How to Prepare for the Euclid Math Contest: A Grade 12 Guide

Each April, about 24,000 students (mostly in Grade 12) in Canada and abroad write the Euclid Mathematics Contest, which the Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo organizes. For applicants to Waterloo's mathematics and computer science programs, a strong Euclid result can matter for entrance scholarships. At top private schools with serious math traditions, it is also a matter of pride and a way to stand out.

This guide is for Grade 11 and 12 students and their parents. It explains what the Euclid demands, how to prepare well, and what a competitive score looks like.

What is the Euclid Math Contest?

The Euclid is a 2.5-hour written exam with 10 questions worth 10 marks each, for 100 points in total. Unlike multiple-choice contests such as the AMC, the full-solution parts of each Euclid question need a complete written solution with every step shown. Partial credit is given, so clear mathematical writing counts throughout.

Each question has several parts, and the parts are either short answer (3 marks each) or full solution (the remaining marks). The early parts of a question are more approachable and test core ideas directly, while the later parts are much harder and reward deeper insight. Many students do well on the early parts and struggle with the later ones, which means steady accuracy on the early parts plus occasional success on the later parts can already add up to a competitive mark.

The contest draws on the full Ontario senior math curriculum and goes beyond it, including:

• Algebra and functions, including logarithms and exponential functions
• Trigonometry, including identities and non-right triangle applications
• Sequences and series, including geometric and arithmetic patterns
• Analytic geometry and coordinate geometry
• Combinatorics and counting principles
• Number theory, including divisibility, primes and modular arithmetic
• Proof-based reasoning and mathematical argumentation

Which Euclid score makes an application stand out?

A Certificate of Distinction goes to every writer in the top 25%. The cutoff changes with the difficulty of the paper, and in 2026 it was 66 out of 100. The 2026 average score was 52.2 out of 100. A mark well above the cutoff is truly exceptional.

Score Range	Standing in 2026	Significance for Applications
66 to 100	Certificate of Distinction (top 25%)	A strong credential for Waterloo and other programs that value math achievement
53 to 65	Above the 2026 average of 52.2	A modest contribution to an application; still demonstrates participation
Below 52	At or below the 2026 average	Participation is still valuable experience

Experienced math educators and contest coaches say that a student aiming for a distinction-level result generally needs strong MHF4U (Grade 12 Advanced Functions) skills, a solid base from earlier contests such as the AMC 10, AMC 12 or CEMC's Cayley and Fermat, and the ability to write clear, complete solutions.

How do you begin preparing for the Euclid?

The best approach is to build a firm foundation first and then move to deliberate contest practice. For a student aiming at a distinction-level score, 3 to 6 months of steady work is a realistic timeline.

Months 1 to 2: close content gaps and review the core topics. The Euclid checks how deeply you understand Grade 11 and 12 math. Find your weak spots by trying 2-3 past part (a) questions in each topic area. Frequent trouble spots are logarithm rules, trigonometric identities, geometric sequences and combinatorics. Use your school textbook and CEMC's free online resources to firm these up before turning mostly to contest problems.

Months 2 to 4: targeted problem practice. Work through the past 10 years of Euclid contests. CEMC publishes every past contest with full solutions, free, at cemc.uwaterloo.ca. For each problem you cannot solve alone, make sure you understand how the solution works. With part (b) problems, aim to grasp the key insight or technique instead of memorizing the solution.

The final 4 to 6 weeks: full timed practice in exam conditions. Do at least 3 to 5 complete past Euclid papers the way the real thing runs: 2.5 hours, with only the calculator you would be permitted on the day, and pen or pencil and paper. Then go over the results carefully and look for patterns in your mistakes. Are marks slipping away through arithmetic slips, unclear reasoning or real gaps in understanding? Each kind of error needs a different fix.

Which topics matter most on the Euclid?

Looking at past Euclid papers, some topics turn up in most years and repay preparation time best:

1. Sequences and series: Arithmetic and geometric sequences appear on nearly every Euclid. Know the standard formulas and be comfortable deriving sums. Questions often combine sequences with algebra or number theory.
2. Trigonometry: Expect at least one problem on trigonometric identities, the sine and cosine rules, or the area of a triangle. The Euclid often sets trigonometry in unfamiliar situations that call for mixing identities with algebraic manipulation.
3. Counting and combinatorics: Questions range from simple combinations to clever counting arguments. Practise casework, complementary counting and arrangements with restrictions.
4. Analytic geometry: Circles, lines, parabolas and where they intersect come up regularly. Be at ease with the general equation of a circle and with finding tangent lines.
5. Number theory: Divisibility arguments, prime factorization, modular arithmetic and digit problems keep appearing in part (b) questions. They usually need ingenuity more than a particular formula.

How is Euclid preparation different from AMC preparation?

Students who have prepared for the AMC 10 or AMC 12 start the Euclid with a real advantage, but the two contests differ in important ways. The AMC is multiple choice, with 25 problems that reward quick pattern recognition. The Euclid is a written-solution contest of 10 problems, and it rewards communication, methodical thinking and the ability to build a clear argument.

A student moving from AMC preparation to the Euclid should deliberately practise writing solutions, not just reaching the right answer. The Euclid gives partial credit for sound reasoning that is incomplete. A student who lays out a clear approach but makes a small arithmetic error might earn 7 or 8 out of 10, while one who writes a correct answer with no justification might get 2 or 3.

How can a tutor help with Euclid preparation?

A math tutor who specializes in contests can speed up Euclid preparation a great deal. One-on-one, a tutor can pinpoint gaps in core curriculum knowledge, teach contest techniques for areas like combinatorics and number theory that schools often cover only lightly, and give feedback on how clear and well organized written solutions are.

The students who gain most usually begin with a contest specialist in September or October of Grade 12, which leaves 5 to 6 months of steady preparation before the April contest. Private school students often carry heavy course loads on top of the Euclid, and a tutor can help build a focused, efficient schedule that fits around their other commitments.

If you want expert help preparing for the Euclid or other CEMC contests, see our tutoring subjects or book a free consultation with Bosen Academics to be matched with a contest math specialist.