YOU are better than YOU think. Show yourself  how: 

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 Logic chapters 1 to 5  re- appear not in sequence, as is or longer,  in  Volume 1A,  Pattern Based Reason, Bon Appetite.

Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and
writing

Logic mastery makes the hard, easier. Logic mastery  leads to better, stronger and richer comprehension.  Logic mastery  improves reading and writing.  Logic mastery ease learning difficulties.  Logic mastery gives a headstart.  In sum, logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

After logic,   (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

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What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.

Try the Twiddla Whiteboard. In principle, it  allows to people to draw and chat together online on a copy of this webpage or a clean sheet. The chat may be via text or audio.  Visit www.twiddla.com to set up whiteboards to work with the webpage of your choice.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

Area Introduction and Map

Analytic Geometry covers many topics. The multi-page coverage of straight lines, quadratics, operations on polynomials, and functions can be read in any order.

Optional Reading. Site pages on  Euclidean Geometry. with this area pages on real numbers,  Vectors and  Polar Coordinates lead to a lean, self-contained thought-based development of Complex Numbers and  Unit circle Trigonometry. It is possible to infer or suggest the properties of real numbers from geometric considerations, considerations not part of pure mathematics.- that will be posted online.

Study Tip: The excellent (ad-supported) Kyrgyz-Turkish High Schools Mathematics Pages [lecturen Notes] [worksheets] [review exercises] in pdf form, textbook style,  cover from arithmetic to calculus at a high level in a comprehensive manner. Pages  here at www.whyslopes.com focus on developing the algebraic reasoning and writing skills needed to appreciate the Kyrgyz-Turkish High Schools Mathematics Pages.

Top Level Pages.

1. Equal Sign Use & Perils <== Do not get bitten.

2. Real Numbers

3. Say More Positive

4. Solving linear Inequalities

5. 1 &  2D Triangle Inequalities

6. Absolute Value Calculation |x|

7. Absolute Value Equations Inequalities

8. Rectangular Coordinates

9. Distance Formulas

10. Triangle Inequality

11. Shortest Path with one
    bounce off a wall

Major Topics.

Analytic Geometry of Lines in the plane (start here)

1. (L)  Numerical Introduction

2. (L)  Point-Slope Equations for

3. (L)  Slopes of Perpendicular Lines

4. (L)  More Equations Forms

5. (L)  Algebraic View

6. (L) Intersection of Lines

7. (L) Geometry without drawings.

8. (L) Exercises

9. (L) Summary

10. (L) Lessons Elsewhere

This is the simplest area topic for students able to solve two equations in two unknowns using exact arithmetic with integers and whole numbers, efficiently.

Operations on Polynomials

Polynomials - Multiplication, Addition, Subtraction and Long Division . - are explained efficiently in five lessons.

• The first lesson is on the area view of the distributive law.

• The second lesson is on multiplication, addition and subtraction.

• The third and fourth  lessons are on long division by linear and then nonlinear polynomials.

• The fifth lesson revisits column multiplication methods.

Readers are assumed to be familiar with the definition of what is a polynomial and what is the degree of  polynomial. Links are provided to explanations elsewhere. Two views are better than one.

Quadratic Functions

1. Quadratic expressions, equations and formula, what is here (and not).

2. Introductory Graphing Exercises

3. Discussion of the standard form for graphing.

4. Factoring Quadratics by inspection

5. Difference of Two Squares

6. Completing the Square

7. Factorization, Arithmetic Approach

8. Factorization, Algebraic Approach (Quadratic Formula)

9. Summary of Main Ideas

10. More Exercises

The site coverage of quadratic factorization and the quadratic formula is almost complete. Sign analysis of quadratics (factored) and discussion of axes of symmetry may come later.

