Precalculus Test Out Practice Exam

Part 2 Test 1 Time: 3 hours

  1. Simplify the expression tex2html_wrap_inline189 to the from a+bi.


    Answer: tex2html_wrap_inline193 .

  2. Solve the equation tex2html_wrap_inline195 for x. List the exact answer(s), not approximation(s).


    Answer: The exact solutions are: tex2html_wrap_inline199 .

  3. A picture frame has a total perimeter of 3 feet. The width of the frame is 0.62 times its height. Find the exact dimensions of the area of the frame.


    Answer: The height of the frame is tex2html_wrap_inline201 feet, its width is tex2html_wrap_inline203 feet.

  4. Which of the following is a function:
  5. Find the exact solution(s) to the equation tex2html_wrap_inline213 .


    Answer: The exact solution is x=1.

  6. Find the exact solution(s) to the equation tex2html_wrap_inline217 .


    Answer: The exact solutions are x=1, and x=-3.

  7. Find the exact non-real solutions(s), if any, to the equation tex2html_wrap_inline223 .


    Answer: The exact non-real solutions are: tex2html_wrap_inline225 .

  8. Solve tex2html_wrap_inline227 for x.


    Answer: The values of x that make the inequality true are the real numbers contained in the interval (-1,3).

  9. Solve tex2html_wrap_inline235 for x.


    Answer: The values of x that make the inequality true are 5<x<15, or in interval notation, (5,15).

  10. Find the exact vertex of the parabola tex2html_wrap_inline245 .


    Answer: The vertex is (4,-15).

  11. Find an equation of the parabola that has its vertex at (2,3) and passes through the point (1,1).


    Answer: The equation is tex2html_wrap_inline249 .

  12. Find the maximum height of a ball that follows the path defined by the equation tex2html_wrap_inline251 .


    Answer: The maximum height is 81.125.

  13. Find an equation of a polynomial that has 3+i as a zero.


    Answer: One solution is the polynomial tex2html_wrap_inline255 .

  14. Find the zeros of the polynomial tex2html_wrap_inline257 .


    Answer: The zeros are: x=-5, x=4, and x=5.

  15. Divide tex2html_wrap_inline265 by x-4. What is the remainder?


    Answer: The remainder is 0.

  16. What is the largest rational (exact) zero of the polynomial

    displaymath179


    Answer: The largest rational zero is tex2html_wrap_inline269 .

  17. How many real zeros does the polynomial tex2html_wrap_inline271 have?


    Answer: There are three real solutions, which are: x=-2, and x=1 (double solution).

  18. Find an equation of the slant asymptote to the graph of

    displaymath180


    Answer: The equation is y=x-6.

  19. Is tex2html_wrap_inline279 a zero of the polynomial

    displaymath181


    Answer: Yes, tex2html_wrap_inline279 is a zero.

  20. Find the inverse of the function tex2html_wrap_inline283 . If the domain needs to be restricted, state such a restricted domain. If the domain does not need to be restricted, explain.


    Answer: There are two solutions.

    displaymath182

    when the domain is restricted to the interval tex2html_wrap_inline285 , or

    displaymath183

    when the domain is restricted to the interval tex2html_wrap_inline287 .

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Wed Jul 9 15:08:24 MDT 1997

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