Introduction

Here you will find links to my Study Notes as .pdf files.   Each file will open in a new window.  To return to the web-site when you finish reading a file,  close the file  window or click on the tab to the left of the file-window tab. 

These notes were mainly generated in response to students' problems.  They frequently address a topic  by slowly developing a topic based on material which the students already understand and can apply.  I use a range of resources.

My text can be ʍopǝpᴉsd∩ if I wish
or coloured or even animated

I can compose some work in another package and import it, like this ...

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All Grades
  1. AG1 -Why some students fail mathematics.  My commentary on a paper by Helen A Marshal - The Mathematics Teacher 1918 and other sources.
  2. AG2 - Why Algebra.  An unusual approach to why we use algebra
  3. AG3 - Real Numbers and Beyond.  This note contains useful insights but may need to be supported by a tutor.
  4. AG4 - Negative Numbers. An investigation of negative numbers.  Why does Negative x Negative = Positive?
  5. AG5 - Ancient Arithmetic l - A Scientific Fable - Lots of fun
  6. AG6 - Ancient Arithmetic ll  The perils of living with the decimal system.
  7. AG7 - Lost Marks, reasons for; cancelation, elimination and numeracy
  8. AG8 - How to write a Science Exam
  9. AG9 - Learning and being Examined
  10. AG10 - Teaching Children with Learning Disabilities
  11. AG11 - Numbers and Arithmetic  A Story for Primary School Students.
  12. AG12 - Maths Reasoning  I found this series of slides on the Internet.  Interesting.  Sometimes contentious.  Useful for students and teachers?
  13. AG13 - What is a Square Root?  Defining.  Other roots.  Limitations on.  Finding without a calculator.
Grade 6
1.  AG600 Numbers and Arithmetic  A Story
Grade 7

1. AG700 Numbers and Arithmetic  A Story

Grade 8
Grade 9

1. AG40 - Algebraic Operations

2. AG41 - Solar System  A few interesting calculations

3. AG42 - Area of Triangle  and area of a parallelogram

4. AG43 - Geometry + Algebra  An interesting problem

5. AG44 - Indices Growth Test - exercises which lead to discovery

6. AG45 - Rational Numbers  Decimal to fraction form

7. AG46 - The Volume of a Sphere 

8.  AG47 - An Introduction to Trigonometry

9.  AG48 - The Lune of Hypocrates


 

