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 Senior Mathematical Challenge (SMC) is for students in grade 12 and below. It focuses on the development of students' ability to fully mobilize logical thinking and use mathematical skills to solve problems accurately and fluently, with challenging and flexible questions that usually cover key high school mathematics knowledge such as geometry, number theory, permutation and combination, and a few algebraic and problem solving, as well as some other more challenging questions (not involving advanced mathematics), which greatly expands the mathematical horizons of the students. SMC is the assessment challenge before BMO.