## Precalc Stuff

Last year I presented "Teaching with Trig Tricks." This year look at much of the rest of my precalculus resources. Examine a spreadsheet for writing tests, quizzes, doing computation. Kinesthetically explore functions in 3 ways. Take an inverse in the visual, auditory, symbolic, and kinesthetic modalities. Examine a library of precalc resources in topics like quadratics, logs/exponents, trig, polynomial and rational functions.

Pre Precalculus

Syntax, numbers, expressions, computation
number systems
how to use calculator to express or simplify
*use compute.xls to complete arithmetic from proportions to solving trig equations
basic precalc functions from an order of operations standpoint
Heronian Triangles and Pythagorean Triples

Graph
*graph paper
Solve Algebraically & Graphically

Formulas
distance
midpoint
*Slope in sound and pictures
compute distances w/ web page
Model for Distance     model info

Solving Equations
calculator to solve
solving equations and inequalities: algebraically, graphically
solving equations and inequalities: technologically
linear equation solver
*linear inequality notation and "proofs"

Lines
Who Has? ----- Lines
Lines Library
Lines Classes

Non-Functions
*Conics

Functions
*Exploring Functions Through the Use of Manipulatives, the entire book

*Function Library
most important functions -- IDENTITY, OPPOSITE, RECIPROCAL
smile odd/even/neither
definition odd/even graphics and questionbook
symmetry definition

*curve shifting -- translations, dilations, reflections: algebraically and graphically

# Place the wax paper on top of the coordinate plane to graph:  1. y= (x)  2. y= - (x)  3. y= ( - x)  4. y= - (- x)  5. y= (x - 3)  6. y= (x + 2) - 1  7. y= - (x + 2) - 1  8. y= (x - 6) + 2  9. the inverse of y= (x - 6) + 2

* more graphing
* solving
* raw masters
*absolute value dilator in hand
*absolute value dilator w/movement
Math Exercises (later)
notes: joer16b.gif , joer16c.gif

Inverse Functions
*Inverse Notes
*Inverse Problems
Take An Inverse In 4 Language Families

More on composition of functions

Dilation -- multiplication of functions
dilation of a function
*(Line)(line)=(quadratic)
animation on hundreds board and coordinate plane

Quadratic Functions
"Why = a(x - h)² + k?" -- EVERYTHING
Function Library -- Quadratics
quadratic dictionary definition
quadratic formula
standard and general forms
solve quadratic by calculator
completing the square summary sheet
solve a quadratic equation vs. simplify a radical expression
quadratic equation
discriminant

Complex Numbers
*00
off site: Elizabeth Stapel on Complex Computation I & II

Polynomial Functions
increasing/decreasing, end behavior definition
Functions Home Page
polynomials
more polynomials
*poly.xls by degree & coeff or in factored, synthetic division, solves
roots of polynomial functions
*Pass or Touch
*Who Has? Polynomial F(x)

Rational Functions
(Line)/(line)=(rational function) another kind of dilation
*asymptote definition
rational functions , harder problem, factors
*ratl.xls top vs bottom, graph, endbehavior, A(x)/B(x) + C(x), asymptotes
Notes on Rational and Polynomial Graphing Individual Graphics
Log & Exponential Functions
*e by area
Log use
log-log paper
semi log paper
log laws
*slide rule
exp.xls pay, 2 curves
Who Has? Exoponential

Trig Functions
*Lessons 330 - Trig Functions
Last year's "Trig Tricks"
Sine Law Ambiguous Case
· web page & text
· just the master
· *sinelaw.xls -- sine law digital manipulative
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
*sine.xls -- Asin(Bx-C)+D, sine, cosine, tangent, or sine & cosine
· sine & cosine animation only
Inverse Trig Functions Graphic
*solvtrig.xls all sorts of triangles

Vector
Addition
vector.xls -- completes scalar addition, multiplication, and vector addition
polrect.xls -- A DIGITAL MANIPULATIVE for drawing and addition of vectors.
*cramers.xls 2x2, 3x3, systems, minors, augmented columns

Matrices
*maytrix computation, inverse, solve systems

Other
*tiles.xls all stuff & hot
Writing To Learn Assignments
· Writing Assignments
· Writing Project Questions
· Possible Projects
· Coversheet
Precalc Notes

Algebra Notes
*Lessons
* graph paper
high school and college stuff
*Connect-the-Dots
*Who Has Games

*Math Exercises

# It's time for "Math Exercises." Please stand.Use your body particularly your hands and arms to represent: The line y = 0, the x-axis. Represent the y-axis: x = 0 Represent: y = x, the identity. Represent: y = -x, the opposite. Represent: y = x², the squaring function. Represent: y = |x|, the absolute value. Represent: y = -2x². Represent: y = 1/x, the reciprocal. Represent: x = y². Represent: y - |x-1|, the distance between a number and 1. Represent: y = |x| - 1, the absolute value, less 1. Represent: y = |x| + 1, the absolute value, plus 1. Please take your seat.

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