Category: Blog

I. Key Changes in the 2026 Euclid Contest

1. Major adjustments in content distribution:
- The algebra section has reached its highest proportion in recent years: functions, equations, polynomials, sequences, and other algebraic content run throughout the paper, particularly dominating questions 7–10.
- Permutations & combinations and analytic geometry are significantly reduced: traditional high-frequency topics such as complex combinatorial counting and conic section problems in coordinate systems have almost disappeared.
- Changes in the assessment of trigonometry: no standalone trigonometric equation problems appeared; instead, they were integrated into composite function contexts, emphasizing conceptual understanding over mechanical solving.
Trend interpretation: Euclid is shifting from "broad coverage" to "deep exploration," with algebraic thinking and logical rigor becoming the keys to high scores.

II. Question-by-Question Style Analysis

First 5 Questions: Steady with Changes, Foundation is King

Following the style of previous years, they mainly tested:
- Algebraic operations and proportional applications (e.g., speed, concentration problems)
- Parabola vertex and axis of symmetry properties
- Prime factorization and base-10 expansion
- Basic probability (classical probability, independent events)
Although they are foundational, computational details are prone to errors; you must secure full marks on the first 5 questions.

Questions 6–8: Sudden Style Shift, Difficulty Spike

Question 6:
Combines logarithms and composite functions: no longer directly asks to solve logarithmic equations, but requires understanding the structure and reasoning using logarithmic monotonicity and domain restrictions.
Skills required: awareness of function composition + flexible use of logarithmic properties.

Question 7:
A traditional algebra synthesis problem involving inequalities and parameter discussions, but no traps; it's a "conquerable" medium-level problem.

Question 8 (the biggest difficulty this year!):
- Part (a): Tests the Inscribed Angle Theorem and the Right Triangle Altitude Theorem; no tangents are examined, and auxiliary lines need to be constructed.
- Part (b): Uniquely combines the triangle inequality and the floor function, requiring students to have relatively rich experience in handling the floor function.
Overall difficulty: Significantly higher than previous year's question 8, becoming a key differentiator between Distinction (top 25%) and Honor Roll (top 5%).

Questions 9–10: Final Tough Problems Remain, Algebra and Combinatorics as Main Tracks

Question 9 (Algebra final problem):
- Part (a): Simple graph analysis, easy points.
- Part (b): Tests understanding of polynomial roots, requiring a good grasp of Vieta's formulas and their applications.
- Part (c): Requires the ability to analyze solutions of quadratic Diophantine equations, demanding a relatively high level of number theory.

Question 10 (Combinatorics final problem):
- Part (a): Small-scale enumeration, intuitive.
- Parts (b) and (c): Relatively traditional permutations and combinations problems; constructing a recursive function for n solves them.
Although it is combinatorics, the thinking is more algebraic, reflecting the trend of "algebraization of combinatorics."

III. Difficulty and Cutoff Predictions

Indicator	2026 Trend
Overall difficulty	Higher than 2024–2025, especially questions 8 and 9 raising the bar
Distinction cutoff	Expected around 68 points
Honor Roll cutoff	Expected around 90 points

IV. Preparation Suggestions for 2027 and Beyond

1. Solidify the Six Fundamental Modules

Ensure no blind spots in:
- Exponents and logarithms (including applications in composite functions)
- Functions and systems of equations (including cubic equations, Vieta's formulas)
- Trigonometry (properties, graphs, identities)
- Sequences (arithmetic/geometric, recursion, summation)
- Counting and probability (permutation and combination models, expectation)
- Elementary number theory (divisibility, modular arithmetic, Diophantine equations)

2. Strengthen Two Core Areas of Attack

Area	Key Focus Points
Plane Geometry	- Inscribed angles, tangent-chord angles, Altitude Theorem - Auxiliary line construction (perpendiculars, medians, similar triangles) - Integration with algebra (e.g., coordinate method, vectors)
Counting & Probability	- Recursive modeling (state transitions) - Inclusion-Exclusion Principle, introduction to generating functions - Problems integrating with sequences/inequalities

3. Special Plan for Final Problems

Questions 7–8: Practice 2 medium-to-high difficulty problems each week, focusing on multi-knowledge point integration.
Questions 9–10: Develop strategies based on target awards:
- Pursuing Distinction: Ensure parts (a) and (b) of question 9 and parts (a) and (b) of question 10 are correct.
- Pursuing Honor Roll: Must conquer question 8(b), question 9(c), and question 10(c); systematic study of elementary number theory and advanced recursion techniques is recommended.

I. Why Do Oxbridge G5 Universities Value the Euclid Contest So Much?

1. Assessment of "Mathematical Expression" and "Logical Rigor"

Unlike multiple-choice competitions like the AMC, the Euclid Contest features a significant number of full-solution questions. The evaluation focuses not only on the final result but also on the process: examiners award points based on the completeness of the solution steps and the rigor of the logic. This assessment style is highly consistent with Oxbridge interviews and admissions tests like the MAT/STEP—elite universities do not want "calculators" who can only do drills; they seek students who can express mathematical thinking clearly and logically.

2. Bridging the "Depth of Thinking" Required at the University Level

The last two questions (Q9, Q10) of the Euclid Contest are extremely difficult, often requiring strong creativity and a deep understanding of the essence of mathematics. This design aims to screen for students who possess "sustained resilience" when facing unknown and complex problems—a quality essential for the demanding STEM coursework at G5 universities.

3. Authoritative "Academic Endorsement"

The University of Waterloo holds an excellent reputation in the global mathematics community. For G5 admissions officers, the Euclid Contest serves as a globally standardized and highly credible benchmark. Earning a Certificate of Distinction (top 25% globally) is a powerful academic credential in itself.

II. How to Leverage Your Euclid Results?

Many students simply file away their certificates after the contest, which is a significant waste of this resource. Below is the proper way to leverage your results:

1. Include It in the UCAS System

When filling out your UCAS application, you can enter your Euclid award in the "Extra-curricular activities" or "Awards" section. This is particularly beneficial if you are applying for Mathematics, CS, Engineering, or Physics, as strong contest results can significantly enhance your academic competitiveness.

2. Mention It in Your Personal Statement

This is the most valuable way to use your results. Instead of simply stating "I participated in the Euclid Contest and won an award," describe:

Specific intellectual growth: Detail your logical reasoning process when tackling a challenging full-solution problem.

Transferable skills: Explain how the logical abilities honed through the competition have helped you better understand advanced A-Level/IB concepts.

3. Use It as a Tool for "Borderline Admission"

Special for the University of Waterloo: If you apply to its Mathematics or Computer Science programs, your Euclid score directly influences borderline admission decisions and entrance scholarships. For reference by G5 universities: If your predicted grades are on the borderline, a strong Euclid score could be the deciding factor that leads an admissions officer to issue an offer.

4. Use It as Preparation for Admissions Tests (MAT/STEP/TMUA)

The assessment style of the Euclid Contest (a mix of short-answer and full-solution questions) is very similar to the additional admissions tests required by top UK universities, such as Cambridge's STEP and Oxford's MAT. The problem-solving mindset and mental resilience you develop while preparing for Euclid can be seamlessly transferred to these high-stakes university assessments.

III. Summary: What Score Should You Aim For?

For applications to general prestigious universities: Earning a Certificate of Distinction (top 25% globally) is a solid foundation, demonstrating strong mathematical literacy. For those aiming for G5 universities, the Ivy League, or competitive programs at Waterloo: Your target should be a score of 85+ (typically the top 5% or higher). This score is sufficient to prove to admissions officers that you possess top-tier logical reasoning and mathematical communication skills.