Maths Important Questions Class 10 CBSE 2026 — Chapter Wise
Class 10 Maths important questions 2026 — algebra, trigonometry, geometry, and statistics problems expected in CBSE board exam.
CBSE Class 10 Maths: 80 marks theory + 20 marks internal assessment. Algebra and Trigonometry together are nearly 50% of the paper. Below are the most expected questions from each chapter — solve all of these before your board exam.
Chapter-Wise Marks Distribution
| Unit | Chapters | Marks |
|---|---|---|
| Number Systems | Real Numbers | 6 |
| Algebra | Polynomials, Linear Equations, Quadratic Equations, AP | 20 |
| Coordinate Geometry | Coordinate Geometry | 6 |
| Geometry | Triangles, Circles, Constructions | 15 |
| Trigonometry | Trig Ratios, Trig Identities, Heights & Distances | 12 |
| Mensuration | Areas (Circles), Surface Areas & Volumes | 10 |
| Statistics & Probability | Statistics, Probability | 11 |
Real Numbers & Polynomials
| Question | Marks |
|---|---|
| Find the HCF and LCM of 306 and 657 using prime factorisation. Verify HCF × LCM = Product of numbers. | 3 |
| Prove that √2 is irrational. | 3 |
| Prove that 3 + 2√5 is irrational. | 3 |
| Find a quadratic polynomial whose zeroes are 3 and −2. Verify the relation between zeroes and coefficients. | 3 |
| If α and β are zeroes of x² − 5x + 6, find α² + β² and 1/α + 1/β. | 3 |
| Find the zeroes of 6x² − 3 − 7x and verify the relationship. | 3 |
Linear Equations & Quadratic Equations
| Question | Marks |
|---|---|
| Solve: 2x + 3y = 11, 2x − 4y = −24 (by substitution and elimination). | 3 |
| The sum of two numbers is 15 and sum of their reciprocals is 3/10. Find the numbers. | 5 |
| A train travels 360 km at a uniform speed. If speed increased by 5 km/h, it would take 1 hour less. Find the original speed. | 5 |
| Solve using quadratic formula: 2x² − 7x + 3 = 0 | 3 |
| Find the nature of roots of 3x² − 4√3x + 4 = 0 using discriminant. | 2 |
| The product of two consecutive positive integers is 306. Find the integers. | 3 |
| For what values of k does kx² + 6x + 1 = 0 have equal roots? | 2 |
Arithmetic Progressions
| Question | Marks |
|---|---|
| Find the 20th term of the AP: 3, 8, 13, 18, ... | 2 |
| Which term of AP 3, 15, 27, 39, ... is 132 more than its 54th term? | 3 |
| Find the sum of first 25 terms of AP: 7, 10.5, 14, ... | 3 |
| If sum of first n terms of AP is 3n² + 5n, find the AP and its 25th term. | 3 |
| How many terms of AP 24, 21, 18, ... must be taken so that their sum is 78? | 3 |
Practise Maths chapter-wise
Super Tutor has chapter-wise Maths problems for Class 10 — Algebra, Trigonometry, Geometry. Solve with step-by-step solutions.
