Using GeoGebra for A level Further Mathematics

GeoGebra Institute of MEI, May 19, 2016

This GeoGebra Book provides ideas and suggestions for using GeoGebra to enhance teaching and learning A level Further Mathematics.

Table of Contents

  1. Complex Numbers
    1. The graph of the completed square form of a quadratic
    2. Complex roots of quadratic equations
    3. Locus in the complex plane: |z-w|=k
    4. Complex Plane Transformation: w=1/z
    5. Construction: Locus of |z1-w|=|z2-w|
    6. Entering Complex Numbers
  2. Matrices
    1. Matrix Transformations
    2. Rotation Matrix
    3. Invariant lines of matrix transformations
    4. Construction: Transformation Matrix
    5. Entering Matrices
  3. Roots of polynomials
    1. Roots of a cubic: α, β, γ (real)
    2. Roots of a cubic: α, β, γ
    3. Roots of related cubics: α+k, β+k, γ+k
    4. Roots of related cubics: kα, kβ, kγ
  4. 3D Vector Geometry
    1. Vector equation of a line in 3D
    2. Skew lines: finding the distance (dot product)
    3. Skew lines: finding the distance (cross product)
    4. 3 planes: unique point of intersection
    5. 3 planes: 2 parallel
    6. 3 planes: 3 parallel
    7. 3 planes: prism
    8. 3 planes: sheaf
    9. Entering Vectors
  5. Polar Curves
    1. Polar curve: r = a + b cosθ
    2. Polar curves: wrapping a function around the pole
    3. Area under polar curves
    4. Entering polar coordinates and curves
  6. Maclaurin Series
    1. Entering Maclaurin series
    2. Maclaurin series
  7. Differential equations
    1. 2nd order differential equations
    2. Second Order Linear DE solver
    3. Coupled Differential Equations
  8. Student Tasks
    1. Student tasks for using GeoGebra

1.

Complex Numbers

  • 1. The graph of the completed square form of a quadratic
  • 2. Complex roots of quadratic equations
  • 3. Locus in the complex plane: |z-w|=k
  • 4. Complex Plane Transformation: w=1/z
  • 5. Construction: Locus of |z1-w|=|z2-w|
  • 6. Entering Complex Numbers

1.1.

The graph of the completed square form of a quadratic

Vary the sliders to change b and c in y=x²+bx+c.
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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Matrices

  • 1. Matrix Transformations
  • 2. Rotation Matrix
  • 3. Invariant lines of matrix transformations
  • 4. Construction: Transformation Matrix
  • 5. Entering Matrices

2.1.

Matrix Transformations

Vary the points A' and B' to change the matrix M.
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2.2.

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2.3.

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2.4.

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2.5.

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3.

Roots of polynomials

  • 1. Roots of a cubic: α, β, γ (real)
  • 2. Roots of a cubic: α, β, γ
  • 3. Roots of related cubics: α+k, β+k, γ+k
  • 4. Roots of related cubics: kα, kβ, kγ

3.1.

Roots of a cubic: α, β, γ (real)

Drag the points [math]\alpha[/math], [math]\beta[/math] and [math]\gamma[/math] to vary the function.
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3.2.

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3.3.

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3.4.

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4.

3D Vector Geometry

  • 1. Vector equation of a line in 3D
  • 2. Skew lines: finding the distance (dot product)
  • 3. Skew lines: finding the distance (cross product)
  • 4. 3 planes: unique point of intersection
  • 5. 3 planes: 2 parallel
  • 6. 3 planes: 3 parallel
  • 7. 3 planes: prism
  • 8. 3 planes: sheaf
  • 9. Entering Vectors

4.1.

Vector equation of a line in 3D

– GeoGebra Institute of MEI

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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5.

Polar Curves

Polar curves can be entered using r=f(θ)

  • 1. Polar curve: r = a + b cosθ
  • 2. Polar curves: wrapping a function around the pole
  • 3. Area under polar curves
  • 4. Entering polar coordinates and curves

5.1.

Polar curve: r = a + b cosθ

– GeoGebra Institute of MEI

5.2.

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5.3.

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5.4.

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6.

Maclaurin Series

  • 1. Entering Maclaurin series
  • 2. Maclaurin series

6.1.

Entering Maclaurin series

[list=1][br][*]Enter a function for y=f(x) such as [b]y=sin(x)[/b].[br] [br][/*][*]Add a variable: [b]n = 1[br][/b]Set the limits of the slider to: [b]1 ≤ n ≤ 15, Step 20[/b][b] [/b][/*] [*]In the input bar enter: [b]TaylorPolynomial(f, 0, n)[/b] [br] [/*][/list]
– GeoGebra Institute of MEI

6.2.

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7.

Differential equations

  • 1. 2nd order differential equations
  • 2. Second Order Linear DE solver
  • 3. Coupled Differential Equations

7.1.

2nd order differential equations

– GeoGebra Institute of MEI

7.2.

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7.3.

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8.

Student Tasks

  • 1. Student tasks for using GeoGebra

8.1.

Student tasks for using GeoGebra

A set of student tasks are available at: [url=https://mei.org.uk/resource/ab80a69d-e6fd-4954-9d46-08d9d6b4f934/]https://mei.org.uk/resource/ab80a69d-e6fd-4954-9d46-08d9d6b4f934/[/url]
– GeoGebra Institute of MEI

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