A Level 2-style Maths challenge can feel different from an ordinary workbook question. It may combine two familiar ideas, hide the useful number in a story, or ask you to explain why a pattern always works. You do not need to learn secret tricks: begin by drawing, estimating, testing a small case and checking every result. This 2026–27 guide offers twenty original, fully explained Maths questions for Classes 3–12, with techniques you can use in school, at home or during carefully chosen extra practice. The goal is to become a more thoughtful problem solver—whether or not you have qualified for a formal second-round competition.
First, what does ‘Maths Olympiad Level 2’ really mean?
‘Level 2’ can describe a second round for students selected after Level 1, or simply harder practice material. These are not interchangeable. A learner can try demanding puzzles without qualifying for any formal second round. Entry to a real Level 2 assessment must follow the specific organiser’s current selection rules and invitation.
On older SCO awards and eligibility information, selection examples include high grade-level scores and qualifying school toppers, while Classes 1 and 2 are described as ranked from Level 1 rather than sitting its second stage. The page contains historic rules, and other published details are not fully consistent. Treat the current result notice, class-wise instructions and invitation as authoritative for your actual exam rather than assuming that an old percentage applies to every 2026–27 session.
For broader guidance on choosing the right round, Maths and Science together, read the companion Olympiad Level 2 preparation guide. This article takes a different approach: learn twenty distinct Maths methods and see exactly how the answers are obtained.
What the published 2026–27 dates and fees do—and do not—establish
| Public information | What is supported | What is still unconfirmed |
|---|---|---|
| SCO WINTER 2027 Maths subject schedule | The published Maths subject-cycle dates include 18 October, 6 November, 14–15 November, 4 December, 12 December and 20 December 2026. | Whether these are separate Level 2 dates, a qualifying student’s approved sitting or a guaranteed available seat. |
| Maths entry fee | The current registration catalogue displays ₹200 / US$12 for the listed Maths Olympiad registration. | A universal extra Level 2 fee, exemption or second-round payment method. |
| Results and invitations | SCO has a results page and published awards guidance. | A student’s Level 2 qualification before their cycle-specific results and invitation are confirmed. |
| Past papers | The portal has grade-specific 2026 syllabus, sample paper and answer-key landing pages. | That any PDF called ‘2026’ or ‘previous year’ was an administered Level 2 paper in that exact year. |
The older promise of a fixed ‘first week of February’ Level 2 exam and INR 200 / USD 11 is not a reliable current fact. Current Maths entry information shows ₹200 or US$12, while the cycle calendar does not separately establish Level 2. Neither a public award table nor a sample paper should be treated as an individual examination invitation.
Seven ways to tackle a harder Maths question
- Draw before calculating. Use boxes, equal groups, number lines or a sketch when the quantities are hidden inside a story. For perimeter, trace the boundary rather than thinking about the space inside.
- Work backwards. If a number is doubled and then increased by nine, reverse those steps to discover the original. Undo adding before undoing multiplication.
- Look at differences as well as terms. For 2, 5, 10, 17, 26, differences 3, 5, 7, 9 suggest the next difference 11. The pattern rule should explain every given term.
- Write a simple equation. A ‘larger number and smaller number’ problem becomes easier with x+y and x−y rather than repeated guessing.
- Check the order of operations. A discount followed by tax has a different base for the second percentage. Keep a short line of working for each step.
- Test a small case. For ratios or sequences, use a simpler total first to understand the method, then apply it to the actual numbers.
- Verify independently. Substitute a solution, add the parts to check the total, estimate an answer, or solve using a second method. A letter alone does not show understanding.
