Precalculus 2 Practice Exam

Test 4 Time: 1.5 hours

  1. Find the center, foci, and vertices of the ellipse


  2. Find the magnitude and direction angle of the vector tex2html_wrap_inline78 .

  3. Each cable of a suspension bridge is suspended (in the shape of a parabola) between two towers that are 480 feet apart and 60 feet above the roadway. The cables touch the roadway midway between the towers. Find an equation for the parabolic shape of each cable.

  4. Convert the polar equation tex2html_wrap_inline80 to rectangular form.

  5. Consider the equation


  6. Find two sets of polar coordinates for the point (-4,3), where tex2html_wrap_inline92 .
  7. Let tex2html_wrap_inline94 , and tex2html_wrap_inline96 .
  8. Find an equation for the hyperbola with vertices at (-1,5) and (-1,1), and with asymptotes tex2html_wrap_inline98 , and tex2html_wrap_inline100 .

  9. Follow these instructions carefully: Sketch the graph of tex2html_wrap_inline102 by hand. Have a table of at least seven appropriate values for r and tex2html_wrap_inline82 . Use exact values for tex2html_wrap_inline82 (no decimals). Sketch your graph by plotting the ordered pairs from your table (use the graph paper below). The shape of the curve must be apparent from your table of values. If it isn't, you must choose more appropriate values for tex2html_wrap_inline82 . You may use symmetry to avoid plotting too many points.

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Sun Jul 20 23:02:10 MDT 1997

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