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Class 10 Maths PYQ chapter wise: marks per chapter in the 2025 and 2026 board papers
In short: we read two real CBSE Class 10 Mathematics Standard board papers question by question, set 30/1/1 of 2025 and set 30/4/1 of 2026, and counted the marks each NCERT chapter carried. Every chapter appeared in both papers, and the totals for each unit matched CBSE's official unit marks exactly. Below are the counts, where to download the papers free from CBSE, how to use them chapter by chapter, and 8 questions of our own in the same styles, with worked answers.
The 8 practice questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us. We do not copy past-paper questions here; for those, use CBSE's own files linked below.
Where to get the official papers
CBSE puts its board question papers on its website, free, as one zip file per subject and year: the "Question Paper" page of cbse.gov.in lists Class X papers for 2022 to 2026, for the main exam and the supplementary (compartment) exam. Mathematics Standard (code 041) and Mathematics Basic (code 241) are separate files, and each zip holds several sets, such as 30/1/1, 30/1/2 and 30/1/3. The sets of one year are different papers of the same design, so a chapter's marks can change a little from set to set.
Marks per chapter in two real papers
Both papers have 38 questions for 80 marks: Section A has 20 one-mark questions (18 multiple choice and 2 assertion-reason), Section B 5 two-mark questions, Section C 6 three-mark questions, Section D 4 five-mark questions and Section E 3 four-mark case studies. Where a question had an internal choice, both options came from the same chapter in these two sets, so the counts do not depend on which option a student picked.
| NCERT chapter | 2025 (set 30/1/1) | 2026 (set 30/4/1) |
|---|---|---|
| 1 Real Numbers | 6 | 6 |
| 2 Polynomials | 4 | 3 |
| 3 Pair of Linear Equations (two variables) | 6 | 4 |
| 4 Quadratic Equations | 5 | 8 |
| 5 Arithmetic Progressions | 5 | 5 |
| 6 Triangles | 8 | 8 |
| 7 Coordinate Geometry | 6 | 6 |
| 8 Introduction to Trigonometry | 7 | 7 |
| 9 Some Applications of Trigonometry | 5 | 5 |
| 10 Circles | 7 | 7 |
| 11 Areas Related to Circles | 6 | 5 |
| 12 Surface Areas and Volumes | 4 | 5 |
| 13 Statistics | 6 | 6 |
| 14 Probability | 5 | 5 |
| Total | 80 | 80 |
Add the chapters up by unit and both papers give Number Systems 6, Algebra 20, Coordinate Geometry 6, Geometry 15, Trigonometry 12, Mensuration 10 and Statistics and Probability 11: exactly the unit marks in CBSE's 2026-27 curriculum. So the unit marks are fixed, and only the split between the chapters of a unit moves. In 2026, for example, Quadratic Equations carried 8 marks and Pair of Linear Equations 4; in 2025 it was 5 and 6, and Algebra was 20 both times. (We counted 2025's one-mark question on powers of −1 under Real Numbers.)
Where the big questions came from. The four 5-mark questions were Pair of Linear Equations, Triangles, Quadratic Equations and Statistics in 2025, and Quadratic Equations, Circles, Some Applications of Trigonometry and Statistics in 2026. The three case studies were Arithmetic Progressions, Areas Related to Circles and Applications of Trigonometry in 2025, and Triangles, Arithmetic Progressions and Coordinate Geometry in 2026. Statistics gave a 5-mark question both years, and every chapter had at least one question each year.
How to use past papers chapter by chapter
- Finish the chapter first. Do the NCERT exercises and our chapter guide before you open past questions on it; a past paper tests, it does not teach.
- Sort by chapter, then by marks. Take two or three papers, list each chapter's questions under it, and note the marks. You will see the same question types come back: a value from the zeroes of a polynomial, a ratio from the section formula, a proof of a trigonometric identity, a height and distance problem, the median or mode of grouped data.
- Time yourself. About 1 to 1.5 minutes for a 1-mark question, 3 for 2 marks, 5 for 3 marks, 8 to 10 for 5 marks and 7 for a case study keeps you inside 3 hours with time to check.
- Mark your own work against the marking scheme. CBSE also publishes the marking schemes on its website; check where the step marks go, not only the final answer.
- Plan by unit. Algebra (20) and Geometry (15) carry 35 of the 80 marks in every paper, so give them the most time; our weightage guide has the full table.
8 PYQ-style questions, our own, with answers
Question 1 (1 mark, Real Numbers). If HCF(84, 126) = h and LCM(84, 126) = l, find l ÷ h.
Answer: 6. 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. HCF: the common primes with their lower powers, 2 × 3 × 7 = 42. LCM: every prime with its higher power, 2² × 3² × 7 = 252. So l ÷ h = 252 ÷ 42 = 6. (Prime factorisation method, Chapter 1.)
Question 2 (1 mark, Polynomials). α and β are the zeroes of x² − 9x + 14. Find α² + β² without finding the zeroes.
Answer: 53. α + β = −(−9)/1 = 9 and αβ = 14/1 = 14. Then α² + β² = (α + β)² − 2αβ = 81 − 28 = 53. Check: the zeroes are 2 and 7, and 4 + 49 = 53. (Relation between zeroes and coefficients, Chapter 2.)
Question 3 (2 marks, Coordinate Geometry). The point P(2, y) lies on the segment joining A(−4, 9) and B(6, −1). Find the ratio in which P divides AB, and the value of y.
