In the landscape of mathematics competitions, the Euclid Mathematics Contest, organized by the University of Waterloo, stands as a unique landmark. It not only tests candidates’ mathematical computation skills but also serves as a deep examination of logical construction and written expression.
Many students often wonder during preparation: “Why do I get the correct answer but still receive a disappointing score?” or “I always have no idea how to approach the last few long-answer questions—where exactly are the marking points?” In reality, the Euclid’s scoring system is fundamentally different from that of the Gaokao. Today, we will provide an in-depth analysis of the scoring difficulties and mark-winning techniques for the Euclid’s long-answer questions.
I. Why Are Long-Answer Questions “Hard to Score”? — Core Difficulty Analysis
The Euclid Contest consists of 10 questions, each worth 10 points, for a total of 100 points. Among these, the long-answer questions are the key to opening up score differences. Their difficulties lie in:
From “Finding the Result” to “Presenting a Logical Argument”: Domestic math exams typically focus on the “final answer,” but in the Euclid’s scoring criteria, “completeness, clarity, and presentation style” carry significant weight. A correct solution with a messy process often fails to earn full marks.
Continuity of Thought: The latter part of the contest (e.g., Q8-Q10) no longer tests single knowledge points, but rather combinatorial questions that require logically connecting multiple modules such as algebra, geometry, and sequences. Candidates often get stuck at the very first step, preventing them from developing subsequent steps.
The Grader’s “Logical Following”: When graders review long-answer questions, they are reading your “thinking trajectory.” If the logic leaps too much, the grader cannot understand your argument within a short time, and even if the conclusion is correct, you will be penalized for “insufficient argumentation.”
II. Golden Mark-Winning Techniques: How to Efficiently Earn “Step Marks”
In the Euclid Contest, even if you cannot fully solve a difficult problem, you can still earn a significant number of step marks through reasonable answer-writing strategies.
1. Standardized Expression — “Convey Meaning with Words”
Do not just write equations: Use simple logical connectors such as “Since…”, “Therefore…”, “Because…”. This clearly demonstrates your derivation direction to the grader.
Define variables: When introducing variables, be sure to clearly write a sentence like “Let x be the radius of…”. Clear variable definitions are the foundation of logical rigor.
2. Embrace “Partial Marks”
Even if you cannot calculate the final result, show your progress: If you do not have a complete approach for a long-answer question, you can first write down the geometric properties you observe, known mathematical theorems, or simple algebraic transformation steps. As long as your attempts are logically sound, the grader will give you as many step marks as possible.
Never leave it blank: In a competition, a blank answer sheet means 0 points, but writing down any relevant and reasonable derivation could earn you 2-3 points.
3. The Art of Structured Layout
Separate scratch work from the final answer: The Euclid allows the use of calculators, but strictly forbids submitting scratch work as your final answer. On the answer booklet, keep your layout clear. You can divide complex derivations into “Step 1, Step 2” or “Case 1, Case 2” for presentation.
Clearly mark the conclusion: The final conclusion must be prominent. You can underline it or put it in a box so that the grader can quickly locate it.
III. Exam Strategy: The Game of Time
The Five-Minute Trap: If you have spent more than 5 minutes on a long-answer question without any progress, decisively mark it and temporarily skip it. First, ensure that you secure full marks on the questions you are good at and have a high scoring rate (such as Q1-Q5). These questions have the same point value as the difficult ones and offer much higher cost-effectiveness than stubbornly grinding away at a tough problem.
The Reverse Backtracking Method: For students with a strong mathematical foundation, consider working backwards—starting with the long-answer questions and then returning to fill in the earlier parts. This ensures that you tackle the most complex logical arguments when your mind is at its sharpest.
Frequently Asked Questions
Why are the long-answer questions where scores separate?
Because they carry most of the marks and those marks follow the writing. Each of the ten questions is worth ten marks; on the full-solution questions the final value is a small part of that. Two students who reach the same answer can score very differently, and the difference is entirely in how the reasoning was set out.
What is the fastest way to earn step marks?
Standardise how you open. Define the symbols, state what is given and what you are proving, then show each transformation rather than compressing several into one line. If a step relies on a construction or a substitution, say so explicitly. None of this requires more mathematics; it requires writing the mathematics you already did in a form a grader can follow.
What should I do when a question stalls?
Set a limit before you start. If several minutes pass with no progress, mark it and move on — the marks still available on later questions are usually easier than the ones you are stuck on. Come back with whatever time remains and write down the partial reasoning you do have, because an incomplete but legible argument scores and a blank page does not.