| Week |
Tuesday | Wednesday |
Thursday
|
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|---|---|---|---|---|---|
| I. Introduction: Backgrounds and Key concepts | 8-24 Introduction : How to succeed in this course. Sensible Precalc Ch 1.A |
8-25 Pre-Test |
8-26 What are Numbers? Comparing Numbers:=,< Operations. |
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| II. More
Backgrounds: Beginning Functions-Linear functions and key concepts. |
8-31 Number Operations, equation, inequality properties. Types of Numbers Visualizing: numbers- intervals. |
9-1 Rational numbers and decimals. See Moodle for worksheet. |
9-2
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. Plane Coordinates. Similar triangles. Introduction to Winplot. Points, Animation.. |
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| III.Functions
and
lines |
9-7 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. |
9-8 Linear
functions. Linear Functions and Visualization of data. |
9-9
Lines. Slopes and equations of lines. Y and X intercepts. Midpoints with coordinates. |
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| IV. Start
Trigonometry |
9-14 Circles Equations for circles. Inequalities and absolute values. MORE on functions! Graphs and mapping figures. |
9-15 Quiz
#1 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. |
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| V.
Triangle Trig |
9-21
Modeling
with
quadratic
functions. 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. Inverse trig |
9-22 Law of sines sine for obtuse angles. Law of Sines. |
9-23 More on Solving
triangles/
applications. More Inverse trig (sine obtuse). Graph piecewise functions. Visualize triangle trig and unit circle. |
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| VI.Finish Triangle Trig- Trig function graphs | 9-28 More on Law of Sines. Radian measure and circles in general. |
9-29 Quiz #2 |
9- 30 Start Law of cosines. Trig functions for all angles - with radian measure.(sine and cosine)(tan) |
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| VII
Trig Equations Trig Identities |
10-5 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 |
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| VIII. More trig identities.:) | 10-12 More on graphs of trig functions, identities and equations. Graphs for tangent and secant. Graphically solving trig equations. Identity games.. |
10-13 Quiz #4 |
10-14 Addition formulae double angles! |
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| IX More trig identities,
equations, and graphs! |
10-19 More Trig functions and equations: Addition formulae. Double and half angles |
10-20 | 10-21 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. |
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| X End of trig! |
10-26 graphs and elementary functions More on graphs and basic properties of trig functions. |
10-27 |
10-28 Phase shifts. Periodic functions .Phase Shift - trig and linear compositions. Continued! graph SinAX graph A sin(BX+C) |
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| XI Begin
Exponential and logs |
11-2 Misc. Trig. 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. |
11-3 |
11-4Reference 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 |
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| XII.Finish
exponents and Logarithmic functions. What are elementary functions? |
11-9 e! 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 VETERAN'S DAY |
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| XIII. Begin Polynomial and Rational Functions | 11-16More
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. |
11-17 | 11-18 Logarithmic scales log scales (simple) Log scales |
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| XIII-XIV |
11-23
Fall Break |
11-24 Fall Break | 11-25 Fall Break | ||
| XIV More on rational functions. |
11-28 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. |
11-29 |
11-30 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. . |
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| XV Pre-Calculus! | 12-4 Inequalities. Linear.
Quadratic.
Polynomial. Absolute value functions and inequalities Intermediate value theorem. Complex numbers, The fundamental theorem of algebra Composition & Inverse functions |
12-5 Quiz #8! |
12-6 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. |
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| Final Exam Review Session Sunday and Room BSS TBA |
Tuesday, December 14 @ 10:20 am. |
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| 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?? |
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