Mathematics Placement/Pretest 2

26 Questions | Total Attempts: 40

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Mathematics Placement/Pretest 2

This is Part 2 of the Mathematice Placement/Pre-test.


Questions and Answers
  • 1. 
    Expand the expression   log (6x5 / y)   as a sum, difference, and/or constant multiple of logarithms.
    • A. 

      5(log 6x - log y)

    • B. 

      30(log x) - log y

    • C. 

      5(log 6x) - log y

    • D. 

      Log 6 + 5(log x) - log y

    • E. 

      Log (6x^5 / y)

  • 2. 
    Find all solutions of the following equation in the interval [0, 2π).  
    • A. 

      X = 0, π/6, 5π/6, 7π/6, 11π/6

    • B. 

      X = 0, π/2, π, 3π/2

    • C. 

      X = 0, π/4, 7π/4

    • D. 

      X = 0, π/3, 2π/3, π, 4π/3, 5π/3

    • E. 

      X = 0, π/4, 3π/4, π, 5π/4, 7π/4

  • 3. 
    Solve the following equation. 2 cos x -1 = 0
    • A. 

      X = (π/6) + 2nπ and x = (5π/6) + 2nπ, where n is an integer

    • B. 

      X = (π/3) + 2nπ and x = (5π/3) + 2nπ, where n is an integer

    • C. 

      X = (π/4) + 2nπ and x = (5π/4) + 2nπ, where n is an integer

    • D. 

      X = (π/6) + 2nπ and x = (7π/6) + 2nπ, where n is an integer

    • E. 

      X = (2π/3) + 2nπ and x = (4π/3) + 2nπ, where n is an integer

  • 4. 
    Using the factors (x - 1) and (x + 4), find the remaining factor(s) of F(x) = x3 + 5x2 + 2x – 8.   and write the polynomial in fully factored form.
    • A. 

      F(x) = (x - 1)(x + 4)(x + 2)

    • B. 

      F(x) = (x - 1)(x + 4)^2

    • C. 

      F(x) = (x - 1)(x + 4)(x - 2)

    • D. 

      F(x) = (x - 1)^2(x + 4)

    • E. 

      F(x) = (x - 1)(x + 4)(x + 6)

  • 5. 
    Find the exact value of log4 12 – log4 3 without using a calculator.
    • A. 

      1/2

    • B. 

      1

    • C. 

      3

    • D. 

      3/2

    • E. 

      4

  • 6. 
    The point (7, 24) is on the terminal side of an angle in standard position. Determine the exact value of tan θ.
    • A. 

      Tan θ = -7/24

    • B. 

      Tan θ = 25/24

    • C. 

      Tan θ = 24/25

    • D. 

      Tan θ = -25/24

    • E. 

      Tan θ = 24/7

  • 7. 
    State the quadrant in which θ lies if cos θ < 0 and csc θ < 0.
    • A. 

      Quadrant IV

    • B. 

      Quadrant I

    • C. 

      Quadrant II

    • D. 

      Quadrant III

  • 8. 
    Write the quadratic function, f(x) = -x2 + 2x + 8, in standard form.
    • A. 

      F(x) = - (x + 1)^2 + 9

    • B. 

      F(x) = (x - 9)^2 - 1

    • C. 

      F(x) = (x - 1)^2 - 9

    • D. 

      F(x) = -(x - 1)^2 + 9

    • E. 

      F(x) = -(x + 9)^2 - 1

  • 9. 
    Condense the expression 1/3[log x + log 7] - [log y] to the logarithm of a single term.
    • A. 

      Log ((7x)^3/y)

    • B. 

      Log (7x/3y)

    • C. 

      Log ((7x / y)^(1/3))

    • D. 

      Log (((7x)^(1/3)) / y)

    • E. 

      Log ((7x)^(1/3)) - log y

  • 10. 
    Find the exact value of csc θ, using the triangle shown in the figure below, if a = 7 and b = 24.
    • A. 

      25/24

    • B. 

      25/7

    • C. 

      7/24

    • D. 

      24/25

    • E. 

      7/25

  • 11. 
    Determine the exact value of sin θ when cot θ = (7/24) and csc θ > 0.
    • A. 

      Sin θ = 26/25

    • B. 

      Sin θ = 24/25

    • C. 

      Sin θ = 49/25

    • D. 

      Sin θ = 48/25

    • E. 

