Precalculus Test Out Practice Exam

Part 2 Test 2 Time: 3 hours

  1. Simplify the expression tex2html_wrap_inline247 to the from a+bi.


    Answer: tex2html_wrap_inline251 .

  2. Solve the equation tex2html_wrap_inline253 for x. List the exact answer(s), not approximation(s). A decimal answer is not an exact answer; it is an approximation. No credit will be given for an approximation.


    Answer: The exact solutions are: tex2html_wrap_inline257 .

  3. A farmer wants to construct a rectangular livestock pen so that he maximizes the area with 14,884 feet of fencing. Find the exact dimensions of the pen.


    Answer: The fence should be a square with side length 3721 feet.

  4. Why are the following not functions:
  5. Find the exact solution(s) to the equation tex2html_wrap_inline271 . Find the extraneous solution.


    Answer: The solution is tex2html_wrap_inline273 . The extraneous solution is tex2html_wrap_inline275 .

  6. Find the exact solution(s) to the equation tex2html_wrap_inline277 . Find the extraneous solution.


    Answer: The solutions are: tex2html_wrap_inline279 and tex2html_wrap_inline281 . The extraneous solutions are tex2html_wrap_inline283 and tex2html_wrap_inline285 .

  7. Find the exact non-real solutions(s), if any, to the equation tex2html_wrap_inline287 .


    Answer: The exact non-real solution is tex2html_wrap_inline289 .

  8. Solve tex2html_wrap_inline291 for x.


    Answer: The solutions are the numbers satisfying tex2html_wrap_inline295 ,


    or in interval notation, tex2html_wrap_inline297 .

  9. Solve tex2html_wrap_inline299 for x.


    Answer: x>6.

  10. Find the exact vertex of the parabola tex2html_wrap_inline305 . (No decimals)


    Answer: The vertex is tex2html_wrap_inline307 .

  11. Find an equation of the parabola that has a vertex at (8,3) and passes through the point (4,1).


    Answer: tex2html_wrap_inline309 .

  12. Find the maximum height of a ball that follows the path defined by the equation tex2html_wrap_inline311 .


    Answer: The maximum height is 9820.

  13. Find an equation of a polynomial of degree 10 that has 3+i as a zero.


    Answer: tex2html_wrap_inline315 .

  14. Find the zeros of the polynomial tex2html_wrap_inline317 .


    Answer: tex2html_wrap_inline319 and tex2html_wrap_inline321 .

  15. Divide tex2html_wrap_inline323 by x-6. What is the remainder?


    Answer: The remainder is 22.

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

    displaymath237


    Answer: The largest zero is tex2html_wrap_inline327 .

  17. How many real zeros does the polynomial tex2html_wrap_inline329 have?


    Answer: It has 3 real zeros, which are x=-2 and x=1 (double root).

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

    displaymath238


    Answer: y=x-6.

  19. Is tex2html_wrap_inline337 a zero of the polynomial

    displaymath239


    Answer: Yes, it is a zero.

  20. Find the inverse of the function tex2html_wrap_inline339 . If the domain needs to be restricted, state the restricted domain. If the domain does not need to the restricted explain.


    Answer: There are two solutions:

    displaymath240

    when the domain is restricted to the interval tex2html_wrap_inline341 , or

    displaymath241

    when the domain is restricted to the interval tex2html_wrap_inline343 .

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Wed Jul 9 16:04:51 MDT 1997

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