The United Kingdom Mathematics Trust (UKMT) is a charity founded in 1996 to help with the education of children in mathematics within the UK.
History The national mathematics competitions had existed prior to the formation of the trust, but the foundation of the UKMT in the summer of 1996 enabled them to be run collectively. The Senior Mathematical Challenge was formerly called 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 Tony Gardiner in 1987, and were run by him under the name of the United Kingdom Mathematics Foundation until 1996. In 1995, Gardiner 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 organization.
Mathematical Challenges The UKMT runs a series of mathematics challenges to encourage children's interest in mathematics and to develop their skills. The three main challenges are: Junior Mathematical Challenge (UK year 8/S2 and below) Intermediate Mathematical Challenge (UK year 11/S4 and below) Senior Mathematical Challenge (UK year 13/S6 and below) United Kingdom Mathematics Trust, Thursday 19 April 2012 Primary Mathematical Challenge (UK year 6/S2 and below)
Certificates In the Junior and Intermediate Challenges the top scoring 50% of the entrants receive bronze, silver or gold certificates based on their mark in the paper. In the Senior Mathematical Challenge these certificates are awarded to top scoring 66% of the entries. In each case bronze, silver and gold certificates are awarded in the ratio 3 : 2 : 1. So in the Junior and Intermediate Challenges The Gold award is achieved by the top 8-9% of the entrants. The Silver award is achieved by 16-17% of the entrants. The Bronze award is achieved by 25% of the entrants. United Kingdom Mathematics Trust, Tuesday 10 May 2022
In the past, only the top 40% of participants received a certificate in the Junior and Intermediate Challenges, and only the top 60% of participants received a certificate in the Senior Challenge. The ratio of bronze, silver, and gold have not changed, still being 3 : 2 : 1.
Junior Mathematical Challenge The Junior Mathematical Challenge (JMC) is an introductory challenge for pupils in Years 8 or below (aged 13 or below), taking place in late April or early May each year. 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. The last five questions are intended to be the most challenging and so are also 6 marks. Questions to which no answer is entered will gain (and lose) 0 marks. United Kingdom Mathematics Trust, Junior Challenge, Thursday 19 April 2012 However, in recent years there has been no negative marking so wrong questions will be given 0 marks. Previously, the top 40% of students (50% since the 2022 JMC) get a certificate of varying levels (Gold, Silver or Bronze) based on their score. The Junior Mathematical Challenge has follow-on rounds called the: Junior Kangaroo and the more difficult Junior Mathematical Olympiad (JMO). The average score for to qualify for the Junior Kangaroo is 88 and the JMO is 104. However, please note that the pass marks for certificates and follow-on rounds have been at an all-time high, making it increasingly difficult to achieve a qualification for the Junior Kangaroo and JMO. +Summary of UKMT Junior ChallengesChallengeEligibilityWhenDurationNo. of QsQuestionsMax ScoreCertificatesJunior Mathematical Challenge(JMC)England Wales and Overseas: Y8 or below Scotland: S2 or below Northern Ireland: Y9 or belowLate April60 mins25Questions 1-15 (multi-choice) 5 marks each
Questions 16-25 (multi-choice)
6 marks each135Top 50% of candidates in ratio 3:2:1 get: Bronze, Silver, Gold.Junior KangarooGood performance (at least Gold certificate) in JMC OR discretionary entry at some fee.weeks after JMC135Top 10% get Gold Kangaroo Certificate, the next 20% get Silver Kangaroo Certificate, and the next 30% get a Bronze Kangaroo Certificate. Remaining 40% get Certificate of Qualification or Participation.Junior Mathematical OlympiadAround top 1,200 performers in JMC invited. Discretionary entry also available.120 mins16 (From 2025, 10)Section A Questions 1-10 (correct answer only) 1 mark each
Section B
Questions 11-16 (answer with solution)
0~10 marks each
From 2025 onwards, Section A (Questions 1-10) was removed and there were only be 6 questions (Section B). The format and marking stayed the same. 70 (From 2025, 60)Top 25% get Certificate of Distinction. Next 40% get Certificate of Merit. Remaining 35% get Certificate of Qualification or Participation. Top 40 get a gold medal, the next 60 a silver medal, the next 100 a bronze medal. All medalists receive a book prize. Only questions 11-16 are considered for medals
Junior Kangaroo Over 10,000 participants from the JMC are invited to participate in the Junior Kangaroo. Most of the Junior Kangaroo participants are those who performed well in the JMC, however the Junior Kangaroo is open to discretionary entries for a fee. Similar to the JMC, the Junior Kangaroo is a 60 minute challenge consisting of 25 multiple-choice problems. Correct answers for Questions 1-15 earn 5 marks, and for Questions 16-25 earn 6 marks. Blank or incorrect answers are marked 0; there is no penalty for wrong answers.
