4 - √5)(4 + √5) = 42 - √5 2 = 16 - 5 = 11
  15. In a standard (x,y) coordinate plane, the point (-2 , -6) is located

    Solution

    Both coordinates are negantive, therefore the point (-2 , -6) is located in quadrant III

  16. | -7 - 9 | =

    Solution

    Simplify as follows

    | -7 - 9 | = |-16| = 16

  17. If the ratio of 7 to x is equal to 42/30, then x =

    Solution

    We are given

    7 / x = 42 / 30

    Solve for x

    7 * 30 = 42 * x

    x = 5

  18. If x = 1/3, then 4 x2 - 2x + 2 =

    Solution

    Substitute

    4 x2 - 2x + 2 = 4 (1/3)2 - 2(1/3) + 2 =

    Simplify using common denominator

    4 * (1/9) - 2/3 + 2 = 4 / 9 - 6 / 9 + 18 /9 = 16 / 9

  19. Which equations corresponds to a line that is perpendicular to the line 2y + 3x = 6

    A) y = -(2/3)x + 9
    B) y = (3/2)x + 4
    C) y = -(3/2)x - 5
    D) y = 2/3
    E) y = (2/3)x + 3

    Solution

    Write in slope intercept form and find the slope of given line

    2y + 3x = 6

    2y = -3x + 6

    y = (-3/2) x + 2 , slope = - 3 / 2

    Slope of line perpendicular to the given line is equal to

    -1 / (-3/2) = 2 / 3

    Hence line E) given by y = (2/3)x + 3 is perpendicular to the given line

  20. (√128) / 2 + (5√2) / 4 =

    Solution

    Use 128 = 2 * 64 to write

    (√128) / 2 + (5√2) / 4 = (√(2*64)) / 2 + (5√2) / 4 =

    = (√2 √64) / 2 + (5√2) / 4

    = 8 √2 / 2 + 5√2 / 4

    = 16 √2 / 4 + 5√2 / 4 = 21 √2 / 4

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