Mathematics
Primary Mathematics Challenge (UKPMC)
(UKPMC)
The Primary Mathematics Challenge (PMC) is organised by The Mathematical Association in the United Kingdom. It is designed for primary school pupils aged 9–11 and encourages mathematical reasoning, problem-solving and creative thinking through an accessible but progressively challenging paper.
CURRENT OPPORTUNITIES
UKPMC 2026
Format
Registration Deadline (NZ Time)
Eligible Years
Remote online
15 November 2026 at 11:00:00 am
Year 5–6
Nationwide
Competition Date (NZ Time)
17:00–17:45, Thurs 19 Nov 2026
Location
NZ Nationwide
Competition Gallery
Course Information
Optional preparation courses or resources for this round (if available)
Submission and Confirmation
Please check your email address carefully before submitting the registration form.
Once you submit the form, you will receive a confirmation email automatically.
All other important communications (including the Exam Instructions, Results and Certificates, etc) will be sent to the email address you submitted to us. Please check your email inbox and junk mail / spam folder regularly!
What Happens Next?
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2
3
4
Registration Received
We will send you a confirmation email
We may review your registration if required
Eligibility Review
You will receive the Exam Instructions closer to the date
Exam Instructions
Participate and do your best!
Competition Day
Competition Overview
Primary Mathematics Challenge (UKPMC)
The Primary Mathematics Challenge (PMC) is an international primary-level mathematics competition created by The Mathematical Association in the United Kingdom. It is designed to encourage young students to enjoy mathematics, develop confidence, and experience mathematical questions that go beyond routine classroom exercises.
Rather than functioning as a conventional school test, the Challenge places a strong emphasis on problem solving, logical reasoning and mathematical thinking. Students are encouraged to explore unfamiliar problems, recognise patterns, select efficient strategies and apply their existing mathematical knowledge in creative ways.
The PMC is primarily aimed at primary-school students year 5-6 and is open to participating schools worldwide. The questions are deliberately designed so that success does not depend heavily on advanced mathematical knowledge; instead, students are encouraged to think carefully and reason logically.
The Primary Mathematics Challenge provides students with an opportunity to experience mathematics in a different and engaging way.
Participation can help students:
Develop stronger logical reasoning and problem-solving skills.
Learn to approach unfamiliar problems systematically.
Improve confidence when working with challenging mathematical questions.
Strengthen numerical fluency and mathematical intuition.
Practise identifying patterns, relationships and efficient strategies.
Experience mathematics beyond standard classroom exercises.
Develop perseverance and resilience when a solution is not immediately obvious.
Gain experience in a recognised international mathematics challenge.
Potentially qualify for the PMC Bonus Round through a strong performance.
The Challenge can also help students discover that mathematics is not simply about performing calculations—it involves observation, experimentation, reasoning and finding creative approaches to problems.
The PMC is officially aimed at students year 5-6 who are attending primary school. International schools are also welcome to participate.
It is particularly suitable for students who:
Enjoy mathematics and mathematical puzzles.
Show confidence with core primary-school mathematics.
Enjoy solving problems that require several stages of thinking.
Are curious about patterns and relationships.
Like explaining how or why an answer works.
Would benefit from mathematical extension beyond normal classroom exercises.
Are interested in progressing towards more advanced mathematics challenges in the future.
Students do not need to be experienced mathematics competitors. The Challenge begins with relatively accessible questions before gradually increasing in difficulty, allowing students with different levels of experience to engage with the paper.
Preparation for the PMC should focus primarily on developing mathematical thinking rather than memorising advanced formulas.
1. Complete Past Papers
Official PMC past papers are one of the most effective preparation resources.
Students should become familiar with:
The style of questions.
The progression in difficulty.
The 45-minute time limit.
Different problem-solving approaches.
Official past papers and accompanying answer materials are available through the PMC website.
2. Review Solutions Carefully
Preparation should not stop after checking whether an answer is correct.
Students should ask:
Why does this method work?
Is there a faster way to solve the problem?
What information in the question was most important?
Could the problem be solved using a diagram or table?
What mistake would someone commonly make?
Understanding the reasoning behind a solution is more valuable than simply memorising an answer.
3. Strengthen Core Number Skills
Good numerical fluency allows students to spend more time reasoning and less time performing basic calculations.
Useful areas to review include:
Mental arithmetic
Multiplication and division
Fractions
Factors and multiples
Measurement
Simple geometry
Number patterns
4. Practise Problem-Solving Strategies
Students should become comfortable using strategies such as:
Drawing a diagram.
Making an organised list or table.
Looking for a pattern.
Working backwards.
Eliminating impossible answers.
Trying a simpler example first.
Breaking a problem into smaller steps.
Checking whether an answer is reasonable.
5. Develop Time Management
With 25 questions in 45 minutes, students should avoid spending too long on one difficult problem.
