2.  Pre-requisites

3.  Real Numbers, Estimation, & Logic

4.  Be able to calculate with rational numbers (expressed as either repeating or terminating decimals) or irrational numbers (decimals that do NOT terminate or repeat)  Be able to ESTIMATE answers before pushing a button on a calculator! Use good mental mathematics.  Much done in math must be proven, and different methods of proof can be employed.

5.  Inequalities and Absolute Value

6. Solve by comparing the inequality to zero, factor if possible, and solve.

7.  Consider absolute value as distance, if the distance is greater than a constant, you must get further away in both directions. If the distance is less than a constant, the solution values must be within a certain range of values.

8.  The Rectangular Coordinate System

9.  Graphs are done in the x-y system. You can find distance between any 2 points using Pythagorean theorem and midpoint of 2 any 2 points simply as the average.  In both instances, a graph is often helpful in understanding the situation, prior to calculating.

10.  General form: Ax + By + C = 0  Slope-intercept form: y = mx + b  Point-slope form y – y1 = m(x – x1)

11.  Graphs of Equations

12.  Graphs to a parabola  Vertex at (h,k)  Graph has reflection symmetry

13.  Reflects through the origin

14.  Functions & Their Graphs

15.  Domain (x-values): real numbers which can be placed for x  Range (y-values): real numbers which are created from the values for x  Even functions: Reflect through the y-axis, f(x) = f(-x)  Odd functions: Reflect through the origin, f(x) = -f(-x)

16.  Operations on Functions

17.  Only consideration? Operations cannot result in a zero denominator  Composition of functions: When g is composed on f, the range of f becomes the domain for g.

18.  Trigonometric Functions

19.  t = real number (length of arc on unit circle) that corresponds to pt (x,y)  y = sin x y = cos x

20.  sec x = 1/cos x csc x = 1/sin x  cot x = 1/tan x  Pythagorean identity (main one, others may be developed from this one)