I'm currently 18 years old and only as of the part year taken a strong interest in maths. I'm working with my school curriculum (UK a-level) and receiving A grades so I am happy with this. However I want to study competition style problems (or problems that are harder than the usual level tested at school). I want to do this for the pleasure required from solving and not for the competitive nature itself.

Having read the previous questions posted, I have seen that the AoPS books/brilliant.org resources seem good to improve problem solving capability. Of which of the AoPS books do I require? I wish to be able to succeed at solving algebra/equality/geometry/factorization style problems.

Is the book by Paul Zeitz (art and craft of problem solving) a good place to start? I feel intimidated by the problems in many papers like the BMO/senior maths challenge and feel it maybe a big jump. Is there a set list of requirements prior to attempting any type of these competition problems?



1 Answer 1


You need to find your own level - but one thing to learn: don't be intimidated by how problems are badged. Solving problems yourself is worth about a hundred times as much as reading solutions. When I was your age I sat in front of some of these problems for hours before I solved them.

Try the BMO - the idea is that they are elementary - don't require sophisticated knowledge. The Geometry tends to be beyond what you might do at school. There are some key inequalities to learn - they are rewarding to solve, but take resilience.

Try also the STEP papers, which are tougher tests of the UK syllabus.

  • $\begingroup$ may I also ask, Im applying to university in the UK in a year or 2 depending on how well my maths/further maths go. How do I prepare for STEP I/II/AEA? I actually wanted to get into competition maths in order to complement my chances of doing well on STEP (there isn't a guideline of topics/what to study). I also haven't finished Core 3/Core 4/Further pure 2, should I do that prior to studying for STEP? $\endgroup$
    – salman
    Aug 28, 2013 at 20:51
  • $\begingroup$ @user90771 For STEP, do STEP questions - look at some old papers and see what topics come up. Pick the topics you know, or ones you think you can learn. STEP tends to require resilience and accuracy - read the examiners reports, which are available online. Others will be more current than I am. As between STEP and competition - STEP often gives you a hint how to start, and the bit at the end is where you are on your own - doing problems helps you to become familiar with the kind of link between start and end. In a competition there are no hints, and you have to work out how to get started. $\endgroup$ Aug 28, 2013 at 21:01
  • $\begingroup$ do you suggest that I should not worry too much about competition maths, and just work on general problem solving/a-levels/STEP I/II practice on the side? Have you done STEP yourself? $\endgroup$
    – salman
    Aug 28, 2013 at 21:07
  • $\begingroup$ @user90771 STEP is after my time - I did BMO 1980/1981 and IMO 1981, and I did the old Cambridge Entrance Papers. I would try a range of problems from various sources - but don't aim low - the only way you ever learn to do tough problems is to get stuck in. On the old equivalent of STEP, what I did was to pick three years and I then tried to do all the questions on every paper. If you are preparing for STEP read the examiners reports which come along with the old papers - they suggest practice on STEP problems. You should not "worry" - I hope you will enjoy - so give youself some variety. $\endgroup$ Aug 28, 2013 at 21:19
  • $\begingroup$ brilliant, I will try to do STEP problems. My final problem is that what is the best step to do if you do not understand what the question is saying (I feel this way for all STEP questions - which makes me feel I lack the knowledge to solve the questions). $\endgroup$
    – salman
    Aug 28, 2013 at 21:29

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