Preparing for the Euclid Mathematics Contest requires more than just mathematical talent. It requires access to the right resources, the right tools, and the right guidance. With so many study materials, websites, textbooks, and online platforms available, it can be overwhelming to know where to start and which resources are most valuable.
In this comprehensive guide, we curate the essential resources and tools that every serious Euclid student should know about. From official CEMC materials to third-party textbooks, from online problem databases to study group strategies, we cover everything you need to build a complete preparation toolkit.
Official CEMC Resources: Your Foundation
The Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo provides the most authoritative and valuable resources for Euclid preparation. These should be the foundation of your study plan.
1. Past Euclid Contests and Solutions
The CEMC publishes complete past contests with official solutions dating back many years. This is the single most valuable resource available.
Website: cemc.uwaterloo.ca/contests/past-contests.html
What to do: Download at least 10 years of past contests. Work through them under timed conditions (2.5 hours). Study the official solutions carefully to understand the expected level of detail and mathematical communication.
Pro tip: Do not just check your answers. Read the solutions thoroughly and understand why each step was taken. The marking scheme shows exactly how marks are allocated.
2. CEMC Workshop Materials
The CEMC occasionally hosts free workshops and webinars for students preparing for their contests. These are excellent opportunities to learn directly from the contest organizers.
Check the CEMC website in February and March for workshop schedules
Workshops often cover contest strategies, common mistakes, and topic-specific problem-solving techniques
Some workshops provide additional practice problems not available elsewhere
3. CEMC Newsletter and Updates
Subscribe to the CEMC newsletter to stay informed about contest dates, rule changes, and new resources. This is especially important in contest year (Grade 12) when deadlines matter.
Essential Textbooks and Books
While past exams are the most important resource, textbooks provide structured learning and additional practice problems. Here are the most highly recommended books for Euclid preparation:
For Building Foundation (Grade 9-10)
"Art of Problem Solving, Vol. 1: The Basics" by Sandor Lehoczky and Richard Rusczyk. An excellent introduction to problem-solving techniques for beginning contest students.
"The Art and Craft of Problem Solving" by Paul Zeitz. A classic text that develops mathematical thinking and problem-solving strategies.
"Challenge and Thrill of Pre-College Mathematics" by V. Krishnamurthy et al. A comprehensive book covering algebra, geometry, number theory, and combinatorics.
For Advanced Preparation (Grade 11-12)
"Art of Problem Solving, Vol. 2: and Beyond" by Sandor Lehoczky and Richard Rusczyk. The advanced companion to Vol. 1, covering topics that appear in the harder Euclid questions.
"Problem-Solving Strategies" by Arthur Engel. A rigorous text that covers advanced problem-solving techniques used in olympiad-level competitions.
"Euclid Contest Preparation Guide" (various authors). Several publishers offer Euclid-specific preparation books with topic reviews and practice problems. Check reviews before purchasing.
For Topic-Specific Study
Algebra: "Algebra" by I.M. Gelfand and A. Shen. A deep dive into algebraic techniques.
Geometry: "Geometry" by I.M. Gelfand et al. Excellent for developing geometric intuition and proof skills.
Trigonometry: "Trigonometry" by I.M. Gelfand and Mark Saul. A thorough treatment of trigonometric concepts.
Combinatorics: "102 Combinatorial Problems" by Titu Andreescu and Zuming Feng. Advanced but valuable for the hardest Euclid questions.
Online Problem Databases and Practice Platforms
Beyond past Euclid exams, several online platforms provide valuable practice problems and additional resources:
1. Art of Problem Solving (AoPS) Community
Website: artofproblemsolving.com
What it offers: A massive community of contest math students, discussion forums, problem databases, and online classes. The Alcumus adaptive learning system provides personalized practice problems.
Best for: Students who want to engage with a community, ask questions, and access a wide variety of problems at all difficulty levels.
2. CEMC Course Materials and Outreach
The CEMC offers online courses and outreach programs for students. These often include video lectures, problem sets, and interactive materials.
Check the CEMC website for current offerings, especially in the months leading up to the contest.
3. Khan Academy
Website: khanacademy.org
What it offers: Free video lessons and practice exercises covering all the topics that appear in the Euclid (algebra, functions, trigonometry, geometry, etc.)
Best for: Students who need to strengthen their understanding of specific topics. Khan Academy is excellent for building foundational knowledge, though it does not focus specifically on contest-style problems.