Class-wise Maths problem-solving map
| Class range | Ideas to develop | How to practise |
|---|---|---|
| Classes 3–4 | Multiplication, sharing, number patterns, digits, simple geometry and time. | Draw equal groups and convert story problems into two clear steps. |
| Classes 5–6 | Fractions of a whole, ratios, area and perimeter, percentage ideas, and missing numbers. | Estimate first, simplify fractions and label units in every answer. |
| Classes 7–8 | Linear equations, simultaneous clues, probability, proportional reasoning and right-triangle geometry. | Write the relationship before calculating and check by substitution. |
| Classes 9–10 | Factorisation, arithmetic sequences, combined percentage changes, similarity and probability. | Explain formulas, assumptions and why a method applies. |
| Classes 11–12 | Functions, sequences and series, calculus basics and probability without replacement. | Show every algebraic step, define variables and verify the final expression. |
This is a teaching progression, not an exact paper blueprint. The actual grade-wise Maths syllabus can vary by organiser and cycle. For younger students, a challenging two-step addition problem may be suitable; a Class 3 learner does not need to attempt derivatives to ‘train for Level 2’.
Five worked strategies before the question set
Strategy 1 — Split a number into helpful parts
When subtracting 18 from 42, subtract 20 first and add back two: 42−20+2 = 24. This mental calculation is often quicker and less error-prone than subtracting individual digits without understanding place value.
Try next: Write three different methods for finding 62−29; check that all give the same answer.
Strategy 2 — Convert a pattern into its rule
For the sequence 2, 5, 10, 17, 26, you might notice that each term is one more than a square: 1²+1, 2²+1, 3²+1 and so on. The next term is 6²+1 = 37. Another check is the growing odd-number differences.
Try next: Explain both the square-plus-one rule and the odd-difference rule to a friend.
Strategy 3 — Treat a ratio as equal-sized parts
A class has 48 pupils and a boys-to-girls ratio of 3:5. There are eight equal parts, each worth six pupils. Boys are 3×6=18 and girls 5×6=30. Check 18+30=48 and that 18:30 reduces to 3:5.
Try next: Make a similar puzzle for 56 counters split in the ratio 2:5, then check both quantities.
Strategy 4 — Draw similarity instead of guessing area
When every side of a figure grows by a factor of 3/2, the area grows by (3/2)² = 9/4. If a smaller triangle’s area is 24 cm², the larger area is 54 cm². It is a mistake to multiply the area by only 3/2.
Try next: Draw a square with side 2 cm and another with side 3 cm. Compare side and area ratios.
Strategy 5 — Make probability outcomes visible
For a fair coin tossed twice, write the outcomes HH, HT, TH and TT. Exactly one head occurs twice, so the probability is two out of four, or one half. For balls chosen without replacement, remember that the total in the bag changes after the first selection.
Try next: Draw two branches for the second coin toss or colour five circles to model choosing beads.
20 original Maths Olympiad Level 2-style questions and worked answers
Try the questions for your own class range first. These exercises are newly written for this guide. They have not been copied from an official SCO Level 2 paper or the International Mathematical Olympiad. Difficulty is intentionally mixed; a question’s suggested class is a teaching guide, not proof that the question appears in that class’s actual second-round examination.
Question 1 (Class 3 · doubling pattern). A sequence begins 4, 8, 16, 32. What is the next number?
A. 64 | B. 48 | C. 36 | D. 72
Answer: A — 64. Every term is twice the previous one: 32 × 2 = 64. Writing the doubling rule prevents guessing from the last two numbers alone.
Question 2 (Class 3 · multi-step sharing). Twenty-four stickers are shared equally among four friends. Each friend gives two stickers to a sibling. How many stickers does each friend keep?
A. 6 | B. 4 | C. 8 | D. 3
Answer: B — 4. Each friend gets 24 ÷ 4 = 6 stickers. Giving away two leaves 6 − 2 = 4. Divide before subtracting.
Question 3 (Class 4 · rectangle reasoning). A rectangle has a perimeter of 30 cm and one side is 9 cm. How long is the other side?
A. 12 cm | B. 3 cm | C. 6 cm | D. 21 cm
Answer: C — 6 cm. Opposite sides match. Half the perimeter is 30 ÷ 2 = 15, so 9 + width = 15 and width = 6 cm.
Question 4 (Class 4 · digit puzzle). The tens digit of a two-digit number is three greater than its units digit. The digits total 11. What is the number?
