 Pre-requisites

 Real Numbers, Estimation, & Logic

 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.

 Inequalities and Absolute Value

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

 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.

 The Rectangular Coordinate System

 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.

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

 Graphs of Equations

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

 Reflects through the origin

 Functions & Their Graphs

 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)

 Operations on Functions

 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.

 Trigonometric Functions

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

 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)