Precalculus 2 Practice Exam

Test 4 Time: 1.5 hours

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


    Answer: The center is (-5,4), the foci are (-5,2), and (-5,6), and the vertices are (-5,8), (-5,0).

  2. Find the magnitude and direction angle of the vector tex2html_wrap_inline123 .

    Answer: The magnitude is tex2html_wrap_inline125 , and the direction angle is approximately tex2html_wrap_inline127 .

  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.

    Answer: The equation is tex2html_wrap_inline129 , if the midpoint on the roadway is chosen as the origin of the coordinate system.

  4. Convert the polar equation tex2html_wrap_inline131 to rectangular form.

    Answer: The rectangular equation is


  5. Consider the equation


  6. Find two sets of polar coordinates for the point (-4,3), where tex2html_wrap_inline145 .

    Answer: The two sets of polar coordinates are tex2html_wrap_inline147 , and tex2html_wrap_inline149 .

  7. Let tex2html_wrap_inline151 , and tex2html_wrap_inline153 .
  8. Find an equation for the hyperbola with vertices at (-1,5) and (-1,1), and with asymptotes tex2html_wrap_inline159 , and tex2html_wrap_inline161 .

    Answer: The equation for the hyperbola is


  9. Follow these instructions carefully: Sketch the graph of tex2html_wrap_inline163 by hand. Have a table of at least seven appropriate values for r and tex2html_wrap_inline133 . Use exact values for tex2html_wrap_inline133 (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_inline133 . You may use symmetry to avoid plotting too many points.


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Sun Jul 20 23:05:21 MDT 1997

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