Navigational Mathematics

Hisham Amir, 05.04.2018

Inhaltsverzeichnis

  1. Basic Arithmetic
    1. BODMAS Practice
    2. Prime Factorization
    3. Order of operations - addition, subtraction, division, multiplication and brackets
    4. Percentages and Equivalent Fractions and Decimals
  2. Algebra
    1. Basic Algebra Terms
    2. Polynomials
    3. Proof: Difference of two squares
    4. Proof: Perfect Square Trinomials
    5. Sum And Difference of 2 Cubes
    6. Guided Example: Multiplying Binomials
    7. Example: Factorising Polynomials
    8. Summary Practice: Factorising Polynomials
    9. Guided Example: Solving Quadratic Equations using Factorization
    10. Quiz: Solving Quadratic Equations by factorising.
    11. Solving Quadratic Equations using Quadratic Formula
    12. Multiply and Division of Fractions
    13. Practice: Addition and Substraction of Algebraic Fractions Ex1
    14. Exercise: Simplify Complex Fractions
  3. Law of Indices
    1. Indices
    2. Product of Powers Law
    3. Power of a power law
    4. Division of Powers Law
    5. Solving Equations Involving Indices
    6. Practice with steps: Indices Equation types Ex 1
    7. Practice with Steps: Indices Equation Types Ex2
    8. Practice with steps: Indices Equation Types Ex3
    9. Practice with steps: Solving Indices Equation types Ex4
    10. Practice with steps:Solving Indices Equation types Ex 5
  4. Using of straight line graphs
    1. Graph Equations
    2. Variables
    3. Identifying variables
    4. Graph of a Straight Line
    5. Gradient of a Straight Line
    6. The Y Intercept
    7. Vertical Line Graph
    8. Drawing a Graph using known equations
    9. Drawing a Straight Line Graph using known points
    10. Reading from the graph
    11. Lets do some practice
    12. Let's Do Some Practice
    13. Let's Do Some Practice
  5. Trigonometry
    1. Definitions used in Trigonometry
    2. Proof: Pythagora's Theorem
    3. Proof: Law of Sines
    4. Exercise: Using Sine Rule Ex 1
    5. Exercise: Using Sine Rule Ex 2
    6. Proof: Law of Cosines
    7. Introduction: Radians
    8. Convert Radians to Degrees
    9. Basic Trig Functions of the Unit Circle
    10. Values of points on the Unit Circle
    11. CAST Rule
    12. Explore the Sine Function
    13. Explore the Cosine Function
    14. The Sine, Cosine, Tangent and the Unit Circle
  6. Angles
    1. Bearing Relationship
  7. Vectors
    1. Intoduction: Vectors
    2. Explore:Vectors
    3. Unit Vectors
    4. Vectors: Addition and Subtraction (Graphically)
    5. Vectors: Algebraic Representation
    6. Exercise: Vectors, Algebraic Representation
    7. Exercise: Vector Exercise Including Scalar Product
    8. Dot And Cross Products
    9. Explore: Dot Product
    10. 3 Dimensional Vectors
    11. Explore: Cross Product
  8. Geometry
    1. Angles in Same Segment
    2. Angles in Alternate Segment
    3. Angle at Centre and Circumference
    4. Angles In Cyclic Quadrilaterals
    5. Angle in Semicircle
    6. Perpendicular Bisector to Chords of Circles
  9. Trigo Identities
    1. The Pythagorean Identities
    2. Trigonometric Identity Explorer
    3. Proving Trigonometric Identities
    4. Solving Trigonometric Equations
    5. Deducing the Relationship: A sin x + B sin x= R cos (x+a)
    6. Asin(wt)+Bcos(wt)=Rsin(wt+a)
    7. Solving Trigonometric Equations in Harmonic Form
    8. Practice: Solve Trig Eqn in form of Acosx-Bsinx=C
    9. Practice: Solve Trig Eqns in form of Asinx-Bcos=C

1.

Basic Arithmetic

  • 1. BODMAS Practice
  • 2. Prime Factorization
  • 3. Order of operations - addition, subtraction, division, multiplication and brackets
  • 4. Percentages and Equivalent Fractions and Decimals

1.1.

BODMAS Practice

– Hisham Amir, Waddy

1.2.

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1.3.

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1.4.

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2.

Algebra

  • 1. Basic Algebra Terms
  • 2. Polynomials
  • 3. Proof: Difference of two squares
  • 4. Proof: Perfect Square Trinomials
  • 5. Sum And Difference of 2 Cubes
  • 6. Guided Example: Multiplying Binomials
  • 7. Example: Factorising Polynomials
  • 8. Summary Practice: Factorising Polynomials
  • 9. Guided Example: Solving Quadratic Equations using Factorization
  • 10. Quiz: Solving Quadratic Equations by factorising.
  • 11. Solving Quadratic Equations using Quadratic Formula
  • 12. Multiply and Division of Fractions
  • 13. Practice: Addition and Substraction of Algebraic Fractions Ex1
  • 14. Exercise: Simplify Complex Fractions

2.1.

