Make notation, calculation and proof feel familiar. Begin at the first unfamiliar idea; the prerequisite links help you find a shorter route. You can open any lesson.
- F01
Mathematical language and sets
Read a statement, name its domain, and distinguish for every from there exists.
Inside: Number systems and intervals · Sets, quantifiers and function notation
- F02
Arithmetic and exact calculation
Calculate accurately and retain exact values until approximation is requested.
Inside: Signed numbers and fractions · Ratios, percentages and exact values
- F03
Powers, radicals and logarithms
Transform expressions with all domain restrictions visible.
Inside: Exponent laws and restrictions · Radicals and conjugates · Logarithms only when needed
- F04
Algebraic identities and factorisation
Factor expressions and verify each identity by expanding back.
Inside: Distributive law and identities · Common factors and hidden products
- F05
Equations and quadratic tools
Solve equations while preserving and checking the full solution set.
Inside: Linear equations and simultaneous equations · Quadratic formula and discriminant · Equivalence and extraneous roots
- F06
How to write a proof
Write a connected argument with a reason for each decisive step.
Inside: Examples and counterexamples · Direct proof and cases · Contradiction, converses and completeness
- F07
Geometric language and ratios
Read only the given geometric facts and use a consistent ratio convention.
Inside: Points, lines and labelled diagrams · Proportion, area and transformations
- F08
Sequences and sums
Compute terms, state index ranges and explain a finite-sum method.
Inside: Sequence notation and indexing · Arithmetic and geometric sums · Telescoping
- F09
Complex numbers: optional bridge
Interpret complex roots before the advanced algebra branches.
Inside: The imaginary unit and conjugates · Complex roots of real polynomials
- F10
Trigonometry foundations
Use right-triangle ratios, angle units and trigonometric identities with valid domains.
Inside: Right-triangle ratios · Angle units, identities and domains
These original lessons introduce the methods and give practice with solutions. A single short session is not a full assessment of Olympiad readiness. Build depth through the written challenges and your country’s official past papers.