4. YouTube Channels
Numberphile: Engaging videos on advanced mathematical topics that develop mathematical thinking.
3Blue1Brown: Beautiful visual explanations of mathematical concepts, especially useful for geometry and calculus intuition.
Michael Penn: Problem-solving videos that cover contest-style problems at various difficulty levels.
The Math Sorcerer: Clear explanations of algebra, calculus, and other topics relevant to the Euclid.
Study Strategies and Techniques
Having the right resources is only half the equation. How you use those resources determines your success. Here are proven study strategies that top Euclid students use:
The 3-Pass Method for Past Exams
Do not just work through past exams once. Use the 3-Pass Method to maximize learning:
Pass 1 (Timed): Complete the exam under strict 2.5-hour conditions. Do not look at solutions. Grade yourself honestly.
Pass 2 (Review): Review the official solutions. For every problem you got wrong or did not fully solve, understand the correct approach. Write out the solution yourself.
Pass 3 (Re-attempt): A week later, re-attempt the problems you struggled with. This time, do not look at the solutions. See if you can solve them independently.
Error Journal
Keep a detailed error journal where you record every mistake you make on practice exams. For each error, note:
The problem and what you did wrong
The correct approach
The underlying concept or skill you need to strengthen
A plan to address this weakness (e.g., "Review logarithm rules" or "Practice factoring techniques")
Review your error journal weekly and use it to guide your study priorities.
Study Groups
Forming or joining a study group of 3-5 motivated students can significantly enhance your preparation:
Meet regularly (weekly or biweekly) to work through problems together
Take turns presenting solutions to the group
Discuss different approaches to the same problem
Quiz each other on key concepts and formulas
Keep each other accountable and motivated
Spaced Repetition for Formulas and Concepts
Use spaced repetition to memorize key formulas, identities, and problem-solving techniques. Tools like Anki or physical flashcards can help you retain information over the long term.
Tools for Contest Day
On contest day, you need to have the right materials and be in the right mindset. Here is a checklist:
Required Materials
Pencils and erasers: Bring multiple pencils in case one breaks. Mechanical pencils are fine.
Ruler: Useful for geometry problems, especially coordinate geometry.
Approved calculator: Check the CEMC website for the current list of approved calculators. Note that many Euclid problems can be solved without a calculator, so do not rely on it excessively.
Watch: Bring a non-smart watch to track your time. Do not rely on wall clocks, which may not be visible from your seat.
Water and snacks: The contest is 2.5 hours long. Stay hydrated and bring a small snack if allowed.
Mental Preparation
Get adequate sleep the night before (7-9 hours)
Eat a nutritious meal before the contest
Arrive early to settle in and reduce stress
Practice relaxation techniques such as deep breathing if you feel anxious
Focus on the process, not the outcome. Your goal is to do your best, not to achieve a specific score.
Resources for Parents and Teachers
If you are a parent or teacher supporting a student preparing for the Euclid, here are additional resources:
CEMC Educator Resources: The CEMC provides resources for teachers, including suggestions for supporting students preparing for contests.
School Registration: Ensure your school is registered with the CEMC and that all interested students are signed up by the deadline.
Encourage consistent practice: Help students establish a regular study schedule and provide access to the resources listed above.
Provide emotional support: Contest preparation can be stressful. Encourage students, celebrate their progress, and help them maintain perspective.
Building Your Personal Resource Library
Do not try to use all of these resources at once. Instead, build a personalized resource library based on your current level and goals:
If you are just starting (Grade 9-10): Focus on mastering your school curriculum, working through AoPS Vol. 1, and attempting easier Euclid questions (Questions 1-4) from past exams.
If you are in serious preparation (Grade 11): Work through 10+ past Euclid exams, strengthen weak areas with topic-specific resources, and consider joining a study group.
If you are aiming for top scores (Grade 12): Complete 15-20 past exams under timed conditions, maintain an error journal, attend CEMC workshops, and focus on the hardest questions (8-10).
Final Advice
The most important resource for Euclid preparation is consistent, deliberate practice. No textbook, website, or video can replace the value of working through problems yourself, making mistakes, learning from those mistakes, and improving over time.
Use the resources listed in this guide as tools to support your practice, not as substitutes for it. The students who succeed in the Euclid are those who put in the work, day after day, week after week, month after month.
Start now, use these resources wisely, and give yourself the best possible chance of success. Good luck!
