How to start your IMO journey in Pakistan — a complete guide

School mathematics asks you to apply a method you were shown. Olympiad mathematics asks you to find a method nobody showed you, and then prove it always works. Those are different subjects that happen to share a name.

This guide covers the whole route for a student in Pakistan: what the competition is, how Pakistan selects its team, what the four subjects are, and exactly what to read in what order.

What the IMO actually is

The International Mathematical Olympiad has run annually since 1959 and is the most prestigious mathematics competition for school students in the world. More than 100 countries send teams of up to six students to solve six exceptionally hard problems across two days.

An IMO medal — bronze, silver or gold — is recognised by every top university on earth as one of the strongest signals of mathematical ability that exists. Gold medalists are recruited directly by MIT, Cambridge, Oxford, Harvard, and leading technology companies.

Six problems. Two days. Three problems per day, four and a half hours per day. Each problem is worth seven points, and a full solution requires a complete, rigorous proof.

How Pakistan selects its team

Pakistan selects its IMO team through a national mathematics olympiad process, run under the Federal Board and referred to as the Pakistan Mathematical Olympiad (PMO) / National Mathematics Talent Contest (NMTC).

There are three stages.

Stage 1 · Registration. You need an aggregate of 60% or more in core subjects in your most recent examination. Registering completes this stage.

Stage 2 · Screening test. Held around March for the following year's competition. Roughly 1,000–1,500 students sit it. It covers O Level and A Level mathematics plus introductory olympiad topics; around 50 students are shortlisted.

The format is an MCQ section (around 50 marks, school syllabus plus introductory olympiad) and a subject section (around 25 marks, olympiad problems — geometry appears most often).

Stage 3 · Camps and selection tests. Shortlisted students attend training camps, online or physical. Each camp ends with an exam that narrows the field, repeating until six students remain: the Pakistan IMO team.

Look closely at Stage 2. Around 1,000–1,500 students sit a test that draws heavily on geometry, and about 50 clear it. A student who has properly worked through one good geometry book is already competing against a field where most people have not.

Eligibility

Under 20 on 30 June of the competition year. Open to Grade 9, 10 and 11 students (Matric/O Level) and FSc-1/AS students. A2 students may register if age-eligible and planning a gap year.

The four subjects

Geometry. The most heavily tested area in Pakistan's screening. Euclidean geometry, circles, triangles, transformations. Highly learnable with the right book: Evan Chen's covers what you need, and its first four chapters are enough for the screening test.

Number theory. Primes, divisibility, modular arithmetic, Diophantine equations. Appears in almost every IMO.

Combinatorics. Counting, probability, graph theory, combinatorial proof. Rewards creative thinking over memorised technique, and it is the area Pakistani students have usually seen least of.

Algebra. Functional equations, inequalities, polynomials.

Every IMO problem requires a proof. Whatever the subject, you are proving a statement or proving your answer is complete. Writing proofs is not an extra skill on top of the mathematics — it is the mathematics.

That last point deserves emphasis, because it is where students trained on Pakistani school exams lose the most marks. An answer with no argument scores close to nothing, even when the answer is right.

A subject-by-subject reading order

This is the order to actually work through, rather than a list to collect.

Geometry

Evan Chen, Euclidean Geometry in Mathematical Olympiads. The first four chapters cover what the screening test asks for. It is widely regarded as the best olympiad geometry book written, and geometry is both the most-tested area in Pakistan's screening and the most learnable from a book.

Start here. If you only do one thing this year, do this.

Number theory

1. Modern Olympiad Number Theory
2. Number Theory — Structures, Examples, Problems
3. Introduction to Diophantine Equations
4. Titu Andreescu, 104 Number Theory Problems

Andreescu coached multiple US gold-medal IMO teams. Work every one of the 104 problems — it is the most effective single number theory resource for IMO preparation.

Combinatorics

1. Olympiad Combinatorics
2. A Path to Combinatorics for Undergraduates
3. 102 Combinatorial Problems
4. University lecture notes on discrete mathematics

This is the area Pakistani students have usually seen least of, which cuts both ways: it is unfamiliar, and it is where an hour of work buys the most.

Algebra

1. The Little Fermat playlist for functional equations
2. OTIS Excerpts
3. Advanced Olympiad Inequalities
4. 117 Polynomial Problems

General problem solving

Yufei Zhao's handouts · Evan Chen's handouts · IMOmath · Problem-Solving Strategies (Engel) · the AoPS forum · The IMO Compendium

One more thing worth knowing about

OTIS is Evan Chen's olympiad training programme. It is genuinely excellent, and financial aid is available for it — which is worth knowing before you assume it is out of reach.

Twelve free books

WonderWhyPk hosts twelve olympiad books on Google Drive — no sign-in, no account, no cost. They are listed in reading order, starting with the syllabus, on the IMO Track page.

Read the syllabus first. It states exactly which topics IMO tests, so that every hour after it is aimed at the right target. Students who skip it routinely spend months preparing the wrong material.

How to study

Do not open the solution until you have finished the problem. If you are stuck for more than half an hour, leave it and return days later. The stuck time is the training.

Do not rely on the camps. They are pitched at beginners. If you are aiming for the team, assume you will self-study the entire syllabus.

Two or three hours a day, consistently, is enough. Persistence and creative thinking beat volume. A student doing two focused hours daily for a year will beat one doing twelve-hour weekends.

Start this week

Download the syllabus. Open Evan Chen's geometry book at chapter one. Solve the first problem set without looking at the answers.

March comes round faster than it looks.