Mathematics Placement/pretest 2 Robotics

26 Questions

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Mathematics Quizzes & Trivia

The study of mathematics is always an interesting one. It’s extremely daunting and complex to look at when you’re just starting off with the study but once you’re able to wrap your head around the applications of the numbers, letters and everything in between, and respect the fact that everything in mathematics always follows a set number of rules, it’ll certainly help. What do you know about maths? Take this placement test now!


Questions and Answers
  • 1. 
    Find the exact value of 
    • A. 

      3/4

    • B. 

      8/5

    • C. 

      3/5

    • D. 

      3/8

    • E. 

      4/3

  • 2. 
    If x = 4 tan θ, use trigonometric substitution to write  as a trigonometric function of θ, where 0 < θ < π/2. 
    • A. 

      4sinθ

    • B. 

      4cosθ

    • C. 

      4cscθ

    • D. 

      4secθ

    • E. 

      4tanθ

  • 3. 
    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.

  • 4. 
    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

  • 5. 
    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)

  • 6. 
    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

  • 7. 
    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

  • 8. 
    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

  • 9. 
    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

  • 10. 
    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.

  • 11. 
    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

  • 12. 
    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)

  • 13. 
    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

  • 14. 
    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

  • 15. 
    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)

  • 16. 
    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

  • 17. 
    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

  • 18. 
    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

  • 19. 
    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

  • 20. 
    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

  • 21. 
    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

  • 22. 
    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

  • 23. 
    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)

  • 24. 
    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)

  • 25. 
    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

  • 26. 
    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