ICSE Class 10 Maths Important Questions 2027 — Chapter-Wise
Chapter-wise ICSE Class 10 Maths important questions for 2027: GST, banking, quadratics, progressions, trigonometry, coordinate geometry and mensuration.
ICSE Class 10 Maths is an 80-mark paper plus 20 marks of internal assessment. Section A is compulsory, with short questions from every chapter; Section B gives you a choice of longer questions. Below are important questions from each chapter for the 2027 exam.
Paper Structure
| Section | Details | Marks |
|---|---|---|
| Section A | Compulsory — short answer questions from all chapters | 40 |
| Section B | Longer problems with a choice of questions (the latest specimen paper shows how many to attempt) | 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 ₹12,650 at maturity. Find the period. | 3 |
GST/Banking tip: these are formula-based. Learn the formulas, substitute carefully and show each step; they are some of the quickest 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 |
| From a point on the ground, the angle of elevation of the top of a tower is 30°. After walking 50 m towards the tower, it becomes 60°. Find the height of the tower. | 4 |
ICSE Maths chapter-wise practice
Super Tutor has chapter-wise ICSE Class 10 Maths practice quizzes, revision notes and an AI doubt solver. Free trial, no card needed.
Start 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 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 and 4 green balls. One ball is drawn at random. Find the probability that it is (a) red, (b) not blue, (c) red or green. | 3 |
| 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 |
| 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 every Section B question first | Use the reading time to pick the ones you are strongest in. |
| Attempt your best question first | Start with your strongest chapter to build confidence. |
| Show all working | Examiners give credit for correct working, so never skip steps. |
| Keep a backup question in mind | If you get stuck, switch to your next choice rather than losing time. |
Questions follow the ICSE Class 10 Mathematics syllabus; marks per question are indicative. Check cisce.org for the latest specimen paper and syllabus.
Turn this into exam marks
Super Tutor gives you chapter summaries, revision notes, practice quizzes and an AI doubt solver matched to your board syllabus — so you revise smarter, not longer.
Start freeFrequently Asked Questions
Which ICSE Maths chapters carry the most marks?
CISCE doesn't publish chapter-wise marks for ICSE Maths, and the compulsory first section has short questions from every chapter. Commercial mathematics (GST, banking, shares) is formula-based and quick to score; quadratic equations, trigonometry, coordinate geometry and mensuration often appear in longer questions. Prepare every chapter.
How is ICSE Maths different from CBSE?
ICSE Maths includes topics CBSE Class 10 doesn't, such as GST, banking, shares and dividends, matrices, reflection and the equation of a line. Both papers are 80 marks with 20 marks of internal assessment. ICSE gives a choice of longer questions in the second section, but the compulsory first section still covers every chapter.
How do I prepare for ICSE Maths Section A?
Section A is compulsory and has short questions from all chapters, so you can't skip any. Make sure you can solve basic problems from every chapter; even in a weak chapter, learn the formulas and solve a handful of basic problems.
What books should I use for ICSE Maths?
Use the textbook your school follows (many use Selina Concise or ML Aggarwal) and finish every exercise. Then solve CISCE's specimen paper and past ICSE papers, which are the best guide to how questions are framed. Publishers' sample papers are useful extra practice.