Maths Olympiad Level 2: Preparation, Strategies and Solved Questions
Maths Olympiad Level 2 preparation helps students become confident with multi-step problems, mathematical reasoning, patterns and unfamiliar questions. The most useful preparation combines strong foundations with the habit of explaining why each step works.
Explore 24 Maths Olympiad Level 2 practice questions with fully worked answers, organised into four learning stages. You will also find strategies for tackling difficult questions, a revision timetable and guidance for students, parents and teachers.
Start with the School Connect International Maths Olympiad subject resources and the current Olympiad rules to confirm the exam stage, grade eligibility and applicable instructions for your registration.
What makes Level 2 Maths Olympiad preparation different?
More challenging maths questions often connect several familiar ideas. A ratio question may require fractions and algebra; a geometry problem may require both measurement and logical reasoning. Learning how to organise a solution is just as important as knowing the formula.
| Skill | What to practise | A helpful habit |
|---|---|---|
| Patterns and number sense | Sequences, divisibility, remainders and digit puzzles | Test a pattern against every given term |
| Algebra and arithmetic | Equations, fractions, percentages, ratios and inequalities | Check answers by substitution or estimation |
| Geometry and measurement | Angles, lengths, areas, similarity and diagrams | Sketch and label all known measurements |
| Data and probability | Tables, means, combinations and counting | Count outcomes systematically to avoid omissions |
| Advanced mathematics | Functions, sequences, calculus and vectors when age-appropriate | Explain every transformation and check its conditions |
Choose topics that match your class’s Maths Olympiad syllabus. For Level 2 stage participation, use your school or individual result information together with the applicable SCO exam rules.
Five strategies for harder Olympiad questions
- Read for conditions: underline the quantities, constraints and exact value requested.
- Draw a model: use a labelled diagram, a short table or a number line to make relationships visible.
- Work backwards: if an answer or target is given, test which earlier step could have produced it.
- Check an alternative: substitute the result into the original conditions or estimate to catch arithmetic mistakes.
- Build timed confidence: master the method without rushing, then practise similar problems within a reasonable time.
24 Maths Olympiad Level 2 Practice Questions with Solutions
Try each question before reading the explanation. Begin with the class group that fits your learning level, then progress to harder problems. Every answer shows the main reasoning, so you can learn from each calculation.
Classes 3–5: patterns and number puzzles
Question 1. Find the next number in the pattern 4, 9, 19, 39, __.
A. 79 | B. 69 | C. 59 | D. 89
Answer: A. 79. Each term doubles and then increases by 1: 39 × 2 + 1 = 79.
Question 2. A two-digit number has digits adding to 11. Its tens digit is 3 greater than its ones digit. What is the number?
A. 65 | B. 74 | C. 83 | D. 92
Answer: B. 74. Let the ones digit be u. Then u + (u+3) = 11, so u = 4 and the tens digit is 7. The number is 74.
Question 3. What is 2/3 of 45, minus 8?
A. 20 | B. 24 | C. 22 | D. 30
Answer: C. 22. Two-thirds of 45 is 30. Subtract 8 to obtain 22.
Question 4. A rectangle has perimeter 42 cm and length 13 cm. What is its width?
A. 7 cm | B. 10 cm | C. 9 cm | D. 8 cm
Answer: D. 8 cm. Perimeter = 2(length+width). Divide 42 by 2 to get 21, then subtract length 13 to get width 8 cm.
Question 5. Six friends shake hands once with each other friend. How many handshakes occur?
A. 15 | B. 12 | C. 18 | D. 30
Answer: A. 15. Each of the six friends shakes hands with five others, giving 30 counts. Each handshake is counted twice, so 30 ÷ 2 = 15.
Question 6. In a box the ratio of red to blue counters is 2:3. There are 35 counters in total. How many are red?
A. 12 | B. 14 | C. 18 | D. 21
Answer: B. 14. There are 2+3=5 equal parts. Each part is 35 ÷ 5 = 7. Red counters = 2 × 7 = 14.
Classes 6–8: multi-step arithmetic and algebra
Question 7. Solve 3(2x − 1) = 4x + 13.
A. 7 | B. 9 | C. 8 | D. 10
Answer: C. 8. Expand to 6x − 3 = 4x + 13. Subtract 4x and add 3: 2x = 16, so x = 8.