A. 47 | B. 83 | C. 65 | D. 74
Answer: D — 74. Let the units digit be u and tens digit u + 3. Then 2u + 3 = 11, so u = 4 and tens digit = 7. The number is 74.
Fractions, ratios and two-step thinking
Question 5 (Class 5 · fractions of a whole). A class reads two-fifths of a 60-page booklet on Monday and one-third on Tuesday. How many pages remain?
A. 16 | B. 20 | C. 24 | D. 44
Answer: A — 16. Two-fifths of 60 is 24; one-third is 20. Altogether 44 pages are read, leaving 60 − 44 = 16.
Question 6 (Class 5 · odd differences). Which number follows 2, 5, 10, 17, 26?
A. 35 | B. 37 | C. 36 | D. 42
Answer: B — 37. The increases are +3, +5, +7, +9; the next increase is +11, giving 26 + 11 = 37.
Question 7 (Class 6 · ratio partitions). A group has boys and girls in a 3:5 ratio. There are 48 students altogether. How many are girls?
A. 18 | B. 24 | C. 30 | D. 32
Answer: C — 30. The ratio has eight equal parts. Each is 48 ÷ 8 = 6 students. Girls account for five parts: 5 × 6 = 30.
Question 8 (Class 6 · time calculation). An imaginary train leaves at 9:45 am and the journey lasts 2 hours 35 minutes. When does it arrive?
A. 11:20 am | B. 12:10 pm | C. 12:30 pm | D. 12:20 pm
Answer: D — 12:20 pm. 9:45 + 2 hours is 11:45. Adding 35 minutes reaches 12:20 pm after crossing midday.
Algebra and geometry connections
Question 9 (Class 7 · simultaneous clues). Two numbers have sum 17 and difference 5. What is the larger number?
A. 11 | B. 12 | C. 10 | D. 6
Answer: A — 11. Adding the equations x + y = 17 and x − y = 5 gives 2x = 22. Therefore x = 11 and the other number is 6.
Question 10 (Class 7 · percentage steps). A fictional item costs 180 units. Its price is reduced by 20%, then 10% tax is applied to the reduced price. What is the final price?
A. 162.00 | B. 158.40 | C. 160.00 | D. 144.00
Answer: B — 158.40. After discount: 180 × 0.8 = 144. After tax: 144 × 1.1 = 158.4. Applying both percentages to the original total would be incorrect.
Question 11 (Class 8 · consecutive integers). Three consecutive integers total 96. What is the middle integer?
A. 30 | B. 31 | C. 32 | D. 33
Answer: C — 32. Write the numbers as n−1, n, n+1. Their sum is 3n = 96, so n = 32; the numbers are 31, 32, 33.
Question 12 (Class 8 · Pythagoras). A right triangle has perpendicular sides measuring 9 cm and 12 cm. Find its hypotenuse.
A. 21 cm | B. 10 cm | C. 14 cm | D. 15 cm
Answer: D — 15 cm. For a right triangle, c² = 9² + 12² = 81 + 144 = 225. Thus c = 15 cm.
Sequences and probability
Question 13 (Class 9 · factorisation). Solve x² − 7x + 12 = 0. Which pair gives both roots?
A. 3 and 4 | B. 2 and 6 | C. −3 and −4 | D. 1 and 12
Answer: A — 3 and 4. Factor the equation as (x−3)(x−4) = 0. Thus x = 3 or x = 4; both make the equation equal zero.
Question 14 (Class 9 · nth term). An arithmetic sequence is 7, 11, 15, 19, … . Find its twentieth term.
A. 79 | B. 83 | C. 87 | D. 80
Answer: B — 83. The first term is 7 and difference is 4. T₂₀ = 7 + (20−1) × 4 = 7 + 76 = 83.
Question 15 (Class 10 · probability). A fair coin is tossed twice. What is the probability of getting exactly one head?
