Junior Maths Olympiad-Style Paper: 6 Problems with Full Written Solutions

A full Junior Mathematical Olympiad-style mock: 6 original problems, 2 hours, 10 marks each (60 in total), written in the style, format and difficulty of the UKMT Junior Olympiad, the follow-on round for top scorers in the Junior Maths Challenge (Year 8 and below).

Every problem comes with a complete model write-up that shows a student exactly how an olympiad answer should be presented: letters defined, every step justified, one idea per line, with right-margin notes and mark allocations showing where the marks are won. Each solution closes with a ‘What a marker wants to see’ box covering the common ways strong students drop marks, such as testing an example instead of proving, missing a case, or reading a fact off a diagram that is not to scale.

Inside: algebraic proof with consecutive integers and last-digit arguments; a coins problem solved with simultaneous equations and inequalities; a football-table logic proof; probability without replacement with a full tree diagram leading to a quadratic; rectangle area geometry with a TikZ diagram; and a powers-of-two problem proving how many digits 2^100 has and finding its last two digits, all without a calculator.

Also includes an instructions page, a key-facts box and an answers-at-a-glance grid. Ideal for able Year 7 and 8 students preparing for the JMC follow-on rounds, maths clubs and enrichment sessions.

Original UKMT-style practice material written by Locus Tutors. Not official UKMT material and not affiliated with or endorsed by the UK Mathematics Trust.