Grade 10

1. AG60 - Domain and Range 

2. AG61 - Factorize Trinomial 

3. AG62 - Perpendicular Intersection 

4. AG63 - Canonical forms of Functions 

5. AG64 - Grade 10 Resources - Various Topics

6 AG65 - Solving Triangles 

7 AG66 - Circle Geometry Grade 10 and higher

8 AG67 - Geometry Revision Tool

9 AG68 -  Uphill with Gradients  Gradient and Angle of Inclination

10 AG69 - Oktoberfest etc  Venn Diagram problems

11 AG70 - Probability  Boolean Algebra (Algebra of Sets) and Venn diagrams

12 AG71 - Venn Diagram problem

13 AG72 - Statistics  Frequenccy table, Histogram, Frequency Polygon, Ogive, Standard Deviation

14 AG73 - Translation, Reflection, Rotation  Analytical Geometry

15 AG74 - Canonical Forms of Functions

16 AG75 - Grade 10 Maths Resources (incomplete)

17 AG76 - 2+Cos2T = 1,5  Trig. Equation

18 AG77 - Trig and Geometry  Worked examples

19 AG78 - Indices, Surds, Factorization  Worked examples

20 AG79 - An Equation with 2 variables 1.  An introduction to Simultaneous Equations.  Baiboard Slide

21 AG80 - Simultaneous Equations 2.  A Baiboard Slide Show.

22 AG81 - Working with Algebraic Fractions  Baiboard slides

23 AG82 - Functions  Domain and Range  Sketching a function  Finding Quadratic Parameters.  Worked Examples

23 AG83 - Parallelogram Problems including congruent triangles

24 AG84 - Reflection in a Straight Line in the Cartesian Plane

25 AG85 - Statistics, Frequency Tables

26 AG86  Factorising and Binomial Expansion

27  AG87 Sierpinski Triangles

Grade 11
  1. AG100 - Analytical Geometry Gradient of straight line.  Average gradient of a curve.  Gradient at a point on a curve foreshadowing Differential Calculus
  2. AG101 - 'k' substitution for solving complex equations
  3. AG102 - Binomial expansions - very important applications
  4. AG103 - Equations with square roots
  5. AG104 - Determining the conditions for the square root of the quotient of two binomials to be real
  6. G105 - Hyperbolae and other Functions.  Transformations of points, lines and functions.
  7. AG106 - Root of an Algebraic Fraction  Interesting
  8. AG107 - A Hyperbola Reflected
  9. AG108 - Completing the Square
  10. AG109 - Division  A study of long division leading to algebraic long division and 'Syntetic Division'
  11.  AG110 - Word Problems
  12.  AG111 - Quadratic Equations  Worked examples
  13.  AG112 - Sequences and Series  Worked Examples.  The question is not always stated.
  14.  AG113 - Probability Grade 11  Theory and Examples
  15.  AG114 - Synthetic Division.  Worked example
  16.  AG115 - Analytical Geometry  Gradient, Distance, Midpoint
  17.  AG116 - Angle of Inclination  Definition, AOI in Trigonometry, Example
  18.  AG117 - Find the Vertex (or turning point) of a parabola.  Two Methods
  19.  AG118 - Quadratic Equations, Exponents, Surds (incomplete)
  20.  AG119 - Quadratic Equation Intercepting a Straight line
  21.  AG120 - Completing the Square (worked Examples), Indices (in detail)  Incomplete but very useful.
  22.  AG121 - When a (Non Monic)Quadratic Expression will not Factorize Easily  The depreciated "Los Dit" method.
  23.  AG122 - Simultaneous Equations.   Different Situations and Their Solution Methods
Grade 12
  1. AG120 - Euclid and Similar Triangles created by a line cutting two sides of a triangle and parallel to the third side.  The Side-Splitter Theorem
  2. AG121 - Cubic Equations
  3. AG122 - The Factor Theorem
  4. AG123 - Monotonic Increasing Cubic
  5. AG124 - Quadratic Inverse
  6. AG125 - Sketching a Cubic.  Includes Algebraic Division and Synthetic Division
  7. AG126 - Circle Geometry Question and Solution
  8. AG127 - Financial Maths Summary
  9. AG128 - Loan Repayment including graphical treatment.
  10. AG129 - Find the equation of a parabola given its graph.
  11. AG130 - Understanding Logarithms
  12. AG131 - Maths G12 Competancy Assessment
  13. AG132 - Arithmetic Series Last Term
  14. AG133 - Geometric Series
  15. AG134 - More Complex Series
  16. AG135 - Sequences and Series
  17. AG136 - Sigma Notation
  18. AG137 - Fundamental Counting Principle
  19. AG138 - Trig. Equations Examples
  20. AG139 -Trig. Equations More Worked Examples
  21. AG140 - Graph Interpretation and Analysis
  22. AG141 - Trig. Equations, The General Solution
  23. AG142 - Tan 15 as a compound angle function.
  24. AG143 - The Lune of Hippocrates
  25. AG144 - The Lune of Hippocrates  Solution.  Hand written.  JPG image file
  26. AG145 - x^3 + x^2 - x -10  Sketch the cubic
  27. AG146 - A Nice Trig Problem
  28. AG147 - Geomtry Similar Triangles.  Worked Example
Unsorted

1. AG200 - Root Determination  A Root Characteristic Problem using the Discriminant. G11?

2 AG201 - Simultaneous Equations  Word Problem G10?

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