These tasks are designed to help students in understanding mathematical relationships better through exploring dynamic constructions. They can be accessed using the computer-based version of GeoGebra or the tablet/smartphone app. They have been designed with the following structure:

• Construction: step-by-step guidance of how to construct the objects in GeoGebra.
• Questions for discussion: The emphasis is on students being able to observe mathematical relationships by changing objects on their screen and being able to describe what happens, and explain why.
• Problem: The purpose is for them to formalise what they have learnt through exploration and discussion and apply this to a “standard” style question.
• Further tasks: Extension activities with less structure for students who have successfully completed the first three sections.

### AS/A level Mathematics: Pure Mathematics (AS)

Surds and indices (AS)
Quadratic functions (AS) Plot y=ax2+bx+c in and vary a, b and c.
Equations and inequalities (AS) Intersection of a line and a curve
Coordinate geometry (AS) Perpendicular lines
Trigonometry (AS) Solution of trig equations
Polynomials (AS) The Factor Theorem (GeoGebra Classic)
The Factor Theorem (GeoGebra graphing app)
Graphs and transformations (AS) Functions - Transformations
Functions - Transformations of y=1/x curves
The binomial expansion (AS)
Differentiation (AS) Exploring the gradient on a curve
Introduction to Stationary Points
Integration (AS) Area under a curve
Vectors (AS) Introduction to vectors
Exponentials and logarithms (AS) Graph of y=kax
Derivate of exponential functions y=ekx

Between April and July 2019 MEI trialled the use of GeoGebra exam mode with a selection of schools and colleges. The materials included practice questions and guidance based on the pure content of AS Mathematics. These materials can be used by students to learn how to use GeoGebra to support their studies.

### AS/A level Mathematics: Pure Mathematics (Full A level only)

Sequences and series Sum of an AP
Sum of a GP
Functions The Modulus Function
Inverse functions
Differentiation Points of inflection
Trigonometric functions
Algebra Partial Fractions
Trigonometry identities Double Angle formulae
Rcos(θ−α)
Further Differentiation Differentiating trigonometric functions
Integration Gradient of tangent to y=lnx
Parametric equations Tangents to parametric curves
Vectors
Differential equations
Numerical methods Change of sign
Fixed point iterations
Newton-Raphson

### AS/A level Further Mathematics

Complex numbers Roots of quadratic equations
Addition and subtraction in the Argand diagram
Roots of polynomial equations Roots of polynomial equations
Matrices Transformation matrices
Determinants and inverse matrices
3x3 matrices and transformations
Polar curves Polar curves
Vectors Intersection of three planes
Conic sections Parabolas, hyperbolas and ellipses
Rational functions Sketching the curves of rational functions

## Problem solving activities using GeoGebra

These problem solving activities are constructions that test students' understanding of connections between representations and reinforce generalisation