O level papers from 1957, 1962, and 1968

I found these old 1968 GCSE [then called O’ level] Maths papers in my study. Try them and see what you think.

1968 O Level Maths Paper 1   * 1968 O Level Maths Paper 2

And these are 1962 Ordinary Level Maths papers – passed to me by my dear friend, Frank.

1962 O Level Maths Paper 1 * 1962 O Level Maths Paper 2

And Graham’s  1957 Ordinary  Level Maths Papers

[Originally posted at Maths Answers]

The UK at the 53rd International Mathematical Olympiad

This year, the UK participated in the 53rd International Mathematical Olympiad, which was held this time in Mar del Plata, Argentina (about 500km south of Buenos Aires). The UK has been participating every year since 1967; it is now one of about a hundred countries which attend regularly.

The format is standard. Each country may send a team of up to six school-age students. However, all of them sit the competition on their own: it consists of two papers, each giving four-and-a-half hours for three questions. Medals are awarded according to rank order, conforming to the ratio gold:silver:bronze:no medal = 1:2:3:6.

Performance in the IMO depends on many factors. While we perform strongly compared to western European social democracies with similar or smaller populations, it has not been usual for the UK to outperform highly organised countries with larger populations than ours (such as Germany), or countries with elite state school systems that are able to provide intensive relevant education (such as Hungary). However, this year we did better than both Germany and Hungary.

In terms of the average scores achieved, this year was the hardest IMO for some years. It was gratifying to see our students trying hard, producing many ingenious ideas, and — often enough — succeeding in solving the problems where many others couldn’t. Indeed, all our students this year obtained a medal.

Of course, national one-upmanship is not the aim of the competition. One significant benefit is that it brings together like-minded students from all over the world. Indeed, the organisers did an excellent job of facilitating social interaction, providing a large room with all manner of games and diversions, and after the exams keeping it open (and supervised) almost permanently except for a few short hours around breakfast each day.

In my view, however, the best thing about the IMO is the quality of the mathematics: it exposes students to mathematical topics which are genuinely challenging yet approachable in a short timescale. Research inspired by IMO problems, both of a conventional and an experimental sort, has been on the rise in the last five years. Of this year’s problems, Q3 is an fascinating topic for further enquiry: is it possible to improve the bounds beyond those which are hinted at by the two parts of the problem, namely (2-ε)k and 2k?

The value extends beyond the six students who make it onto the UK’s team each year. More than a thousand students each year take part in our national olympiad, as an end in itself or with the hope of further participation.

It is also worth advertising the problems as a teaching resource. Recently, I have enjoyed using Q5 from IMO2010 as an introduction to Ackermann-style notations for large numbers: the problem provides a natural example of their use which students can enjoy experimenting with for themselves.

Those who are interested can read a blow-by-blow account of our participation in this year’s IMO. It remains to mention that, from an academic point of view, the UK’s olympiad activities are entirely volunteer-led. We are dependent on the goodwill and time of mathematicians all over the country: if you wish to join us, please send our organisation an email to let us know.

More calls for A level national curriculum

House of Lords Select Committee on Science and Technology published report
Higher Education in Science, Technology, Engineering and Mathematics
(STEM) subjects
. Some of the recommendations:

41. The Education Committee recommended that the Government should pilot a national syllabus in one large entry subject as part of the forthcoming A level reforms. We would recommend that maths should be the subject of such a pilot. […]

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