|I. Introduction: Backgrounds and Key concepts||8-24
Introduction : How to succeed in this course.
Sensible Precalc Ch 1.A
What are Numbers?
Beginning Functions-Linear functions and key concepts.
Number Operations, equation, inequality properties. Types of Numbers
Visualizing: numbers- intervals.
Rational numbers and decimals. See Moodle for worksheet.
The Pythagorean theorem. [Over 30 proofs
[Many Java Applets proofs ]
Sqr(2) is not a rational #.
Solving linear inequalities
Applications of linear inequalities
Simplifying and Rationalizing
Visualizing variables and plane coordinate geometry.
Introduction to Winplot. Points, Animation..
More Algebra review.
Review Polynomials. (Factoring)
Introduction to Excel.
Linear and quadratic "Functions" and Visualization of data.
What's a function?
More on functions.
Linear Functions and Visualization of data.
Slopes and equations of lines.
Y and X intercepts.
Midpoints with coordinates.
Equations for circles.
Inequalities and absolute values.
MORE on functions!
Graphs and mapping figures.
Quadratic Functions and Visualization of data.
|9-16 Quadratic Functions
Other function qualities.
Winplot:Demonstation: Lines as equations and "functions".
Exploring functions with Winplot:
Primary Descriptive features of functions. (Increasing/decreasing/max/min)
Overview of Core functions...elementary functions.
Review of Key Triangles.
Secant line slopes.
[Using winplot to graph and find key function feature and solve equations graphically for zeros.?]
Start trig. Trigonometric functions for Right Triangles
Solving Right triangles.
Triangle trig: Inverse sine, cosine, tangent for acute triangles.
|9-22 Law of sines
sine for obtuse angles.
Law of Sines.
|9-23 More on Solving
More Inverse trig (sine obtuse).
Graph piecewise functions.
Visualize triangle trig and unit circle.
|VI.Finish Triangle Trig- Trig function graphs||9-28
More on Law of Sines.
Radian measure and circles in general.
|9-29 Quiz #2
Start Law of cosines.
Trig functions for all angles - with radian measure.(sine and cosine)(tan)
More on law of cosines.
A visual proof for "The Law of Cosines"
Dynamic proof :The Law of Cosines
Applications of triangle trig
Begin Trig Identities
|10-6 Quiz #3
||10-7 Begin Graphs of trig functions. Sine and cosine.
Begin trig equations and review of inverse trig functions(Asin and Acos)
Simple use of identities: relating trig function values on unit circle.
Solving Simple Trig Equations
|VIII. More trig identities.:)||10-12 More on graphs of trig functions, identities and equations.
Graphs for tangent and secant. Graphically solving trig equations.
|10-13 Quiz #4
|IX More trig identities,
equations, and graphs!
More Trig functions and equations:
Double and half angles
Other Trig identities: Product to sum trig.
Applications of Sum to slopes and trig function graphs for sine and cosine..
Identities and Equations
Phase Shift - trig and linear compositions.
|X End of trig!
graphs and elementary functions
More on graphs and basic properties of trig functions.
.Phase Shift - trig and linear compositions. Continued!
graph A sin(BX+C)
Exponential and logs
Inverse trig functions.
More on inverse trig functions(Asin and Acos):
Graphs for inverse trig. (esp'lly Inverse tangent function)
More on inverse and trig functions.
graphs of combining trig functions.
Compound interest? What is e?
Applications of Exponential functions
Solving simple exponential equations.exponential functions and graphs.
Graphs of exponential functions.
More on Exponential Applications- compound interest and growth.Exponential graphs
exponents and Logarithmic functions.
What are elementary functions?
Logarithms: Introduction and definition.
Basic properties of logs... and applications and exponents-solving equations
Models using Exponential Functions
Continuously compounded interest: Pert.
|11-10||11-11 No Class
|XIII. Begin Polynomial and Rational Functions||11-16More
Logs and Graphs of logs, exps with graphs of trig functions
Logarithmic calculations in equations and computations. "Transforming equations."
More applications of logs/exponential functions.
log scales (simple)
||11-24 Fall Break||11-25 Fall Break|
|XIV More on rational functions.
||11-28 Long division and
The remainder Theorem.
The Factor theorem
Roots and more on Polynomials.Functions The big picture on functions: Core functions and elementary functions
Symmetry [wrt origin....(axes).]
Quadratics and 1/x.
Translation, symmetry and scales for quadratics
Difference quotients-Slopes of secant lines-
roots and positive and negative values.
Roots of polynomials in general - inequalities.
|XV Pre-Calculus!||12-4 Inequalities. Linear.
Absolute value functions and inequalities
Intermediate value theorem.
The fundamental theorem of algebra
Composition & Inverse functions
Final comments on elementary functions- algebraic, logrithmic exponential, and trignometric.
Some of my "favorite functions."
A pre-calculus view of some calculus problems.
Review Session Sunday and Room BSS TBA
Tuesday, December 14 @ 10:20 am.
|Inventory of topics and materials
Worksheet on log scales
Music and log scales
Earthquake Magnitude and logs.
On-line java sliderule
More Slide rules
More applications of logs
Trisection of angles, trig and algebra!
Complex arithmetic and trig
Properties of roots and exponents.
More on Complex Numbers, trig and roots??
or in SC on line.
|Special Instructions & Interesting but Optional|
|Sensible Precalc Ch 1.A|
Purple Math on Converting between Decimals,
More on Similar triangles.
|Dynamic Geometry® Exploration SimilarTriangles|
|Ch 1.B.1: 1c, 2, 16|
|Law of Sines.|
proof for "The
Demonstrations of the laws of sines and cosines
|History of Pi|
|sin(A+B) proof illustrated.|
|Summary of trig identities|
|graph SinAX graph A sin(BX+C)|
angles, trig and algebra!
|History of the number e|
|How and Why a Slide
On-line java sliderule
|History of the Function concept|