# Student Tasks: Autograph

These tasks are designed to help students in understanding mathematical relationships better through exploring dynamic constructions. They have been designed with the following structure:

• Construction: step-by-step guidance of how to construct the objects in Autograph.
• 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)

Topic Classroom tasks
Quadratic functions (AS) Plot y=ax2+bx+c in and vary a, b and c.
Graphs of quadratic functions
Equations and inequalities (AS) Intersection of a line and a curve
Coordinate geometry (AS) Perpendicular lines
Trigonometry (AS) Trigonometric equations
Polynomials (AS) The Factor Theorem
Graphs and transformations (AS) Functions - Transformations
Functions - Transformations of y=1/x curves
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
Derivative of exponential functions y=ekx

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

Topic Classroom tasks
Trigonometry Trig equations in radians
Functions The Modulus Function
Inverse functions
Differentiation Points of inflection
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 Converting parametric equations to cartesian equations
Numerical methods Change of sign
Fixed point iterations
Newton-Raphson