What maths olympiads test
Most school maths olympiads are built on the maths a student learns in school that year. The difference is in how they ask. A textbook exercise tells you which method to use; an olympiad question leaves you to work it out. It may combine two chapters, wrap a simple sum in a long story, or ask the question backwards (“the answer is 24; what was the starting number?”).
Speed matters, but not as much as people think. A student who knows basic facts fluently, such as tables, squares, simple fractions and place value, has more time left for thinking, and thinking is what the harder questions need.
For older students, the national maths olympiad pathway is a different kind of exam. It goes well beyond the school syllabus into number theory, combinatorics, algebra and geometry, and its problems take a long time each. The practice ideas for Classes 8–12 below cover both kinds.
Common question types
School maths olympiads tend to draw on the same families of questions, described here in general terms:
- Number sense and place value: comparing, ordering and building numbers, and spotting the largest or smallest number that fits a rule.
- Patterns and series: finding the next number or the missing one in a sequence, where the rule may be adding, multiplying, or a mix.
- Word problems: money, time, distance, sharing and age, often with two or three steps.
- Measurement: length, mass, how much a container holds, clocks and calendars, with conversions between units.
- Shapes and space: counting shapes in a figure, area and perimeter on grids, angles, symmetry and nets of solids.
- Fractions, decimals and percentages: comparing, converting and using them in real situations.
- Data handling: reading a table, bar graph or pictograph and answering a question from it.
- Logic within maths: questions where you must test each option, or reason from what is impossible.
Most papers also include a reasoning section and a few harder questions at the end. The harder ones often reward a neat idea over a long calculation.
Practice ideas by age
Classes 2–4
- Make maths spoken. “We need 3 packets of 6 eggs. How many eggs?” at the shop does more than a worksheet.
- Clocks and money at home. Reading a real clock, working out “how long until dinner?”, and counting change are all common question types.
- Shape hunts. Count the triangles in a drawing, fold paper to find symmetry, build shapes from matchsticks.
- Read word problems aloud and ask your child to say what the question wants before solving it.
- Ten minutes, not an hour. Short and regular is far better at this age.
Classes 5–7
- Fluency first. Tables to at least 12, squares to 20 and common fraction–decimal–percentage pairs (½ = 0.5 = 50%) save time throughout a paper.
- Draw the problem. Bar diagrams for ratio and fraction questions make many “hard” problems simple.
- Estimate before solving. A quick estimate catches answers that are ten times too big.
- Work backwards on questions that give the end result. It is a skill worth practising on its own.
- Keep a mistakes notebook, one line per error, and reread it before each paper.
Classes 8–10
- For school olympiads, make sure algebra, linear equations, mensuration and geometry from school are solid. Then practise mixing chapters in one question.
- For the pathway, work through one good problem-solving book slowly. Two or three problems a session, with full written reasoning, is plenty.
- Stay with hard problems. Give a difficult problem twenty minutes before looking at a hint. The struggle is the practice.
- Write solutions as if for someone else. Later pathway stages ask for proofs, and clear writing takes practice.
Classes 11–12
- Know which exam the week is for. Entrance exams reward speed across a wide syllabus; olympiad problems reward depth on a few hard ones.
- Past pathway papers, done under time and then reviewed problem by problem, are the most useful resource at this stage.
- Keep a problem log: the problem, the key idea, and what blocked you. Rereading it shows patterns in your own thinking.
- Find someone to discuss problems with, such as a teacher, a senior student or a friend preparing too.
Example questions
These are original practice questions written for this page, not taken from any exam.
1. The film (Classes 2–4)
A film starts at 4:45 pm and lasts 1 hour 30 minutes. At what time does it end?
Answer: 6:15 pm. One hour after 4:45 is 5:45, and 30 minutes more is 6:15.
2. The stickers (Classes 2–4)
Riya has 3 rows of 4 stickers. She gives 5 stickers to her brother. How many does she have left?
Answer: 7. She starts with 3 × 4 = 12 stickers, and 12 − 5 = 7.
3. The pattern (Classes 5–7)
What number comes next: 2, 6, 12, 20, 30, …?
Answer: 42. The gaps are 4, 6, 8 and 10, growing by 2 each time, so the next gap is 12, and 30 + 12 = 42.
4. The remainder (Classes 5–7)
What is the smallest number greater than 1 that leaves a remainder of 1 when divided by 2, by 3 and by 4?
Answer: 13. The smallest number divisible by 2, 3 and 4 is 12, so one more than that, 13, leaves a remainder of 1 each time.
5. Counting multiples (Classes 8–10)
How many two-digit numbers are divisible by 7?
Answer: 13. The two-digit multiples of 7 run from 14 (7 × 2) to 98 (7 × 14), which is 14 − 2 + 1 = 13 numbers.
Mistakes worth watching
- Answering a different question. A problem asks for the difference, and the student gives the larger number. Rereading the last line catches this.
- Units. Mixing centimetres and metres, or minutes and hours, is one of the most common slips.
- Stopping one step early. Multi-step problems often have a tempting option that matches an intermediate answer.
- Ignoring the options. In multiple choice, the options themselves are clues. If your answer isn’t among them, check your working before guessing.
For routines, mock papers and reviewing mistakes in general, see the olympiad prep guide. The reasoning guide covers the logic questions that often sit beside maths.
Where daily practice fits
A few quick questions a day keep number facts fluent between longer sessions. Ado’s free daily quiz of 8 questions, including a 60-second sprint, covers maths alongside science, English, GK and reasoning, ranked only against students the same age; it is a habit, not an olympiad course.