Whole Past Papers · Competitions

Every free past paper from the UK Mathematics Trust’s Challenges, Kangaroos, Olympiads and Team Challenges, with solutions and video solutions where UKMT provides them. All papers open on UKMT’s own website. Papers © UKMT.

New to UKMT? Start with the Challenge for your year group (Junior, Intermediate or Senior). The Kangaroos and Olympiads are follow-on rounds for the highest scorers, so they are harder. Older papers (Junior before 2004, Senior before 2005) are only sold in the UKMT shop. For more competitions and puzzles, see Enrichment: Competitions & Challenges.

Jump to a competition

UKMT

Junior (Years 7–8)

Junior Mathematical Challenge23 papers · 2004–2026
Junior Kangaroo11 papers · 2015–2026
Junior Mathematical Olympiad11 papers · 2015–2026

Follow-on round for top JMC scorers.

Primary Kangaroo2 papers · 2025–2026

For Years 5–6.

UKMT

Intermediate (Years 9–11)

Intermediate Mathematical Challenge23 papers · 2004–2026
Grey Kangaroo12 papers · 2015–2026

Years 9–10 follow-on round.

Pink Kangaroo12 papers · 2015–2026

Year 11 follow-on round.

Cayley Olympiad12 papers · 2015–2026

Year 9 follow-on round.

Hamilton Olympiad12 papers · 2015–2026

Year 10 follow-on round.

Maclaurin Olympiad12 papers · 2015–2026

Year 11 follow-on round.

UKMT

Senior (Years 12–13)

Senior Mathematical Challenge22 papers · 2005–2026
Senior Kangaroo11 papers · 2015–2025

Follow-on round from the SMC.

British Mathematical Olympiad Round 18 papers · 2018–2025

Follow-on round from the SMC.

British Mathematical Olympiad Round 29 papers · 2018–2026

Invitation round after BMO1.

UKMT

Girls’ competitions

Mathematical Competition for Girls5 papers · 2025–2026

For girls in Years 7–9.

Mathematical Olympiad for Girls16 papers · 2011–2026

For girls in Years 10–13.

UKMT

Team challenges

Team Maths Challenge (Years 8–9)6 sets · 2016–2025
Senior Team Maths Challenge (Years 12–13)6 sets · 2014–2019

Practice answer sheets

Print one to practise filling in answers the way you will on the day.

Junior & Intermediate Challenges and Kangaroos · Senior Mathematical Challenge · Senior Kangaroo · Olympiads (written answers) · Primary Kangaroo