A. 1/4 | B. 3/4 | C. 1/2 | D. 1/3
Answer: C — 1/2. The equally likely outcomes are HH, HT, TH, TT. Exactly one head occurs in HT and TH: 2/4 = 1/2.
Question 16 (Class 10 · similar areas). Two similar triangles have corresponding side lengths in the ratio 2:3. The smaller has area 24 cm². What is the larger triangle’s area?
A. 36 cm² | B. 48 cm² | C. 81 cm² | D. 54 cm²
Answer: D — 54 cm². Area scales with the square of the side factor. Larger area = 24 × (3/2)² = 24 × 9/4 = 54 cm².
Advanced senior-grade reasoning
Question 17 (Class 11 · function evaluation). For f(x) = x² − 3x + 2, find f(4).
A. 6 | B. 10 | C. 2 | D. 18
Answer: A — 6. Substitute x=4: 4² − 3×4 + 2 = 16 − 12 + 2 = 6.
Question 18 (Class 11 · arithmetic series). The first term of an arithmetic series is 3 and each next term is 4 larger. What is the sum of the first ten terms?
A. 190 | B. 210 | C. 230 | D. 200
Answer: B — 210. The tenth term is 3 + 9×4 = 39. Sum = 10×(3+39)/2 = 210.
Question 19 (Class 12 · derivative). If f(x) = x³ − 2x², what is f′(2)?
A. 12 | B. 8 | C. 4 | D. 0
Answer: C — 4. Differentiate term by term: f′(x) = 3x² − 4x. At x = 2, the value is 12 − 8 = 4.
Question 20 (Class 12 · without replacement). A bag has three red and two blue beads. Two beads are chosen without replacement. What is the probability both are red?
A. 9/25 | B. 1/5 | C. 2/5 | D. 3/10
Answer: D — 3/10. The first red probability is 3/5. After it is taken, two red remain among four beads: 2/4. Multiply: 3/5 × 2/4 = 3/10.
Make your mistake notebook genuinely useful
After checking a worked answer, write more than a tick or cross. Was the problem difficult because you misread a relationship, used the wrong arithmetic operation, forgot a formula, mixed units, or made a careless calculation? The answer tells you which skill to practise next. A corrected explanation is stronger evidence of improvement than repeating the same answer letter.
| I noticed… | A helpful next action | A check that builds confidence |
|---|---|---|
| I used addition instead of multiplication | Draw equal groups; write repeated addition, then multiplication. | Count the groups and the items per group separately. |
| The fractions did not make sense | Find each fraction of the same original whole before subtracting. | Re-add the used and remaining parts to equal the original. |
| I forgot to change the percentage base | Write one line for the discounted total and another for tax. | Estimate whether the result should be above the reduced price. |
| The algebra answer was wrong | Rearrange one step at a time and keep both sides balanced. | Substitute the answer into the original equation. |
| The geometry unit was missing | Label length in cm or m, area in cm² or m². | Use a sketch to decide if it asks for boundary or inside space. |
Four weeks of deeper Maths practice
| Week | Focus | A realistic practice activity |
|---|---|---|
| Week 1 | Find two topics you understand and one that needs stronger foundations. | Read the appropriate class syllabus, then solve six untimed examples and explain the steps. |
| Week 2 | Patterns, multi-step stories and geometry diagrams. | Try four related problems, including one you can check with a different approach. |
| Week 3 | Algebra, fractions or probability suited to your class. | Attempt a small mixed set, keep a mistake notebook and revisit it after two days. |
| Week 4 | Accuracy, checking and calm time management. | Complete a short self-selected timed practice only after you understand the questions; use the answer key for a careful review. |
Taking more mock tests does not automatically lead to better reasoning. Some learners will progress faster with a teacher-led conversation, a page of sketches or one difficult question explained properly. Make space for breaks and avoid treating practice scores as a guarantee of an Olympiad award.
