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Thursday 21st March 2024, 12:00:00 AM

UKMT Cayley Olympiad

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Thursday 21st March 2024, 12:00:00 AM

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Thursday 21st March 2024, 12:00:00 AM

UKMT Hamilton Olympiad

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Monday 1st January 2024, 12:00:00 AM

UKMT Intermediate Challenge

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Wednesday 24th April 2024, 11:00:00 PM

UKMT Junior Challenge

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Tuesday 11th June 2024, 11:00:00 PM

UKMT Junior Kangaroo

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Tuesday 11th June 2024, 11:00:00 PM

UKMT Junior Olympiad

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Thursday 21st March 2024, 12:00:00 AM

UKMT Maclaurin Olympiad

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Thursday 21st March 2024, 12:00:00 AM

UKMT Pink Kangaroo

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Wednesday 15th November 2023, 12:00:00 AM

UKMT Senior BM01

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Wednesday 24th January 2024, 12:00:00 AM

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Monday 2nd October 2023, 11:00:00 PM

UKMT Senior Challenge

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Wednesday 15th November 2023, 12:00:00 AM

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The UKMT was established to advance the education of children and young people in mathematics. UKMT Challenges are only open to entry from institutions that are registered UKMT centres, and not to individual students or parents, nor to private tutors. A school selects their top performing pupils and enters them into either the junior, intermediate or senior challenge.

The UKMT challenges are seen as the UK's most popular school maths competitions. Everything you could possibly need or want to know is explained below.

This is for students in years 5-6 (ages 9-11) although anyone from year 6 and below can do this. There is no certificate nor categories awarded for this (just a particiation certificate). The Primary Challenge contains resources for teachers to use in class at schools and is for teams, not individuals.

**Junior Challenge (JMC) - Years 7 and 8**

This is for students in **years 7- 8** (ages 11-13) although anyone from year 8 and below can enter (around 250,000 students take this challenge). This takes place in late April each year. The schools enter for students and usually select students from the top 2 sets (everyone in the top set is often forced to do it). Normally a student will have 2 attempts at it (in both years).

It is designed to make students think and is fun. Its purpose is to encourage mathematical reasoning, precise thinking, and the ability to use basic maths techniques to solve basic problems. These problems are designed to help students think and use their maths knowledge in interesting ways, and they are designed to be accessible yet still challenging.

The exam is a **1 hour multiple choice** paper with **25 questions** worth a **total of 135 marks**. The first 15 questions are designed to be easier. Questions 16-20 are more difficult and the last 5 questions are intended to be the most challenging. You are not expected to complete all the questions during the time. You should bear this in mind when deciding which questions to tackle.

The questions on this paper are designed to challenge you to think, not to guess. You will gain more marks, and more satisfaction, by doing one question carefully than by guessing lots of answers. This paper is about solving interesting problems, not about lucky guessing.

Marks are awarded as follows:

**5 marks for correct answers to questions 1-15****6 marks for correct answers to questions 16-25****0 marks for incorrect/unanswered answers to questions 1-25**

Note: In previous years there was negative marking (pre 2020 papers), but this no longer applies. It used to be -1 marks for incorrect answers to questions 16-20 and -2 marks for incorrect answers to questions 21-25.

**Certificates Awarded:**

These are based on where students rank compared to others.

1) **Participation**

2) **Bronze** - This is usually the level of getting questions 1-8 correct and on average around 49-60 marks which is roughly 8 correct and is achieved by 25% of students.

3) **Silver** - This is usually the level of getting questions 9-16 correct and on average around 61-74 marks which is roughly 10-12 correct and is achieved by 16-17% of students.

4) **Gold** - This is usually the level of getting questions 17-25 correct and on average around 75+ marks which is roughly 15+ correct and is achieved by the top 8-9% of students.

The top 50% get a certificate of Bronze, Silver, or Gold in the ratio 3 : 2 :1, with Bronze being most common and Gold being least. The thresholds change each year (see the boundaries below).

There are invitation only merit challenge papers sat afterwards

- Junior Kangaroo
- Junior Olympiad

These invitational papers are dependent on how students have scored in the the Junior Challenge above and are offered to the pupils who achieve the very top scores in the Junior Challenge.

