ICSE Maths Important Questions Class 10 2026 — Chapter Wise
ICSE Class 10 Maths important questions 2026 — quadratic equations, GST, banking, probability, and mensuration with solutions.
ICSE Class 10 Maths: 80 marks external (2.5 hours) + 20 marks internal assessment. Section A (40 marks) is compulsory — short questions from all chapters. Section B (40 marks) gives choice: attempt any 4 out of 7 detailed questions. Below are the most expected questions from each chapter.
Paper Structure
| Section | Details | Marks |
|---|---|---|
| Section A | Compulsory — short answer questions from all chapters | 40 |
| Section B | Attempt any 4 out of 7 — detailed problems | 40 |
| Total (External) | 80 | |
GST & Banking (Easy Marks)
| Question | Marks |
|---|---|
| A shopkeeper buys an article for ₹5,000 and sells it for ₹6,500. If GST is 12%, find: (a) CGST and SGST paid by shopkeeper, (b) amount paid by customer, (c) GST paid to government by shopkeeper. | 4 |
| A manufacturer sells goods worth ₹50,000 to a wholesaler at 18% GST. Wholesaler sells to retailer at ₹60,000 at 18% GST. Find: Input Tax Credit for wholesaler and tax paid to government. | 4 |
| Ramesh deposits ₹2,500 per month in a recurring deposit for 2 years at 8% p.a. Find the maturity value. | 3 |
| Mrs Gupta opens a recurring deposit of ₹1,000 per month at 10% p.a. She gets ₹12,715 at maturity. Find the period. | 3 |
GST/Banking tip: These are pure formula-based questions. Memorise the formulas, substitute carefully, and you get full marks. Easiest marks in the paper.
Quadratic Equations
| Question | Marks |
|---|---|
| Solve: x² − 7x + 12 = 0 using the quadratic formula. | 3 |
| The product of two consecutive positive integers is 240. Form and solve the quadratic equation. | 4 |
| A two-digit number is such that the product of its digits is 12. When 36 is added, the digits interchange. Find the number. | 4 |
| For what values of k does the equation 2x² + kx + 3 = 0 have equal roots? | 3 |
| If the roots of 3x² − 5x + q = 0 are equal, find q. Also find the roots. | 3 |
Arithmetic & Geometric Progression
| Question | Marks |
|---|---|
| Find the sum of the first 20 terms of AP: 3, 11, 19, 27, ... | 3 |
| How many terms of GP: 3, 9, 27, ... are needed to get a sum of 363? | 3 |
| The 4th term of AP is 11 and the 8th term is 23. Find the first term and common difference. | 3 |
| Find the sum of all natural numbers between 100 and 300 which are divisible by 7. | 4 |
| If a, b, c are in GP, prove that a², b², c² are also in GP. | 3 |
Trigonometry
| Question | Marks |
|---|---|
| Prove: (sin A + cosec A)² + (cos A + sec A)² = 7 + tan²A + cot²A. | 4 |
| Prove: (1 + cot A − cosec A)(1 + tan A + sec A) = 2. | 4 |
| Without using trigonometric tables, evaluate: sin²20° + sin²70° + tan 45° × (tan 10° × tan 80°). | 3 |
| From the top of a cliff 80m high, the angles of depression of two ships are 30° and 60°. Find the distance between the ships. | 4 |
| A vertical tower stands on a horizontal plane. From a point on the ground 36m away, the angle of elevation of the top is 60° and from the top of a pole 12m high, the angle of elevation is 30°. Find the height of the tower. | 4 |
ICSE Maths chapter-wise practice
Super Tutor has chapter-wise ICSE Maths questions — Quadratics, Trigonometry, Mensuration. Practise with step-by-step solutions.
