Maths Olympiad preparation: a guide for students and parents

Maths Olympiads and competitions are different from school exams. Instead of repeating a method you have been taught, you are asked to explore a problem, try ideas and explain why your answer works. That is what makes them exciting, and a little daunting at first. Here is how to start.

What competitions test

Competition questions are often non-routine: they use familiar ideas in unfamiliar ways. They reward:

• Number sense: spotting patterns, estimating and checking whether an answer makes sense.
• Problem-solving habits: trying small cases, drawing diagrams, working backwards and looking for a pattern.
• Clear reasoning: knowing why something is true, not only getting the answer.
• Accuracy under time limits, especially in multiple-choice rounds.

Formats and rules differ by competition and level (school, regional, national, international), so check the official source for the contest you are entering.

The core topic areas

Most competitions draw on four areas:

1. Number theory: divisibility, primes, factors, remainders, LCM and HCF. Try the prime number checker and the LCM and HCF calculator, and learn the divisibility rules in our mental maths guide.
2. Algebra: patterns, sequences, equations and inequalities.
3. Geometry: angles, triangles, circles, area and the Pythagorean theorem. The Pythagoras calculator is handy for checking.
4. Combinatorics and counting: arrangements, choices and probability.

A good weekly routine

• Two or three short sessions of 30 to 45 minutes, rather than one marathon.
• Start with a warm-up of mental maths or a puzzle such as the 24 game.
• Work on one hard problem for a proper attempt, say 15–20 minutes, before looking at a hint.
• Always review. Read the full solution even if you got it right, and look for a neater method.
• Keep a problem notebook of ideas and tricks that came up.

How to attack a hard problem

1. Understand it: restate it in your own words and list what is given.
2. Try small cases: substitute small numbers and look for a pattern.
3. Draw a diagram or make a table.
4. Work backwards from the answer you want.
5. Check and explain: does the answer make sense? Can you say why it must be true?

If you are stuck, take a break. Many solutions appear after a walk.

Building speed and accuracy

Competition time is short, so fast, accurate basics help a lot: tables, squares, fractions and percentages. Practise with the mental maths practice and check working with the fraction calculator and ratio calculator.

Staying motivated

• Treat it as a puzzle, not a test. Enjoy the problems you cannot solve yet.
• Celebrate progress, such as solving a problem you could not last month.
• Practise with friends. Explaining your solution deepens understanding.
• Do not compare yourself with others. Compare with your own earlier self.

For parents

Encourage curiosity, ask your child to explain their thinking, and keep sessions friendly. You do not have to solve the problems yourself. Praise effort and strategies, not only scores.

Getting guidance

A coach can choose problems at the right level, show better methods and give feedback on how you think, not just on the final answer. Our maths competition and Olympiad preparation uses non-routine problems, careful reasoning and feedback on the approach. Share the competition and level, and we confirm what fits.

Common questions

What age should a child start preparing for a maths Olympiad?

There is no fixed age. Many children begin with puzzles and problem-solving games in primary school and move to competition-style questions as they grow. Look at the contest's eligibility rules.

How is Olympiad maths different from school maths?

School maths often practises a taught method. Olympiad maths asks you to choose and combine ideas in new ways and to explain why they work.

How many hours a week should I practise?

Quality matters more than quantity. Two to four focused hours a week is a sensible routine for many students, adjusted for schoolwork and rest.

Do I need to be a "maths genius"?

No. Curiosity, practice and persistence matter more than natural talent. Everyone improves with good problems and feedback.

What should I do if I get stuck on every problem?

Move to slightly easier problems to build confidence, review the key ideas and ask for a hint. Progress comes from steadily stretching, not from always struggling.

This guide is general information. For exams, follow your school, teacher and official exam board, and use your own judgement about what suits your child.