Free Maths Olympiad Study Materials for Classes 1–12
Good Maths Olympiad preparation starts with understanding important ideas and practising questions that make you think. Here you can find free class-wise Maths study resources, a 2026 syllabus, practice-paper links and 24 questions with worked answers, all in one place.
Choose the learning level that matches your class, solve a few questions before checking the answers, and use the explanations to improve your methods. Parents and teachers can use the topic table and study plan to guide practice without overwhelming younger learners.
Begin with the School Connect International Maths Olympiad subject page and 2026 Maths Olympiad syllabus to choose topics for your grade.
Free Maths Olympiad Resources: Where to Start
Start with a syllabus, practise a few questions on a topic, then try a sample paper when you are ready for a longer session. Use the answer key after completing your attempt to check your reasoning.
| Study resource | How it helps | Open resource |
|---|---|---|
| Class-wise syllabus | Choose maths topics suited to your class | Maths Olympiad Class 1–12 guide |
| 2026 syllabus overview | Plan learning in a clear sequence | Maths Olympiad syllabus |
| Grade-wise practice questions | Learn the methods behind tricky answers | Class 1–12 questions and papers |
| Class 5 sample paper | Try a longer set after revising the topics | Class 5 Maths sample paper |
| Exam preparation guide | Organise study and exam-readiness activities | 2026 Maths Olympiad exam guide |
Maths Topics to Practise for Your Class
| Class group | Study topics | How to practise |
|---|---|---|
| Classes 1–3 | Number sense, arithmetic, shapes, patterns, time | Use counters, drawings and short problems |
| Classes 4–6 | Fractions, decimals, factors, area, measurement, data | Write calculations and check units |
| Classes 7–9 | Integers, equations, algebra, geometry, probability | Show each reasoning step and check your answer |
| Classes 10–12 | Functions, trigonometry, algebra, calculus and statistics | Explain formulas and apply them to new problems |
Students can also build confidence with our Maths Olympiad Level 1 practice and Level 2 problem-solving exercises.
24 Free Maths Olympiad Practice Questions with Answers
Try these questions before reading their solutions. Begin at the level that suits your learning, and move to the next section when you feel ready. Each answer includes the calculation or reasoning used to solve the question.
Classes 1–3: numbers, shapes and patterns
Question 1. What is 36 + 27?
A. 63 | B. 53 | C. 73 | D. 83
Answer: A. 63. 36+20=56 and 56+7=63.
Question 2. Which number comes next: 3, 6, 12, 24, __?
A. 30 | B. 48 | C. 42 | D. 36
Answer: B. 48. Every number is twice the previous number, so 24×2=48.
Question 3. A ribbon is 25 cm long. You cut away 9 cm. How long is the remaining ribbon?
A. 14 cm | B. 18 cm | C. 16 cm | D. 34 cm
Answer: C. 16 cm. Subtract the amount cut from the total: 25−9=16 cm.
Question 4. Four equal boxes contain six counters each. How many counters are there altogether?
A. 10 | B. 18 | C. 30 | D. 24
Answer: D. 24. Four groups of six contain 4×6=24 counters.
Question 5. Which 2D shape has five straight sides?
A. Pentagon | B. Triangle | C. Rectangle | D. Hexagon
Answer: A. Pentagon. A pentagon is a polygon with five sides.
Question 6. The clock shows 3:20 p.m. What time will it be after 45 minutes?
A. 3:55 p.m. | B. 4:05 p.m. | C. 4:00 p.m. | D. 4:15 p.m.
Answer: B. 4:05 p.m.. Add 40 minutes to reach 4:00 p.m., then 5 more minutes to get 4:05 p.m.
Classes 4–6: fractions, measurement and data
Question 7. Calculate 5/6 − 1/3.
A. 1/6 | B. 2/3 | C. 1/2 | D. 4/3
Answer: C. 1/2. Change 1/3 to 2/6; then 5/6−2/6=3/6=1/2.
Question 8. Find the least common multiple of 9 and 12.
A. 18 | B. 24 | C. 108 | D. 36
Answer: D. 36. Multiples of 9 are 9,18,27,36, and multiples of 12 are 12,24,36. The first common one is 36.
Question 9. A rectangle measures 14 cm by 6 cm. What is its perimeter?
A. 40 cm | B. 20 cm | C. 42 cm | D. 84 cm
Answer: A. 40 cm. Perimeter=2×(14+6)=40 cm.
Question 10. A shop reduces a price of 600 units by 15%. What is the sale price?
A. 490 | B. 510 | C. 500 | D. 540
Answer: B. 510. Fifteen percent of 600 is 90, so the sale price is 600−90=510.
Question 11. The mean of four numbers 6, 10, 14 and x is 12. Find x.
A. 12 | B. 14 | C. 18 | D. 16
Answer: C. 18. A mean of 12 for four numbers requires a total of 48. The known numbers total 30, so x=18.
Question 12. A 3:5 ratio is shared among 40 counters. How many counters are in the smaller group?
A. 12 | B. 25 | C. 20 | D. 15
Answer: D. 15. There are eight equal parts, each 40/8=5; the smaller group has 3×5=15.
Classes 7–9: algebra, geometry and probability
Question 13. Solve 5x−7=28.
A. 7 | B. 6 | C. 5 | D. 8
Answer: A. 7. Add 7 to both sides to get 5x=35, then divide by 5 to find x=7.
