# Competition Details

Here is a summary of the details of our competitions. Click on the buttons below to skip to different sections. Last edited 30 January, 2016.

# The curriculum - what students will be expected to know

- The level of content in questions will follow the NZQA curricula for the corresponding year levels.
- If additional knowledge is required for a particular question, all relevant information will be provided so that no student is disadvantaged.
- Students may assume basic results depending on the level of the question.
- Basic geometry such as angle relationships, basic number theory such as divisibility, basic algebra such as factorisation, and basic combinatorics such as the pigeonhole principle may be used without proof
- More advanced results, not commonly encountered by students of the corresponding level, such as the midpoint-of-arc lemma, Fermat's little theorem, AM-GM or the Cauchy-Schwarz inequality, and graph theory, are
**not expected**and should not be required for a problem. - Other results, such as factorisation identities not commonly encountered in the high school curriculum, should be substantiated with proof where possible.

# Monthly Competitions

## Entries and due dates

- Problems will be released on the first day of the month.
- Entries are due at 23:59 on the last day of the months.
- Entries should be typed up or scanned then emailed to problems@nzmosa.org. Please include student name, school and school year.
- Entries arriving later than the due date will not be marked.

## Problem details (significantly changed, effective August 2015)

- There are six problems of generally increasing difficulty. All students can attempt all problems.
- Questions 1 and 2 are "answer only" questions (worth 3 marks each).
- Only the answer is required, but working is welcome.
- A correct answer will score 3 points; an incorrect answer will score 0 points.

- Questions 3, 4, 5 and 6 are "working" questions (worth 5 marks each).
- Students are expected to provide clear written explanation of their work.
- The correct answer will earn at most 1 point; the other 4 points are allocated based on the student's working.

- Students can work on the problems all throughout the month, with no time restriction. However, they
**must not receive any assistance from anyone**, including teachers, parents, friends, siblings or anyone else. Students must work on the problems individually and without collaboration. - Creative/inventive solutions will perform better than brute-force solutions, and will get special mentions in our solutions!

## Marking and prizes (SIGNIFICANTLY CHANGED, EFFECTIVE AUGUST 2015)

- Students are pooled into three divisions:
- Junior (Years 7-8)
- Intermediate (Years 9-11)
- Senior (Years 12-13)

- Divisions are for determining prizewinners only, and there are no restrictions on which problems a student can work on.
- Students are eligible for prizes from only their division or a higher division.
- Students who win prizes will be contacted by email for proof of identity (scanned image of school ID), and postage address.
- Students are assigned to the correct division automatically on their first submission.
- If a student wins a prize twice in the same division, they will be automatically moved to the next division after receiving their second prize.
- If the student is already in the Senior division, they will still continue to be eligible for prizes.

# New Zealand Mathematical Olympiad

The official regulations for the NZMO can be found here.

## Registration

- Students may register either through their school or individually (to take the NZMO at an alternative testing centre).
- The cost of registration is $2.00 per student.

## The competition

- Duration: 90 minutes
- Examination conditions:
- No cheating, communication or collaboration is permitted.
- No calculators or any electronic devices are permitted, except for a wristwatch that does not have memory storage or computational capabilities.
- Closed book: no textbooks or notes are permitted.

## Problem details

- There are four divisions. In ascending order of difficulty:
- Junior, aimed at Years 7-8
- Intermediate, aimed at Years 9-11
- Senior, aimed at Years 12-13
- Olympiad, aimed at students in any year level that have, at any point in the past, attended the NZMOC Residential January Maths Camp.

- There will be a different paper for each division.
- Students may take a paper of a higher division, but
**must not take a paper of a lower division**. This will result in an "unofficial" result, because their participation in an easier division will disadvantage other students in that division.- Examples of unofficial entries: (1) A Year 12 student takes the Intermediate paper. (2) A Year 11 student who has previously attended the NZMOC Maths Camp takes the Intermediate paper. (3) A Year 11 student who has previously attended the NZMOC Maths Camp takes the Senior paper.

- Junior, Intermediate and Senior: each paper will have six problems, with marks allocated for a total of 60 marks.
- Olympiad: there will be three problems, with 7 marks each for a total of 21 marks.
- All working is expected for all questions. A correct answer (if one is required) will earn at most one point.

## Marking and prizes

- Every valid submission will be marked, but statements which cannot be interpreted (due to illegibility or poor explanation) will be ignored.
- Clear explanation is expected for every key step of the solution.
- Students are eligible for prizes from their division only, unless they wish to compete in a higher division.
- Medals will be presented for the top students of each division (gold, silver and bronze medals).
- Certificates will be presented to all students:
- Gold/Silver/Bronze,
- Honourable Mention,
- Highly Commended, and
- Commended.

- Badges and other prizes (such as books, t-shirts, Rubik's cubes) may also be presented to accomplished students.
- Special awards, for example the Golden Pen Award (for the most convoluted yet completely correct solution) and the Ingenuity Award (for the most inventive, creative solution), may also be awarded.