Competitions · Mathematics · Euclid
The Euclid Mathematics Contest.
Ten questions and two and a half hours, set by the Faculty of Mathematics at the University of Waterloo. Unlike a multiple-choice paper it awards marks for method, so a sound argument that ends in the wrong number still scores - which makes it a test of how a student reasons rather than of what they can recall.
At a glance
What the contest is, and who sits it.
Euclid has run since the 1970s. Over recent years it has drawn more than 20,000 students a year from around 2,000 schools, of whom roughly 8,000 are international candidates - the largest group of them from China.
- Organiser
- The Faculty of Mathematics at the University of Waterloo, through its Centre for Education in Mathematics and Computing
- Who can enter
- High-school students in grade 12 and below. The paper is written with grade 12 in mind, which is worth knowing if you enter earlier
- When
- Once a year, in early April. The 2026 contest was held on 1 April
- Format
- An individual written paper, sat on site with pen and paper. Scripts are posted back to Waterloo after the sitting
- Duration
- 2.5 hours
- Questions
- 10 questions for 100 marks, in two kinds: short-answer questions wanting only the result, and full-solution questions wanting the complete argument
- Marking
- Marks are awarded for method and working. Incomplete working cannot earn full marks, and correct reasoning that reaches a wrong answer still earns credit
- Language
- English throughout, for both reading and answering
- Calculators
- Permitted, and most models qualify. Excluded are any with internet access, storage, a computer algebra system, the ability to communicate with other devices, or dynamic geometry software
- Registration
- Through a registered centre school only. Students cannot register themselves and must sit the paper at a centre
- Entry fee
- A registration fee applies, set out in the official notice at the time of registration
- Results
- Published in late May
Why it carries weight
What makes Euclid different from a multiple-choice contest.
Its standing in Canada is high enough that it is sometimes described there as the TOEFL of mathematics, and the reasons are structural rather than reputational.
Method is marked, not just the answer
Full-solution questions are marked on the argument. A student who sets out a correct approach and slips at the end still scores, and one who writes down a right answer with no working does not score fully. Few contests at this level read the reasoning.
Waterloo asks for it directly
Waterloo’s mathematics and engineering faculties state that they strongly recommend applicants sit Euclid, and a Euclid result is a condition of applying for the Faculty of Mathematics entrance scholarships. That is an unusually explicit link between a contest and an admission.
A short preparation cycle
The syllabus sits close to a solid middle-school and early high-school foundation rather than reaching into olympiad material, so a student with secure fundamentals can prepare for it in a manageable window and can enter more than once across their school career.
Read across North America
Beyond Waterloo, the result is widely recognised by Canadian, British and American universities as evidence of mathematical ability for international applicants, and the top-quarter certificate is frequently cited in science and engineering applications.
Syllabus
What the paper covers.
The questions are not confined to testing whether a topic is known. They are built to extend it, which is why familiar content can still produce an unfamiliar problem.
Equations and algebra
Equations, systems of equations and inequalities, and polynomial functions - including solving cubics, the remainder theorem and the factor theorem. This is the most reliably represented area of the paper and the one worth securing first.
Functions
Elementary functions in general, with exponential and logarithmic functions treated in their own right, and trigonometric functions covered through their graphs, their properties, and the sine and cosine rules.
Sequences and counting
Sequences and the summation of series, alongside permutation and combination problems. These questions tend to sit in the middle of the paper where the difficulty starts to climb.
Geometry and number theory
Plane geometry and analytic geometry, together with elementary number theory. Geometry questions here reward a clear diagram and a willingness to switch between a synthetic and a coordinate approach.
Awards
Two certificates, both decided on percentile.
Because the awards are percentile-based, the mark that earns them moves each year with the difficulty of the paper.
Score cutoffs
Where the two lines have fallen since 2011.
A fifteen-year run is unusually long for a published cutoff series, and it is the most useful thing on this page for setting a target. Note how much steadier the Distinction line has been since 2016 than before it.
| Year | Certificate of Distinction (top 25%) | Honor Roll (top 2.5%) |
|---|---|---|
| 2026 | 66 | 87 |
| 2025 | 68 | 87 |
| 2024 | 69 | 89 |
| 2023 | 65 | 87 |
| 2022 | 68 | 86 |
| 2021 | 69 | Not published |
| 2020 | No contest data, owing to the pandemic | - |
| 2019 | 68 | 80 |
| 2018 | 64 | 78 |
| 2017 | 64 | 79 |
| 2016 | 65 | 80 |
| 2015 | 52 | 72 |
| 2014 | 60 | 79 |
| 2013 | 60 | 79 |
| 2012 | 56 | 78 |
| 2011 | 59 | 80 |
Since 2016 the Distinction line has sat between 64 and 69 and the Honor Roll line between 78 and 89. Aiming at the upper end of the recent range rather than at last year’s figure is the safer way to plan.
