Our Euclid preparation courses come with exclusive self-developed teaching materials, and all instructors are graduates of top universities at home and abroad with extensive experience in competition training. We offer different class levels tailored to students with varying backgrounds, ensuring targeted instruction and helping you achieve better results with less effort!
Instructor Team
Teacher Zhang
PhD in Pure Mathematics, University of Rochester, USA
Postdoctoral Researcher, Shanghai Center for Mathematical Sciences, Fudan University
During his junior high school years, he won First Prize in the National Junior High School Mathematics League and Second Prize in the National Junior High School Chemistry League, and was directly admitted to the Science Competition Experimental Class at Chongqing Nankai Middle School.
In his first year of high school, he won First Prize in the Chongqing Mathematics Competition and placed third in the city. In his third year, he earned First Prize in the National High School Mathematics League and Second Prize in the National High School Biology League.
He has 7 years of experience in theoretical mathematics research and teaching and has systematically taught most of the undergraduate and graduate professional courses in university mathematics departments.
During his PhD studies, he participated extensively in lectures and training sessions for various math competitions, including the AMC and major American university contests such as the Putnam and Virginia Tech.
Coaching Achievements:
In November 2021 among his AMC students, the highest score was 150 (full marks). 4 students scored above 10 in AIME, 12 students scored above 7 and 5 students reached the USA(J)MO cutoff score.
In the 2022 Euclid Mathematics Contest four of his students achieved scores of 91, 90, 88, and 87 respectively.
Teacher Gao
Master's degree from Peking University
Winner of the National Undergraduate Mathematical Modeling Contest (First Prize); National High School Mathematics League (Second Prize); National Hope Cup Mathematics Competition (Third Prize).
Tutoring Achievements:
Over 65% of students in the US AMC 12/10/8 competitions advanced to the semi-finals or won awards. The highest score in AMC 12 was 150, with many scoring 140+. The highest score in AMC 10 was 144. For example, in 2022, 17 students advanced to the AIME, with 4 achieving top 1%. In 2023, over twenty students advanced to the AIME, mostly in the top 5% or 1%. In the Euclid competitions, approximately 75% of students won awards (top 25%), with a highest score of 94. Australian AMC students also achieved top awards.
Over 96% of A-Level students achieved A or A* grades. In Advanced Mathematics, some students were only one point away from a perfect score in FP1, FM, and FP2. 95% of AP Calculus students achieved a 5-point score. IB students improved rapidly; currently, most IB HL students have reached 7 points, and some SL students improved from 1-2 points to 5-6 points in about 3 months.
Student performance
🏆 2025
233 students achieved Distinction
8 students scored 90+, 97 students scored 80+
🏆 2024
177 students achieved Distinction
17 students scored 90+, 75 students scored 80+
🏆 2023
165 students achieved Distinction, with a 70% success rate among participating students;
8 students scored 90+, 63 students scored 80+
🏆 2022
96 students achieved Distinction, with a 75% success rate among participating students;
The passing score was 68. 7 students scored 90-93, 16 scored 85-89, 26 scored 80-84, and 47 scored 68-79.
🏆 2021
33 students achieved Distinction, with a 50% award rate among participating students;
4 students scored above 90 (94, 93*2, 90), and 12 students scored above 80.
Euclid Mathematics Competition Tutoring Course
Suitable for: Students in Grade 12 and below.
Course Description:
The Euclid Mathematics Competition Tutoring Course is a mathematics competition tutoring course designed for junior and senior high school students. This course covers all aspects of the Euclid Mathematics Competition, including mathematical reasoning, geometric proofs, and problem-solving techniques, aiming to help students improve their mathematical literacy, expand their mathematical thinking, and enhance their mathematical abilities. Whether you are a beginner or an experienced competition participant, you can find suitable content in our course. Our teaching team consists of experienced and highly capable mathematics competition teachers, providing personalized instruction and truly tailoring teaching to individual needs.
Course Outline
(Materials with * are aimed for the potential last Problems)
Number Theory
(1) Prime factorization
——Number of factors, Sum/Product of factors
——LCM and GCD, *Euclidean Algorithm and Bézout's Theorem
(2) Congruence and Modular Algebra
——Principles of Modular Calculations
——*Euler’s Theorem/Fermat’s Little Theorem
——*Chinese Remainder Theorem(CRT)
(3) Digits and Base-n Representation
——Mutual Conversion between different bases
(4)Diphantine Equations
——Estimation and Molular Method
Algebra
(1)Sequences
——Arithemetic and Geometric Sequences
——Periodic Sequences, *Recursive Sequences and Characteristic Equation Method
——*Conjecture and Mathematical Induction Proof
(2) Functions and Equations
——Elementary Functions (Linear, Quadratic, Exponential, Logarithmic, Trigonometric) and their properties
——Functional Equations
——*Gaussian/Floor function
(3) Inequalities and Extreme Value Problems
——Simple Polynomial Inequalities
——AM-GM Inequality, *Cauchy inequality
(4)Polynomials
——Division Algorithm of Polynomials and the Remainder's Theorem
——Fundamental Theorem of Algebra (Polynomial Factorization) and Vieta's Theorem
——The Rational Root Theorem
Geometry
(1) Triangles and Polygons
——The Law of Sines, The Law of Cosines
——Area Method and Heron's formula
——*Menelaus's theorem, Ceva's theorem, Stewart Theorem
——Centers of triangle
(2) Circles
——Chords, Arcs, Tangents, Inscribed and Central accepted angles
——Cyclic Quadrilateral
——Power of a Point Theorem, *Ptolemy's theorem
(3)Basic Coordinate Geometry
——Coordinate System and Equations of lines, Circles
(4)Basic Solid Geometry
——Lines in space, Planes; Rectangular Box, Pyramids, Prisms, Sphere and Cones, Frustums
Combinatorics
(1)Basic Counting Principle
——Sum Rules and Product Rules
(2) Permutations and combinations
——Combinatorics numbers and *Combinatorics identities
——Grouping Theorems, Boards Method and the Problem of Balls into Boxes
(3) Logic reasoning
——*Pigeonhole principle
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