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

$library$ *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)� + 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

$[tutorials & resource material arranged by topic$

*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
$[tutorials & resource material arranged by topic$ *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.

$[MC,i. Home]$ $[Applications]$ $Classes$ $[Words]$
© 2015, 2017 A² www.mathnstuff.com/papers/joer16.htm

Precalc Stuff

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

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