Year |
Brone |
Silver |
Gold |
To Qualify for Kangaroo |
To Qualify for Olympiad |

1999 | 43 | 56 | 71 | 97 | |

2000 | 52 | 66 | 82 | 106 | |

2001 | 58 | 73 | 88 | 114 | |

2002 | 45 | 57 | 73 | 100 | |

2003 | 44 | 57 | 75 | 105 | |

2004 | 47 | 60 | 75 | 100 | |

2005 | 51 | 64 | 79 | 102 | |

2006 | 39 | 51 | 66 | 92 | |

2007 | 43 | 54 | 69 | 94 | |

2008 | 45 | 56 | 71 | 99 | |

2009 | 45 | 57 | 72 | 100 | |

2010 | 44 | 56 | 73 | 102 | |

2011 | 49 | 61 | 77 | 104 | |

2012 | 56 | 71 | 86 | 110 | |

2013 | 49 | 63 | 82 | 113 | |

2014 | 50 | 63 | 79 | 108 | |

2015 | 51 | 62 | 78 | 88 | 105 |

2016 | 51 | 65 | 81 | 93 | 113 |

2017 | 52 | 63 | 77 | 86 | 107 |

2018 | 49 | 61 | 75 | 82 | 105 |

2019 | 41 | 54 | 71 | 78 | 106 |

2020 (online) | 70 | 86 | 102 | n/a | |

2021 (online) | 45 | 57 | 73 | 73 | 98 |

2022 (online) | 52 | 66 | 92 | 92 | 120 |

2023 | 52 | 66 | 88 | 88 | 113 |

**Junior Mathematical Kangaroo (JMK):**

Over 10,000 participants out of the 250,000 participants from the JMC are invited to participate (around the top 4% of all who sit the JMC). Entry to the Junior Kangaroo is by invitation based on a qualifying JMC score (at least Gold - see required scores above ), or by discretionary entry. This challenge takes places weeks after the JMC.

This exam is a **1 hour multiple choice** paper with **25 questions** worth a total of **135 marks**.

Marks are awarded as follows:

**5 marks for correct answers to questions 1-15****6 marks for correct answers to questions 16-25****0 marks for incorrect/unanswered answers**

Certificates are awarded as follows:

1) **Qualification **(bottom 75%). This is just for be able to get to this stage and all entries receive this.

2) **Merit** (top 25%). Recall that the top 4% of the students from the Junior Challenge get invited for the Kangaroo Challenge. This means that on average, a Kangaroo merit would be ranked 99 out of 100 people taking the Junior Challenge. The other (half) person who scores bettter would qualify for the Junior Olympiad below. Perhaps, more accurately, a kangeroo merit would reflect a ranking in the interval (98.5%, 99.5%).

Year |
Kangaroo Merit |

2015 | 96+ |

2016 | 95+ |

2017 | 89+ |

2018 | 96+ |

2019 | 89+ |

2020 (online) | n/a |

2021 (online) | 97+ |

2022 (online) | 97+ |

2023 | 90+ |

**Junior Mathematical Olympiad (JMO):**

The highest 1,200 scorers are invited to take part in this challenge (around the top 0.5% of all who sit the Junior Challenge). Students usuallty qualify for this if they score around 105 marks in the Junior Challenge. Though like all assessments, the ranking/placements need to be taken with a pinch of salt.

Another way of looking at it is if 125,000 kids take the Junior Challenge in each year group (typically both year 7 and 8 take JMC so 250,000 in total) out of a rough total of 750,000 students in the uk (each year group) and an average high school has approximately 200 kids in each year group. So roughly 60 take the JMC per school (year 7 and 8) and on average, you'd expect 1 of those 60 to be roughly kanagaroo merit/olympiad.

Another way of looking at it is there are roughly 5,000 high schools in the uk, so if roughly 3,500 get kangaroo merit/olympiad, there is again about 1 per school. These figures could be made more precise and some schools put more effort into supporting/promoting the challenges etc, but if there is a reasonable chance that one student gets kangaroo merit/olympiad per school, it should be less surprising.

This exam is a** 2**** hour paper** worth **70 marks** with **16 questions**. For the first 10 questions (part A) only the answer is required and for the next 6 (Part B), full written solutions must be given.

