United Kingdom Mathematics Trust
The United Kingdom Mathematics Trust is a charity founded in 1996 to help with the education of children in mathematics within the UK.
History
The national mathematics competitions existed prior to the formation of the UKMT, but the foundation of the UKMT in the summer of 1996 enabled them to be run collectively. The Senior Mathematical Challenge was formerly the National Mathematics Contest. Founded in 1961, it was run by the Mathematical Association from 1975 until its adoption by the UKMT in 1996. The Junior and Intermediate Mathematical Challenges were the initiative of Dr Tony Gardiner in 1987 and were run by him under the name of the United Kingdom Mathematics Foundation until 1996. The popularity of the UK national mathematics competitions is largely due to the publicising efforts of Dr Gardiner in the years 1987-1995. Hence, in 1995, he advertised for the formation of a committee and for a host institution that would lead to the establishment of the UKMT, enabling the challenges to be run effectively together under one organisation.Mathematical Challenges
The UKMT runs a series of mathematics challenges to encourage children's interest in mathematics and develop their skills:- Junior Mathematical Challenge
- Intermediate Mathematical Challenge
- Senior Mathematical Challenge
Certificates
So in the Junior and Intermediate Challenges
- The Gold award is achieved by the top 6-7% of the entrants.
- The Silver award is achieved by 13-14% of the entrants.
- The Bronze award is achieved by 21% of the entrants.
Junior Mathematical Challenge
The Junior Mathematical Challenge is an introductory challenge for pupils in Years 8 or below or below. This takes the form of twenty-five multiple choice questions to be sat in exam conditions, to be completed within one hour. The first fifteen questions are designed to be easier, and a pupil will gain 5 marks for getting a question in this section correct. Questions 16-20 are more difficult and are worth 6 marks, with a penalty of 1 point for a wrong answer which tries to stop pupils guessing. The last five questions are intended to be the most challenging and so are also 6 marks, but with a 2 point penalty for an incorrectly answered question. Questions to which no answer is entered will gain 0 marks.Junior Mathematical Olympiad
The top 40% of students get a certificate of varying levels based on their score. The highest 1200 scorers are also invited to take part in the Junior Mathematical Olympiad. Like the JMC, the JMO is sat in schools. This is also divided into two sections. Part A is composed of ten questions in which the candidate gives just the answer, worth 10 marks. Part B consists of 6 questions and encourages students to write out full solutions. Each B question is marked out of 10 and students are encouraged to write complete answers to 2-4 questions rather than hurry through incomplete answers to all 6. If the solution is judged to be incomplete, it is marked on a 0+ basis, maximum 3 marks. If it has an evident logical strategy, it is marked on a 10- basis. The total mark is out of 70. Everyone who participates in this challenge will gain a certificate ; the top 200 or so gaining medals ; with the top fifty winning a book prize.Intermediate Mathematical Challenge
The Intermediate Mathematical Challenge is aimed at school years equivalent to English Years 9-11. Following the same structure as the JMC, this paper presents the student with twenty-five multiple choice questions to be done under exam conditions in one hour. The first fifteen questions are designed to be easier, and a pupil will gain 5 marks for getting a question in this section correct. Questions 16-20 are more difficult and are worth 6 marks, with a penalty of 1 point for a wrong answer which tries to stop pupils guessing. The last five questions are intended to be the most challenging and so are also 6 marks, but with a 2 point penalty for an incorrectly answered question. Questions to which no answer is entered will gain 0 marks.Again, the top 40% of students taking this challenge get a certificate. There are two follow-on rounds to this competition: The European Kangaroo and the Intermediate Mathematical Olympiad.
Intermediate Mathematical Olympiad
To prevent this getting confused with the International Mathematical Olympiad, this is often abbreviated to the IMOK Olympiad.The IMOK is sat by the top 500 scorers from each school year in the Intermediate Maths Challenge and consists of three papers, 'Cayley', 'Hamilton' and 'Maclaurin' named after famous mathematicians. The paper the student will undertake depends on the year group that student is in.
Each paper contains six questions. Each solution is marked out of 10 on a 0+ and 10- scale; that is to say, if an answer is judged incomplete or unfinished, it is awarded a few marks for progress and relevant observations, whereas if it is presented as complete and correct, marks are deducted for faults, poor reasoning, or unproven assumptions. As a result, it is quite uncommon for an answer to score a middling mark. This makes the maximum mark out of 60. For a student to get two questions fully correct is considered "very good". All people taking part in this challenge will get a certificate. The mark boundaries for these certificates change every year, but normally around 30 marks will gain a Distinction. Those scoring highly will gain a book prize; again, this changes every year, with 44 marks required in the Maclaurin paper in 2006. Also, the top 100 candidates will receive a medal; bronze for Cayley, silver for Hamilton and gold for Maclaurin.
In addition to the book prize, each year approximately 48 students are chosen to go to a National Mathematics Summer School in July. At this summer school the students are stretched, with daily lectures going beyond the normal GCSE syllabus and exploring some of the wider aspects of mathematics.
