### Introduction to Advanced Problem Solving

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.

### How to use Advanced Problem Solving

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.

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!

### Worked examples

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.

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

### Welcome to the NRICH Advanced Problem Solving pages.

**This is an archive resource. For our current STEP preparation programme please visit maths.org/step.**

These resources are designed to help potential university applicants develop their advanced problem-solving skills and prepare for sitting examinations such as STEP. The material has been carefully selected to provide an accessible and supportive introduction to advanced problem-solving, and to help you build
your confidence, fluency and speed.

Start by reading about the materials, or scroll down to get started on the modules.

The 24 modules below begin with general problem-solving skills and gradually introduce new techniques, ideas and advice to help you to solve advanced problems.

You may also be interested in Stephen Siklos's book, Advanced Problems in Mathematics: Preparing for University, which can be downloaded for free.