|I. Introduction: Backgrounds and Key concepts||8-23
Introduction : How to succeed in this course.
Sensible Precalc Ch 1.A
What are Numbers?
|8-25 Finish course info?
Beginning Functions-Linear functions and key concepts.
R.1, R.2, R.5, 1.5
Number Operations, equation, inequality properties.
Types of Numbers
Rational numbers and decimals. See Moodle for worksheet.
Sqr(2) is not a rational #.
Visualizing: numbers- intervals.
Solving Linear Equations
Solving linear inequalities
Simplifying and Rationalizing
|9-1 R.7, (1.5), 1.6,
Applications of linear inequalities
The Pythagorean theorem. [Over 30 proofs !]
[Many Java Applets proofs ]
||9-6 R.4, 1.1, 1.2
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.
Sensible Precalc Ch 1.B.1 (Firefox Preferred)
Linear Functions and Visualization of data.
Slopes and equations of lines.
Y and X intercepts.
Midpoints with coordinates.
||9-13 1.1,1.6, (3.5)
Equations for circles.
MORE on functions!
Graphs and mapping figures.
|9-14 Quiz #1
Visualization of data.
Overview of Core functions...elementary functions.
Review of Key Triangles.
|V. Triangle Trig
||9-20 3.3, (2.2)
Other function qualities.
Winplot:Demonstation: Lines as equations and "functions".
Exploring functions with Winplot:
Primary Descriptive features of functions. (Increasing/decreasing/max/min)
Graph piecewise functions.
Secant line slopes.
[Using winplot to graph and find key function feature and solve equations graphically for zeros.?]
||9-22 6.1, 6.2
Modeling with quadratic functions.
Start trig. Trigonometric functions for Right Triangles
Solving Right triangles.
Triangle trig: Inverse sine, cosine, tangent for acute triangles.
Inverse trig/ applications.
More Inverse trig (sine obtuse).
More on Solving triangles
Areas with trig.
|9- 29 8.1, 6.4, 6.1, 6.3, (6.5)
Law of sines
sine for obtuse angles.
Law of Sines. in general.
|VII Finish Triangle
Start General trig Functions and radian Measure
More on Law of Sines.
Start Law of cosines.
A visual proof for "The Law of Cosines"
Dynamic proof :The Law of Cosines
Applications of triangle trig
Visualize triangle trig and unit circle.
Radian measure and circles
Trig functions for all angles - with radian measure.
(sine and cosine)(tan)
More on law of cosines
Trig function graphs
|10-11 6.5, 7.1,
Begin Trig Identities
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.
|10-12 Quiz #3
More on graphs of trig functions, identities and equations.
Solving Simple Trig Equations
|10-13 7.1, 7.2, 7.5, (7.3)(7.4, 7.5)
Graphs for tangent and secant.
Graphically solving trig equations.
Begin Addition formulae
|IX More trig identities, equations, and
||10-18 7.1, 7.2
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 Trig Graphs
graphs and elementary functions
|10-26 More on graphs and basic properties of trig functions.||10-27
A sin(x) and sin(x) + D
|XI End of trig!
Misc..Phase Shift - trig and linear compositions. Continued!
Trig. graph A sin(BX+C)
|11-2 Quiz #5||11-3 Review of
More on compostions of trig functions-
cosine tangent, secant.
|XII. Begin Exponential and
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.
Logarithms: Introduction and definition.
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
Models using Exponential Functions
Continuously compounded interest: Pert.
|XIII. Finish exponents and Logarithmic
What are elementary functions?
Begin Polynomial and Rational Functions
of logs... and applications and exponents-solving
More exponential models (Growth/Decay)
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.
Slide Rule Reference
log scales (simple)
Start Polynomials and rational functions
||11-22 Fall Break
||11-23 Fall Break||11-24 Fall Break|
|XIV More on rational functions.
||11-29 Long division and factors of
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!||12-6 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
|Thursday, December 15 @ 3:00 pm.|
|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|
||Extra help from Purple Math on
Converting between Decimals, Fractions,
More on Similar triangles.
|Dynamic Geometry® Exploration SimilarTriangles|
|Ch 1.B.1: 1c, 2, 16|
|Law of Sines.|
visual 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)|
of angles, trig and algebra!
|History of the number e|
Why a Slide Rule Works
On-line java sliderule
|History of the Function concept|