The top 10% of participants in the Junior Kangaroo receive a Gold Kangaroo Certificate, the next 20% receive a Silver Kangaroo Certificate, and the next 30% receive a Bronze Kangaroo Certificate
Junior Mathematical Olympiad The highest 1200 scorers are also invited to take part in the Junior Mathematical Olympiad (JMO). Like the JMC, the JMO is sat in schools. Students are given 120 minutes to complete the JMO. This is also divided into two sections. Part A is composed of 10 questions in which the candidate gives just the answer (not multiple choice), worth 10 marks (1 mark each). Part B consists of 6 questions and encourages students to write out full solutions. Each question in section B is worth 10 marks 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 for the whole paper is 70. Everyone who participates in this challenge will gain a certificate (Participation 75%, Distinction 25%); the top 200 or so gaining medals (Gold, Silver, Bronze); with the top fifty winning a book prize. United Kingdom Mathematics Trust, Junior Mathematical Olympiad, Thursday 19 April 2012
From 2025, this has changed as Part A has been omitted. Section B has stayed the same, though it is no longer called Section B (it is now the only section). This changes the total number of questions to 6 from 16 and the marks to 60 from 70. However the time given for the JMO has stayed at 120 minutes.
Intermediate Mathematical Challenge The Intermediate Mathematical Challenge (IMC) is aimed at school years equivalent to English Years 9-11, taking place in winter each year. 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 (and lose) 0 marks. United Kingdom Mathematics Trust, Intermediate Challenge, Thursday 19 April 2012
Again, the top 50% of students taking this challenge get a certificate. There are two follow-on rounds to this competition: The Pink and Grey Kangaroo and the 3 Intermediate Mathematical Olympiads, dependent on year group. Additionally, top performers can be selected for the National Mathematics Summer Schools. +Summary of UKMT Intermediate ChallengesChallengeEligibilityWhenDurationNo. of QsQuestionsMax ScoreCertificatesIntermediate Mathematical Challenge(IMC)England Wales and Overseas: Y11 or below Scotland: S4 or below Northern Ireland: Y12 or belowFebruary60 mins25Questions 1-15 (multi-choice) 5 marks each
Questions 16-20 (multi-choice)
6 marks each / penalty of 1 if wrong answer chosen
Questions 21-25 (multi-choice)
6 marks each / penalty of 2 if wrong answer chosen135Top 50% of candidates in ratio 3:2:1 get: Bronze, Silver, Gold.Grey KangarooInvitation from good IMC performance (around 8,000 invitations), OR discretionary entry at a fee.Y9 or belowMarchQuestions 1-15 (multi-choice) 5 marks each
Questions 16-25 (multi-choice)
6 marks eachSeparately awarded for each Kangaroo's cohort:Top 25% of candidates receive a Certificate of Merit. Remaining 75% get Certificate of Qualification or Participation.Pink KangarooY10/11Cayley Mathematical OlympiadInvitation from good IMC performance (usually top 1,500), OR discretionary entry at a fee.Y9 or below120 mins6Questions 1-6 (answer with solution) 0~10 marks each60Separately awarded for each Olympiad's cohort:Highest-scoring participants receive Certificates of Distinction or Merit. Remaining participants receive Certificate of Qualification or Participation. Top 20 get a gold medal, the next 30 a silver medal, the next 50 a bronze medal. All medalists receive a book prize.Hamilton Mathematical OlympiadY10Maclaurin Mathematical OlympiadY11
Intermediate Mathematical Olympiad To prevent this getting confused with the International Mathematical Olympiad, this is often abbreviated to the IMOK Olympiad (IMOK = Intermediate Mathematical Olympiad and Kangaroo).
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 (Cayley for those in year 9 and below, Hamilton for year 10 and Maclaurin for year 11). United Kingdom Mathematics Trust, Intermediate Mathematical Olympiad, Saturday 26 May 2012
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 (e.g. 4–6). 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 (participation for the bottom 50%, merit for the next 25% and distinction for the top 25%). The mark boundaries for these certificates change every year, but normally around 30 marks will gain a Distinction. Those scoring highly (the top 50) 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. United Kingdom Mathematics Trust, Intermediate Mathematical Olympiad, Thursday 19 April 2012
European Kangaroo