Euclid Mathematics Contest Preparation: Waterloo Full-Solution Training

A contest where the writing carries the marks

The Euclid Mathematics Contest is run by the Centre for Education in Mathematics and Computing at the University of Waterloo, and it differs from most competitions an international student will have met. Part of the paper asks for full written solutions. The final answer alone is not the submission; the argument is.

For students arriving from AMC-style multiple-choice contests, this is a significant adjustment. They are used to a format where reaching 17 is the entire job. On Euclid, reaching 17 without a justified argument can earn very little, while a well-presented partial attempt that never reaches the answer can earn a good deal.

Why it is worth writing

Beyond the mathematics, Euclid carries practical weight. The University of Waterloo considers contest performance in admission and scholarship decisions for its mathematics and computing programmes, which makes it one of the few competitions with a direct and stated bearing on an admission outcome.

The specific weighting is set by the university and changes between cycles, so we point students to the official Waterloo pages rather than printing a claim here that may not hold next year. What is stable is the general point: for a student considering Waterloo, this contest is not optional enrichment.

The shape of the paper

Euclid builds. The early questions are accessible to any well-prepared senior student, and the later ones are genuinely demanding. Since the later questions are worth the same as the earlier ones but take considerably longer, time allocation becomes a real strategic decision rather than an afterthought.

Students who spread their time evenly across the paper tend to do worse than students who secure the early questions quickly and then commit the remaining time deliberately. We practise this explicitly in the closing weeks, because it is a decision best made before the exam rather than during it.

Writing a solution that earns full marks

Most of what separates a good Euclid score from a mediocre one is not additional mathematics. It is the discipline of writing an argument that a marker can follow and award.

That means stating what is being assumed, justifying the steps that are not self-evident, handling the cases that the problem actually contains rather than the one convenient case, and finishing with a clear conclusion. Students almost never do this naturally, because school examinations rarely require it.

From the first weeks, written work is marked the way the contest marks it. The feedback is usually uncomfortable at first and is the most valuable part of the course.

Syllabus coverage

The contest draws on senior secondary mathematics worked to greater depth rather than on material beyond the school syllabus. Algebraic manipulation underpins everything. Functions, particularly quadratics and their behaviour, appear constantly. Trigonometry, sequences and series, number sense and geometry all feature, with analytic and three-dimensional geometry appearing in the harder later questions.

We work from past papers throughout rather than saving them for the end. The Waterloo style is consistent enough across years that familiarity with it is itself worth marks.

How the classes run

Sessions are live and online, one-on-one or in small groups of two to six. Students write solutions during the session and have them critiqued immediately, which is far more useful than submitting work and receiving a score days later.

The closing weeks are full past papers under timed conditions, marked to contest standard, so the student knows what their written work is actually worth before it counts.

Who this suits

Students in their final two school years who are comfortable with senior algebra, functions and trigonometry. Prior contest experience helps but is not required. What matters is a willingness to be marked strictly on presentation, which is the part most students resist and most need.

Registration is usually arranged through a school and the details vary by country and year. Check cemc.uwaterloo.ca for the current cycle rather than relying on dates reproduced elsewhere.