Precalculus 2 Practice Exam

Final Exam Time: 3 hours

  1. If tex2html_wrap_inline115 , and tex2html_wrap_inline117 , give exact values for:
  2. Find the angle between the vectors tex2html_wrap_inline127 and tex2html_wrap_inline129 .
  3. Using the given sketch of the function tex2html_wrap_inline131 , find the values for a, b, c, and d.

  4. A kennel raises Doberman pinschers and German shepherds. The kennel can raise no more than 40 dogs and wishes to have no more than 24 Doberman pinschers. The cost of raising a Doberman pinscher is $50, the cost of raising a German shepherd is $30, and the kennel can invest no more than $1500 for this purpose. Find a system of inequalities which describes the number of Doberman pinschers and German shepherds that can be raised by the kennel.
  5. Find all angles tex2html_wrap_inline133 between tex2html_wrap_inline135 and tex2html_wrap_inline137 that satisfy tex2html_wrap_inline139 . Write your answers in the degree-minute-second format.
  6. Find the partial fraction decomposition of


  7. Let tex2html_wrap_inline141 .
  8. Verify the identity


    Show all steps.

  9. Consider the parametric equations tex2html_wrap_inline147 , and tex2html_wrap_inline149 .
  10. Sketch the graph of tex2html_wrap_inline155 tex2html_wrap_inline157 . Include three cycles (periods) and label each asymptote.
  11. Find the sum of the sequence given below. Show your work:


  12. Find the all exact solutions for tex2html_wrap_inline159 on the interval tex2html_wrap_inline161 .
  13. A manager must select 4 employees for promotion: 12 employees are eligible.
  14. If tex2html_wrap_inline163 , and tex2html_wrap_inline165 , find exact values for the following:
  15. Write an expression for the nth term of the sequence. (Assume n begins with 1.)


  16. Find the equation of the tangent line to the parabola given by tex2html_wrap_inline177 at the point (-1,1).
  17. Find a unit vector in the direction of v= tex2html_wrap_inline179 .
  18. Use mathematical induction to prove the given formula for every positive integer n:


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Mon Jul 21 15:30:58 MDT 1997

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