Precalculus Test Out Practice Exam

Part 4 Test 1 Time: 3 hours


  1. Find the exact solution(s) to the equation

    displaymath108


    Answer: There is no solution because x=3 is not in the domain of the original equation.

  2. If tex2html_wrap_inline132 , find tex2html_wrap_inline134 .


    Answer:

    displaymath109

  3. Write the following trigonometric expression as an algebraic expression in x:

    displaymath110


    Answer:

    displaymath111

  4. Find two angles that have the point (-3,7) on the terminal side of the angle.


    Answer: The two angles are tex2html_wrap_inline136 , and tex2html_wrap_inline138 .

  5. Building A and Building B are 100 feet apart. If the angle of depression from the top of Building A to the top of Building B is 10 degrees, how much taller is Building A than Building B?


    Answer: Building A is 17.6 feet higher than Building B.

  6. Find the exact value of

    displaymath112


    Answer: The exact value is 1.

  7. Concerning the following function

    displaymath113

  8. Where do the graphs of the functions tex2html_wrap_inline148 , and tex2html_wrap_inline150 intersect on the interval [6,14]?


    Answer: The are two points of intersection which are approximately (9.032,7.791) and (9.605,7.027).

  9. Find the approximate range of the function

    displaymath114


    Answer: The range of the function f(x) is approximately [-2.889,2.889].

  10. The graph of the function

    displaymath115

    is bounded by two graphs. What are the equations of the boundary graphs?


    Answer: The graph of the function is bounded above by the line tex2html_wrap_inline154 , and below by the line tex2html_wrap_inline156 .

  11. What is the phase shift of the graph of

    displaymath116


    Answer: The phase shift of the graph is tex2html_wrap_inline158 .

  12. Restrict the domain of the function tex2html_wrap_inline160 so that its inverse exists.


    Answer: The restricted domain is tex2html_wrap_inline162 . There are many other solutions, e.g. tex2html_wrap_inline164 .

  13. Find tex2html_wrap_inline166 .


    Answer: The expression is not defined, since the domain of the function tex2html_wrap_inline168 is [-1,1], and 2 does not lie in this interval.

  14. If point A is located at (2,3) and point B is located at (-8,14), give the bearing and distance from point A to point B.


    Answer: The bearing from point A to point B is tex2html_wrap_inline170 . The distance from point A to point B is tex2html_wrap_inline172 .

  15. In triangle ABC, angle tex2html_wrap_inline174 equals 40 degrees, angle tex2html_wrap_inline176 equals 30 degrees, and side AB equals 10 inches. Find the exact value of side AC.


    Answer: The exact value of side AC is

    displaymath117

  16. Convert 150 radians to degrees in the degree-minute-second format.


    Answer: tex2html_wrap_inline178 .

  17. Find the equation of the circle that passes through the points (2,3), (7,1), (9,5).


    Answer: The equation of the circle is

    displaymath118

  18. If tex2html_wrap_inline180 , and the terminal side of t is located on the second quadrant, find tex2html_wrap_inline184 .


    Answer: tex2html_wrap_inline186 .


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Wed Jul 16 15:55:54 MDT 1997

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