Precalculus Practice Exam

Part 2 Test 1 Time: 1 hour

  1. Factor tex2html_wrap_inline103 completely over the complex numbers.

    Answer: tex2html_wrap_inline105

  2. Solve for x in the expression tex2html_wrap_inline109 .

  3. In certain cases in which patients have rapidly increasing body temperature, powerful drugs are used to decrease the temperature. Suppose that t minutes after the injection of such a drug, a patient's temperature is y degrees above normal, where tex2html_wrap_inline117 . What is the patient's maximum temperature above normal?

    Answer: After 30 minutes the temperature is maximal, 9.6 degrees Fahrenheit above normal.

  4. Find all roots, real and complex, of the function tex2html_wrap_inline119 . Show all work and identify what techniques you use.

    Answer: tex2html_wrap_inline121 .

  5. Divide tex2html_wrap_inline123 using long division or synthetic division.

    Answer: tex2html_wrap_inline125 with a remainder of -137

  6. Find all asymptotes of the following functions:

    Answer: tex2html_wrap_inline133 is the vertical asymptote, y=2 the horizontal asymptote of the first function; the second function has a vertical asymptote at x=-1, and has tex2html_wrap_inline135 as its oblique asymptote.

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Mon Jun 16 12:10:04 MDT 1997

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