By Geoff Smith This text will enable enthusiastic students to deal with confidence with secondary school mathematics competitions at the highest level. The book is a sequel to A Mathematical Olympiad Primer by the same author, but contains harder problems drawn from round 2 of the British Mathematical Olympiad. Like other volumes in The Handbooks series this book provides ready access to directly relevant material. All these books are characterised by the large number of carefully constructed exercises for the reader to attempt.