Advanced Mathematical Problem Solving Resources

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During 2013/14, thanks to generous support from the Citi Foundation, the NRICH Stage 5 team created a collection of linked materials to help students prepare for sitting their STEP Mathematics examinations. 

The STEP Preparation page consists of 24 modules which we suggest students work through at the rate of 1 per fortnight from the summer of Year 12 to the end of Year 13.

Each module consists of problems, articles, worked examples, advice for STEP candidates and much more. By working through these modules, students will be able to start their STEP preparation in a timely manner, and have a good idea what to expect by the time they sit the exam at the end of Year 13.

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The Advanced Problem Solving resources are designed to take you from being a keen mathematics student without much experience in answering STEP and other advanced mathematics examinations questions to being a confident mathematician capable of passing your examinations with flying colours and making the transition to studying mathematics at a top university.

If you have come to this page as a Year 12 student, you're in a great position - past STEP and other advanced mathematics examinations candidates often say they wish they'd started their preparation earlier. The early modules of this collection are designed to ease you into problem solving and teach you new mathematical techniques, and should be accessible to anyone who has done the first year of their A levels, or equivalent. Don't worry if you're a little closer to sitting the exams when you start your preparation though - it just means that you might need to work through the modules a little more quickly.

The preparation modules consist of a brief explanation of the contents of the module, and then a small selection of resources. These usually consist of an article explaining some mathematics or offering some problem-solving advice, together with a variety of activities including short problems, in-depth investigations and suggested past advanced examination paper questions on a particular theme.

It is important to begin your exam preparation by consolidating your mathematical knowledge and building your fluency and speed, so even if a problem seems straightforward, it's worth working through! As the year goes on, you may find the difficulty level of the problems will increase, so that by the summer, you will be well prepared to tackle full STEP or other advanced mathematics examinations questions.

 

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We suggest that you get a folder to file your STEP and other advanced mathematics examinations work in, so that you can easily look back on your work. Work through the modules at your own pace; our suggestion is one module per fortnight. It is a good idea to look back on earlier modules every few weeks to remind yourself of what you've already learned. This can be a great confidence boost too, as you look back and see how much you've achieved!

Keep aside two or three recent years' exam papers to use as timed tests for yourself in the weeks immediately before your exams. 

In addition to this general advice, each module will contain lots of helpful tips to help you to become a stronger and more confident mathematician. All that remains to be said here is good luck!

Here are some worked examples of a selection of Pure Mathematics STEP questions from the 2010 papers.

They are not intended to be perfect model answers, but rather are intended to give you a flavour of how your written STEP answers might look. Our students used some scrap paper for workings out which are not included here, so don't panic if your work doesn't look as neat as theirs!

We asked the students who completed their questions to annotate in red pen any useful techniques or clever tricks they used when solving the problems. We hope you find it useful to see some of their thought processes.

REMEMBER: You will get much more out of the STEP preparation process if you tackle the questions for yourself first before looking at hints, answers or worked solutions.

With that in mind, we suggest you download the 2010 papers and work through the questions before looking at the worked examples.

STEP 1 2010

STEP 2 2010

STEP 3 2010

Other documents which might be useful are the 2010 Examiner's Report, the 2010 solutions from the exam board and the 2010 Mark Scheme.

The STEP Support Programme gives structured support to help students prepare for STEP.  You can also find out more about STEP on the OCR STEP website.

2010_I_1.pdf

2010_I_2.pdf

2010_I_3.pdf

2010_I_4.pdf

2010_I_5.pdf

2010_I_6.pdf

2010_I_7.pdf

2010_I_8.pdf

2010_II_1.pdf

2010_II_2.pdf

2010_II_3.pdf

2010_II_4.pdf

2010_II_5.pdf 

2010_II_7.pdf

2010_II_8.pdf

2010_III_1.pdf

2010_III_2.pdf

2010_III_4.pdf

2010_III_8.pdf