Precalculus Test Out Practice Exam

Part 4 Test 2 Time: 3 hours

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

    displaymath115


    Answer: There is no solution because of the domain restriction.

  2. If tex2html_wrap_inline135 , find tex2html_wrap_inline137 .


    Answer: tex2html_wrap_inline139 .

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

    displaymath116


    Answer:

    displaymath117

  4. Find two angles that have the point (5,-4) on the terminal side of the angle.


    Answer: The angles are: tex2html_wrap_inline141 , and tex2html_wrap_inline143 .

  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 20 degrees, how much taller is Building A than Building B?


    Answer: Building A is 36.4 meters higher than Building B.

  6. Find the exact value of

    displaymath118


    Answer: The exact value is 1.

  7. Concerning the following function

    displaymath119

  8. Where do the graphs of the functions tex2html_wrap_inline147 , and tex2html_wrap_inline149 intersect on the interval [6,14]?


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

  9. Find the approximate range of the function

    displaymath120


    Answer: The approximate range is [-2.889,2.889].

  10. The graph of the function

    displaymath121

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


    Answer: The graph of the function of y is bounded above by the graph of tex2html_wrap_inline153 , and below by the graph of tex2html_wrap_inline155 .

  11. What is the phase shift of the graph of

    displaymath122

    Give the answer in terms of a combination of one ore more of a, b, c, and d.


    Answer: The phase shift is tex2html_wrap_inline165 .

  12. Restrict the domain of the function tex2html_wrap_inline167 so that its inverse exists.


    Answer: In the restricted domain tex2html_wrap_inline169 , the graph has an inverse. There are many other solutions, e.g. tex2html_wrap_inline171 .

  13. Find tex2html_wrap_inline173 .


    Answer: The expression is not defined, since the domain of the function tex2html_wrap_inline175 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 (10,-14), give the bearing and distance from point A to point B.


    Answer: The bearing from point A to point B is tex2html_wrap_inline177 . The distance from point A to point B is tex2html_wrap_inline179 .

  15. In triangle ABC, angle tex2html_wrap_inline181 equals 40 degrees, angle tex2html_wrap_inline183 equals 30 degrees, and side AB equals 10 inches. Find the exact value of side AC.


    Answer: The exact value of side AC is

    displaymath123

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


    Answer: tex2html_wrap_inline185 .

  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

    displaymath124

  18. If tex2html_wrap_inline187 , and the terminal side of t is located on the second quadrant, find tex2html_wrap_inline191 ans tex2html_wrap_inline193 in the interval tex2html_wrap_inline195 . Find the reference angle and the real angle in terms of degrees in the degree-minute-second format.


    Answer: The reference angle is tex2html_wrap_inline197 . The real angle is tex2html_wrap_inline199 .

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Wed Jul 16 16:19:34 MDT 1997

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