CEMC Fryer, Galois and Hypatia Preparation: Waterloo Written-Solution Contests

Contests where the writing is marked

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

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. For a student arriving from AMC-style contests the second part is a substantial adjustment: there, reaching 17 is the whole job, while here a correct answer with no justification can earn very little, and a clearly written partial attempt that never reaches the answer can earn a good deal.

Writing a solution that earns full marks

CEMC is explicit about how the written questions are judged: each solution is assessed for completeness, clarity and presentation style, and a correct solution that is poorly presented will not earn a full score. That sentence is worth reading twice, because it means marks are available to be lost by students who have done the mathematics correctly.

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

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

Written work is marked to contest standard from the first week. The feedback is usually uncomfortable at first and is the most valuable part of the course.

Multi-part problems are a single 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 it was meant to be, and sometimes impossible. We teach reading the whole problem before starting, and asking what the earlier part is there to give you — a habit that pays again at RMO and INMO, where problems are built the same way.

Topic coverage, written out

With only four questions in the paper, each one 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.

Why this matters beyond Waterloo

For students on the Indian olympiad pathway, these contests are unusually useful preparation. RMO and INMO are written-proof examinations, and most students arrive at RMO having spent years producing answers and never arguments. The transition catches them at exactly the wrong moment.

The Waterloo full-solution contests give that practice earlier and at lower stakes, which makes the later step considerably less abrupt.

What strict marking feels like at first

It is worth being honest about the first month. A student who is used to being right hands in a solution they believe is complete and gets it back with half of it questioned. Not because the mathematics is wrong, but because steps were assumed, a case was ignored, or the conclusion was never actually stated.

Most students find this deflating for a few weeks, and some parents ask whether the marking is too harsh. It is the marking the contest uses. A student who meets it 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.

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 teaches far more than a score returned days later.

The closing weeks are past papers under timed conditions, marked to contest standard.

Who this suits

Students comfortable with Class 9 algebra and geometry who are willing to be marked on presentation as well as correctness. It suits students who already solve well but have never been asked to write, which describes most capable students at this stage.

Contest levels, dates and registration are set by CEMC and vary; check cemc.uwaterloo.ca for the current cycle.