Precalc  Notes

Resources
- Algebra Notes
Classes, Tutorials & Resource Material
graph paper

Projects: Project Questions
Some Possible Projects
qb coversheet

Model for Distance
compute distances w/ web page
model info

Solve Algebraically & graphically
Solving Equations Graphically, Solutions to Linear Equations
"Why = a(x - h)² + k?" -- EVERYTHING
Solve w/Graphing Calulator

Syntax, numbers, expressions
number systems
calculator express or simplify
compute.xls arith to trig and stat
calculator solve

Functions function library
basic functions, expressions
odd/even/neither , odd/even ,
increasing/decreasing, end behavior
asymptote
symmetry ,
most important functions -- IDENTITY, OPPOSITE, RECIPROCAL: ,

Lines
linear.xls graphs, slope
Slope Song
graph.xls
lines
Who Has? Lines , ,
linear inequality notation , =poi++--+
solving equations and inequalities: algebraically, graphically technologically ,
linear equation solver
solving equations and inequalities: algebraically, graphically, technologically in 1, 2, 3 dimensions: solve linear ,

Families of functions ,
function notation
basic curve shifting and composition of functions:
shift square root functions
shift reciprocal function ,
translations, dilations, reflections: algebraically and graphically
Who Has? Curve Shift
more on composition of functions

Inverse Functions inverse functions: verbally, analytically, algebraically
Inverse Notes ,     Inverse Problems     Take An Inverse In 4 Language Families

Dilation
dilation of a function , Dilation creates functions ,
animation

quadratic functions: graphs, equations, features, vocabulary , ,
regions bounded by curves: pcdraw , fx8 (precalc drawing required in calc)

Polynomial Functions
, , ,
poly.xls by degree & coeff or in factored, synthetic division, solves
roots of polynomial functions ,
Who Has? Polynomial F(x)

Complex Numbers
more on complex numbers: Elizabeth Stapel on Complex Computation I II

Rational Functions
rational functions
ratl.xls top vs bottom, graph, endbehavior, A(x)/B(x) + C(x), asymptotes
Who Has? Rat'l F(x)

Log & Exponential Functions
Function Library
Exponential or Power Functions
A Bit about e, the base of the Natural Logs
Even More About e, the base of the Natural Logs
Linear vs Exponential Growth
Parent Functions, Their Slope Functions, and Area Functions
Questionbook questions on exponents and logs:
graph exponentials
solve exponentials
A LOG IS AN EXPONENT - exponential and natural log are inverse functions ,
exp.xls pay, 2 curves
Who Has? Exoponential
Logs without Feeling Out on A Limb
Log Papers

Trig Functions

Triangle Sides & Angles Vocabulary
opposite
hypotenuse

Right Triangle Sides & Angles --
equilateral triangle
30-60-90 triangle
the square
45-45-90 triangle

the 90s
45s
60s
30s

Trig Functions of Reference & Special Angles
trig30s
trig45s
trig60s
trig90s
All Students Take Calculus

Six Trig Functions and the Unit Circle
Six Trig Functions and the Unit Circle
· The Animated Unit Circle. - Words w/text.
· *jig1.xls -- UNIT CIRCLE JIG SAW PUZZLE
· *unit circle jig saw puzzle master
Black Unit Circle - Each function is the length of a leg or hypotenuse of a right triangle.
Colored Unit Circle - w/6 Trig Functions
central angle animation only
sine & cosine animation only
tangent and secant animation only
cotangent and cosecant animation only
all 6 functions animation only
all 6 functions with segments labeled animation only

Inverse Trig Functions graphic
Pythagorean Trig Identities
sine-cosine, sin2(A) + cos2(A) = 1
tangent-secant, tan2(A) + 1 = sec2(A)
cotangent-cosecant, cot2(A) + 1 = csc2(A)

Cheat Sheets of Trig Identities --
Pythagorean Identities, Cofunctions, Odd/Even Functions
Sine, Cosine, & Tangent of the Sums & Differences
Double & Half Angle Formulas
(Signs of the Trig Functions)

Trig Functions Summary Pages
*Lessons 330 - Trig Functions
Last year's "Trig Tricks"

Sine Law & Asin(Bx-C)+D & Solve Triangles
Sine Law Ambiguous Case
· web page & text
· just the master
master sinelaw.xls DIGITAL MANIPULATIVE
solvtrig.xls -- solve all sorts of triangles
sine.xls -- Asin(Bx-C)+D, sine, cosine, tangent, or sine & cosine
· sine & cosine animation only
Inverse Trig Functions Graphic
Solving Equations Graphically, Solutions to Linear Equations
More Trig Equations to Solve

Vector