GCSE Extension Materials

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


  • To introduce students to new ideas so as 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 so as to encourage students to continue their studies.

Format of the materials

  • 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.

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 after-school maths 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.

Do you have any feedback on these resources?

We welcome feedback on our materials; if you have any thoughts and ideas that you would like to share please contact Kevin Lord.




GCSE topic

NA 1

Graphs of quadratic equations

NA 2


NA 3

Interpreting graphs

NA 4

Trial and improvement

NA 5


NA 6


NA 7

Simultaneous equations

NA 8

Solving quadratic equations

NA 9

Adding fractions

NA 10


NA 11*

Plotting curves

* NA 11 features a separate extension sheet

Shape, Space and Measure


GCSE topic


Trigonometry 1


Trigonometry 2



SSM 4*

Pythagoras' theorem



SSM 6*


* SSM 4 and SSM 6 consist of two sheets to be copied for the students.

Handling Data


GCSE topic


The mean from a frequency table


Interquartile range


Tree diagrams

Accessing the Teachers' Notes

Teachers' notes, including solutions, can be accessed on the Integral Mathematics resources site. The KS4 Extension and Enrichment resources on this site have been developed as part of a DfE funded project providing resources and continuing professional development to extend and enrich the mathematical experiences of KS4 students.

The KS4 Extension and Enrichment resources available to all schools who already subscribe to the Integral online resources or who register with the Further Mathematics Support Programme. Please see our Integral Mathematics Resources page for information about subscribing to our Integral resources. English schools and colleges can register free with the Further Mathematics Support Programme to receive limited access to the Integral resources.