Remainders and Cycles
Use repeating patterns and remainders to replace large calculations with small ones.
3 problemsMATHS4U · OLYMPIAD MATHEMATICS
Intermediate · Years 9–10 Olympiad Problems
Develop methods in algebra, number theory and geometry.
112 problems · Hints and worked solutions
LATEST PRACTICE
Number Theory
A 12-problem lesson, from a warm-up to a complete proof.
Number Theory
Divisibility and Prime Factors
Factor integers, track prime exponents and organise possible divisors.
5 problemsDigits and Place Value
Combine place value, digit sums and divisibility tests in number puzzles.
18 problemsInteger Equations
Find every integer solution using factorisation, substitutions and bounds.
9 problemsAlgebra
Sequences and Recurrences
Translate a progression or recurrence into a formula you can reason with.
1 problemAlgebraic Reasoning and Bounds
Use simple equations, comparisons and inequalities to justify an answer.
2 problemsAlgebraic Identities
Use identities and symmetry to reveal the structure of an expression.
5 problemsFactorisation
Factor expressions and turn a complicated condition into a useful product.
5 problemsQuadratic Equations
Use roots, coefficients, substitutions and complete solution sets.
14 problemsInequalities
Prove bounds using squares, AM–GM and related inequalities.
5 problemsGeometry
Visual Geometry
Read diagrams, compare areas and reason about geometric constructions.
24 problemsRight Triangles
Explore right triangles, lengths, areas and geometric proofs.
30 problemsNo matching topic. Try a shorter search.
Lesson lists and worksheets
Use a prepared sequence when teaching or practising a complete lesson.
Number Theory — Intermediate12 problemsUse identities to see more5 problemsMake a useful product appear5 problemsFind all the possibilities5 problemsSquares give bounds5 problemsDigits and decimal notation — Years 8-913 problemsQuadratic equations — Year 1013 problemsVisual geometry — Years 8-924 problemsRight triangles — Years 10-1130 problems
Previous weekly lists
The original club lists are still available in their original order.