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.
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.
This takes the form of twenty-five multiple choice questions to be sat in exam conditions, to be completed within one hour.
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.
Similar to the JMC, the Junior Kangaroo is a 60 minute challenge consisting of 25 multiple-choice problems.
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.
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 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.
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%).
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.
(The puzzles along with solutions)[19] Selected by lottery, 48 of the top 1.5% of scorers in the IMC are invited to participate in one of three week-long National Mathematics Summer Schools in July.
Each from a different school across the UK, the 24 boys and 24 girls are facilitated with a range of activities, including daily lectures, designed to go beyond the GCSE syllabus and explore wider and more challenging areas of mathematics.
[20] The Senior Mathematical Challenge (SMC) takes place in late-autumn each year, and is open to students who are aged 19 or below and are not registered to attend a university.
[21] Further, the top 1000 highest scorers who are eligible to represent the UK at the International Mathematical Olympiad, together with any discretionary and international candidates, are invited to compete in the British Mathematical Olympiad and the next around 6000 highest scorers are invited to sit the Senior Kangaroo.
Discretionary candidates are those students who are entered by their mathematics teachers, on payment of a fee, who did not score quite well enough in the SMC, but who might cope well in the next round.
[22] Scotland: S6 or below Northern Ireland: Y14 or below 4 marks each / penalty of 1 if wrong answer chosen All participants start on 25 points Bronze, Silver, Gold.
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' problem-solving skills.
Approximately 100 highest scoring candidates from BMO1 are invited to sit the BMO2, which is the follow-up round that has the same time limit as BMO1, but in which 4 harder questions are posed.
The top 24 scoring students from the second round are subsequently invited to a training camp at Trinity College, Cambridge or Oundle School for the first stage of the International Mathematical Olympiad UK team selection.
[27] The Senior Kangaroo is a one-hour examination to which the next around 6000 highest scorers below the Olympiad threshold are invited.
One team from each participating school, comprising four pupils selected from year 8 and 9 (ages 12–14), competes in a regional round.
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.
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.