GCSE Extension Materials

The GCSE Extension materials are aimed at students who are working towards GCSE Mathematics and would benefit from exposure to mathematics beyond the GCSE specifications.


The aims of the materials are:

  • To introduce students to new ideas to stimulate their interest in the subject;
  • To reinforce some of the concepts in GCSE so as to improve students’ understanding of them;
  • To highlight how some areas of GCSE are developed at A level to encourage students to continue their studies.

Format of the materials

All of the materials have the following format:

  • Starts from a topic or idea that is in GCSE Mathematics and features a ‘What you should know’ section;
  • A ‘New idea’ that is an extension to GCSE Mathematics;
  • A task for students to attempt so they can investigate the idea;
  • Ideas for further investigation suggested in a ‘Take it further section’;
  • A brief explanation of how this topic is developed at A level;
  • All the materials are based on a single sheet of A4 (except for NA 11, SSM 4 and SSM 6) which can be copied and given to students;

Teachers’ notes, including solutions, are available for free from the Integral Online Resources website. To access these resources, schools/colleges must register with the FMSP.  Registration is free and will also provide access to other resources and information about local events to support teachers and students.  To register go to online registration.

Ways to use the materials

Some suggestions for ways to use the materials:

  • As a whole-class activity when students have finished studying the topic;
  • As extra materials to stretch and challenge some of the more able students within a class;
  • As a regular, possibly optional, homework task;
  • As a basis for study in lunchtime or at an after-school mathematics club.


  • The tasks are not intended to be linear. Students will benefit from the investigations even if they do not ‘complete’ them.
  • In each of the three sections the resources are ordered by accessibility; however, it is inevitable that some students will progress further with some tasks than with others.
  • The materials are based on interesting mathematical ideas and are not designed to provide extension to every aspect of the GSCE specifications.


  GCSE topic
NA 1 Graphs of quadratic equations
NA 2 Surds
NA 3 Interpreting graphs
NA 4 Trial and improvement
NA 5 Functions
NA 6 Indices
NA 7 Simultaneous equations
NA 8 Solving quadratic equations
NA 9 Adding fractions
NA 10 Inequalities
NA 11* Plotting curves

* NA 11 features a separate extension sheet

Shape, Space and Measure

  GCSE topic
SSM 1 Trigonometry 1
SSM 2 Trigonometry 2
SSM 3 Circles
SSM 4 Pythagoras’ theorem
SSM 5 Loci
SSM 6 Vectors
SSM 4 and SSM 6 consist of two sheets to be copied for the students.

Handling Data

  GCSE topic
HD1 The mean from a frequency table
HD2 Interquartile range
HD3 Tree diagrams

Do you have any feedback on these resources?

If you have used the resources with students and have feedback or suggestions as to how to make the resources more useful, then please contact Phil Chaffe at [email protected].