Find class-wise Maths learning resources
Begin with the current grade-specific syllabus and actual sample-paper landing page. A landing page marked ‘2026’ may link to a PDF from an earlier set, so check the opened document’s cover and date rather than describing every file as a freshly administered 2026 Level 2 exam.
| Class | Syllabus / learning scope | Sample or answer resource |
|---|---|---|
| Class 3 | Syllabus listing | Sample Paper 1 |
| Class 5 | Syllabus listing | Sample Paper 1 |
| Class 6 | Syllabus listing | Answer key |
| Class 9 | Class 9 subject guide | Sample listing |
| Class 12 | Class 12 subject guide | Sample listing |
For Classes 3–12, students can explore the SCO Maths subject hub, Maths sample-paper collection and free learning materials guide. School Connect Olympiad provides free chapter-wise learning materials, linked educational videos and practice questions. The learning resources are continually updated and improved. Students can use the twenty worked examples here without registering for an exam.
Frequently asked questions about Maths Olympiad Level 2
Is this an official Level 2 Maths Olympiad examination paper?
No. The twenty questions are original problem-solving exercises written for this guide. They are not official SCO Level 2 questions, a leaked paper or a complete match for any particular competition’s difficulty.
Who can take a Level 2 Maths Olympiad?
It depends on the actual organiser and year. SCO’s older information describes qualifying students from Level 1 in certain grades, but published historical criteria are not always consistent. A student’s current invitation or verified organiser instruction is the final authority.
Can Classes 1 and 2 take Level 2?
SCO’s historical awards page says that Classes 1 and 2 are ranked from Level 1 rather than sitting its second stage. Verify the rule for the actual cycle. Younger students may still enjoy harder Maths puzzles without entering Level 2.
What marks or ranking do I need to qualify?
Do not assume a universal top-five-percent cut-off, state ranking or school topper rule. Older SCO pages describe several methods; selection rules and score thresholds may differ by year and event. Use current results and the organiser’s confirmed guidance.
Is the Level 2 exam definitely held in February 2027?
That has not been confirmed from the current public schedule. The published WINTER 2027 calendar lists Maths subject sessions during October–December 2026, not a distinct verified second-round date. Do not arrange travel or payment from a historic February claim.
Is there a separate fee for Level 2?
The current SCO Maths registration catalogue shows ₹200 or US$12 for the listed Maths entry. It does not establish a standard fee for a separate second round. Ask for the current Level 2 instruction before paying anything extra.
Are there authentic Level 2 previous-year Maths papers for every class?
Several blog posts are labelled as previous-year or Level 2 practice, but a title alone does not prove a file was administered in that round. Check the cover, edition, organiser and actual PDF before treating it as an authentic past exam.
How is this guide different from the Maths and Science Level 2 preparation page?
This page concentrates on twenty Maths-only worked problems and techniques, from patterns and fractions through algebra and probability. The linked wider Level 2 page discusses selection, planning and both Maths and Science.
Should I time every problem?
No. Learn the method first, then try short timed sets after you understand the idea. A hard problem solved carefully is often more useful than several random guesses made quickly.
Which Maths topics matter most?
Match your grade’s current syllabus first. Common teaching themes include number patterns, fractions, geometry, algebra, ratios, data and probability; this guide’s mixed-grade exercises do not claim to reproduce one official level’s full syllabus.
Can a School Connect Level 2 award qualify me for the official International Mathematical Olympiad national team?
No. The official IMO uses separate country-by-country national-team selection. SCO’s independent school-level International Maths Olympiad is not the same event.
Are chapter-wise lessons, videos and practice questions free?
School Connect Olympiad provides free chapter-wise learning materials, linked educational videos and practice questions. The learning resources are continually updated and improved. For any separate timed exam or student-specific competition report, follow the current event and account instructions.
Your best next step is one well-explained question
Choose a Maths idea that feels just beyond your comfort zone, make a sketch and work through it carefully. A student who can explain a solution, find a mistake and check an answer is already building the habits that make advanced Maths enjoyable. If you have a real Level 2 invitation, follow the organiser’s specific current instructions; otherwise you can keep learning with class-appropriate practice. School Connect’s Maths subject pages provide one optional set of further resources.
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