Question 8. Calculate 1/2 + 3/4 − 2/3.
A. 5/12 | B. 13/12 | C. 11/12 | D. 7/12
Answer: D. 7/12. Use the common denominator 12: 6/12 + 9/12 − 8/12 = 7/12.
Question 9. A jacket costs 800 units. It is reduced by 20%, then a 10% sales tax is added to the reduced price. What is the final price?
A. 704 | B. 700 | C. 680 | D. 720
Answer: A. 704. After the discount, the price is 800 × 0.8 = 640. Add 10% tax: 640 × 1.1 = 704.
Question 10. What is the sum of the interior angles of a pentagon?
A. 360° | B. 540° | C. 450° | D. 720°
Answer: B. 540°. An n-sided polygon has angle sum (n−2) × 180°. For five sides: 3 × 180° = 540°.
Question 11. The mean of four numbers 12, 18, x and 26 is 20. Find x.
A. 20 | B. 22 | C. 24 | D. 26
Answer: C. 24. The four numbers sum to 4 × 20 = 80. The known three sum to 56, so x = 80 − 56 = 24.
Question 12. What is the units digit of 7 raised to the power 2026?
A. 1 | B. 3 | C. 7 | D. 9
Answer: D. 9. The units digits of successive powers of 7 cycle 7,9,3,1. Since 2026 leaves remainder 2 when divided by 4, the units digit is 9.
Advanced Maths Olympiad Problems for Higher Classes
Classes 9–10: geometry, equations and probability
Question 13. Find the two roots of x² − 9x + 20 = 0.
A. 4 and 5 | B. 3 and 6 | C. 2 and 10 | D. −4 and −5
Answer: A. 4 and 5. Factor the expression: (x−4)(x−5)=0, giving roots 4 and 5.
Question 14. An arithmetic sequence begins 7, 11, 15, … . What is its 12th term?
A. 47 | B. 51 | C. 49 | D. 55
Answer: B. 51. The common difference is 4, so the 12th term is 7 + 11 × 4 = 51.
Question 15. Two similar triangles have corresponding sides in the ratio 6:15. If the smaller triangle has area 24 cm², what is the larger area?
A. 60 cm² | B. 96 cm² | C. 150 cm² | D. 120 cm²
Answer: C. 150 cm². Area scales with the square of the side ratio: 24 × (15/6)² = 24 × 6.25 = 150 cm².
Question 16. A bag contains four red and three blue counters. Two are drawn without replacement. What is the probability that both are blue?
A. 3/7 | B. 1/6 | C. 2/7 | D. 1/7
Answer: D. 1/7. P(first blue) = 3/7 and P(second blue given first blue) = 2/6. Multiply to get 6/42 = 1/7.
Question 17. A straight line passes through (2,7) and (5,16). Where does it meet the y-axis?
A. 1 | B. 0 | C. −2 | D. 3
Answer: A. 1. The slope is (16−7)/(5−2)=3. Write y=3x+b; using (2,7) gives 7=6+b, hence b=1.
Question 18. Which monic quadratic polynomial has two roots with sum 8 and product 15?
A. x²+8x+15 | B. x²−8x+15 | C. x²−15x+8 | D. x²+15x−8
Answer: B. x²−8x+15. For roots r and s, the monic polynomial is x²−(r+s)x+rs, which gives x²−8x+15.
Classes 11–12: functions, calculus and combinations
Question 19. If f(x)=2x−1 and g(x)=x²+3, find g(f(3)).
A. 22 | B. 25 | C. 28 | D. 34
Answer: C. 28. First calculate f(3)=5. Then apply g: 5²+3=28.
Question 20. How many ways can three students be chosen from seven distinct students when order does not matter?
A. 21 | B. 28 | C. 42 | D. 35
Answer: D. 35. Use combinations: 7C3 = (7×6×5)/(3×2×1) = 35.
Question 21. For f(x)=x³−3x²+2, find f'(2).
A. 0 | B. −2 | C. 2 | D. 6
Answer: A. 0. Differentiate to f'(x)=3x²−6x. Substitute x=2: 12−12=0.
Question 22. Evaluate the definite integral of 2x+1 from x=0 to x=2.
A. 4 | B. 6 | C. 5 | D. 8
Answer: B. 6. An antiderivative is x²+x. Evaluate at 2 and 0: (4+2)−0=6.
