Olympiad 1 (O1) Course

Lessons: 40
Fee: $40
Duration: 2
Current Time(s): Tue 07:00–09:00, Sun 07:30–09:30
Workload: 3–4 hours

There will be 2 hours of teaching per week over 40 weeks, and I expect students to spend about 3–4 hours per week reviewing the material and doing homework. The total time spent in this course should be around 220 hours over the year. As this is the first Olympiad course, there will be a heavy emphasis on understanding and writing proofs, as well as a discussion of different problem-solving strategies more relevant to proofs.

Classes

Click on the class to see the week-by-week schedule.

Name	Time	Students	Duration (h)	Status
2026-O1	Tue 07:00–09:00	6	2	Active
2025-07-O1	Sun 07:30–09:30	4	2	Active

Syllabus

Proofs (4 weeks): proof writing, contradiction, induction.
Problem-Solving Strategies (12 weeks): try small cases, case bashing, extremal principle, pigeonhole principle, backsolving, representation and visualisation techniques, problem exploration.
Combinatorics (6 weeks): double counting, bijections, invariants and monovariants, game theory, graph theory.
Number Theory (6 weeks): prime factorisations, infinite descent, Euclidean algorithm, modular arithmetic, Fermat’s little theorem, Euler’s theorem, Diophantine equations.
Algebra (6 weeks): graphing, sequences, polynomials, Vieta’s formulas, inequalities, functional equations.
Geometry (6 weeks): geometry strategies and techniques, angle chasing, length chasing, important configurations, reverse reconstruction.

Learning Outcomes

Understand what a proof is and be able to write one with an appropriate level of detail.
Use contradiction and induction effectively in proofs.
Be able to use a variety of soft and hard techniques in problem-solving.
Apply a range of theorems and techniques across algebra, combinatorics, geometry, and number theory to prove results, especially in the areas covered in the C2 course.
Understand what game theory, graph theory, and functional equations are.
Understand how to manipulate inequalities.

Prerequisites

Before starting this course, students should be familiar with most of the concepts taught in the Competition 2 (C2) course. In particular, students should:

have at least some experience with creative thinking and problem-solving in maths done outside the classroom,
be able to use permutations and combinations, including the supermarket principle (aka stars and bars) to solve counting problems,
be able to apply binomial theorem to determine coefficients of binomial expansions,
be able to apply modular arithmetic (addition, subtraction, multiplication, exponentiation) in problems,
be able to solve simultaneous equations and quadratic equations,
be able to sum arithmetic and geometric series,
understand the relationships between the equations and graphs of lines, quadratics, and circles,
be able to angle chase on parallel lines, in triangles, in circles, and in cyclic quads, and
be able to spot and utilise similar triangles to solve geometry problems.