Olympiad preparation
Original mock papers, full written solutions to official competitions, and geometry you can move. Everything on this page is free.
Original mock papers
Sit them cold under the stated time limit, then read the solutions.
Kevin's Mathematical Olympiad, Round 1
An original mock in the style of BMO Round 1, across geometry, number theory, algebra and combinatorics. Each question is worth 10 marks.
Mock Senior Mathematical Challenge
An original mock in the style of the UKMT Senior Mathematical Challenge, marked out of 150. The questions get much harder towards the end.
Solutions to official competitions
Original write-ups of real competition papers. Find the official problems, try them first, then compare.
UKMT Senior Mathematical Challenge 2026
Full solutions to all 25 problems, with every diagram redrawn in tkz-euclide.
Purple Comet! Math Meet 2026, High School
The thirty official High School problems, with solutions and remarks.
British Mathematical Olympiad Round 2, 2011
Solutions and insights for the four problems of BMO2 2011.
IMO Shortlist 2025, G1 to G3
Original, rigorous solutions to the first three geometry problems of the 2025 IMO Shortlist.
The HU Collection
Short, elite-level problem sets on topics the standard curriculum skips. They train the habits olympiads reward, and they also suit MAT, TMUA and interview preparation.
Part 1: Pure Elegance and Structural Logic
Recognising invariants, exploiting symmetry and building creative arguments.
Part 2: Combinatorial Processes and Invariants
Combinatorial processes, algorithmic operations and state changes.
Geometry tools and proof marking
Geometry Lab
One triangle with its five centres, three circles and the Euler line. Drag a vertex and watch OI stay equal to √(R²−2Rr), whatever shape you force the triangle into.
Conjecture sandbox
Build a figure from twenty-seven constructions and drag it. The page reports what stays true under perturbation, then exports tkz-euclide code.
Proof marker
Paste a written solution and have it marked against a BMO, STEP, MAT or interview scheme by Claude, ChatGPT or Gemini. The arithmetic is checked exactly.
Going further in geometry? Beyond the Incenter is a full monograph on olympiad geometry, from the triangle's centres to projective geometry and spiral similarity. Read the sample chapter on cross ratios.