In 2007 the Australian Mathematics Competition was held for the 30th time. This event was introduced in Australia in 1978 as the first Competition in Australian Schools. In this time it has served almost all Australian secondary schools, providing feedback and enrichment to schools and students. It has become the largest single event on the Australian Education Calendar, allowing students to attempt the same tasks, on the same day in about 40 countries. It has become a truly international event, with countries throughout the Pacific and South East Asia, and some from even further afield taking part.

The Competition is administered by the non-profit Australian Mathematics Trust, which has representatives on its Board of the Australian Association of Mathematics Teachers, Australian Academy of Science and Australian Mathematical Society. A vast network of volunteers from these professional societies and from the teaching profession in particular ensures the highest quality of question paper, renowned over its lifetime for its originality and mathematical and typographical accuracy. This reputation is ensured by an extensive moderation process, which not only exhaustively checks the mathematics in the problems but also ensures the suitability of the tasks for students in all Australian States and New Zealand. The problem creators and moderators include the most experienced mathematics educators in the country.

When the Australian Mathematics Competition first started in 1978 it was sponsored by the Bank of New South Wales, Australia's oldest bank, which later became the Westpac Banking Corporation. This has been a remarkable and unique partnership, over 30 years, between an educational activity and a major Australian corporation.

The aims of the Competition are three-fold:

1. To highlight the importance of mathematics as a curriculum subject
2. To give students an opportunity to discover talent in mathematics
3. To provide resources for the classroom and general discussion

The AMC is for students of all standards. Students are asked to solve thirty problems in 60 minutes (Years 3 to 6) or 75 minutes (Years 7 to 12). Students mark their responses on a mark-sense sheet and these are processed by computer. The earliest problems are very easy. All students should be able to attempt them. The problems get progressively more difficult until the end, when they are challenging to the most gifted student. Students of all standards will make progress and find a point of challenge.

We believe this to be the largest event in Australia for which participants pay an entry fee. It is the original competition which started in 1978 and has been run every year since then. The number of entrants in Australia alone in recent years has been of the order of 400,000, enough to fill the MCG four times! There is a Middle Primary Paper (Years 3 and 4), Upper Primary Paper (Years 5 and 6), a Junior Paper (Years 7 and 8), an Intermediate Paper (Years 9 and 10) and a Senior Paper (Years 11 and 12).

We would like the AMC to be available to all students who wish to participate. There is no minimum entry from a school and we have special arrangements for visually impaired students and distance education organisations. Home schooled students or students whose school chooses not to participate are free to make arrangements to sit under the supervision of another school.

As a national mathematical body, whose main aims are to help mathematics learning, the Australian Mathematics Trust is qualified to provide the best type of questions to help identify the strengths and weaknesses of students in mathematical thinking, skills and application. The reports for each student show the student's performance in all main categories, such as arithmetic, algebra, geometry, problem solving and various sub-categories.

The International Commission on Mathematical Instruction has recently identified challenge as having a key role in mathematics learning and has appointed Trust Executive Director Professor Peter Taylor as one of two co-convenors of this Study, which is expected to report in 2009.

The AMC, given the style of problems posed, in which mathematics is often used to solve problems in the real world to which students can relate, is not only providing challenge by the style of these problems, but as a competition involving several hundreds of thousands of students on the same day will often ask students to respond to a situation which might be new (even though they should have the underlying mathematical knowledge).

The Trust conducts a range of activities up to full international Olympiad level, The next step up is the Mathematics Challenge for Young Australians, which attracts tens of thousands of students each year. So in addition to diagnosis and challenge for the students at the average level, the AMC provides talent identifiction and the basis for continuing to develop that talent with the full range of activities which the Trust supplies.

Students receive a score based on different weightings for questions in different parts of the paper. These scores become the basis for determining awards. For further details, see

• Scoring System
• Awards Criteria

• English
• French
• Chinese (simplified and traditional character sets both available)

French is not available for the primary versions, and in Australia it is assumed students write the paper in English (unless there is a special school).

The first 20 questions are intended to be directly familiar to students from their classroom experience. The problems are carefully moderated by experienced teachers in each state each year to ensure that the problems are suitable for students in their respective states. The later problems are more difficult and may be in unexpected contexts, but they have been graded to ensure that the skills required are commensurate with those taught at that level.

The problems are designed to test mathematical thinking rather than focus on calculations themselves, and as such questions are designed so that they answered just as quickly without a calculator as with one. Whereas calculators are thus seen to not provide an advantage, due to equity reasons they should not be used in years 7 to 12. For younger students, in Years 3 to 6, students are permitted to access any aids normally available to them in the classroom. Such students will be permitted to use any teaching aids such as MAB blocks, counters, currency, calculators, play money, etc. All students are allowed to work on scrap paper and teachers may help explain the meaning of words in the paper.

The problems are set by two volunteer committee of Australia's most experienced teachers and academics. The process of setting the paper commences 18 months in advance, to allow the extensive moderation which has given the paper its reputation for mathematical and typographical accuracy over the years.

• All students receive a detailed report showing how they went on each problem, with comparisons as to wider statistics.
• All students receive a certificate or award commensurate with their performance.
• The AMC provides the student an extra opportunity for external recognition. The certificates are often kept by students for their folios. They are well understood by employers and so can be used as evidence of problem solving ability.
• Unlike formal examinations in mathematics, many of the problems are set in situations to which students can relate, indicating the relevance of mathematics in their everday lives. Above all the competition is designed to be enjoyable, even for those students who might not have performed as well as they may have hoped. Certainly the event is intended to be conducted in a pressure-free environment (not normally affecting school assessment) and the questions are designed to be of sufficient interest to stimulate discussion at a later time, with friends, parents or in the class.
• Competitions can inspire a greater interest in the subject and a love of learning.
• Students are given an opportunity to participate in a large event attempting the same problems as students in other schools and other countries.

In addition to the direct benefits to students, all schools which enter the AMC receive, free of charge, a confidential set of statistics which the school can use in checking its performances overall, and by topic, with statistics overall for their state or region.

It is also possible that results from past years can be retrieved.

Students receive few opportunities to attempt problems in common with those of students at other schools, in their own region or internationally. The Competition is such an opportunity. In recent years about half a million students per year from 35 countries have taken part. As a result of the size of the competition, the statistics are meaningful, and students can obtain a good guide to the standard they have reached.

There is an entry fee, but this is modest compared with costs of sport and entertainment, and it is set in a non-profit environment. More details on how to enter can be found here.

The AMC is not a stand-alone event but provides opportunity for students to attempt further enrichment activities offered by the Trust, including the Mathematics Challenge for Young Australians and the opportunity to progress to national and international Olympiad projects supported by the Federal Government through its Department of Education, Science and Training (DEST).