A useful approach is to:
Complete accessible questions efficiently.
Mark difficult problems and return to them later.
Reserve time for the final five questions.
Check answers when time permits.
6. Focus on Reasoning, Not Advanced Content
Students do not need to rush into secondary-school mathematics to prepare successfully.
The official philosophy of the PMC is that questions should not depend heavily on formal advanced knowledge. Developing logical reasoning, flexibility and confidence with familiar mathematics is therefore the most effective preparation strategy.
7. Discuss Problems
PMC problems are particularly useful for discussion.
Students can compare different solution methods and explain their reasoning to teachers, parents or classmates. The organisers themselves recommend using PMC questions as a starting point for mathematical discussion and investigation beyond the competition itself.
The Primary Mathematics Challenge consists of 25 questions to be completed in 45 minutes.
The paper is structured progressively:
Questions 1–20: Multiple-choice questions.
Questions 21–25: Questions requiring students to provide their own answers rather than selecting from given options.
Questions generally progress from more accessible problems to increasingly challenging ones.
The first part of the paper is intended to help students build confidence before tackling more demanding problems.
The official Challenge can be administered by participating schools through online access, a downloadable PDF paper, or official printed paper packs, depending on the entry method selected by the school.
Students may receive:
Gold Certificate
Silver Certificate
Bronze Certificate
Participation / Took the Challenge Certificate
For the main November PMC, Gold, Silver and Bronze awards are determined within each participating school rather than through fixed national score boundaries.
The organisers provide Gold, Silver and Bronze certificates and encourage teachers to recognise students according to the performance and ability profile within their own school. This approach allows schools with students of different mathematical levels to recognise achievement appropriately.
A strong performance in the November Primary Mathematics Challenge may lead to progression to the PMC Bonus Round.
Stage 1 — Primary Mathematics Challenge
Students complete the 25-question, 45-minute November Challenge.
Stage 2 — Results Submission
Participating schools submit their students' scores to the organisers.
Stage 3 — Bonus Round Qualification
Once national results have been reviewed, the organisers establish a qualification boundary for the Bonus Round.
The qualification score is normally communicated to schools in December.
Stage 4 — PMC Bonus Round
Students who meet the required score are invited to participate in the PMC Bonus Round, which is free for qualifying students.
The next Bonus Round following the 2026 November Challenge is scheduled for February 2027.
The Bonus Round follows a similar structure to the main Challenge:
25 questions
45 minutes
Progressively challenging mathematical problems
Available through approved online or PDF formats
The Bonus Round is intended to provide high-performing students with an additional opportunity to extend their mathematical thinking and problem-solving skills.
Preparation for the PMC should focus primarily on developing mathematical thinking rather than memorising advanced formulas.
1. Complete Past Papers
Official PMC past papers are one of the most effective preparation resources.
Students should become familiar with:
The style of questions.
The progression in difficulty.
The 45-minute time limit.
Different problem-solving approaches.
Official past papers and accompanying answer materials are available through the PMC website.
2. Review Solutions Carefully
Preparation should not stop after checking whether an answer is correct.
Students should ask:
Why does this method work?
Is there a faster way to solve the problem?
What information in the question was most important?
Could the problem be solved using a diagram or table?
What mistake would someone commonly make?
Understanding the reasoning behind a solution is more valuable than simply memorising an answer.
3. Strengthen Core Number Skills
Good numerical fluency allows students to spend more time reasoning and less time performing basic calculations.
Useful areas to review include:
Mental arithmetic
Multiplication and division
Fractions
Factors and multiples
Measurement
Simple geometry
Number patterns
4. Practise Problem-Solving Strategies
Students should become comfortable using strategies such as:
Drawing a diagram.
Making an organised list or table.
Looking for a pattern.
Working backwards.
Eliminating impossible answers.
Trying a simpler example first.
Breaking a problem into smaller steps.
Checking whether an answer is reasonable.
5. Develop Time Management
With 25 questions in 45 minutes, students should avoid spending too long on one difficult problem.
A useful approach is to:
Complete accessible questions efficiently.
Mark difficult problems and return to them later.
Reserve time for the final five questions.
Check answers when time permits.
6. Focus on Reasoning, Not Advanced Content
Students do not need to rush into secondary-school mathematics to prepare successfully.
The official philosophy of the PMC is that questions should not depend heavily on formal advanced knowledge. Developing logical reasoning, flexibility and confidence with familiar mathematics is therefore the most effective preparation strategy.
7. Discuss Problems
PMC problems are particularly useful for discussion.
Students can compare different solution methods and explain their reasoning to teachers, parents or classmates. The organisers themselves recommend using PMC questions as a starting point for mathematical discussion and investigation beyond the competition itself.
Resources & Downloads
Access all available competition information, preparation materials, past papers and official documents.