Sitting it in China
What candidates in China need to know.
Euclid cannot be sat at home or entered individually, so the practical questions are about centres and registration rather than about the paper.
Centres across nine cities
Hanlin is an authorised Euclid centre, with in-person sittings available in Shanghai, Shenzhen, Beijing, Hangzhou, Chengdu, Changsha, Hefei, Wuhan and Xi’an. Candidates attend a centre in person; there is no remote option.
Registration runs through the centre
Registration is handled by the centre school, not by the student. Anyone planning to enter needs to be attached to a centre before the March deadline, which is roughly two weeks before the paper itself.
No authorised proxy registration
Hanlin has not authorised any centre or individual to offer proxy registration services for this contest. Anyone offering to register a student on Hanlin’s behalf is not acting with its authority, and should be treated accordingly.
Checking your result
Results appear in late May. Candidates can check through the CEMC website using the school registration number and password issued at registration, or by asking the school or centre that registered them.
Preparation
How Hanlin prepares students for Euclid.
The single biggest difference from AMC preparation is that students have to learn to write, not only to solve.
Writing a solution that scores
Full-solution questions are marked on the working, and students arriving from multiple-choice contests routinely lose marks by writing too little. Practice focuses on setting out an argument a marker can follow to the end.
Past papers, read in sequence
Waterloo publishes decades of papers and official solutions. Reading them in order shows both how the questions are phrased and, more usefully, what a full-credit solution is expected to look like.
Pacing ten questions over 2.5 hours
Fifteen minutes a question on average, but the paper is not evenly weighted. Students practise banking the early short-answer questions quickly so the full-solution questions at the end get the time they need.
Working to the cutoff
For most candidates the target is the Distinction line rather than a maximum. Preparation is planned backwards from that mark, which usually means securing complete credit on the first six or seven questions.
Why Hanlin
Hanlin has been entering students for Euclid for years, and publishes what they got. The record is further down this page.
Programme formats
Five ways this is taught.
Group size is the whole difference between these. It decides how much of the tutor's attention a student gets and how far the course can bend to them, so it is worth choosing rather than accepting.
| Format | Group size | What it suits |
|---|---|---|
| One-to-one | One student | Content, pace and emphasis set by what this student actually needs rather than by a syllabus. The only format that can be rebuilt mid-course. |
| Small group | Three to eight | Opens at three. Frequent discussion, and the tutor can slow down or move on according to what the group has absorbed. Most students chasing a higher award are taught in this one. |
| Class | Eight to twelve | Taught by the subject lead or a medal coach. Less back-and-forth, so it suits a student who will say when something is unclear. |
| Large class | Ten to twenty | For students in the middle of the placement range, and a way to try a competition before committing. Students often move to a small group or to one-to-one afterwards. |
| Past-paper class | No cap | Past papers worked through in sequence in the weeks before the sitting. Free to students already enrolled. |
Course length for Euclid is set after a placement paper. The gap between where a student is and what the paper asks for is what the course has to close, and that gap is not the same for two students in the same year group.
How it runs
Six steps, four people on your side.
The same process for every student, so that nothing depends on one tutor remembering to do it.
Step 1Pre-course assessment
A placement paper before anything is booked, so the course tier is chosen on evidence rather than on a year group.
Step 2Tutor matching
A subject tutor is matched to the result, and their full background is provided before you agree to it.
Step 3Plan and group
A study group opens with four people on one student: the tutor, a planner, a supervisor and an academic manager.
Step 4Scheduled teaching
The teaching office sets the timetable around the competition date and school term, and teaching begins.
Step 5After-class reports
What was covered, and how the student handled it, reported after every lesson.
Step 6Homework follow-up
The teaching assistant and the form teacher both check that homework is done, which is where most preparation quietly fails.
Free resource pack
Euclid past papers and preparation pack
The same material our own Euclid students work from. Scan the code, say what you need, and an advisor sends it.
Tell an advisor which competition and year group, and the material comes back the same day. Free, and you do not have to enrol in anything. If we do not already hold what you need, we will go and find it.
- PDFPast Euclid papers with full official solutions
- PDFThe Distinction cutoff, year by year
- PDFHow the full-solution questions are marked
- PDFRegistration checklist and the dates for the current cycle
Teaching team
Who would teach it.
Three of the twenty-two tutors on the published Hanlin roster - the ones whose subject this is.
