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:
Topic | Classroom tasks |
---|---|
Surds and indices (AS) | |
Quadratic functions (AS) | Plot y=ax^{2}+bx+c in and vary a, b and c. Graphs of quadratic functions |
Equations and inequalities (AS) | Intersection of a line and a curve Quadratic inequalities |
Coordinate geometry (AS) | Perpendicular lines |
Trigonometry (AS) | Solution of trig equations |
Polynomials (AS) | The Factor Theorem |
Graphs and transformations (AS) | Functions - Transformations |
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=ka^{x} Derivate of exponential functions y=e^{kx} |
Topic | Classroom tasks |
---|---|
Trigonometry | Trig equations in radians |
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 |
Topic | Classroom tasks |
---|---|
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 |
These problem solving activities are constructions that test students' understanding of connections between representations and reinforce generalisation