Pascal Contest: Format, Eligibility, Registration and Preparation

The Pascal Contest is a 60-minute mathematics competition consisting of 25 questions, administered each February by the Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo. It is designed for students in Grade 9 or below, covering topics from the standard Grade 9 curriculum: number sense, algebra, geometry, and basic problem-solving. The contest is written at individual schools worldwide on the same date, with results returned within weeks.

Who Can Write the Pascal Contest

The Pascal Contest is open to any student in Grade 9 or below. There is no upper age limit, and younger students in Grades 7 or 8 are explicitly encouraged to participate if they feel ready. Many schools register students from multiple grade levels, and the contest organizers publish separate honour rolls for Grade 9 students and for those in Grade 8 or below.

Students do not need to qualify or sit a preliminary round. Any school that registers can administer the contest to as many students as it wishes. Home-schooled students can write the contest if a supervising adult registers as a "school" or if a nearby school agrees to include them.

The contest is curriculum-based, meaning it tests material typically taught by the end of Grade 9 in Canada. Students from other countries can write it, and many international schools do, but they should verify that they have covered equivalent topics: linear equations, exponent rules, perimeter and area of polygons, basic counting, and logical reasoning.

Contest Format and Scoring

The Pascal Contest contains exactly 25 questions, divided into three sections:

• Part A: Questions 1–10, each worth 5 marks. These are straightforward computational or one-step problems.
• Part B: Questions 11–20, each worth 6 marks. These require more reasoning, often two or three steps, and may involve algebraic manipulation or geometric insight.
• Part C: Questions 21–25, each worth 8 marks. These are the most challenging, demanding creative problem-solving, multi-step reasoning, or insight into structure.

The maximum possible score is \( 10 \times 5 + 10 \times 6 + 5 \times 8 = 150 \) marks. All questions are multiple-choice with five options (A, B, C, D, E). There is no penalty for incorrect answers, so guessing is always better than leaving a question blank.

Each student begins with 150 marks. For each question answered incorrectly or left blank, the corresponding point value is subtracted. This means a student who answers all questions incorrectly receives 0 marks, and a student who answers all correctly receives 150 marks. In practice, the median score typically falls between 60 and 80 marks, depending on the year.

Calculators are not permitted. Students may use rulers, compasses, and protractors, but these are rarely necessary. All work must be done on the question paper or on blank paper provided by the school; no formula sheets or notes are allowed.

When the Pascal Contest Is Offered

The Pascal Contest is held once per year, on a Wednesday in late February. The exact date is announced by CEMC in the preceding autumn, usually by October. For example, recent contests have been held in the third or fourth week of February.

All schools worldwide write the contest on the same date, though the local time varies by time zone. Schools must administer the contest during school hours, and CEMC provides guidelines to ensure fairness: students may not communicate with one another, and the question paper must not be shared before the official release time.

Results are typically released four to six weeks after the contest date. CEMC publishes honour rolls (top scorers) and mails certificates to all participants. Schools receive detailed statistics showing how their students performed relative to the global cohort.

How Registration Works

Registration for the Pascal Contest is managed by individual schools, not by students directly. A teacher or administrator at the school must register the school with CEMC, usually by completing an online form on the CEMC website. Registration opens in the autumn and closes in early February, a few weeks before the contest date.

The school pays a registration fee per student. As of the most recent information available, this fee is modest, but the exact amount can change year to year, so schools should verify the current fee on the CEMC website. The fee covers printing costs, administration, and the certificate sent to each participant.

Once registered, the school receives the contest papers by mail or secure electronic delivery, along with instructions for administration. The school is responsible for printing copies if needed, invigilating the contest, and returning answer sheets to CEMC by mail or online submission.

If your school has not registered in the past, a teacher or parent can contact CEMC directly to initiate registration. Home-schooled students or those whose schools do not participate can sometimes arrange to write the contest at a nearby participating school by contacting that school in advance.

How to Prepare Effectively

Preparation for the Pascal Contest should focus on fluency with Grade 9 curriculum topics and practice with problem-solving under time pressure. The contest rewards both speed and accuracy, so students benefit from working many practice problems rather than studying theory alone.

Master the Core Topics

Review the following areas thoroughly:

• Number sense: Integer arithmetic, fractions, decimals, percentages, ratios, exponents, and roots. Be comfortable with mental arithmetic and estimation.
• Algebra: Solving linear equations, simplifying expressions, substitution, and basic manipulation of formulas. Occasionally, simple quadratic expressions appear.
• Geometry: Perimeter, area, and volume of standard shapes (triangles, rectangles, circles, rectangular prisms, cylinders). Angle properties in triangles and parallel lines. Pythagorean theorem.
• Counting and logic: Systematic counting, Venn diagrams, simple probability, and reasoning through multi-step word problems.

The contest does not require calculus, trigonometry beyond basic ratios, or formal proof. It does require comfort with translating word problems into mathematical expressions and checking answers quickly.

Work Through Past Papers

CEMC publishes past Pascal Contest papers and solutions on its website, free of charge. These are the single best preparation resource. Working through five to ten past papers under timed conditions gives students a clear sense of question style, difficulty progression, and pacing.

When working a past paper, simulate contest conditions: no calculator, 60 minutes, no interruptions. After finishing, review the solutions carefully, paying special attention to questions you found difficult or slow. Many Part C questions have elegant solutions that are not immediately obvious; studying these builds problem-solving intuition.

Build Speed Without Sacrificing Accuracy

Sixty minutes for 25 questions allows an average of 2.4 minutes per question, but the difficulty is not evenly distributed. Students should aim to complete Part A in 15–20 minutes, leaving 30–35 minutes for Parts B and C. This requires quick recall of basic facts and efficient calculation.

