CEE Editorial Team · 31 Oct 2026, 1:15 pm PKT
School maths rewards knowing the method. Competition maths rewards working out which method, or inventing one, when the question does not look like anything in the textbook. Students who are good at the first are often shocked by the second. This guide explains how to prepare, whether you are aiming for a school round, the SEG Math League, or an international olympiad.
What competition problems are actually like
A typical competition problem has a short statement, no hint about the chapter it comes from, and a solution that takes several steps of reasoning rather than one formula. The topics are familiar: number theory, algebra, geometry, counting and probability. What is unfamiliar is the need to explore, try small cases, spot a pattern and then prove or justify it.
That means preparation is less about learning new content and more about learning to think with content you already have.
A training plan by stage
Grades 5–7: build fluency and curiosity. Mental arithmetic, factors and multiples, fractions and ratios, basic angle facts. Start with puzzle-style problems: a few a week, done slowly, with the rule that a wrong answer explained is worth more than a right answer guessed.
Grades 8–10: learn the standard competition toolkit. Divisibility and remainders, prime factorisation, simple inequalities, algebraic manipulation, angle chasing and similar triangles, systematic counting. Work through past papers from well-known junior competitions. Time yourself only after you can solve the problems untimed.
Grades 11–12 and college: proof-based problems, functional equations, combinatorics arguments, number theory with modular arithmetic, geometry with constructions. Join or form a problem-solving group; explaining a solution to a peer is the fastest way to find the gap in it.
How to practise
Do fewer problems, more thoroughly. One hard problem worked on for forty minutes, with a written solution and a note on what the key idea was, is worth more than twenty routine exercises.
Keep a problem journal. For each problem: the statement in your own words, what you tried, what worked, and the idea you would want to remember. Students who keep journals improve faster because they start recognising problem types.
Read solutions actively. After an honest attempt, read the official solution and ask at which line you would have been stuck, and why. Then put it away and write the solution yourself the next day.
Get the easy marks. In most competitions the first third of the paper is accessible to anyone with sound basics. Students lose more marks to careless slips on those than to the hard problems at the end.
What parents can do
Protect time. A regular ninety-minute slot each week beats a cram before the paper.
Resist solving it for them. The struggle is the training.
Ask them to explain a solution to you, even if you do not follow the maths. Explaining is practice.
Treat results as information. A low score on a hard paper is normal and tells you what to work on.
What parents should avoid
Signing a child up for every competition on the calendar. One or two serious ones a year, with real preparation, is better.
Buying a shelf of books. One good problem collection worked through is enough for a year.
Making it about the certificate.
The SEG Math League
The SEG Math League is CEE’s problem-solving competition for school and college students in Pakistan, set by level so that a Grade 6 student and an A-level student each face appropriate problems. Dates are announced on the SEG calendar and to registered schools first. If your school is not yet registered, ask your maths coordinator to contact CEE, or register your own interest through the Math League page.