Something in Common: A Level Pure Mathematics

This sub-collection of resources from the ‘Something in Common’ collection contains 17 resources designed to bring a problem solving approach to the teaching of A Level Pure Mathematics. Each resource has an introductory presentation, printed materials, and supporting files. The topics covered are:

  • Equation of a circle and midpoints

  • Tangent to a circle

  • Normal to a tangent

  • Turning points
  • Solids of revolution
  • Expanding brackets

  • Factor theorem
  • Geometric sequences

  • Transformation of graphs

  • Hyperbolas

  • Roots of a cubic


A Circle Journey

The initial task involves using factors of 12 and -12 to set up two points. Compasses are used to draw a circle that has the two points as its diameter. An interesting feature of the resulting...

Annulus Volume of Revolution

A segment of a circle is created using a chord parallel to the x-axis. The resulting segment of the circle is then revolved 360° about the x-axis. The problem is to calculate the volume of the resulting annulus.

To find a general solution to the problem involves using an elemental disc ring and integrating...

Brackets Out, Brackets In

The problem starts with choosing three distinct, non-zero integers between -5 and 5 that do not sum to zero. These are then used in a six factorisations that make use of...

A Geometric Progression Problem

There is an initial investigation of geometric progressions where the interval between the first and second, and the third and fourth terms are given, with the challenge of discovering two possible values for the first term and associated common ratio. There are ten examples to work on to enable collaboration...


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