Marks are awarded as follows:

**Section A:**1 mark for correct answers to questions 1-10. They are not multiple choice but have a single numerical answer.**Section B:**up to 10 marks for questions 11-16. Partial marks are given for correct working and depend on the clarity of presentation and explanation (i.e. your working out!) as much as the answers themselves. A solution with a correct answer may only score 2 out of 10 if not accompanied by any working. An incomplete solution without the right answer might score 2 or 3 marks, and near complete and complete solutions could score 8,9 or 10 marks each. If a solution is judged to be incomplete, it in marked on a 0+ basis, maximum 3 marks. If it has an evident logical strategy, it is marked on a 10-basis. Rather than to try to rush through the section and answer everything, it is advised that students should fully answer the questions that they can. This is because incomplete answers can only score a maximum of 3 marks. Students are encouraged to write complete answers to 2-4 questions rather than hurry through incomplete answers to all 6.

Everyone who completes the Junior Olympiad receives a certificate, with those who gained the most points also receiving medals or book prizes. There are two sets of boundaries. The top 25% of participants receive a certificate of Distinction, and the next 40% receive a Merit. The top 200 students also receive a book prize and a Gold, Silver or Bronze medal.

NB: Prior to 2023 things were slightly different. There were still two sets of boundaries – one for Merit and Distinction and then more for Gold/Silver/Bronze medals. The top 50 (50 people not percent!) scorers also received a book prize. Then the top scoring 25% of candidates receive a certificate of Distinction, and all candidates who have made a good attempt receive a Certificate of Merit. Any student who qualified directly from the Junior Maths Challenge will receive a Certificate of Qualification

Certificates are awarded as follows:

1) **Participation** (bottom 75%). This is just for be able to get to this stage and all entries receive this.

2) **Merit** (next 40% after the top 25%)

3) **Distinction **(top 25%)

4) **Book Prize **(top 200 scorers). The top 200 scorers also get an additional medal.

**Bronze Medal**(top 100 scorers)**Silver Medal**(top 60 scorers)**Gold Medal**(top 40 scorers)

Year |
Merit |
Distinction |
Book Prize |

2015 | 8 | 28 |
45 |

2016 | 8 | 34 | 52 |

2017 | |||

2018 | 8 | 32 | 48 |

2019 | 8 | 45 | 59 |

2020 (online) | n/a | ||

2021 (online) | 12 | 37 | 56 |

2022 (online) | 16 | 29 | |

2023 | 21 | 36 | all medalists |

There are also boundaries for Gold/Silver/Bronze medals. The top 40 scorers receive a Gold Medal, the next 60 a Silver Medal and the next 100 a Bronze medal. All medallists will also receive a book prize. Since 2023, only Section B marks count towards the medals.

NB: Prior to 2023 things were slightly different. Previously Gold medals were awarded to the top 30 students, Silver to the next 60 students and Bronze to the next 120 students taking the paper. Section B scores of 4 marks or lower did not count towards the medal scores, only attempts to individual questions scoring 5 or above.

Year |
Bronze Medal |
Silver Medal |
Gold Medal |

2015 | 27 | 37 |
46 |

2016 | 35 | 44 | 55 |

2017 | |||

2018 | 33 | 40 | 48 |

2019 | 45 | 55 | 59 |

2020 (online) | n/a | n/a | n/a |

2021 (online) | 37 | 47 | 57 |

2022 (online) | 34 | 41 | 48 |

2023 | 36 | 44 | 51 |

This is for students in **years 9 - 11** (ages 13-16) and takes place in February each year. It encourages mathematical reasoning, precision of thought and fluency to make students think. Again students from the top 2 sets get entered. Normally a student will have 3 attempts at it (in all 3 years).

The problems on the Intermediate Maths Challenge are designed to make students think, most are accessible yet still challenge those with more experience.

The exam is a **1 hour multiple choice** paper with **25 questions** worth a total of **135 marks**. Unlike the Junor Challenge, marks are deducted for wrong answers. The first 15 questions are designed to be easier. Questions 16-20 are more difficult and the last 5 questions are intended to be the most challenging. You are not expected to complete all the questions during the time. You should bear this in mind when deciding which questions to tackle.