Start Maths Practice — FreeTrigonometry
| Question | Marks |
|---|---|
| Prove: (sin A − cos A + 1)/(sin A + cos A − 1) = 1/(sec A − tan A) | 5 |
| Prove: (1 + tan²A)/(1 + cot²A) = tan²A | 3 |
| If tan(A+B) = √3 and tan(A−B) = 1/√3, find A and B (0° < A+B ≤ 90°). | 3 |
| From the top of a 7m building, the angle of elevation of a tower is 60° and angle of depression of its foot is 45°. Find tower height. | 5 |
| A 1.5m tall boy is standing at a distance of 20m from a 30m high building. Find the angle of elevation from his eyes to the top. | 3 |
| Two poles of heights 6m and 11m stand on a plane. If distance between feet is 12m, find distance between tops. | 3 |
Coordinate Geometry
| Question | Marks |
|---|---|
| Find the distance between points (2, 3) and (4, 1). Also find the midpoint. | 3 |
| Find the ratio in which line 3x + y − 9 = 0 divides the segment joining (1, 3) and (2, 7). | 3 |
| Find the area of triangle with vertices (2, 3), (−1, 0), (2, −4). | 3 |
| Show that points (1, −1), (5, 2), (9, 5) are collinear. | 3 |
Triangles & Circles
| Question | Marks |
|---|---|
| State and prove the Basic Proportionality Theorem (Thales theorem). | 5 |
| Prove that the ratio of areas of two similar triangles equals the ratio of squares of their corresponding sides. | 5 |
| Prove that the tangent at any point on a circle is perpendicular to the radius at the point of contact. | 5 |
| Two tangents from an external point to a circle are equal. Prove. | 3 |
| In ΔABC, DE ∥ BC. If AD = 2cm, DB = 3cm, AE = 3cm, find EC. | 2 |
| Construct a triangle similar to a given triangle with sides 3/5 of the corresponding sides. | 3 |
Mensuration
| Question | Marks |
|---|---|
| A solid is in the shape of a cone on a hemisphere. If radius = 1cm, height of cone = 2cm, find volume and surface area. | 5 |
| A metallic sphere of radius 4.2cm is melted and recast into a cylinder of radius 6cm. Find the height. | 3 |
| Find the area of the shaded region where a square of side 14cm has 4 equal circles inscribed. | 3 |
| A well of diameter 3m, depth 14m has earth spread around forming a 4m wide embankment. Find height of embankment. | 5 |
| Water in a cylindrical tank of radius 1.5m rises by 3.5cm when a sphere is submerged. Find sphere radius. | 3 |
Statistics & Probability
| Question | Marks |
|---|---|
| Find mean of the following data using assumed mean method: [frequency distribution table]. | 5 |
| Find median of: [grouped frequency table]. Draw ogive and verify. | 5 |
| Find mode of: [grouped frequency table]. | 3 |
| Two dice are thrown simultaneously. Find the probability of getting: (a) same number on both, (b) sum = 8, (c) doublet of even numbers. | 3 |
| A bag has 3 red, 5 black balls. Find probability of drawing: (a) a red ball, (b) not red, (c) neither red nor black. | 3 |
Must-Know Theorems & Proofs
| Theorem | Expected |
|---|---|
| BPT (Thales Theorem) | 5-mark proof — comes almost every year |
| Tangent-Radius Perpendicularity | 5-mark proof — very frequent |
| Pythagoras Theorem (converse too) | 3–5 marks — application problems |
| Areas of Similar Triangles | 3–5 marks |
| √2 is irrational | 3-mark proof |
Questions based on analysis of CBSE Class 10 Maths papers (2018–2025) and 2026 sample paper. Marks distribution from CBSE 2025–2026 blueprint. Solve all NCERT exercises before practising these. Last updated: February 2026.
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Start preparing — freeFrequently Asked Questions
Which chapters are most important for Class 10 Maths?
Top 5 by marks: Coordinate Geometry + Linear Equations (14 marks), Trigonometry (12 marks), Circles + Constructions (10 marks), Statistics & Probability (11 marks), Real Numbers + Polynomials (9 marks). Algebra and Trigonometry together cover nearly 50% of the paper.
How to score full marks in Class 10 Maths?
Three rules: (1) Solve NCERT examples + all back exercises — board questions are variations of these. (2) Show every step in numericals — step marks are generous. (3) Practise 10+ previous year papers under timed conditions. Maths rewards practice, not reading.
Is NCERT enough for Class 10 Maths?
Yes for boards — 95%+ questions are from NCERT or slight variations. Solve: all NCERT examples, all exercises, and NCERT Exemplar for extra practice. RD Sharma is useful for additional practice but not necessary. If you finish NCERT thoroughly, you will score 85+.
How many hours should I practise Maths daily?
Minimum 1.5-2 hours daily for Class 10 Maths. Spend 30 minutes on new concepts and 60-90 minutes on problem solving. In the last month before boards: solve 1 full paper every 2 days. Maths is a skill — daily practice is non-negotiable.