European Kangaroo
The European Kangaroo is a competition which follows the same structure as the AMC. There are twenty-five multiple-choice questions and no penalty marking. This paper is taken throughout Europe by over 3 million pupils from more than 37 countries. Two different Kangaroo papers follow on from the Intermediate Maths Challenge and the next 5500 highest scorers below the Olympiad threshold are invited to take part. The Grey Kangaroo is sat by students in year 9 and below and the Pink Kangaroo is sat by those in years 10 and 11. The top 25% of scorers in each paper receive a certificate of merit and the rest receive a certificate of participation. All those who sit either Kangaroo also receive a keyfob containing a different mathematical puzzle each year.Senior Mathematical Challenge
The Senior Mathematical Challenge is open to students who are in Year 13 or below. The paper has twenty-five multiple choice questions. A correct answer is worth 4 marks, while 1 mark is deducted from a starting total of 25 for an incorrect answer. This gives a score between 0 and 125 marks.Unlike the JMC and IMC, the top 60% get a certificate, the 1000 highest scorers are invited to compete in the British Mathematical Olympiad and the next 2000 highest scorers are invited to sit the Senior Kangaroo. Mathematics teachers may also, on payment of a fee, enter students who did not score quite well enough in the SMC, but who might cope well in the next round.
British Mathematical Olympiad
Round 1 of the Olympiad is a three-and-a-half hour examination including six more difficult, long answer questions, which serve to test entrants' puzzle-solving skills. As of 2005, a more accessible first question was added to the paper; before this, it only consisted of 5 questions. Around one hundred high scoring entrants from BMO1 are invited to sit the second round, with the same time limit, in which 4 questions are posed. The twenty top scoring students from the second round are subsequently invited to a training camp at Trinity College, Cambridge for the first stage of the International Mathematical Olympiad UK team selection.Senior Kangaroo
The Senior Kangaroo is a one-hour examination to which the next 1500 highest scorers below the Olympiad threshold are invited and unlike the Olympiad, a fee cannot be paid for entry. The paper consists of twenty questions, each of which require three digit answers. The top 25% of candidates receive a certificate of merit and the rest receive a certificate of participation.Team Challenge
The UKMT Team Maths Challenge is an annual event. One team from each participating school, comprising four pupils selected from year 8 and 9, competes in a regional round. No more than 2 pupils on a team may be from Year 9. There are over 60 regional competitions in the UK, held between February and May. The winning team in each regional round, as well as a few high-scoring runners-up from throughout the country, are then invited to the National Final in London, usually in late June.There are 4 rounds:
- Group Questions
- Cross-Numbers
- Shuttle
- Relay
| Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
| Winner | Magdalen College School, Oxford | St Paul's Girls' School | Harrow School & Orley Farm School | City of London School | City of London School | Westminster Under School | Westminster Under School | St Olave's Grammar School | Westminster Under School |
| 2nd Place | Queen Elizabeth's Grammar School for Boys | Magdalen College School, Oxford | ? | King Edward's School, Birmingham | Reading School & Colchester Royal Grammar School | Bancroft's School | - | The Judd School | - |
| 3rd Place | Clifton College | City of London School | ? | Magdalen College School, Oxford | - | University College School | St Olave's Grammar School | Westminster Under School | - |
Senior Team Challenge
A pilot event for a competition similar to the Team Challenge, aimed at 16- to 18-year-olds, was launched in the Autumn of 2007 and has been running ever since. The format is much the same, with a limit of two year 13 pupils per team. Regional finals take place between October and December, with the National Final in early February the following year.Previous winners are below:
| Year | Winner | Runners-up | Third Place | Poster Competition winners |
| 2007/08 | Torquay Boys' Grammar School | ? | ? | No competition |
| 2008/09 | Westminster School | ? | ? | No competition |
| 2009/10 | Westminster School | King Edward VI Grammar School, Chelmsford | Abingdon School | King Edward VI High School for Girls |
| 2010/11 | Harrow School | Colchester Royal Grammar School | Merchant Taylors' School/ Abingdon School/ Concord College | North London Collegiate School |
| 2011/12 | Alton College | Dean Close School | Headington School | Royal Grammar School, Newcastle |
| 2012/13 | Westminster School | City of London School/ Eton College/ Magdalen College School | - | The Grammar School at Leeds |
| 2013/14 | Hampton School | Alton College | Rainham Mark Grammar School | The Grammar School at Leeds |
| 2014/15 | Hampton School/Harrow School/King Edward's School | - | - | Dunblane High School |
| 2015/16 | King Edward's School/ Ruthin School/ Westminster School | - | - | Backwell School |
| 2016/17 | Ruthin School | Magdalen College School | Headington School | Royal Grammar School, Newcastle |
| 2017/18 | Ruthin School | Tapton School | King Edward's School | The Perse School |
| 2018/19 | Durham School/Westminster School | - | Ruthin School/Concord College | The Perse School |
| 2019/20 | Westminster School | Ruthin School | Winchester College | Bancroft’s School |
British Mathematical Olympiad Subtrust
For more information see British Mathematical Olympiad Subtrust.The British Mathematical Olympiad Subtrust is run by the UKMT, it runs the British Mathematical Olympiad as well as the UK Mathematical Olympiad for Girls, several training camps throughout the year such as a winter camp in Hungary, an Easter camp at Trinity College, Cambridge, and other training and selection of the IMO team.