Marks are awarded as follows:

**5 marks for correct answers to questions 1-15****6 marks for correct answers to questions 16-25****0 marks for incorrect answers to questions 1-15****0 marks for unanswered questions****-1 marks for incorrect answers to questions 16-20****-2 marks for incorrect answers to questions 21-25**

**Certificates Awarded:**

1) **Bronze **-This is usually the level of questions 1-8 and around 48-58 marks which is roughly 8 correct

2) **Silver** -This is usually the level of questions 9-16 and around 59-72 marks which is roughly 10-12 correct

3) **Gold** This is sually the level of questions 17-25 and around 73+ marks which is roughly 15+ correct

There are also invitation only merit challenge papers sat afterwards (like with the Junior Challenge) dependent on whether you've scored highly enough in the Intermediate Challenge. The follow-on rounds are the European Kangaroo (Grey and Pink) and the Intermediate Mathematical Olympiad (Cayley, Hamilton and Maclaurin).

- Grey Kangaroo (GK)
- Pink Kangaroo (PK)
- Cayley Olympiad (CO)
- Hamilton Olympiad (HO)
- Maclaurin Olympiad (MO)

The following lists the scores that must be obtaind in IMC challenge in order to get a brzone, silver or gold medal OR to progress on to the Europen Kangaroo or Intermediate Olympiad Rounds.

Year |
Bronze |
Silver |
Gold |
GK |
PK |
CO |
HO |
MO |

1999 | 50 | 64 | 80 | |||||

2000 | 40 | 55 | 73 | |||||

2001 | 32 | 43 | 57 | |||||

2002 | 53 | 62 | 72 | |||||

2003 | 46 | 58 | 74 | 75 | 86 | 88 | 98 | 101 |

2004 | 40 | 51 | 68 | 67 | 79 | 84 | 93 | 100 |

2005 | 40 | 50 | 65 | 64 | 72 | 76 | 85 | 90 |

2006 | 46 | 58 | 72 | 72 | 80 | 84 | 92 | 99 |

2007 | 50 | 63 | 78 | 78 | 86 | 90 | 97 | 103 |

2008 | 42 | 54 | 70 | 70 | 82 | 85 | 95 | 102 |

2009 | 39 | 51 | 66 | 66 | 77 | 83 | 90 | 99 |

2010 | 45 | 56 | 70 | 70 | 80 | 83 | 91 | 97 |

2011 | 47 | 59 | 78 | 77 | 88 | 92 | 99 | 104 |

2012 | 50 | 62 | 77 | 77 | 87 | 90 | 96 | 101 |

2013 | 47 | 59 | 74 | 73 | 84 | 88 | 96 | 103 |

2014 | 42 | 55 | 72 | 67 | 78 | 90 | 96 | 103 |

2015 | 37 | 49 | 64 | 61 | 68 | 81 | 88 | 95 |

2016 | 40 | 50 | 62 | 60 | 66 | 81 | 89 | 95 |

2017 | 47 | 61 | 78 | 72 | 81 | 97 | 106 | 112 |

2018 | 48 | 59 | 73 | 68 | 76 | 93 | 100 | 104 |

2019 | 43 | 55 | 71 | 65 | 73 | 91 | 99 | 106 |

2020 (online) | 60 | 72 | 89 | 80 | 89 | 110 | 117 | 120 |

2021 (online) | 55 | 68 | 86 | 68 | 86 | 100 | 110 | 118 |

2022 (online) | 50 | 65 | 81 | 65 | 81 | 101 | 111 | 117 |

2023 | 42 | 55 | 71 | 67 | 77 | 95 | 100 | 103 |

The European Kangaroo is sat by the top 500 scorers from each school year in the IMC and consists of 2 papers (Grey Kangaroo and Pink Kangaroo). The paper that the student will undertake depends on the year group that the student is in (Grey Kangaroo for those in year 9 or below and Pink Kangaroo for those in year 10 or 11). The next 5500 highest scorers below the Olympiad threshold (below the top 500) are invited to take part. Both papers are by invitaiton only or discretionary entry. The papers are **multiple choice**.

