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  • Steve Stephenson
    May 6, 2012

A High School Math Reference

Notes on the "why" and "how" of selected high school math concepts.

From my in-service teaching practice; a work in progress.

(Migrated Feb. 1, 2012 from Knol when it had 5,657 pageviews.)

Hope you find this useful,
-SKStephenson, sks23@cornell.edu, © 2009-2012, All Rights Reserved.

  1. Basic Courses

    1. Arithmetic

      1. Ancient Computers

      2. LineAbacus Dynamic Worksheet

    2. Algebra 1

    3. Geometry

      1. Sum of Angles in Triangle is 180°

      2. Triangle Concurrency Points

      3. Pythagorean Theorem

        1. General Graphic Proof
        2. Graphic Quilt Proof for Isosceles Right Triangles

      4. Special Triangles

    4. Algebra 2

      1. Perpendicular Lines

        1. Slopes

  2. Pre-Calculus

    1. Analytic Geometry

      1. Transformations

        1. Translating Graphs of Relations
        2. Reflecting Graphs of Relations
        3. Dilating Graphs of Relations (for February)
        4. Rotating Graphs of Relations by +90°
        5. Summary: The Essence of Transformations

      2. Polynomial Functions

        1. Polynomial Root Theorems
        2. The Remainder Theorem and Synthetic Substitution / Division

      3. Graphing Rational Functions

      4. Exponential & Logarithmic Functions

        1. Base e from Compound Interest

      5. Conic Sections - Video (#21-Kepler's Three Laws) and its Questionnaire

        6. The video has a good animation of cutting a cone to generate the conics from  14:30 to 15:25, then develops straight line directrix forms, then how conics impact modern society to 20:40. And here's my GeoGebra sketch using a circular arc directrix that can dynamically create all four conic sections.

    2. Trigonometry

      1. Why Study Circular Motion? (includes Standard Position)

      2. Angle Measurement

        1. Why Do We Measure Angles in Degrees?
        2. What Are Radians?

      3. Unit Circle With Special Points

      4. Circular Functions = Trig Functions

        1. Trig Function Definitions - "Trig In A Nutshell"
        2. Trig Function Graphs

      5. Coordinate Plane Trig

        1. Trig Functions of Any Angle
        2. Identity cos(α−β), Law of Cosines, Area of Triangle, Law of Sines
        3. Angle Sum & Difference Identities
        4. Double and Half Angle Identities

      6. Triangle Trig

        1. Similar Right Triangles are Historic Basis of Trigonometry
        2. Law of Cosines and Law of Sines from Obtuse Triangle
          with Definitions of sin(180° − θ) and cos(180° − θ).
        3. Heron's Formula for Area of SSS Triangle

  3. Calculus

    1. Differential Calculus

      1. Tangent Line Problem

      2. Derivatives of sin(θ) and cos(θ)
        are the reason we measure angles in radians.

      3. Derivatives of Exponential and Logarithmic Functions

      4. Differentiation Rules and Other Resources

    2. Integral Calculus

      1. Area Problem

      2. Development of Natural Logarithm From Integral Definition
        [Natural Logs were once called Hyperbolic Logs.]


Subpages (1): Line Abacus