EXSS 323
Math Skills Test Solutions

Instructions:

Complete the following problems as completely as you can. Show your work on separate paper. This test is to be taken with books and notes closed. Have a scientific calculator handy for the computations. Results from the test will be used in assessing your readiness for the tasks involved in biomechanics and will help diagnose where additional review and help may be necessary.

  1. On a piece of graph paper, sketch a graph of the equation:
    4X - 2Y = 12
    What is the slope of the line?

    Slope = 2

  2. The equation X3 - 7X2 + 6X = 0 has three solutions. What are they?

    The solutions are the values which make the equation true. In this case the solutions are X = 0, 1 and 6. These can be determined by factoring the expression into X(X-1)(X-6) = 0.

  3. A graph of the the equation Y = 20X - 5X2 will cross the axis in two places. These are called the roots of the equation. What are these root values of X?

    Roots of the equation are 0 and 4. These are the X values where a graph of the equation would cross the axis. Also these are the values which make Y = 0.

  4. How far is the point (9,12) from the origin?

    The point is 9 units horizontally and 12 units vertically from the origin. Using the distance formula which is based on the Pythagorean theorem, the distance d is the square root of 92 + 122.

  5. What is 0.5 radians in degrees?

    A circle contains 2p radians = 360º => 1 radian ~ 57.3º => 0.5 radians ~ 28.6º

  6. Evaluate sin (30°), cos (30°) and tan (30°). What are these values expressed in radical (square root) form?

    Evaluations are: 0.5, 0.866, 0.577
    When expressed in radical form these are: 1/2 , square root of 3 divided by 2, square root of 3 divided by 3

  7. For what angle X is sin X = 0.4 ?

    Angle of 23.6 degrees.

  8. If cos X = 0.8944 what does sin X equal?

    Solving the trigonometric identity sin2X + cos2X = 1 for sinX yields
    sinX = sqrt(1 - cos    2X)
    sinX = sqrt(1 - 0.8944    2)
    sinX = ±0.4473


    Illustration for problems 9-12:

  9. Find a and c if b=4 and A = 30°

    a = 2.31 and c = 4.62 using the tan and cos functions

  10. . Find b and c if a = 9 and B = 45°

    b = 9 and c = 12.73 based on b = a and Pythagorean theorem

  11. . Find a and A if b = 5 and c = 8

    a = 6.24 and A = 51.32 degrees using Pythagorean theorem and cos(A) = 5/8

  12. . If the vertex of angle A is at the origin and B is at (5,4) what is angle A in degrees?

    If B is at (5,4) then side b is of length 5 and side a is of length 4. Tangent of angle A is then 4/5. Hence A is 38.66 degrees.