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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
Surds and indices (AS)
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
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

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

Topic Classroom tasks
Trigonometry Trig equations in radians
Sequences and series
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 Converting parametric equations to cartesian equations
Vectors
Differential equations
Numerical methods Change of sign
Fixed point iterations
Newton-Raphson