CEMC Fryer Preparation: Galois and Hypatia Guide

CEMC Fryer preparation is unusual among competition programmes because a large share of the work is not mathematical. It is learning to write an argument that a marker can follow and award.

What these contests are

Fryer, Galois and Hypatia are the written-solution contests in the University of Waterloo CEMC series. Fryer is for Grade 9, Galois for Grade 10 and Hypatia for Grade 11.

Each is 4 questions in 75 minutes, scored out of 40, and CEMC describes them as a mix of final-answer and full-solution questions rather than a pure proof paper. They are not invitational: schools order and supervise them, normally in April.

That mix is the point. Part of the paper behaves like the contests a student already knows, and part of it asks for an argument.

Presentation is marked, and CEMC says so

This is the sentence that should shape all CEMC Fryer preparation: each solution is assessed for completeness, clarity and presentation style, and a correct solution that is poorly presented will not earn a full score.

Read that twice. Marks are available to be lost by students who have done the mathematics correctly. That is an uncomfortable fact and an entirely fixable one.

For a student arriving from AMC-style contests the adjustment is substantial. There, reaching the right number is the whole job and the working is private. Here the working is the submission.

What a full-mark solution contains

Not additional mathematics, in most cases. The discipline is procedural.

State what is assumed. Justify the steps that are not self-evident. Handle the cases the problem actually contains rather than the convenient one. Finish by reaching the conclusion explicitly rather than leaving it implied.

Students almost never write this way naturally, because school examinations rarely require it. Marked to contest standard from the first week, most students find the feedback deflating for a month and then find themselves pre-empting the objections unprompted.

Multi-part problems are one problem

These contests set problems in parts, and the parts are related by design. Part (a) typically establishes a fact, a small case or a technique that part (c) depends on.

Students who treat the parts as three separate questions make the last one far harder than intended, and sometimes impossible. Reading the whole problem before starting, and asking what the earlier part is there to give you, is a trained habit that pays again at RMO and INMO where problems are built the same way.

Four questions in seventy-five minutes

That is nearly nineteen minutes per problem, which changes the pacing entirely from a 25-question sprint.

There is time to think, so abandoning a problem at two minutes is the characteristic error of a student trained on short papers. There is also a cost students forget: a problem solved in eight minutes may need another six to write properly. A student who allocates only solving time finishes with arguments correct in their head and incomplete on the page.

We practise the split explicitly — solve, then write, with the writing timed as its own task.

Topic coverage, written out

With only four questions, each covers ground. The mathematics is the senior school syllabus worked to competition depth: algebra in extended form, geometry with written proof, number theory and combinatorics with full justification.

What differs from a multiple-choice course is that every topic is practised in writing. A student may reason correctly about an angle chase in their head and still lose marks for a submission that assumes what it should prove. That gap closes only by writing, which is why our geometry course treats written proof as part of the subject rather than an extra.

Why this matters beyond Waterloo

For students on the Indian olympiad pathway, these contests are unusually useful preparation.

RMO is six problems in three hours with detailed proof required, and INMO is six in four and a half hours. Most students arrive at RMO having spent years producing answers and never arguments, and the transition catches them at exactly the wrong moment, with a place at stake.

Fryer, Galois and Hypatia give that practice earlier, at a fraction of the stakes, and in a format where the feedback is specific. The COMC serves a similar purpose with its Part C.

What the first month of marking feels like

It is worth preparing a family for this, because the early feedback is harsher than students expect.

A student hands in a solution they consider complete and gets it back with half of it questioned. Not because the mathematics is wrong, but because a step was assumed, a case was ignored, or the conclusion was never actually stated. Students who are used to being right find this genuinely deflating.

Parents sometimes ask whether the marking is too strict. It is the marking the contest uses, stated plainly by CEMC. A student who meets that standard for the first time on contest day loses those marks when they count, rather than in a session where someone can explain what was missing.

By about the sixth week the same students start pre-empting the objections themselves, and the writing stops being an afterthought. That shift is the whole return on the exercise.

Who should write these

Students comfortable with the mathematics of their year who are willing to be marked on presentation as well as correctness. That describes most capable students, and the ones who resist it hardest usually need it most.

Contest levels, dates and registration are set by CEMC and vary by country. Check cemc.uwaterloo.ca for the current cycle before planning around it.