Dr Zhang
PhD in theoretical mathematics from the University of Rochester and a postdoctoral fellow at the Shanghai Center for Mathematical Sciences at Fudan. An AMC-accredited coach, ASDAN-accredited for DMM and ITCCC, and an accredited UKMT BMO2 and PUMaC coach. His students have gone on to read mathematics and physics at Harvard, MIT, Princeton, Caltech and Cambridge.
Dr Zhuang
PhD in mathematics from the University of Denver, working in mathematical logic, after a first degree in applied mathematics at Southeast University. A repeat conference speaker on his research, with three years lecturing and assisting on undergraduate mathematics at Denver.
He
A Cambridge master's after a computer science degree with a mathematics minor at the University of Nebraska-Lincoln, and a US high school GPA of 4.13. Six years overseas and teaches entirely in English, across AMC, Math League, AP Computer Science and AP Calculus.
Student results
What Hanlin students got.
Taken from Hanlin's published record of student honours and rewritten in English. Figures are as the organisers reported them.
Distinctions in 2025
One line from Hanlin's published Euclid record. The rest of it is below.
Euclid
- 2025233 students earned Distinction, 8 scored above 90 and 97 scored above 80
- 2024177 Distinctions, 17 above 90 - the highest a 99 - and 75 above 80
- 2023165 Distinctions, a 70% award rate, with 8 above 90 and 63 above 80
Earlier years
- 202296 Distinctions, a 75% award rate, and 7 students scoring 90 to 93
- 202133 Distinctions, a 50% award rate, with 4 above 90
The full record, across every subject and year, is on the student honours page.
Where it is taught
Hanlin learning centres.
Teaching runs from Hanlin's own centres in Shanghai, Shenzhen, Chengdu and Hangzhou, and online for students elsewhere.
Talk to an advisor
Everything Hanlin does for Euclid, in one conversation.
Entry, planning, coaching and the past papers. An advisor will tell you which of these a student actually needs, including when the answer is none of them.
Competition entry and planning
Which competitions suit this student, in what order, and by when - then we handle the registration, including the ones that can only be entered through a school or a centre.
Competition coaching
Taught by full-time subject tutors, on a course tier chosen by placement paper rather than by year group.
International curriculum tutoring
IB, AP, A-Level, IGCSE and the US high school curriculum, taught alongside school and timed around the exam calendar.
Competition past papers, free
A large library of past papers, mark schemes and syllabus breakdowns across every competition on this site. No charge and no enrolment.
Scan to add an advisor
Say which competition or course you are asking about. Replies in Chinese or English.
Or call +86 21 6352 6630FAQ
Euclid, briefly answered.
What students and families ask before registering.
Who can sit the Euclid contest?
High-school students in grade 12 and below, from any country. The paper is written with grade 12 students in mind, so entering earlier is allowed and common but means meeting a paper pitched above your year.
Do I get marks for working if my answer is wrong?
Yes, on the full-solution questions. Marks are awarded for method and steps, so a correct approach that ends in an arithmetic slip still scores. The reverse is also true: incomplete working cannot earn full marks even with the right answer.
Can I register for Euclid myself?
No. Registration is handled by registered centre schools, and candidates sit the paper at a centre. Note also that Hanlin has not authorised any centre or individual to provide proxy registration services.
Can I use a calculator?
Yes, and most models are acceptable. Calculators are excluded if they have internet access, storage capability, a computer algebra system, the ability to communicate with other devices, or dynamic geometry software.
What score do I need for a certificate?
The Certificate of Distinction goes to the top 25% and the Honor Roll to the top 2.5%, so the mark moves each year. Since 2016 the Distinction line has fallen between 64 and 69 out of 100, and the Honor Roll line between 78 and 89.
How does Euclid help with a Waterloo application?
Waterloo’s mathematics and engineering faculties state that they strongly recommend applicants sit it, and a Euclid result is required in order to apply for Faculty of Mathematics entrance scholarships.
When is the contest and when do results arrive?
The contest is held once a year in early April - 1 April in 2026 - with registration closing in March. Results are published in late May.
Can I sit Euclid more than once?
Yes. Students commonly enter in more than one year while they remain in grade 12 or below, which is part of why its preparation cycle is considered good value for the effort involved.
Related
The rest of the Waterloo family.
CEMC runs a contest for almost every school year, and Euclid is the senior one.
Euclid enquiries
You need a centre before you need a revision plan.
Registration runs through centre schools and closes in March, weeks before the April paper. Tell us the student’s year group and city, and an advisor will confirm the nearest sitting and what the preparation window allows.