What is The Junior Mathematics Competition?

This competition for students in years 9 to 11 (forms 3 to 5) was initiated in 1985 by Professor Derek Holton of the University of Otago Mathematics and Statistics Department, shortly after his appointment. The competition is administered by a manager from within the Department. Other members of the Department help by writing questions, marking them, and determining the winners.

The National Bank sponsored the competition from 1985 to 2010 inclusive, providing cash prizes for the top students and Merit Certificates for about fifteen percent of the participants at each level. Apparently this competition was the longest running sponsorship activity which The National Bank had been involved in. Now The University of Otago itself generously provides sponsorship of the prizes.

The competition attracts around 10 000 entries from about 250 participating schools each year. It takes place on the same day at schools throughout the country, on a date late in March or early in April. The date is generally the second last Wednesday before Easter, so that schools have time to return the papers before the start of the Easter break. Marking takes place during the week following Easter, and the top papers at each level are later check-marked.

Important dates

Competition rules

Who is eligible to enter?

Anyone who is enrolled in years 9 to 11 in a New Zealand school in a particular year is eligible to enter the competition for that year. Note that it is the overall school year that determines eligibility, and not the year level for which a student is taking Mathematics. For example a year 11 student studying year 13 mathematics (or even University mathematics) is still eligible to enter. As another example a Year 9 student in an 'extension' Year 11 class enters the competition at the Year 9 level, not Year 11. PLEASE INFORM ALL SUCH STUDENTS TO ENTER AT THEIR SCHOOL YEAR LEVEL, not the 'extension' class year.

At this time the competition is restricted to students enrolled in New Zealand schools. (Students not permanently resident in New Zealand but enrolled in a New Zealand school at years 9 to 11 are eligible to enter.) We have no plans yet to let participants from overseas schools enter at this time.

Younger pupils enter as 'honorary' Year 9 students each year.

Format of the Competition

Note the change from 2018.

Students have one hour to answer six questions out of eight. Strong emphasis is placed on their ability to write down good mathematical explanations for their answers.

Q1: 10 marks. Year 9 and below only.

Q2: 10 marks. Year 10 and below only.

Q3 to Q6: 20 marks each. All students.

Q7: 10 marks. Years 10 and 11 only.

Q8: 10 marks. Year 11 only.

Generally speaking the level of mathematics required to do any particular problem should be available to most participants. Naturally, to help sort out the prize winners some of the problems are reasonably difficult. But there are also problems which will be accessible to students of average ability. Well presented work on these problems will often be enough to obtain a Merit Certificate. (Anybody who answers more than three questions fairly well should be eligible for a Merit Certificate during most years.)

Topics in these questions cover a wide spectrum of the Mathematics Curriculum, although there is almost always a logic problem and a geometry problem.

Sample questions

Details of collections of questions

Awards and Prizes

At each level there will be a first prize of $300, a second prize of $250, a third prize of $200, and 27 outstanding awards of $50. Certificates are also awarded for Top 100 and Top 200 placings. In addition, Certificates of Merit will be awarded to approximately the top 15% of students at each level.

Cost of the Competition

The cost of the competition for 2020 is $5 per student. Everything is sent digitally. Schools must print out the questions themselves. Pupils may answer on booklets (also sent digitally), although pad paper will suffice provided the pupil prints out their NAME, SCHOOL, and LEVEL at the top.

Payment should be on line. Details will be on the Initial Invitation.

Please try to be as accurate as possible with the number of students entered. There have been problems in recent years with some schools which have indicated that large numbers of students will sit the competition, but then only a few of them actually take part. The schools then wish to pay only for the smaller number of students at a direct cost to the competition.

The difficulty here is that costs have been calculated for the original number of participants. One major cost, for example, is the payment of the markers. They are happy to be paid for 120 students who did not actually take part, but the result is that the competition runs at a loss and the fee per student may have to be raised in the future.

Once again, please be as accurate as possible with the number of students entered in the competition.

Student Names

The organisers of the competition have made a special effort in recent years to ensure that the student name on the Participation Certificate (sent digitally) is correct. In this regard schools are asked to send accurate electronic lists of students’ names to the organisers.

  • Names should be obtained from the official school roll. Office staff at most schools are able to send this information automatically. Teachers should not have to type out any lists at all!
  • If students are sick on the day of the competition then other students may be substituted to take their place. However updated lists of names will then be essential.
  • Schools supplying no list, or a hand-written list only, will receive blank Participation Certificates. Staff will then have to fill out the student names themselves.
  • The names should be entered into a spreadsheet (such as Excel) in CSV format
  • Schools are urged to run virus checks before they dispatch the student names.