CEMC Pascal Preparation: Cayley and Fermat Guide

CEMC Pascal preparation begins with correcting something most guides still get wrong: these contests are no longer purely multiple choice, and a student who prepares on that assumption gets an unpleasant surprise in the final ten minutes.

Where these contests sit

Good CEMC Pascal preparation starts with knowing where the contest sits. Pascal, Cayley and Fermat are the senior contests in the Centre for Education in Mathematics and Computing series at the University of Waterloo. Pascal is written by Grade 9 students, Cayley by Grade 10 and Fermat by Grade 11, though a younger student who is ready may write a higher one.

Below them sits the Gauss contest for junior students. Above them sits Euclid, which is considered in University of Waterloo admission and scholarship decisions.

These three do not themselves qualify a student for a further round. Their value is preparation: a student who first meets the Waterloo problem style at Euclid is learning the format at the moment it counts towards an application.

Not entirely multiple choice any more

Each contest is 25 questions in 60 minutes, scored out of 150, arranged in three parts.

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.

That removes every technique that makes the earlier questions quick. There are no options to estimate between, nothing to substitute back into the problem, no elimination. 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. A wrong answer costs nothing. But each question left unanswered is worth 2 marks, up to ten of them.

Work through what that means. A blind guess among five options is right one time in five, so it is worth about one mark on average. A blank is worth two. On a question a student genuinely cannot start, leaving it alone beats guessing.

Once they can eliminate even two options, guessing becomes the better bet again. Working this out under time pressure is hard; knowing it in advance is easy, and it separates students of identical ability.

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.

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 rather than flagged.

Twenty-five questions in sixty minutes leaves under two and a half minutes each, so that precision has to be fast. We practise stating what is given and what is asked before starting — a habit that feels slow for a fortnight and then saves time permanently.

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.

What to cover

Algebra to contest standard: expressions, equations, systems, sequences, and the manipulation the early questions assume. Our algebra course covers this depth.

Geometry: angles, triangles, circles, similar figures, coordinate geometry, and reading a figure accurately.

Number sense and number theory: divisibility, remainders, digit problems and the patterns that recur across the series.

Counting, probability and logic: systematic counting and the reasoning problems these contests favour.

Calculators and what is permitted

Calculators are permitted, but without internet access, communication between devices, stored information, computer algebra systems or dynamic geometry software.

Permission is not advantage. The questions are not arithmetic-heavy, so a student reaching for the calculator reflexively loses more time than they save. The useful habit is deciding quickly whether a calculation justifies the keystrokes, and most do not.

How to structure a term of work

A term is enough for a student whose school mathematics is solid, and CEMC Pascal preparation divides naturally into three stretches.

The first covers topic depth untimed, with problems discussed rather than merely marked. The aim is that no technique is unfamiliar, so that later the difficulty is the problem rather than the method.

The second works past papers section by section, still generously timed. This is where a student learns the shape of the paper: that questions 1 to 10 should be quick, 11 to 20 are the real contest, and Part C is effectively a separate event with different rules.

The third is full papers at exact timing with the blank-versus-guess rule applied honestly. A student should know, before they sit down, roughly how many questions they expect to attempt and which they intend to leave.

Sitting the right contest

CEMC Pascal preparation pitched at the wrong level is wasted either way, so confirm which contest a student will write against the current official specification before starting.

A strong student may write up a level, and occasionally that is right. More often it costs them: the extra difficulty is real and the benefit is mostly symbolic. For most students the matching contest, written well, is the better choice.

Dates, the exact scoring scheme, permitted calculators and registration are set by CEMC each year and vary for international candidates. Check cemc.uwaterloo.ca and ask your school for the current cycle.