Precalculus2 Practice Exam

Final Exam Time: 3 hours


  1. If tex2html_wrap_inline361 , and tex2html_wrap_inline363 , give exact values for:
  2. Find the angle between the vectors tex2html_wrap_inline381 and tex2html_wrap_inline383 .


    Answer: The angle is approximately tex2html_wrap_inline385 .

  3. Using the given sketch of the function tex2html_wrap_inline387 , Find values for a, b, c, and d.

    Answer: The values are:

  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.


    Answer: Let x be the number of Doberman pinschers, and y be the number of German shepherds. The system of inequalities is:

    eqnarray37

  5. Find all angles tex2html_wrap_inline401 between tex2html_wrap_inline403 and tex2html_wrap_inline405 that satisfy tex2html_wrap_inline407 . Write you answers in the degree-minute-second format.


    Answer: The angles are tex2html_wrap_inline409 , and tex2html_wrap_inline411 .

  6. Find the partial fraction decomposition of

    displaymath325


    Answer:

    displaymath326

  7. Let tex2html_wrap_inline413 .
  8. Verify the identity

    displaymath331

    Show all steps.


    Answer:

    displaymath332

    displaymath333

  9. Consider the parametric equations tex2html_wrap_inline419 , and tex2html_wrap_inline421 .
  10. Sketch the graph of tex2html_wrap_inline427 tex2html_wrap_inline429 . Include three cycles (periods) and label each asymptote.


    Answer:

  11. Find the sum of the sequence given below. Show your work:

    displaymath335


    Answer: The formula for finding the sum of an infinite geometric sequence is tex2html_wrap_inline431 . In this case a=7 and r=-3/7; thus the sum of the given sequence is tex2html_wrap_inline437

  12. Find the all exact solutions for tex2html_wrap_inline439 on the interval tex2html_wrap_inline441 .


    Answer: There are four solutions:

    displaymath336

  13. A manager must select 4 employees for promotion: 12 employees are eligible.
  14. If tex2html_wrap_inline443 , and tex2html_wrap_inline445 , find exact values for the following:
  15. Write an expression for the nth term of the sequence. (Assume n begins with 1.)

    displaymath337


    Answer: The nth term has the form

    displaymath338

  16. Find the equation of the tangent line to the parabola given by tex2html_wrap_inline465 at the point (-1,1).


    Answer: The equation of the tangent line is tex2html_wrap_inline467 .

  17. Find a unit vector in the direction of v= tex2html_wrap_inline469 .


    Answer: The unit vector is tex2html_wrap_inline471 .

  18. Use mathematical induction to prove the given formula for every positive integer n:

    displaymath339


    Answer:


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Mon Jul 21 17:10:43 MDT 1997

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