CEMC Pascal, Cayley and Fermat Preparation: Waterloo Senior Contests

The middle of the Waterloo series

Pascal, Cayley and Fermat are the senior multiple-choice contests run by the Centre for Education in Mathematics and Computing at the University of Waterloo, written by students at successive grade levels. They sit between the junior Gauss contest and Euclid, which comes in the final school years.

These contests do not themselves qualify a student for a further round; they are written in school and feed CEMC recognition and school awards. Their value is preparation, and it is real. Euclid carries weight in Waterloo admission and scholarship consideration, and a student who first meets the Waterloo problem style at Euclid is learning the format at the moment it counts. A student who wrote Pascal in Class 9 simply sits another paper in a series they already understand.

Cleanly worded, which catches students out

CEMC problems have a recognisable character: carefully written, never deliberately confusing, and dependent on reading precisely what was said. Twenty-five of them in sixty minutes leaves well under two and a half minutes each, so that precision has to be fast.

This sounds easy and is where prepared students lose marks. A student used to skimming a question for its numbers will misread a Waterloo problem, because the condition that makes it interesting is usually stated plainly and in passing. We spend time on reading the problem properly, which is not a skill most students have been asked to practise.

Not entirely multiple choice any more

Most guides still describe these contests as 25 multiple-choice questions. That is now wrong in an important detail, and a student who prepares on that basis gets an unpleasant surprise in the last ten minutes.

Parts A and B are multiple choice with options A to E. Part C, the final five questions, asks for a whole number from 0 to 99 entered directly, written with a leading zero for single digits. There are no options there to estimate between or to substitute back, which removes every technique that makes the earlier questions quick. Part C also carries the heaviest marks, so these are the questions least able to afford a careless slip.

The scoring rewards knowing when to stop

Questions 1 to 10 carry 5 marks, 11 to 20 carry 6, and 21 to 25 carry 8, for 150 in total. A wrong answer costs nothing. But each question left unanswered is worth 2 marks, up to ten of them.

That rule is unusual and most students never think it through. A blind guess among five options is worth about one mark on average, while leaving the question blank is worth two. So on a question a student genuinely cannot start, blank beats guessing. Once they can eliminate even two options, guessing becomes the better bet. Working this out under time pressure is hard; knowing it in advance is easy, and it is worth several marks between students of equal ability.

Multiple choice is a tool, not a safety net

Within Parts A and B, the options are information rather than a fallback.

Several problems are faster to solve by substituting the options back into the question than by solving forwards. Others collapse once two options are eliminated by a rough estimate. Students who treat the option list as a last resort leave time on the table, and that time is exactly what Part C demands.

Sitting the right contest

Pascal is written by Grade 9 students, Cayley by Grade 10 and Fermat by Grade 11, though a younger student may write a higher contest if ready. Preparation pitched at the wrong level is wasted either way, so we confirm the correct contest against the current official specification before beginning.

Why sit a contest that is not an examination

These contests carry no school weight, which leads some families to treat them as optional enrichment. That undervalues them in two respects.

The first is practical. Euclid, later in the same series, is considered in University of Waterloo admission and scholarship decisions, and the students who do well there are generally the ones for whom the format holds no surprises. The second matters more. School mathematics is largely a test of whether a taught method has been learned. These contests ask what a student does when no method has been supplied, which is a different question and a better predictor of how far a student will go in the subject.

How the classes run

Sessions are live and online, one-on-one or in small groups of two to six. Students work problems during the session rather than watching worked examples, and the closing weeks are timed past papers at the student contest level.

Who this suits

Students comfortable with Class 9 algebra and geometry. No prior contest experience is required, and the series is a sensible route for any student who may later want Euclid to count in a Waterloo application.

Registration is normally arranged through a school, and arrangements for international candidates vary. Check cemc.uwaterloo.ca for the current cycle rather than relying on dates reproduced elsewhere.