UKMT Intermediate Mathematical Challenge
The IMC is a school maths competition run by UKMT. The International Mathematics Competition for University Students is a separate event. We help students prepare for the UKMT paper in our weekly Olympiad maths groups and one-to-one lessons.
Your first 30-minute practice session
Use questions 7, 8 and 12 from the 2026 paper. You’ll try divisibility, angles and shaded areas in one sitting.
Open the 2026 IMC paper and solutionsAttempt the questions · 15 minutes
Use blank paper and keep the solutions closed. If you get stuck, write down one thing you know and move on. Put a question mark next to any answer you’re unsure about.
Find the sticking point · 10 minutes
Read the worked solutions for anything you missed or guessed. For each one, write down the step you didn’t see, such as which angle to label or which length you need before you can find an area.
Choose what to practise next · 5 minutes
Close the solutions and redo one of those steps from memory. In your next session, try the investigation after that question. If you solved all three confidently, try question 17.
How to improve before the paper
Make two passes through the paper
On the first pass, take the questions where you can see a way in. Mark the ones you want to revisit. On the second pass, pick the question where your working is closest to an answer and check that you’ve answered what it asks.
Practise when to leave a blank
UKMT deducts marks for wrong answers on questions 16-25. When you mark a practice paper, separate answers you could justify from lucky guesses. On a later question, try ruling out options with an estimate or a small example before deciding whether to answer.
Give each mistake a follow-up
If you missed a diagram clue, redraw and label the diagram. If you missed a method, try one more problem that uses it. Once you can explain the fix, use an unseen paper for a full 60-minute rehearsal.
Prepare with Exact Science
In a trial lesson, we work through unfamiliar problems together so we can see how you choose a method and check your reasoning. We then recommend a group or one-to-one lessons at the right level. If you’ve attempted a past paper, bring a question where you got stuck so we can look at your working together.
What comes after this paper?
Depending on their score, school year and eligibility, students may qualify for the Grey or Pink Kangaroo or for the Cayley, Hamilton or Maclaurin Mathematical Olympiad. If you’re aiming for a written Olympiad, start writing out why each step works when you review your IMC answers.
Frequently asked questions
How do I enter the IMC?
Ask your maths teacher whether your school is entering students. If you’re home educated, UKMT says you can ask a school that is a registered UKMT centre to host you at its discretion.
UKMT advice for parentsDo all wrong answers lose marks?
The first 15 questions carry no penalty for a wrong answer. A wrong answer loses one mark on questions 16-20 or two marks on questions 21-25. A blank scores zero.
UKMT scoring and award thresholdsDo I need to have sat the Junior Mathematical Challenge?
You can start with the IMC. It is a first-round UKMT challenge, and entry is arranged through a registered centre.
UKMT competition structureFind the right level for your preparation
Try a lesson and get a recommendation on what to work on first.