Answer: 3 : 2, and y = 3. Let the ratio be m : n. The x-coordinate gives (6m − 4n)/(m + n) = 2, so 6m − 4n = 2m + 2n, 4m = 6n and m : n = 3 : 2. Then y = (3 × (−1) + 2 × 9)/(3 + 2) = 15/5 = 3. (Section formula, Chapter 7.)
Question 4 (3 marks, Pair of Linear Equations). A school pays ₹6,800 for 4 chairs and 3 tables, and ₹7,600 for 2 chairs and 5 tables. Find the price of one chair and of one table.
Answer: a chair costs ₹800 and a table ₹1,200. Let a chair cost ₹c and a table ₹t. Then 4c + 3t = 6800 and 2c + 5t = 7600. Doubling the second gives 4c + 10t = 15200; subtracting the first leaves 7t = 8400, so t = 1200. Then 2c = 7600 − 6000 = 1600, so c = 800. Check: 3200 + 3600 = 6800. (Elimination method, Chapter 3.)
Question 5 (3 marks, Introduction to Trigonometry). Prove that (1 + tan² A)(1 − sin A)(1 + sin A) = 1.
Answer: Start from the left side. (1 − sin A)(1 + sin A) = 1 − sin² A = cos² A, and 1 + tan² A = sec² A. So the left side is sec² A × cos² A = (1/cos² A) × cos² A = 1, which is the right side. (Identities sin² A + cos² A = 1 and 1 + tan² A = sec² A, Chapter 8.)
Question 6 (5 marks, Some Applications of Trigonometry). From the top of a building 24 m high, the angle of depression of the foot of a pole is 45° and of the top of the pole is 30°. The building and the pole stand on the same level ground. Find the height of the pole (take √3 = 1.732).
Answer: about 10.14 m. The foot of the pole is seen at 45°, so its horizontal distance from the building is d = 24 ÷ tan 45° = 24 m. Looking at the top of the pole at 30°, the drop from the building's top to the pole's top is d × tan 30° = 24 × (1/√3) = 8√3 ≈ 13.86 m. So the pole is 24 − 8√3 ≈ 24 − 13.86 = 10.14 m tall. (Angles of depression, Chapter 9.)
Question 7 (4 marks, case study, Arithmetic Progressions). A stadium has 20 seats in its first row, and each row has 3 seats more than the row in front. (i) How many seats are in the 15th row? (ii) How many seats are there in the first 15 rows? (iii) Which row has 74 seats?
Answer: (i) 62; (ii) 615; (iii) the 19th row. This is an AP with a = 20 and d = 3. (i) a₁₅ = 20 + 14 × 3 = 62. (ii) S₁₅ = 15/2 × (2 × 20 + 14 × 3) = 15/2 × 82 = 615. (iii) 20 + (n − 1) × 3 = 74 gives n − 1 = 18, so n = 19. (nth term and sum of n terms, Chapter 5.)
Question 8 (5 marks, Statistics). Find the median and the mode of this data.
| Class | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 |
|---|---|---|---|---|---|
| Frequency | 5 | 9 | 15 | 12 | 9 |
Answer: median 32⅓ (about 32.33), mode 31⅔ (about 31.67). n = 50, so n/2 = 25. The cumulative frequencies are 5, 14, 29, 41, 50, so the median class is 25-35, with l = 25, cf = 14, f = 15 and h = 10: median = 25 + ((25 − 14)/15) × 10 = 25 + 22/3 = 32⅓. The modal class is also 25-35 (f₁ = 15, f₀ = 9, f₂ = 12): mode = 25 + ((15 − 9)/(2 × 15 − 9 − 12)) × 10 = 25 + 60/9 = 31⅔. (Median and mode of grouped data, Chapter 13.)
Practise more
- More questions of our own, chapter by chapter, with marks: Class 10 Maths important questions 2026-27.
- The paper design for 2026-27: the Class 10 Maths sample paper, section by section, and every formula in one place: the Class 10 Maths formula sheet.
- Free practice, marked instantly in your browser: practice by chapter, and printable worksheets with answer keys: Class 10 worksheets.
- A week-by-week plan for the run-up to the exam: Class 10 board exam revision plan.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 4 November 2026.
- CBSE, Question Paper page (Class X papers 2022 to 2026, main and supplementary exams): www.cbse.gov.in/cbsenew/question-paper.html
- CBSE, Class X Mathematics Standard (041) question papers, 2025 (set 30/1/1 read in full): www.cbse.gov.in/cbsenew/question-paper/2025/X/041_Mathematics_Standard.zip
- CBSE, Class X Mathematics Standard question papers, 2026 (set 30/4/1 read in full): www.cbse.gov.in/cbsenew/question-paper/2026/X/Mathematics_Standard.zip
- CBSE, Marking Scheme page (step marks for the same papers): www.cbse.gov.in/cbsenew/marking-scheme.html
- CBSE, Mathematics curriculum, Class X, 2026-27 (unit marks): cbseacademic.nic.in/web_material/CurriculumMain27/SecPart1/Maths_SecP1X_2026-27.pdf
- NCERT, Mathematics, Textbook for Class X (Reprint 2026-27), Chapters 1 to 14: ncert.nic.in/textbook/pdf/jemh101.pdf to ncert.nic.in/textbook/pdf/jemh114.pdf
The chapter counts are our own reading of the two CBSE papers named above; we have not reproduced any question from them. The 8 practice questions and worked answers are our own, and every answer was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.
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