**Grey Kangaroo **(must be in year 9 or below):

Students qualify for this if they score around 68 marks in Intermediate Challenge (1 hour paper worth 135 marks, 25 questions, 5 or 6 marks for a correct question, 0 marks for incorrect question)

1) **Qualification** (bottom 75%)

2) **Merit** (top 25%)

**Pink Kangaroo** (must be in year 10 or 11):

Students qualify for this if they score around 76 marks in Intermediate Challenge (1 hour paper worth 135 marks, 25 questions, 5 or 6 marks for a correct question, 0 marks for incorrect question)

1) **Qualification** (bottom 75%)

2) **Merit**(top 25%)

Note: All those who sit either Kangaroo receive a keyfob containing a different mathematical puzzle each year.

The Intermediate Mathematical Olympiad is sat by the top 500 scorers from each school year in the IMC and consists of 3 papers (Cayley, Hamilton and Maclaurin named after famous Mathematiciians). The paper that the student will undertake depends on the year group that the student is in (Cayley for those in year 9 and below, Hamilton for year 10 and Maclaurin for year 11). All 3 papers are by invitaiton only.

**Cayley Olympiad** (must be in year 9 or below):

Students qualify for this if they scored around 93 marks in Intermediate Challenge (2 hour paper, 6 questions, each question is worth 10 points, not multiple choice)

1) **Qualification**

2) **Merit** (10+ marks)

3) **Distinction** (46 + marks)

4) **Bronze Medal** (50 + marks - top 100)

5) **Book Prize** (53 + marks - top 50)

**Hamilton Olympiad** (must be in year 10):

Students qualify for this if they scored around 100 marks in the Intermediate Challenge (2 hour paper, 6 questions, each question is worth 10 points, not multiple choice)

1) **Qualification**

2) **Merit** (10+ marks)

3) **Distinction** (41 + marks)

4) **Silver Medal**(46 + marks - top 100)

5) **Book Prize** (52 + marks - top 50)

**Maclaurin Olympiad** (must be in year 11):

Students qualify for this if they scored around 104 marks in Intermediate Challenge (2 hour paper, 6 questions, each question is worth 10 points, not multiple choice)

1) **Qualification**

2) **Merit** (8 + marks)

3) **Distinction** (24 + marks)

4) **Gold Medal** (28 + marks - top 100)

5) **Book Prize** (35 + marks - top 50)

Note: Top performers (students who qualify for the Maclaurin Olympiad) can be selected for the National Mathematics Summer School in July. They get sent to the International Maths Olympiad training camp/squad which is a lot of fun. The top performers are selected by lottery which selects 48 of the top 1.5% of scorers in the IMC.

This is for students in **years 12-13 **(ages 15-18+). The exam is a 1.5 hour multiple choice paper with 25 questions worth a total of 125 marks. All candidates start out with 25 marks in this paper. Marks are awarded as follows:

- 0 marks for each unanswerred question
- 4 marks for a correct question
- -1 marks for incorrect question

**Certificates Awarded:**

1) **Bronze** (usually the level of questions 1-8) around 53-66 marks which is roughly 6 correct

2) **Silver** (usually the level of questions 9-16) around 67-82 marks which is roughly 10-12 correct

3) **Gold **(usually the level of questions 17-25) around 83+ marks which is roughly 15+ correct

There are also invitation only merit challenge papers sat afterwards dependent on whether you've scored highly enough in the Senior Challenge.

- Senior Kangaroo (SK)
- Senior Olympiad (SO)