Question 23. Find the dot product of vectors (2, −1, 3) and (1, 4, 2).
A. 2 | B. 3 | C. 4 | D. 6
Answer: C. 4. Multiply corresponding components and add: (2×1)+(−1×4)+(3×2)=2−4+6=4.
Question 24. Two fair six-sided dice are rolled. Given that their sum is even, what is the probability both show even numbers?
A. 1/4 | B. 1/3 | C. 2/3 | D. 1/2
Answer: D. 1/2. An even sum occurs if both dice are even or both are odd: 9+9=18 outcomes. Nine have both even, so the conditional probability is 9/18=1/2.
Ten-Day Maths Olympiad Level 2 Study Plan
| Days | Focus | Learning outcome |
|---|---|---|
| 1–2 | Review the correct class syllabus and practise 6 mixed questions | Identify topics that need more attention |
| 3–4 | Practise patterns, arithmetic and algebra | Improve multi-step calculations and reasoning |
| 5–6 | Work on geometry, measurement and word problems | Learn to draw useful diagrams and connect formulas |
| 7–8 | Solve a mixed question set and explain each answer | Build accuracy and the confidence to handle unfamiliar problems |
| 9 | Try a timed practice session at a comfortable pace | Strengthen time management and careful reading |
| 10 | Revise mistakes and explain two challenging solutions aloud | Consolidate concepts before the next practice session |
Use an Error Log to Improve Your Solutions
After each session, keep a simple record of your learning. This is especially helpful when several answers look plausible.
| Question | Difficulty | What went wrong? | My next step |
|---|---|---|---|
| Example: fraction equation | Medium | Used different denominators | Practise common denominators and check by substitution |
| Example: triangle similarity | Challenging | Confused side scale with area scale | Square the scale factor before finding area |
| Your question | Easy / Medium / Challenging | Concept / Calculation / Reading / Timing | Write one specific concept to practise |
Class-Wise Maths Olympiad Syllabus and Practice Resources
For your actual examination, select the appropriate class from the SCO Maths Olympiad subject page. You can use the Maths syllabus overview to organise topic revision and the Class 1–12 Maths practice library to find more questions, answers and available papers.
For a foundation in common Olympiad methods, visit our Maths Olympiad Level 1 preparation guide. For a different approach to advanced topics, the class-wise Level 2 solutions guide provides another route for topic practice.
Checking Level 2 Eligibility and Exam Instructions
SCO offers maths participation across school grades, with second-stage or award-round arrangements depending on the selected programme, grade and cycle. Students should check the SCO Maths Olympiad rules and the relevant result or invitation before planning a Level 2 attempt.
For exact exam dates, duration, language, login details and other practical arrangements, use the current examination calendar and the instructions provided for your registered session. The registration page gives subject and fee information where applicable.
Frequently Asked Questions
How can students prepare for Maths Olympiad Level 2?
Practise different types of multi-step problems, explain solutions in writing, review errors and gradually introduce timed practice. Begin with the topics included in your class syllabus.
Which classes can take part in Level 2?
Second-stage eligibility depends on the SCO rules for your class and academic cycle. Check your qualification information and the published rules for the selected exam.
What types of questions are useful for Level 2 preparation?
Problems combining patterns, fractions, geometry, algebra, counting and logical reasoning are good practice. Choose more advanced topics as your school level and syllabus progress.
How long should I spend solving a difficult maths question?
During learning, spend enough time to understand the reasoning. In timed practice, follow the examination’s instructions and return to difficult questions after attempting ones you can solve confidently.
Where can I find Maths Olympiad papers and answers for my class?
Choose your grade in our Maths practice library. You will find questions with worked explanations and downloadable papers where available.
Can parents help with Level 2 maths preparation?
Yes. Parents can ask students to explain each step, encourage short daily practice, and discuss why an alternative answer might be incorrect. Teachers can group learners by topic to offer targeted support.
Should students learn formulas by heart?
Knowing important formulas helps, but understanding when to use them is essential. A labelled diagram and a simple explanation often reveal the correct approach faster than memorisation alone.
Where can I see the latest awards and recognition criteria?
The SCO awards information explains available recognition and applicable eligibility criteria.
Keep practising: Choose six questions above, write out your working and check each explanation. Then move to a new set of problems in the class-wise Maths practice resources.
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