Final Exam Review for
Colorado State University, Pueblo
Math 124 — Pre-calculus Math — Spring 2015

To get started...

New Topics

1. polar coordinates
   1. the definition, particularly including multivaluedness (several polar coordinate expressions for the same point in the plane)
   2. converting from polar to Cartesian coordinates, and vice-versa
   3. graphing equations expressed in polar coordinates (equations involving $r$ and $\theta$, not $x$ or $y$)
   4. graphing polar functions (functions given in the form $r=f(\theta)$), also
      1. how many leaves does a figure have
      2. how many times is each leaf (or is the whole figure) traced out as $\theta$ goes from $0$ to $2\pi$
      3. which intervals of $\theta$ correspond to a single leaf
2. conic sections
   1. parabolæ
      1. geometric definition
      2. terminology: focus, directrix, vertex, latus rectum, focal diameter
      3. equations of parabolæ whose directrices are vertical or horizontal and whose vertices are at the origin
   2. ellipses
      1. geometric definition
      2. terminology: foci, vertices, major and minor axis, eccentricity
      3. equations of ellipses whose major and minor axes are vertical or horizontal and whose foci are symmetric across the origin
   3. hyperbolæ
      1. geometric definition
      2. terminology: foci, vertices, transverse axis, asymptotes, "central box"
      3. equations of hyperbolæ whose transverse axes are vertical or horizontal and whose foci are symmetric across the origin
   4. shifting a conic section left, right, up, or down
      1. getting the new equation
      2. the general equation of a shifted conic: determining which type of conic it is from the coefficients
      3. degenerate conics
   5. rotating a conic
      1. getting the new equation
      2. the general equation of a shifted conic
         1. determining which type of conic it is from the discriminant
         2. performing a rotation to eliminate the $xy$ term

Format of the test

• Thursday, April 30^th, 8-10:30am in our usual classroom This day is in two parts:
  1. A multiple-choice part (which is used for comparison purposes between different sections and years we offer this class) consisting of 30 problems in 30 minutes. This part will count as 45 points out of the 200 total on the final exam. You are not permitted to use a calculator on this part of the final.
  2. A free-response part (just for this section), similar in content, difficulty, and format to the first two midterms we had in this class.
• Friday, May 1^st, 8-10:30am in our usual classroom
  • This day is entirely free-response for this section, based on the material from the last two midterms (all the trig, in all versions and contexts) and a significant additional part on the recent material on polar coordinates and conic sections (for which: make sure you can do all the homework problems which have been assigned on chapters 8 and 11).

As always, to get credit for a solution on the test, you must explain your work; correct answers without explanation usually are worth zero points. Also, whenever possible, give exact answers — e.g, if the answer to a problem is $\sqrt{2}$, please write that, do not write $1.41421356237309504880168$, no matter how tempting.

Don't forget your calculator, you will need it!