Year |
Bronze |
Silver |
Gold |
SK |
SO |

2001 | 56 | 67 | 81 | 91 | |

2002 | 47 | 57 | 70 | 82 | |

2003 | 61 | 72 | 87 | 98 | |

2004 | 55 | 66 | 79 | 92 | |

2005 | 60 | 71 | 84 | 92 | |

2006 | 57 | 66 | 80 | 91 | |

2007 | 52 | 61 | 75 | 88 | |

2008 | 51 | 61 | 74 | 87 | |

2009 | 54 | 64 | 79 | 91 | |

2010 | 58 | 70 | 85 | 96 | |

2011 | 52 | 63 | 79 | 84 | 90 |

2012 | 49 | 62 | 77 | 82 | 93 |

2013 | 53 | 67 | 82 | 86 | 100 |

2014 | 57 | 71 | 84 | 89 | 101 |

2015 | 50 | 65 | 82 | 86 | 104 |

2016 | 55 | 71 | 88 | 90 | 106 |

2017 | 57 | 71 | 86 | 85 | 104 |

2018 | 53 | 67 | 83 | 83 | 102 |

2019 | 49 | 61 | 76 | 76 | 100 |

2020 (online) | 59 | 73 | 91 | 91 | 100 |

2021 (online) | 49 | 66 | 85 | 85 | 108 |

2022 (online) | 48 | 62 | 76 | 76 | 100 |

2023 |

**Senior Kangaroo:**

Students qualify for this if they scored between 83 and 101 marks in senior challenge (1 hour paper worth 100 marks, 20 questions, 5 marks for a completely correct question – not multiple choice)

1) **Qualification** (bottom 75%)

2) **Merit** (top 25%)

**British Mathematical Olympiad **(BMO - Round 1):

The first round of the BMO is held in November each year, and from 2006 is an open entry competition. The qualification to BMO Round 1 is through the Senior Challenge. Students who do not make the qualification through the Senior Challenge may be entered at the discretion of their school for a fee of £40

While around 1000 gain automatic qualification to sit the BMO1 paper each year, the additional discretionary and international students means that since 2016, on average, around 1600 candidates have been entered for BMO1 each year. Although these candidates represent the very best mathematicians in their age group, the difficulty level of the BMO papers mean that many of these attain a very low score.

Students qualify for the BMO if they scored 102 marks or more in the Senior Challenge. The exam is a 3.5 hour paper worth 60 marks, 6 questions, 10 marks for a completely correct question (not multiple choice)/. Candidates are required to write full proofs to the questions. An answer is marked on either a "0+" or a "10-" mark scheme, depending on whether the answer looks generally complete or not. An answer judged incomplete or unfinished is usually capped at 3 or 4, whereas for an answer judged as complete, marks may be deducted for minor errors or poor reasoning but it is likely to get a score of 7 or more. As a result, it is uncommon for an answer to score a middling mark between 4 and 6.

1) **Merit** around 9-21 marks

2) **Distinction** around 22+ marks

3) **Bronze** around 35-40 marks (next 30 students)

4) **Silver** around 41- 47 marks (next 50 students)

5) **Gold** around 48+ marks (top 20 students)

Note: Gold, silver and bronze medals are awarded to the top 100 candidates in the ratio 1 : 2 : 3.

**British Mathematical Olympiad Round 2** (BMO Round 2):

Like the BMO1 paper, it is not designed merely to test knowledge of advanced mathematics but rather to test the candidate's ability to apply the mathematical knowledge to solve unusual problems and is an entry point to training and selection for the international competitions.

Students qualify for this based on how they did in the BMO and which year they are in - see below. The BMO2 is a 3.5 hour paper worth 40 marks, 4 questions, 10 marks for a completely correct question (not multiple choice).

The marks for a distinction vary based on which year you're in:

**Year 10:**

- around 26 marks or more in British mathematical olympiad challenge round 1
- around 19 or more marks in British mathematical olympiad challenge round 2

**Year 11:**

- around 29 marks or more in British mathematical olympiad challenge round 1
- around 19 or more marks in British mathematical olympiad challenge round 2

**Year 12:**

- around 32 marks or more in British mathematical olympiad challenge round 1
- around 19 or more marks in British mathematical olympiad challenge round 2

**Year 13:**

- around 35 marks or more in British mathematical olympiad challenge round 1
- around 19 or more marks in British mathematical olympiad challenge round 2

**International Olympiad:**

Those who qualified for round 2 can ALSO be selected to go on to take the **International Mathematical Olympiad (IMO)** paper (6 questions over 2 days, 7 points each, 42 marks total, 4.5 hours each day to solve 3 questions) and represent UK (IMO). This applies to years 10-13. Teams of up to 6 people are chosen to represent). The individual participants are ranked and given a certificate based on their individual scores.

Certificates awarded:

1) **Bronze**

2) **Silver**

3) **Gold**

Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem. The country with the highest combined team score wins.

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