Question 14. Calculate −3/4 + 5/8.
A. 1/8 | B. −1/8 | C. −11/8 | D. 11/8
Answer: B. −1/8. Write −3/4 as −6/8, then add 5/8 to get −1/8.
Question 15. A right triangle has shorter sides 8 cm and 15 cm. Find the hypotenuse.
A. 16 cm | B. 18 cm | C. 17 cm | D. 23 cm
Answer: C. 17 cm. Pythagoras gives √(8²+15²)=√289=17 cm.
Question 16. Two fair coins are tossed. What is the probability of exactly one head?
A. 1/4 | B. 1/3 | C. 3/4 | D. 1/2
Answer: D. 1/2. The equally likely outcomes are HH, HT, TH, TT. Two of four have exactly one head, so the probability is 1/2.
Question 17. Factorise x²−49.
A. (x−7)(x+7) | B. (x−7)² | C. (x+7)² | D. (x−1)(x+49)
Answer: A. (x−7)(x+7). This is a difference of squares: x²−7²=(x−7)(x+7).
Question 18. Find the slope of the line through (2,3) and (6,11).
A. 1 | B. 2 | C. 3 | D. 4
Answer: B. 2. Slope=(11−3)/(6−2)=8/4=2.
Classes 10–12: advanced maths
Question 19. Find the roots of x²−6x+8=0.
A. 1 and 8 | B. −2 and −4 | C. 2 and 4 | D. 3 and 5
Answer: C. 2 and 4. Factor the polynomial as (x−2)(x−4)=0, giving roots 2 and 4.
Question 20. What is sin 150°?
A. −1/2 | B. −√3/2 | C. √3/2 | D. 1/2
Answer: D. 1/2. 150° lies in the second quadrant; its reference angle is 30°, and sine is positive, so the value is 1/2.
Question 21. Find the derivative of f(x)=x³−4x at x=2.
A. 8 | B. 6 | C. 4 | D. 12
Answer: A. 8. Differentiate to get f'(x)=3x²−4, then substitute x=2: 3×4−4=8.
Question 22. How many ways can two students be selected from six distinct students?
A. 12 | B. 15 | C. 24 | D. 30
Answer: B. 15. Selection order does not matter, so use combinations: 6C2=(6×5)/2=15.
Question 23. Evaluate the definite integral of 2x from x=0 to x=3.
A. 6 | B. 8 | C. 9 | D. 12
Answer: C. 9. An antiderivative is x². Evaluate between 0 and 3: 3²−0²=9.
Question 24. Two fair six-sided dice are rolled. What is the probability that their sum is 7?
A. 1/12 | B. 1/9 | C. 1/3 | D. 1/6
Answer: D. 1/6. Six of 36 ordered outcomes sum to 7, so probability is 6/36=1/6.
How to Use Free Maths Practice Materials Effectively
- Choose one topic: study one idea, such as fractions or patterns, before attempting several questions.
- Work out the answer yourself: write the calculation or draw a simple diagram.
- Compare your reasoning: use the explanation to see which step mattered most.
- Try a similar question: change the numbers to test whether you understand the method.
- Make time for review: practise regularly and revisit difficult questions after a few days.
A Seven-Day Maths Olympiad Study Plan
| Day | Learning activity | Goal |
|---|---|---|
| 1 | Read the class syllabus and choose your first two topics | Set an achievable target |
| 2 | Practise number skills and arithmetic | Improve calculation accuracy |
| 3 | Work on patterns, factors, fractions or algebra | Strengthen mathematical reasoning |
| 4 | Study shapes, measurement or geometry | Understand diagrams and formulas |
| 5 | Try six mixed-topic questions | Apply the concepts together |
| 6 | Attempt a sample paper or longer practice set | Build concentration and sensible pacing |
| 7 | Review mistakes and write your next learning goals | Remember the method and plan ahead |
Free Online Learning and Student Registration
The questions on this page and the linked public study resources are available to explore online. Students who use a School Connect account can follow the learning options displayed for their class and programme. To prepare for an examination, check the exam dates and registration details, including any fee or participation requirements.
Frequently Asked Questions
Where can I find free Maths Olympiad study material?
Use the practice questions above, the Maths Olympiad syllabus and our class-wise Maths question library to start practising.
Do I need to register to practise these 24 questions?
No. Read the questions and worked solutions directly on this page and choose the topics that suit your class.
How can I choose the right Maths Olympiad syllabus?
Select your class from the SCO Maths Olympiad page and match the topics to your school learning.
Can I find Maths Olympiad sample papers online?
Yes. The official Maths Olympiad resource page provides class-wise sample-paper links. You can also begin with the Class 5 example.
How can I improve at difficult Maths Olympiad questions?
Start with simpler examples, show all steps, check your work and try another question that uses the same idea.
Are online study materials the same as examination registration?
You can practise the questions here without registering for an exam. For examination participation, choose the class and subject on the SCO registration page.
Can teachers use these questions in lessons?
Yes. Select questions for the appropriate grade, let students solve them independently and discuss different approaches before reviewing the worked answers.
What should I study after completing this page?
Explore the Level 1 Maths practice guide or try more challenging Level 2 questions when ready.
Keep learning: Choose six questions from your class group and try them without looking at the answers. Then check each solution and decide what to practise next.
Leave a Reply