      Sin θ = 23/24

  • 12. 
    Determine the vertex of the graph of the quadratic function  f(x) = x2 - 3x + 13/4
    • A. 

      (-3/2, 11/2)

    • B. 

      (3, 13/4)

    • C. 

      (3/2, 13/4)

    • D. 

      (3/4, 5/4)

    • E. 

      (-3/2, 1)

  • 13. 
    Identify all intercepts of f(x) = x2 / (x2 + 9).
    • A. 

      X-intercept: none; y-intercept: (0, 4)

    • B. 

      X-intercept: (0, 0); y-intercept: (0, 0)

    • C. 

      X-intercept: none; y-intercept: (0, 1)

    • D. 

      X-intercept: (-3, 0) and (3, 0); y-intercept: (0, 1)

    • E. 

      X-intercept: none; y-intercept: none

  • 14. 
    Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x) = 2 / (x - 3)
    • A. 

      Horizontal: x = 0; vertical: y = 3

    • B. 

      Horizontal: y = -3; vertical: x = 0

    • C. 

      Horizontal: y = 2; vertical: x = 3

    • D. 

      Horizontal: y = 0; vertical: x = 3

    • E. 

      Horizontal: x = 3; vertical: y = -2

  • 15. 
    Identify the vertical asymptote of the function f(x) = 2 + log(x + 3).
    • A. 

      X = 0

    • B. 

      X = -2

    • C. 

      X = -3

    • D. 

      X = 3

    • E. 

      The function has no vertical asymptote.

  • 16. 
    Given  f(x) = x2 + 3x -2    x + 5 determine the equations of any slant and vertical asymptote.
    • A. 

      Slant: y = x - 2; vertical: x = -5

    • B. 

      Slant: y = x + 8; vertical: none

    • C. 

      Slant: y = x + 2; vertical: x = -2

    • D. 

      Slant: y = x - 7; vertical: x = 3

    • E. 

      Slant: none; vertical: none

  • 17. 
    Write F(x) = x3 – 3x2 + 4x - 12 as a product of linear factors.
    • A. 

      X = (x - 3)(x + 2)^2

    • B. 

      X = (x - 3)^2(x - 2i)

    • C. 

      X = (x - 3)(x - 2)^2

    • D. 

      X = (x - 3)(x + 2i)(x - 2i)

    • E. 

      X = (x - 3)(x + 3)(x + 2)

  • 18. 
    If sin x = 1/2 and cos x = √(3)/2, evaluate the following function.   csc x 
    • A. 

      Csc x = √( 3)/2

    • B. 

      Csc x =2

    • C. 

      Csc x = √ 3

    • D. 

      Csc x = 1/3

    • E. 

      Csc x = 2√ 3/3

  • 19. 
    Use an inverse function to write θ as a function of x.
    • A. 

      θ = arctan (4 / (2x + 1))

    • B. 

      θ = arctan ((2x + 1) / 4)

    • C. 

      θ = arctan ((x + 1) / 2)

    • D. 

      θ = arctan (1 / (x + 1))

    • E. 

      θ = arctan (2x + 1)

  • 20. 
    Use the One-to-One Property to solve the following equation for x.  (1/3)7x-1 = 27
    • A. 

      4/7

    • B. 

      -3/7

    • C. 

      1/7

    • D. 

      -2/7

    • E. 

      1/3

  • 21. 
    Which of the following is equivalent to the expression below? cot θ - 1 1 - tan θ
    • A. 

      Cot θ

    • B. 

      Csc θ

    • C. 

      Sec θ

    • D. 

      1

    • E. 

      Tan θ

  • 22. 
    Sketch the graph of the function below. y = cos (x - (π/2))
    • A. 

      Graph A

    • B. 

      Graph B

    • C. 

      Graph C

    • D. 

      Graph D

    • E. 

      Graph E

  • 23. 
    Identify the x-intercept of the function y = 3 + log3 X .
    • A. 

      27

    • B. 

      1/27

    • C. 

      -3

    • D. 

      9

    • E. 

      The function has no x-intercept.

  • 24. 
    An initial investment of $1000 grows at an annual interest rate of 8% compounded continuously. How log will it take to double the investment?
    • A. 

      8.66 years

    • B. 

      9.66 years

    • C. 

      9.00 years

    • D. 

      8.00 years

    • E. 

      1 year

  • 25. 
    Find the exact value of 
    • A. 

      3/4

    • B. 

      8/5

    • C. 

      3/5

    • D. 

      3/8

    • E. 

      4/3