Aims and Objectives

[b]Aims[/b][br]- Explore the use of GeoGebra in GCSE and A-level Maths and Further Maths classes. [br]- Explore some of the tools in GeoGebra classic, and work through some of the problems involving [br]graphs.[br]- Short demonstration on Autograph 4 at the end of this session[br][br][b]Objectives[/b] [br]- Explore linear and non-linear graphs[br]- Extension on 3D graphs[br]- Modelling exercise based on exam questions
Leona So
[b]About me[/b][br]- Teaching A-level Maths and Further Maths at a large FE college in Manchester.[br]- Also an Advanced Practitioner as an ILT Champion, focusing on the use of technology in teaching Maths. [br]- Previously been in different roles, including Level 3 Core Maths Co-ordinator.[br][br]Twitter [url=https://twitter.com/lwyso]@lwyso[/url] Email: [url=mailto:leonawyso@gmail.com]leonawyso@gmail.com[/url][br]

The GeoGebra Classic

This is the GeoGebra Classic.[br][br]You can access the online version: [url=https://www.geogebra.org/classic]https://www.geogebra.org/classic[/url][br]Or download as desktop app: [url=https://www.geogebra.org/download]https://www.geogebra.org/download[/url]

Graphs topics

There are a number of topics we could cover today:[br]- Linear graphs: y = mx +c, intersections between lines, normal[br]- Linear and non-linear, straight line graph with circle[br]- Non-linear: Differentiation by first principles, Differential equations

Equations - GCSE

C is the curve with equation [math]y=x^2-6x+6[/math][br]L is the straight line with equation [math]y=2x-9[/math][br]L intersects C at two points A and B.[br]Calculate the exact length of AB. (6 marks)[br][br]Possible extension question/discussion here?

Vectors

Referred to a fixed origin [math]O[/math], the points [math]A[/math]and [math]B[/math]have position vectors [math]\left(\begin{matrix}\begin{matrix}\begin{matrix}1\\2\\-3\end{matrix}\end{matrix}\end{matrix}\right)[/math]and [math]\left(\begin{matrix}5\\0\\-3\end{matrix}\right)[/math] respectively.[br]a) Find, in vector form, an equation of the line [math]l_1[/math], which passes through [math]A[/math]and [math]B[/math]. (3 marks)[br]The line [math]l_2[/math]has equation [math]r=\left(\begin{matrix}4\\-4\\3\end{matrix}\right)+\mu\left(\begin{matrix}1\\-2\\2\end{matrix}\right)[/math], where [math]\mu[/math] is a scalar parameter.[br]b) Show that [math]A[/math] lies on [math]l_2[/math]. (2 marks)[br]c) Find, in degrees, the acute angle between the lines [math]l_1[/math]and [math]l_2[/math]. (4 marks)[br]The point [math]C[/math] with position vector [math]\left(\begin{matrix}0\\4\\-5\end{matrix}\right)[/math] lies on [math]l_2[/math].[br]d) Find the shortest distance from [math]C[/math]to the line [math]l_1[/math]. (4 marks)

Useful links

[url=https://wiki.geogebra.org/en/Graphics_Tools]GeoGebra Graphics tools manuals[/url][br][url=https://www.geogebra.org/materials][br]GeoGebra Classroom Resources[/url][br][url=http://mei.org.uk/geogebra-tasks][br]MEI GeoGebra Resources[/url]

Demonstration on Autograph 4

[url=http://www.tsm-resources.com/]http://www.tsm-resources.com/[/url]

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