## 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.

- © 2015, 2017 A
^{2}www.mathnstuff.com/papers/joer16.htm- © 2015, 2017 A