Basic Algebra Terms

– Hisham Amir

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2.7.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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3.

Law of Indices

Chapter on the various laws of indices

  • 1. Indices
  • 2. Product of Powers Law
  • 3. Power of a power law
  • 4. Division of Powers Law
  • 5. Solving Equations Involving Indices
  • 6. Practice with steps: Indices Equation types Ex 1
  • 7. Practice with Steps: Indices Equation Types Ex2
  • 8. Practice with steps: Indices Equation Types Ex3
  • 9. Practice with steps: Solving Indices Equation types Ex4
  • 10. Practice with steps:Solving Indices Equation types Ex 5

3.1.

Indices

Move the slider to change the value of the indices
– Hisham Amir

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3.10.

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4.

Using of straight line graphs

Use straight line graph to verify the law connecting two variables

  • 1. Graph Equations
  • 2. Variables
  • 3. Identifying variables
  • 4. Graph of a Straight Line
  • 5. Gradient of a Straight Line
  • 6. The Y Intercept
  • 7. Vertical Line Graph
  • 8. Drawing a Graph using known equations
  • 9. Drawing a Straight Line Graph using known points
  • 10. Reading from the graph
  • 11. Lets do some practice
  • 12. Let's Do Some Practice
  • 13. Let's Do Some Practice

4.1.

Graph Equations

Equations
[i][b]What is an Equation?[/b][/i][br]A conditional equation is a statement of the equality of two expressions that is only true for restricted values of the symbols involved.[br][br]An equation in a single variable can be written as a subject variable (called the dependent variable) being equal to some expression in the single variable (called the independent variable).
– Hisham Amir

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4.9.

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4.11.

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4.13.

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5.

Trigonometry

Chapter on Trigonometry

  • 1. Definitions used in Trigonometry
  • 2. Proof: Pythagora's Theorem
  • 3. Proof: Law of Sines
  • 4. Exercise: Using Sine Rule Ex 1
  • 5. Exercise: Using Sine Rule Ex 2
  • 6. Proof: Law of Cosines
  • 7. Introduction: Radians
  • 8. Convert Radians to Degrees
  • 9. Basic Trig Functions of the Unit Circle
  • 10. Values of points on the Unit Circle
  • 11. CAST Rule
  • 12. Explore the Sine Function
  • 13. Explore the Cosine Function
  • 14. The Sine, Cosine, Tangent and the Unit Circle

5.1.

Definitions used in Trigonometry

This applet shows visually some of the terms used in Trigonometry
– Hisham Amir

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5.7.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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5.14.

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6.

Angles

  • 1. Bearing Relationship

6.1.

Bearing Relationship

– Hisham Amir

7.

Vectors

  • 1. Intoduction: Vectors
  • 2. Explore:Vectors
  • 3. Unit Vectors
  • 4. Vectors: Addition and Subtraction (Graphically)
  • 5. Vectors: Algebraic Representation
  • 6. Exercise: Vectors, Algebraic Representation
  • 7. Exercise: Vector Exercise Including Scalar Product
  • 8. Dot And Cross Products
  • 9. Explore: Dot Product
  • 10. 3 Dimensional Vectors
  • 11. Explore: Cross Product

7.1.

Intoduction: Vectors

– Hisham Amir

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7.7.

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7.9.

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7.10.

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7.11.

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8.

Geometry

  • 1. Angles in Same Segment
  • 2. Angles in Alternate Segment
  • 3. Angle at Centre and Circumference
  • 4. Angles In Cyclic Quadrilaterals
  • 5. Angle in Semicircle
  • 6. Perpendicular Bisector to Chords of Circles

8.1.

Angles in Same Segment

Angles in Same Segment
– Hisham Amir

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8.4.

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8.5.

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8.6.

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9.

Trigo Identities

  • 1. The Pythagorean Identities
  • 2. Trigonometric Identity Explorer
  • 3. Proving Trigonometric Identities
  • 4. Solving Trigonometric Equations
  • 5. Deducing the Relationship: A sin x + B sin x= R cos (x+a)
  • 6. Asin(wt)+Bcos(wt)=Rsin(wt+a)
  • 7. Solving Trigonometric Equations in Harmonic Form
  • 8. Practice: Solve Trig Eqn in form of Acosx-Bsinx=C
  • 9. Practice: Solve Trig Eqns in form of Asinx-Bcos=C

9.1.

The Pythagorean Identities

A video proving the 3 pythagorean identities
– Hisham Amir

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