| Week |
Tuesday | Wednesday |
Thursday
|
||
|---|---|---|---|---|---|
| I. Introduction: Backgrounds and Key concepts | 8-23 Introduction : How to succeed in this course. Sensible Precalc Ch 1.A |
8-24 What are Numbers? |
8-25 Finish course info? R.1 Comparing Numbers:=,< Operations. |
||
| II. More
Backgrounds: Beginning Functions-Linear functions and key concepts. |
8-30
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 |
8-31 R.7 Radicals worksheet. 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 ] Similar triangles. |
||
| III.Functions
and
lines
|
9-6 R.4, 1.1, 1.2 Visualizing variables and plane coordinate geometry. Plane Coordinates. Introduction to Winplot. Points, Animation. More Algebra review. Review Polynomials. (Factoring) Tables. 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) |
9-7 Linear functions. Linear Functions and Visualization of data. |
9-8 1.3 Lines. Slopes and equations of lines. Y and X intercepts. Midpoints with coordinates. |
||
| IV. Start
Trigonometry |
9-13 1.1,1.6, (3.5) Circles Equations for circles. MORE on functions! Graphs and mapping figures. |
9-14 Quiz #1 Visualization of data. |
9-15
3.3 (2.1) Overview of Core functions...elementary functions. Review of Key Triangles. |
||
| V. Triangle Trig |
9-20 3.3, (2.2) 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) Graph piecewise functions. Secant line slopes. [Using winplot to graph and find key function feature and solve equations graphically for zeros.?] |
9-21 More
on Quadratics |
9-22 6.1, 6.2 Modeling with quadratic functions. Start trig. Trigonometric functions for Right Triangles Solving Right triangles. |
||
| VI. |
9-27(2.1)
(6.3) Triangle trig: Inverse sine, cosine, tangent for acute triangles. Inverse trig/ applications. More Inverse trig (sine obtuse). More on Solving triangles |
9-28 Quiz
#2 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
Trig- Start General trig Functions and radian Measure |
10-4 8.1,
7.1,8.2 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. |
10-5 Radian measure and circles |
10-6 6.5 Trig functions for all angles - with radian measure. (sine and cosine)(tan) More on law of cosines |
||
| VIII. Trig Identities Trig function graphs Trig Equations |
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. Identity games. Begin Addition formulae double angles! |
||
| IX More trig identities, equations, and
graphs! |
10-18 7.1, 7.2 More Trig functions and equations: Addition formulae. Double and half angles |
10-19Quiz #4 | 10-20 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 |
10-25 graphs and elementary functions |
10-26 More on graphs and basic properties of trig functions. | 10-27 Periodic functions A sin(x) and sin(x) + D |
||
| XI End of trig! |
11-1graph
SinAX Misc..Phase Shift - trig and linear compositions. Continued! Trig. graph A sin(BX+C) |
11-2 Quiz #5 | 11-3 Review of
Quiz 5 More on compostions of trig functions- cosine tangent, secant. |
||
| XII. Begin Exponential and
logs |
11-8 Inverse
trig functions. More on inverse trig functions(Asin and Acos): Triangles! Graphs for inverse trig. (esp'lly Inverse tangent function) More on inverse and trig functions. graphs of combining trig functions. Exponential Functions. |
11-9 e! Logarithms: Introduction and definition. |
11-10 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
functions. What are elementary functions? Begin Polynomial and Rational Functions |
11-15Basic properties
of logs... and applications and exponents-solving
equations 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. |
11-16Quiz 6 | 11-17
Slide Rule Reference Logarithmic scales log scales (simple) Log scales Start Polynomials and rational functions |
||
| XIII-XIV |
11-22 Fall Break |
11-23 Fall Break | 11-24 Fall Break | ||
| XIV More on rational functions. |
11-29 Long division and factors of
polys. 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. |
11-30 |
12-1 Rational functions.Asymptotes. Translation, symmetry and scales for quadratics Difference quotients-Slopes of secant lines- for Polynomials. Polynomial analysis roots and positive and negative values. Roots of polynomials in general - inequalities. . |
||
| XV Pre-Calculus! | 12-6 Inequalities. Linear.
Quadratic. Polynomial. Absolute value functions and inequalities Intermediate value theorem. Complex numbers, The fundamental theorem of algebra Composition & Inverse functions |
12-7 Quiz #8! |
12-8 Review: Final comments on elementary functions- algebraic, logrithmic exponential, and trignometric. Some of my "favorite functions." A pre-calculus view of some calculus problems. Extremes, tangents,areas. |
||
| Final
Exam 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. Slide rules On-line java sliderule More Slide rules More applications of logs Trisection of angles, trig and algebra! |
Complex numbers? Complex arithmetic and trig Properties of roots and exponents. More on Complex Numbers, trig and roots?? |
|||
|
Reading Textbook or in SC on line. |
Special Instructions & Interesting but Optional | |
|---|---|---|
| Sensible Precalc Ch 1.A | ||
| Sensible
Precalc
Ch
1.B.1
(Firefox
Preferred) |
Extra help from Purple Math on
Converting between Decimals, Fractions, and Percents |
|
|
Similar
triangles. More on Similar triangles. |
|
| Dynamic Geometry® Exploration SimilarTriangles | ||
| Ch 1.B.1: 1c, 2, 16 | ||
| Law of Sines. | ||
| A
visual proof for "The
Law
of
Cosines" Demonstrations of the laws of sines and cosines |
||
| History of Pi | ||
| sin(A+B) proof illustrated. | ||
| Summary of trig identities | ||
| History
of
Trigonometric
functions |
||
| graph SinAX graph A sin(BX+C) | ||
| Trisection
of angles, trig and algebra! Complex Numbers, |
||
| History of the number e | ||
| How and
Why a Slide Rule Works On-line java sliderule |
||
| History of the Function concept | ||