Start ICSE Maths Practice — FreeCoordinate Geometry
| Question | Marks |
|---|---|
| Find the equation of a line passing through (2, −3) and perpendicular to 3x + 4y = 8. | 3 |
| The line y = mx + c passes through (1, 2) and is perpendicular to 2x − 3y + 5 = 0. Find m and c. | 3 |
| Find the coordinates of the point which divides the line segment joining (4, −3) and (8, 5) in the ratio 3:1 internally. | 3 |
| Find the area of triangle with vertices A(1, 2), B(3, −4), C(−2, 3). | 3 |
| Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y = 8, and parallel to x − y + 3 = 0. | 4 |
Probability
| Question | Marks |
|---|---|
| Two dice are thrown simultaneously. Find the probability of: (a) getting a doublet, (b) getting a sum of 9, (c) getting a sum greater than 10. | 4 |
| A bag contains 5 red, 3 blue, 4 green balls. If 2 balls are drawn at random, find P(both red), P(one red one blue). | 4 |
| Cards marked 3 to 50 are placed in a box. A card is drawn at random. Find P(prime number), P(perfect square), P(multiple of 7). | 3 |
| A coin is tossed 3 times. Find the probability of: (a) exactly 2 heads, (b) at least 1 head, (c) at most 2 tails. | 3 |
Mensuration
| Question | Marks |
|---|---|
| A solid is composed of a cylinder (radius 7cm, height 10cm) and a hemisphere at one end. Find total surface area and volume. | 4 |
| A cone of height 24cm and radius 6cm is melted and recast into a sphere. Find the radius of the sphere. | 3 |
| A bucket is in the form of a frustum. Top radius = 28cm, bottom radius = 21cm, height = 45cm. Find capacity in litres and cost of milk at ₹30/litre. | 4 |
| The area of the curved surface of a cone is 60π cm² and its slant height is 10cm. Find: (a) radius, (b) height, (c) volume. | 4 |
| From a solid cylinder of height 7cm and radius 3cm, a conical cavity of same height and radius is hollowed out. Find the volume and total surface area of the remaining solid. | 4 |
Matrices & Ratio/Proportion
| Question | Marks |
|---|---|
| If A = [2 1; 3 4] and B = [1 0; −1 2], find: (a) AB, (b) A², (c) A − 2B. | 4 |
| If a:b = 3:4 and b:c = 8:9, find a:b:c. | 2 |
| Using properties of proportion, if (3a+5b)/(3a−5b) = (3c+5d)/(3c−5d), prove that a/b = c/d. | 4 |
Section B Strategy
| Strategy | Details |
|---|---|
| Read all 7 questions first | Spend 5 minutes reading. Identify your 4 strongest. |
| Attempt easiest first | Start with your best chapter. Build confidence. |
| Show all working | Step marks are generous in ICSE. Never skip steps. |
| Have a backup 5th question | If you get stuck on one, switch to your 5th choice. Do not waste time. |
Questions based on CISCE ICSE Maths specimen papers and previous year papers (2015–2025). Marks distribution is approximate and may vary. Always check cisce.org for the latest specimen paper. Last updated: February 2026.
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Start preparing — freeFrequently Asked Questions
Which ICSE Maths chapters carry the most marks?
Highest-weightage chapters: Quadratic Equations, Trigonometry, Mensuration, Coordinate Geometry, and Probability. GST & Banking are easy marks (formula-based). Section A (40 marks) is compulsory and tests all chapters. Section B (40 marks) gives choice — attempt 4 out of 7 questions, so choose your strongest chapters.
How is ICSE Maths different from CBSE?
ICSE Maths goes deeper in application: GST and Banking (not in CBSE), more challenging Trigonometry problems, and harder Mensuration questions. ICSE also has more choice in Section B (choose 4 of 7), which is an advantage — you can skip weak chapters. The paper is 80 marks in 2.5 hours (vs CBSE's 80 marks in 3 hours).
How to prepare for ICSE Maths Section A?
Section A is compulsory (40 marks) with short questions from ALL chapters. You cannot skip any chapter. Strategy: ensure you can solve basic-level problems from every chapter. Even if you're weak in a chapter, learn the formulas and solve 5 basic problems. Section A questions are generally easier than Section B.
What books should I use for ICSE Maths?
Primary: Your prescribed textbook (Selina or ML Aggarwal). Secondary: Together With ICSE or Oswaal for sample papers. Solve: official CISCE specimen paper + last 10 years' previous year papers. PYQs are the single best resource — ICSE repeats question styles.