UKMT Intermediate Challenge Full Mock — Paper 15
UKMT Intermediate Mathematical Challenge practice paper 15: 30 questions in 60 minutes, marked 5 / 6 with penalties on the harder half, exactly like the real
About this test
UKMT Intermediate Challenge Full Mock — Paper 15 is a full 30-question paper you attempt online in 60 minutes. It follows the American Mathematics Competition 10 pattern, so the timing, the question style and the marking match the real exam. Marks are banded: Q1-18 score 5 with no penalty; Q19-24 score 6 and lose 1 if wrong; and Q25-30 score 6 and lose 2 if wrong. Guessing carries a real cost, exactly as it does on the day.
You get your score the moment you submit, question by question, with a step-by-step solution to every problem. 25 questions in 75 minutes. A high score qualifies for the AIME.
What it covers
Sections
- Linear equations — 2 questions
- Indices — 2 questions
- Ratio — 2 questions
- Pythagoras — 2 questions
- Probability — 2 questions
- Polygons — 2 questions
- Percentage change — 2 questions
- Simultaneous equations — 2 questions
- Combinations — 2 questions
- Multiples — 2 questions
- Trapezia — 2 questions
- Units digits — 2 questions
- Inclusion-exclusion — 2 questions
- Triangle area — 2 questions
- Counting solutions — 2 questions
Difficulty spread
- 14 medium questions
- 13 hard questions
A look at the questions
Questions people ask
How is this paper marked?
Marked 5 / 6 with penalties on the harder half, exactly like the real IMC. A blank always scores zero.
How long should it take?
60 minutes, matching the real challenge. The questions get harder towards the end, so do not expect to finish — deciding which to attempt is part of the skill.
Are solutions included?
Yes, every question has a worked solution that names the method, so a wrong answer tells you what to revise.