School Mathematics

David T, 23. 1. 2021

Topics for school level mathematics.

Obsah

  1. Calculus-Integration
    1. Area between Curves
    2. Area Between Parabolas/Lines
  2. Calculus-Differentiation
    1. Graph Derivatives of sinx and cosx.
  3. Circle-Properties
    1. Circle - angles
    2. Circle - sectors
  4. Functions
    1. Functions - graphs
    2. Domain and Range of a function
    3. Composite Functions
  5. Graph Transformations
    1. Transform Graph
    2. Transform Graph X-Stretch
    3. Transform Graph Y-Stretch
    4. Transform Graph X-Shift
    5. Transform Graph Y-Shift
    6. Quadratic Graph-Completed Square Form
  6. Lines and Circles
    1. Straight Line - gradient
    2. Straight Line - equation
    3. Equation of a Straight Line
    4. Lines Associated with a Triangle
    5. Locus Intro
    6. Equation of a Circle (1)
    7. Equation of a Circle (2)
    8. Equation of a Circle through 3 Points
    9. Equation of Tangent to a Circle
    10. Line and Circle 1
    11. Line and Circle 2
  7. Logs and exponentials
    1. Exponential and Log graphs
    2. Graphs e^x and ln x
  8. Pythagoras' Theorem
    1. Pyth Thm: 3D cuboid
    2. Pyth Thm: Coordinates
    3. Distance Formula
  9. Quadratics
    1. Quadratics - expand brackets
    2. Quadratics - factorise
    3. Quadratic function-graph 1
    4. Quadratic function-graph 2
    5. Quadratic Equations-factorising
    6. Quadratic Equations - Formula
    7. Discriminant
    8. Completing the Square
    9. Completing the Square
  10. Shapes-Area
    1. Area of a Triangle
    2. Area of a Kite
    3. Area of a Parallelogram
    4. Area of a Trapezium
  11. Shapes-Properties
    1. Properties: square
    2. Properties: rectangle
    3. Properties: kite
    4. Properties: rhombus
    5. Properties: parallelogram
    6. Properties: trapezium
  12. Statistics
    1. Standard Deviation Formulae
  13. System of Equations
    1. Simultaneous Equations:Elimination
    2. Simultaneous Equations:Substitution
    3. Simultaneous Equations: Graph input
    4. Simultaneous Equations: Graph move line
  14. Trig Graph Transformations
    1. Trig Graph Transformation 1
    2. Trig Graph Transformation 1 (radians)
    3. Trig Graph Transformation 2
    4. Trig Graph Transformation 2 (radians)
    5. Trig Graph Transformation 3
    6. Trig Graph Transformation 3 (radians)
    7. Trig Graph Transformation 4
    8. Trig Graph Transformation 4 (radians)
  15. Trig. Equations
    1. Trigonometry: equation solution graph 1 (sine)
    2. Trigonometry: equation solution graph 2 (cosine)
    3. Trigonometry: equation solution graph 3 (tangent)
    4. Trigonometry: CAST introduction
  16. Trig-Triangle Formulae
    1. Sine Rule - find a side
    2. Sine Rule - find an angle
    3. Cosine Rule - find a side
    4. Cosine Rule - find an angle
    5. Trigonometry-Area Formula
  17. Vectors
    1. Scalar Product
  18. Wave Function
    1. Wave Function

1.

Calculus-Integration

  • 1. Area between Curves
  • 2. Area Between Parabolas/Lines

1.1.

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1.2.

–

2.

Calculus-Differentiation

  • 1. Graph Derivatives of sinx and cosx.

2.1.

–

3.

Circle-Properties

  • 1. Circle - angles
  • 2. Circle - sectors

3.1.

–

3.2.

–

4.

Functions

  • 1. Functions - graphs
  • 2. Domain and Range of a function
  • 3. Composite Functions

4.1.

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4.2.

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4.3.

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5.

Graph Transformations

  • 1. Transform Graph
  • 2. Transform Graph X-Stretch
  • 3. Transform Graph Y-Stretch
  • 4. Transform Graph X-Shift
  • 5. Transform Graph Y-Shift
  • 6. Quadratic Graph-Completed Square Form

5.1.

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5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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6.

Lines and Circles

  • 1. Straight Line - gradient
  • 2. Straight Line - equation
  • 3. Equation of a Straight Line
  • 4. Lines Associated with a Triangle
  • 5. Locus Intro
  • 6. Equation of a Circle (1)
  • 7. Equation of a Circle (2)
  • 8. Equation of a Circle through 3 Points
  • 9. Equation of Tangent to a Circle
  • 10. Line and Circle 1
  • 11. Line and Circle 2

6.1.

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6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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7.

Logs and exponentials

  • 1. Exponential and Log graphs
  • 2. Graphs e^x and ln x

7.1.

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7.2.

–

8.

Pythagoras' Theorem

  • 1. Pyth Thm: 3D cuboid
  • 2. Pyth Thm: Coordinates
  • 3. Distance Formula

8.1.

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8.2.

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8.3.

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9.

Quadratics

  • 1. Quadratics - expand brackets
  • 2. Quadratics - factorise
  • 3. Quadratic function-graph 1
  • 4. Quadratic function-graph 2
  • 5. Quadratic Equations-factorising
  • 6. Quadratic Equations - Formula
  • 7. Discriminant
  • 8. Completing the Square
  • 9. Completing the Square

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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9.9.

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10.

Shapes-Area

  • 1. Area of a Triangle
  • 2. Area of a Kite
  • 3. Area of a Parallelogram
  • 4. Area of a Trapezium

10.1.

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10.2.

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10.3.

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10.4.

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11.

Shapes-Properties

  • 1. Properties: square
  • 2. Properties: rectangle
  • 3. Properties: kite
  • 4. Properties: rhombus
  • 5. Properties: parallelogram
  • 6. Properties: trapezium

11.1.

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11.2.

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11.3.

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11.4.

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11.5.

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11.6.

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12.

Statistics

  • 1. Standard Deviation Formulae

12.1.

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13.

System of Equations

  • 1. Simultaneous Equations:Elimination
  • 2. Simultaneous Equations:Substitution
  • 3. Simultaneous Equations: Graph input
  • 4. Simultaneous Equations: Graph move line

13.1.

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13.2.

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13.3.

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13.4.

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14.

Trig Graph Transformations

  • 1. Trig Graph Transformation 1
  • 2. Trig Graph Transformation 1 (radians)
  • 3. Trig Graph Transformation 2
  • 4. Trig Graph Transformation 2 (radians)
  • 5. Trig Graph Transformation 3
  • 6. Trig Graph Transformation 3 (radians)
  • 7. Trig Graph Transformation 4
  • 8. Trig Graph Transformation 4 (radians)

14.1.

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14.2.

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14.3.

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14.4.

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14.5.

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14.6.

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14.7.

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14.8.

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15.

Trig. Equations

  • 1. Trigonometry: equation solution graph 1 (sine)
  • 2. Trigonometry: equation solution graph 2 (cosine)
  • 3. Trigonometry: equation solution graph 3 (tangent)
  • 4. Trigonometry: CAST introduction

15.1.

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15.2.

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15.3.

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15.4.

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16.

Trig-Triangle Formulae

  • 1. Sine Rule - find a side
  • 2. Sine Rule - find an angle
  • 3. Cosine Rule - find a side
  • 4. Cosine Rule - find an angle
  • 5. Trigonometry-Area Formula

16.1.

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16.2.

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16.3.

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16.4.

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16.5.

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17.

Vectors

  • 1. Scalar Product

17.1.

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18.

Wave Function

  • 1. Wave Function

18.1.

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Informace