(FN) Functions & Relations

1. (FN) Functions and Relations (intro)

2. (FN) With Formulas Examples

3. (FN) With Sets Examples

4. (FN) Vertical Line Rule Examples

5. (FN) Functions & Sets - Theory

6. (FN) Interval Notation

7. (FN) Functions & Sets - Continued

8. (FN) Relations & Sets I

9. (FN) Relations & Sets II

10. (FN) Source, Target, Domain & Range

11. (FN) Numerical Exercises, Etc

12. (FN) Absolute Value

13. (FN) Step, Sawtooth & Abs. Value

14. (FN) Horizontal Line Rule Examples

15. (FN) Inverse Functions Examples

16. (FN) More Ways to Define  Examples

Site coverage includes a few fresh viewpoints that may complete explanations elsewhere and provide a context for the set-based codification of functions.

Vectors and Coordinates

1. Add & Multiply Points - warm-up for vectors.

2. Polar Coordinates - warm-up for complex numbers and trig.

3. Radians - useful in Calculus

4. (A) Vectors

5. (A) Coordinate Arithmetic

6. (A) Navigation on Maps

7. (A) Addition Geometrically

8. (A) Rotation

Complex Numbers

The development here assumes the properties of real numbers and derives the distributive law from assumptions about geometry.

1. (C) Complex Numbers Intro

2. (C) Distributive Law

3. (C) Properties

4. (C)  Complex Conjugates

5. (C)  Pythagoras New Proof
   The development here is based on the properties of real numbers and some geometric assumptions.

 The older site area on Complex Numbers may also be of interest.

Trigonometry

This development links the unit circle approach to right triangle approach, and to the use of complex numbers. Properties of the latter simplify many explanations (proofs) involving trig and vectors.

1. (T) Unit Circle Trig

2. (T) Complex Numbers & Trig

3. (T) cis or exponential Functions

4. (T) Dot & Cross Products

5. (T) Cosine Law

6. (T) Pythagoras Converse

Conic Sections

1. Conic Sections - a short essay to provide background information for secondary V students in Quebec.  Fuller treatment may come later.

Geometric Transformations

1. (PT) Dilations

2. (PT) Translations

3. (PT) Rotations

Geometric transformation assumptions imply an alternative base for Euclidean Geometry. The number of lesson here will or should be expanded.

www.whyslopes.com
Analytic Geometry
& Functions, etc

Area Entrance
(C) Complex Numbers
(FN) What are Functions?
(FN) Functions - More
SZM: Sign Analysis
(L) Lines Summary
(P) Polynomials (*,+,-)
(Q) Quadratics
(D) Simplify Square Roots
(T) Unit Circle Trig
Conic Sections
Links
More Links 
Entrance + Pages Below this page

Pages at Current Level

Pages at Above this Page

Extras:  Not all perfect.

Equal Sign Use/Abuse
Real Numbers
Say More Positive
Linear Inequalities
Triangle Inequality
Absolute Value |x|
|x| Eq'ns & Inequalities
Rectangular Coords
Shortest Path
Distance Formulas
Add & Multiply Points
Polar Coordinates
Radians
(A) Vectors
(A) Coordinate Arithmetic
(A) Navigation on Maps
(A) Addition Geometrically
(A) Rotation
(PT) Translations
(PT) Dilatations
PT: Rotations

Links to Site Pages outside this site area follow - co- and pre- requisites.

Road Safety Message

Easy Consequences of  this (newest) Complex Number. Starter Lesson follow below to provide an alternate development of HS or college maths.

Vec & Cmplx  No Applet
B2 C. Conjugates
B3 Pythagoras
B4 Distance
B5 Rt Triangle Similarity
B6 Trig., Functions
B7 Dot & Cross Products
B8 Cosine Law
B9 Exponential & cis fns
B10 Easy Trig Identities
B11 Set Viewpoint

Arithmetic Videos - Real Player Format

Decimal Addition Methods
Decimal Subtraction Methods
Decimal Multiplication Methods
Decimal Division Methods

Fractions
Primes
Greatest Common Divisor
Divisors
Least Common Multiples
Square Root
Simplification

Using formulas forwards & Backwards - A unifying theme for algebra skill development - the 4th skill in Volume 2, Three Skills for Algebra!

What is a Variable?

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