Midterm I Review for Math 121, Summer 2012

Topics we covered.

1. basics of manipulating equations -- "equivalent equations"
   1. distributive law
      1. forward: "multiply it out" [FOIL...]
      2. backward: "factoring"
   2. fractions
      1. common denominators
      2. clearing denominators
2. solving linear equations
3. solving quadratic equations
   1. completing the square
   2. the quadratic formula
4. complex numbers
   1. definition, basic manipulation
   2. the "conjugate"
   3. multiplication and division
   4. complex solutions of quadratic equations
5. radical equations... which, when squared give quadratic (or linear) equations
6. equations which become quadratic after some substitution
   1. sometimes $u=x^{1/2}$ (or $\sqrt{x}$)
   2. also $u=x^2$ (or $x^3$ or ...)
   3. maybe $u=(x+17)$
7. factoring by grouping
8. manipulating inequalities, particularly when to flip the direction of the inequality and when not to do so
9. interval notation
10. solving inequalities with the absolute value — two different kinds of behavior
11. word problems
    1. general approach to such problems: particularly important to define all variables, clearly and with units
    2. interest
    3. uniform motion
    4. mixtures
    5. finishing jobs
12. basics of Cartesian coordinates, graphing
13. formula for the distance between two points in the plane
14. formula for the midpoint of a line segment
15. graphing equations in two variables
    1. lots of points
    2. know what certain graphs look like
       1. $y=x^2$ and $x=y^2$
       2. $y=ax+b$
       3. $y=x^3$
       4. $y=1/x$
    3. $x-$ and $y-$intercepts
    4. symmetry
       1. with respect to the $x$ axis
       2. with respect to the $y$ axis
       3. with respect to the origin
16. lines
    1. idea of the slope
    2. slope-intercept equation
    3. parallel and perpendicular lines
    4. the general form of the equation of a line
    5. vertical and horizontal lines