Australian Mathematics Competition

The Australian Mathematics Competition for the Westpac Awards is a mathematics competition run by the Australian Mathematics Trust for students from year 3 up to year 12 in Australia, and their equivalent grades in other countries. Since its inception in 1976 in the Australian Capital Territory, the participation numbers have increased to around 600,000, with around 100,000 being from outside Australia, making it the world's largest mathematics competition.

History

The fore-runner of the competition was first held in 1976, was open to students within the Australian Capital Territory, and attracted 1200 entries. In 1978, the competition became a nationwide event, and became known as the Australian Mathematics Competition with 60,000 students from Australia and New Zealand participating. Westpac Banking Corporation (previously known as the Bank of New South Wales) has been the title sponsor for the entirety of its history, in conjunction with the Canberra Mathematical Society and the University of Canberra (previously known as the Canberra College of Advanced Education).

Since its inception, the competition has spread to countries such as New Zealand, Singapore, Taiwan and Malaysia, which submit thousands of entries each. A French translation of the paper has been available since the current competition was established in 1978, with a Chinese translation being made available to Singapore and Taiwan students in 2000. Large print and braille versions are also available.

In 2004, the competition was expanded to allow two more divisions, one for year five and six students, and another for year three and four students.

In 2005, students from 38 different countries entered the competition.

Format

The competition paper consists of thirty multiple-choice questions, which are ordered in increasing difficulty. Students record their personal details and mark their answers by pencil on a carbon-mark answer sheet, which is marked by computer. There are five divisions in total: Senior (for years 11 and 12), Intermediate (for years 9 and 10), Junior (for years 7 and 8), Upper Primary (for years 5 and 6) and Middle Primary (for years 3 and 4).

Students are allowed 75 minutes to read and answer the questions. Calculators are not permitted, but geometrical aids such as rulers, compasses, protractors and paper for working are permitted.

The original points scheme, which was in operation from inception until 2001, consisted of three groups of ten questions. The first ten questions were worth three marks each, the next ten four marks each, and the last ten five marks each. Students were deducted a quarter of the marks for a given question if they answered incorrectly, so that a student randomly guessing the answers would gain no numerical benefit (on statistical average). Students started with 30 marks, so that a student who answered all questions incorrectly would record a total score of zero, while one who answered all questions correctly would record a score of 150.

In 2002, the format was changed so that no penalties were incurred for incorrect answers to the first twenty questions, and for each of the last ten questions, a correct answer gave eight marks, no answer gave three marks, and no marks were given for an incorrect answer; the total score remained the same at 150.

In 2005, the format was changed once more. This time the first ten questions are still worth three marks each and the next ten are still worth four marks each, however the last ten are now once again worth 5 marks each. To make it harder to guess the most difficult questions, the last 5 questions required integer answers between 0 and 999 inclusive. The total score possible was thus reduced to 120. [http://www.amt.canberra.edu.au/amcnews.html]

The competition is supervised by staff of the individual educational institutions, and the Australian Mathematics Trust reserves the right to conduct re-examinations in order to preserve the integrity of the competition, if it believes that students have not attempted the paper under sufficiently stringent conditions.

Syllabus

There is no official declared syllabus which determines the scope of the problems presented in to the students. However, all problems can be solved without the use of calculus. Topics include arithmetic, number theory, combinatorics, geometry, measurement, algebra and probability.

Awards system

Despite the name of the competition, students are allocated awards for their performance relative to other students in their region, of the same year level. For Australian students, this means their State or Territory, and for other students, their country. Although the personal data such as date of birth and gender are collected, this is not used in the percentile ranking, which is only determined by the raw score. The award scheme is as such
* Prize - Students above the 99.7 percentile
* High Distinction - Students between the 98 and 99.7 percentile
* Distinction -Students between the 85 and 98 percentile
* Credit - Students between the 50 and 85 percentile
* Participation - Students below the 50 percentile

Students who have won a prize may also receive a medal if they are determined to have performed outstandingly well with respect to their region and the competition as a whole; this is restricted to a maximum of three medals per region per year level. All students receive a certificate, and prizewinners are awarded an additional monetary sum. Students who achieve the maximum score are awarded the Bernhard Neumann certificate. In 1998, a record 10 students in Australia, and 23 in Singapore achieved the maximum attainable score. Due to the restriction of three medals per year level, a re-examination was carried out in order to determine the Singaporean medallists.

All students receive an analysis sheet along with their certificate, which records their answers for each question, along with the correct answers. The questions are divided into a four categories: arithmetic, algebra, geometry and problem solving, and the number of questions that the student answered correctly for each category are listed along with the regional mean.

Every school receives a more comprehensive analysis, with a complete record of answers given by all students, as well as the percentage of students choosing any given answer for a given question, and a comparison to the percentage of students choosing any given answer for a given question in the whole region. Schools also receive analysis of their students by mathematical topic, compared to the entire region.

Successful students

Two students have won medals on all six of their opportunities to participate: [ [http://www.amt.edu.au/amcprev.html Australian Mathematics Trust - AMC: Previous Results ] ]
* Geoffrey Chu, Scotch College, Melbourne, Victoria
* Peter McNamara, Hale School, Western Australia

Ivan Guo Sydney Boys High School, New South Wales was the first person to win three consecutive BH Neumann certificates, which are only awarded to those that achieve a perfect score.

Impact

The Australian Mathematics Competition is run by the Australian Mathematics Trust, which also runs the Australian Mathematics Olympiad Committee, which trains and selects students to represent Australia at the International Mathematics Olympiad. Although there is no publicly declared formula for the selection of students, it is possible that the results of the Australian Mathematics Competition are used in identifying students for further training by the Australian Mathematics Olympiad Committee.

External links

* [http://www.amt.edu.au/default.htm Australian Mathematics Trust website]

References

* [http://www.amt.edu.au/AMCFACT2006.pdf An AMC fact sheet from the Australian Mathematics Trust]