Extension Materials

There are a variety of resources that will help to develop yourself as a mathematician - most of these will have been written with the intention of preparing for specific tests but the resources on this page will all help you to improve at tackling questions at the more difficult end of the spectrum. They divide into roughly two groups:

  • University Entrance Paper preparation - these are specifically aimed at improving at the STEP, MAT or TMUA. Whilst the style of these varies, and it will make sense to focus on whatever you need to sit, they will all make you better at applying A Level methods in more difficult contexts.
  • Maths Competition preparation - these are more focussed on more creative problem solving skills often using relatively basic techniques. The UKMT (who run the Senior Maths Challenge) have created an incredible number of resources that rarely even require A Level knowledge but are sometimes fiendishly difficult.

MAT Preparation (mainly Oxford Maths but used by others as well)

MAT is changing in 2024! It is a two-and-a-half hour paper, but unlike previously it will consist of 25 multiple-choice questions and 2 longer questions. The MAT is sat in mid-October.

  • You can find information and past papers going all the way back to 2007 on the official Oxford website. I would recommend saving the most recent few years until nearer the time but that still gives you plenty of practice.
  • There are Livestreams put on every Thursday from 17:00 to 19:00 to discuss how to solve these problems. All these videos get put on YouTube afterwards so you can catch up on missed sessions there.

TMUA Preparation

The TMUA consists of two 75 minutes papers, each made up of 20 multiple-choice questions. The TMUA is sat in mid-October.

STEP Preparation (mainly Cambridge Maths but used by others as well)

There are two STEP papers, called STEP II and STEP III (STEP I used to be a thing but doesn't exist any more). STEP II is based on A Level Single Mathematics and STEP III is based on A Level Further Mathematics. STEP I was a slighlty easier paper based on Single Maths. These papers are sat alongside A Levels at the end of Year 13.

  • The best place to start is the STEP Support Programme - because the STEP papers can be intimidating, this programme tries to ease you in by giving smaller assignments that build in difficulty. The Foundation programme is worth doing even if you ultimately want to do STEP III.
  • A former STEP chief examiner wrote this incredible free online book. It was specifically written to help candidates prepare and to give them an insight into how to think through each question.
  • Make use of the above resources before you start trying full papers - STEP is meant to be very difficult at the end of Year 13 after full preparation, so trying too early can be discouraging. However, there are past papers going all the way back to 1994
  • Papers before 2014 often have hints but not full solutions. You can find hand-written solutions hand-written solutions back to 1996 via this link

Problem Solving Resources

The UKMT (United Kingdom Mathematics Trust) have made some incredible resources that you can use to sharpen your problem solving skills and to prepare for competitions.

  • Senior Maths Challenge past papers going back to 1998 can be found in this Google Drive along with solutions. These a great fun multiple-choice problems that get really hard without ever needing much beyond GCSE knowledge.
  • The British Maths Olympiad is the next step up from the SMC and is made of much more extended and more difficult problems. BMO past papers (and solutions back to 2019) are all available. Only go near Round 2 if you are smashing Round 1!
  • There are mentoring sheets with solutions that are designed to help prepare for the BMO.