Use of GeoGebra in Further Maths: examples
1. Complex numbers
1. The graph of the completed square form of a quadratic
2. Locus in the complex plane: |z-w|=k
2. Matrices
1. Matrix Transformations
2. Rotation Matrix
3. Invariant lines of matrix transformations
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
5. Polar curves
1. Polar curve: r = a + b cosθ
2. Area under polar curves
3. Polar curves: wrapping a function around the pole
6. Differential equations
1. 2nd order differential equations
2. Second Order Linear DE solver
3. Coupled Differential Equations
7. Student Tasks
1. Student tasks for using GeoGebra
2. Construction problems

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Use of GeoGebra in Further Maths: examples

GeoGebra Institute of MEI, Feb 21, 2018

Complex numbers
1. The graph of the completed square form of a quadratic
2. Locus in the complex plane: |z-w|=k
Matrices
1. Matrix Transformations
2. Rotation Matrix
3. Invariant lines of matrix transformations
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
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
Polar curves
1. Polar curve: r = a + b cosθ
2. Area under polar curves
3. Polar curves: wrapping a function around the pole
Differential equations
1. 2nd order differential equations
2. Second Order Linear DE solver
3. Coupled Differential Equations
Student Tasks
1. Student tasks for using GeoGebra
2. Construction problems

1.

Complex numbers

1. The graph of the completed square form of a quadratic
2. Locus in the complex plane: |z-w|=k

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.

1.2.

2.

Matrices

1. Matrix Transformations
2. Rotation Matrix
3. Invariant lines of matrix transformations

2.1.

Matrix Transformations

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

2.2.

2.3.

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.

3.2.

3.3.

3.4.

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

4.1.

Vector equation of a line in 3D

4.2.

4.3.

4.4.

4.5.

4.6.

4.7.

4.8.

5.

Polar curves

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

5.1.

Polar curve: r = a + b cosθ

5.2.

5.3.

6.

Differential equations

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

6.1.

2nd order differential equations

6.2.

6.3.

7.

Student Tasks

1. Student tasks for using GeoGebra
2. Construction problems

7.1.

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]

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