UKMT encourages mathematical reasoning, precision of thought, and influency in using basic mathematical techniques to solve interesting problems. Among many mathematical challenges organized by UKMT, their biggest competitions are the Junior, Intermediate and Senior Mathematical Challenge(JMC/IMC/SMC), which have over 700,000 entries from 6,000 schools each year, and are the UK's most popular school Mathematical Challenges.

The Junior Mathematical Challenge (JMC) is based on the knowledge learned in the classroom, allowing students to apply their mathematical knowledge to solve problems in a novel way. Most questions are easy for primary and secondary school students, but there are still some challenging questions designed to develop students' critical thinking and mathematical reasoning skills, to stimulate their enthusiasm for learning mathematics and to enjoy solving puzzles. Students who achieve excellent results in JMC will be invited to participate in JMO.

The Junior Mathematical Olympiad (JMO) is an advanced challenge to JMC, which invites high achievers in the JMC to participate, encouraging students to improve their mathematical reasoning skills, refine their logical thinking and acquire higher mathematical skills. The top performers in JMC have the opportunity to compete in JMO.