Practice mental arithmetic: multiplying two-digit numbers, finding 10% or 25% of a quantity, simplifying fractions. Avoid over-relying on written work for simple calculations. On contest day, every minute saved on Part A is a minute available for a challenging Part C question.

Learn to Eliminate and Estimate

Because there is no penalty for guessing, students should answer every question. On difficult questions, eliminating one or two obviously incorrect options improves the odds. Estimation is often faster than exact calculation: if a question asks for an area and the options are 12, 24, 36, 48, and 60, a rough sketch and approximation may suffice.

For Part C questions, consider working backward from the answer choices. If a question asks "which of the following could be the value of \( x \)?" try substituting each option into the given conditions. This is often faster than solving algebraically.

Past Papers and Sample Questions

CEMC provides past Pascal Contest papers dating back many years, all available for free download on the CEMC website. Each paper comes with a full solution set, often including multiple solution methods for the harder questions. These solutions are written clearly and are suitable for self-study.

To illustrate the style, here are three sample questions representative of each section:

Part A example: If \( 3x + 7 = 22 \), what is the value of \( x \)?

This is straightforward: subtract 7 from both sides to get \( 3x = 15 \), then divide by 3 to obtain \( x = 5 \).

Part B example: A rectangle has perimeter 40 cm and area 96 cm². What is the length of its longer side?

Let the sides be \( l \) and \( w \) with \( l > w \). Then \( 2(l + w) = 40 \), so \( l + w = 20 \). Also, \( lw = 96 \). Substituting \( w = 20 - l \) into the area equation gives \( l(20 - l) = 96 \), or \( 20l - l^2 = 96 \). Rearranging: \( l^2 - 20l + 96 = 0 \). Factoring: \( (l - 12)(l - 8) = 0 \), so \( l = 12 \) or \( l = 8 \). The longer side is 12 cm.

Part C example: How many two-digit positive integers have the property that the product of their digits is 12?

We need pairs of digits \( (a, b) \) where \( 1 \le a \le 9 \), \( 1 \le b \le 9 \) (since 0 would give product 0), and \( ab = 12 \). The factor pairs of 12 using single digits are \( (2,6), (3,4), (4,3), (6,2) \). Each pair corresponds to a distinct two-digit number: 26, 36, 43, 62. So there are 4 such integers.

Notice that Part C questions require more careful reasoning and often involve counting, case analysis, or insight into number properties.

Tips for Contest Day

On the day of the contest, arrive early, bring several sharpened pencils and a good eraser, and ensure you have a watch or can see a clock. Calculators are not allowed, so leave yours at home to avoid any confusion.

Read each question carefully. Many errors come from misreading the question or missing a word like "not" or "at least." If a question seems unusually difficult for its position in the paper, reread it; you may have misunderstood.

Work through the paper in order, but do not get stuck. If a Part A question takes more than two minutes, circle it and move on. Return to skipped questions after completing the rest of the section. Part C questions are worth the most marks, so budget time to attempt all of them, even if only to eliminate wrong answers and guess.

Fill in your answer sheet carefully. If your school uses a bubble sheet, ensure you mark the correct row for each question number. If you change an answer, erase completely.

With five minutes remaining, ensure you have marked an answer for every question. A blank answer guarantees lost marks; a guess has a 20% chance of being correct.

Frequently Asked Questions

Can Grade 10 students write the Pascal Contest?
No. The Pascal Contest is restricted to students in Grade 9 or below. Grade 10 students should write the Cayley Contest, which is held on the same day and covers similar material at a slightly higher level.

Is the Pascal Contest recognised for university admissions?
The Pascal Contest itself is not typically a significant factor in university admissions, as it is written by Grade 9 students. However, strong performance can build a foundation for later contests (Fermat, Euclid) that are considered by universities, particularly in Canada. Participation demonstrates interest in mathematics and problem-solving.

What score is considered good?
This varies by year, but typically a score above 100 places a student in the top 25% globally, and a score above 120 places them in the top 10%. CEMC publishes honour rolls for the top-performing students, and certificates indicate whether a student scored in the top 25% at their school.

Are there prizes?
All participants receive a certificate. High-scoring students may receive additional recognition from CEMC or their school, but there are no cash prizes or scholarships directly associated with the Pascal Contest. The primary value is the experience and the motivation to continue with mathematics competitions.

Can I write the contest online at home?
No. The Pascal Contest must be written in person at a registered school, supervised by a teacher or invigilator. This ensures fairness and prevents collaboration or use of unauthorised resources.

How is the Pascal Contest different from the Gauss Contest?
The Gauss Contest is for students in Grades 7 and 8, while the Pascal Contest is for Grade 9. The Gauss Contest has 25 questions in 60 minutes, similar to Pascal, but the content is aligned with the Grade 7/8 curriculum. Students in Grade 8 may choose to write either the Gauss or the Pascal, depending on their preparation.

Where can I find more practice problems?
Besides past Pascal papers, students can practice with past Gauss and Cayley papers (also on the CEMC website), or with problem sets from other introductory contests such as the AMC 8 or UKMT Junior Mathematical Challenge. Many of these problems test similar skills.

What happens after the Pascal Contest?
Students who enjoy the Pascal Contest often continue with the Fermat Contest in Grade 11 and the Euclid Contest in Grade 12. The Euclid is particularly significant, as strong performance is considered by Canadian universities, especially Waterloo's mathematics and engineering programs. The Pascal Contest is the first step in a progression of increasingly challenging contests.