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CBSE Class 10 Maths sample paper 2026-27, section by section: what each part tests

CMDLearn · 20 October 2026

CBSE has put out its Class 10 Mathematics sample paper for 2026-27, with a marking scheme to go with it. It is the closest thing you have to a map of the board exam: how many questions there are, how the 80 marks are shared out, where you get a choice, and how an examiner gives marks for working. This guide goes through the paper one section at a time, shows which chapters each part draws on, and ends with a self-check and a way to test an AI's solutions.

Keep CBSE's PDF open next to this page. Our explanations and examples are our own; the paper and its marking scheme are the authority.

Is the 2026-27 paper out?

Yes. When we checked on 20 October 2026, CBSE's Class X sample paper page for 2026-27 listed both Mathematics papers, Standard (code 041) and Basic (code 241), each with a marking scheme. This guide follows the Standard paper:

• Sample paper: cbseacademic.nic.in/web_material/SQP/ClassX_2026_27/MathsStandard-SQP.pdf
• Marking scheme: cbseacademic.nic.in/web_material/SQP/ClassX_2026_27/MathsStandard-MS.pdf

A line at the foot of every page of the paper says that the design of the question paper and the way it is assessed are unchanged for 2026-27. The questions are a fresh set: we compared it with the 2025-26 paper, and only one item repeats, the theorem you are asked to prove in Q33 (with a different follow-up). So last year's paper is still good practice for the format, and this year's is the one to sit as a full mock.

The paper at a glance

From the General Instructions on page 1 of the 2026-27 Standard paper:

• Time: 3 hours. Calculators: not allowed. Take π as 22/7 unless the question gives another value.
• Every question must be answered. There is no overall choice; the only choices are the "OR" pairs in the table.
• The other 20 marks are internal assessment by your school: 10 for pen-and-paper tests and multiple assessment, 5 for a portfolio and 5 for lab activities (CBSE's 2026-27 curriculum). So the subject is out of 100.

Standard or Basic? The 2026-27 Basic paper has the same five sections, the same 38 questions and the same marks per section (its own General Instructions say so). The difference is in the kind of thinking each paper asks for. CBSE's 2026-27 paper design gives:

On the page the two papers look alike. But in Standard, 37 of the 80 marks need you to use a method in a new situation or reason your way through, while Basic is mostly about knowing and explaining what you were taught.

Where the marks come from: the seven units

CBSE's 2026-27 curriculum fixes how many of the 80 marks each unit carries. We matched every question in the sample paper to its chapter. CBSE does not print a chapter against each question, so the matching is ours; the totals come out exactly equal to the curriculum's unit marks.

Two things stand out. Algebra is a quarter of the paper (20 of 80 marks) and turns up in Sections A, C, D and E, including a 5-mark word problem (Q32) and a case study (Q36). And no unit is left out: even the two 6-mark units are asked three and four times, so every chapter needs at least its basics.

Section A: 20 one-mark questions (Q1 to Q20)

What it tests: whether you know a fact or formula and can use it in one or two quick steps. All seven units have at least one question here.

How it is marked: the marking scheme gives no part marks in this section. The right option gets the mark; anything else gets nothing. Rough work still pays, because several of these are two-step sums in disguise. Q1, for example, wants the largest number that divides 134 and 188 leaving remainders of 4 and 6: take the remainders off first (130 and 182), then find the HCF, which is 26.

Assertion-reason (Q19 and Q20). You get two statements, an Assertion (A) and a Reason (R), and pick one of four options:

• (A) both are true, and R explains A;
• (B) both are true, but R does not explain A;
• (C) A is true and R is false;
• (D) A is false and R is true.

Judge each statement on its own first. Then ask one question: is R the reason A is true? Two of our own to try:

1. A: The HCF of 18 and 24 is 6. R: For any two positive integers, HCF × LCM equals their product. Both are true (18 = 2 × 3² and 24 = 2³ × 3, so the HCF is 2 × 3 = 6), but R is not why the HCF is 6. Answer: (B).
2. A: The equation x² + 1 = 0 has no real roots. R: A quadratic ax² + bx + c = 0 has no real roots when b² − 4ac is negative. Here b² − 4ac = 0 − 4 = −4, so R is exactly why A is true. Answer: (A).

The usual slip is choosing (A) every time both statements are true.

Section B: 5 two-mark questions (Q21 to Q25)

What it tests: a short method of two or three steps. In 2026-27 the five questions come from five different units: Real Numbers (Q21), Triangles (Q22), trigonometric ratios (Q23), the area of a sector (Q24) and probability with two dice (Q25).

How it is marked: in halves. For Q21(A), the longest ruler that measures a hall's three sides exactly, the marking scheme gives ½ for seeing that the answer is the HCF of the three lengths in centimetres, 1 for the three prime factorisations, and ½ for the HCF itself, 75 cm. The marks sit on the steps, so write each one down.

Some figure questions here also have a version without a figure for visually impaired candidates (Q22(B) has one).

Section C: 6 three-mark questions (Q26 to Q31)

What it tests: proofs and working of three or four steps. The 2026-27 set: proving a number irrational (Q26), the zeroes of a quadratic polynomial (Q27), an AP word problem (Q28), a proof about tangents to a circle (Q29), the section formula (Q30) and trigonometric identities (Q31).

How it is marked: look at Q28(A), where the exterior angles of a polygon form an AP. Setting up the sum of the exterior angles as 360° earns 1 mark, factorising earns 1, the two roots earn ½, and keeping only the positive one (n = 12) earns the last ½. Rejecting an impossible answer is a step with its own mark.

A question type to expect: find the error. Q31(A) shows a student's working in four steps and asks you to find the wrong step, put it right and finish. Here is one of our own. A student simplifies (sin θ + cos θ)² + (sin θ − cos θ)²:

1. (sin θ + cos θ)² = sin²θ + 2 sin θ cos θ + cos²θ
2. (sin θ − cos θ)² = sin²θ + 2 sin θ cos θ + cos²θ
3. Adding the two: 2(sin²θ + cos²θ) + 4 sin θ cos θ = 2 + 4 sin θ cos θ

The mistake is in step 2: the middle term of (sin θ − cos θ)² is −2 sin θ cos θ. With that fixed, the middle terms cancel and the answer is 2(sin²θ + cos²θ) = 2. Check with θ = 45°: sin θ = cos θ = 1/√2, so the first bracket squared is 2, the second is 0, and the total is 2.

Section D: 4 five-mark questions (Q32 to Q35)

What it tests: long problems that join a method to a situation. A quadratic word problem (Q32: a park, a pool and a grass strip of equal width), a theorem proof followed by using it (Q33: the Basic Proportionality Theorem, then a trapezium), a solid made of two shapes (Q34: a tent or a toy), and heights and distances (Q35: a kite or a lighthouse).

How it is marked:

• Q33: 1 mark for the figure, given, to prove and construction; 2 for the proof; 2 for using it on the trapezium. The curriculum marks this theorem "(Prove)", so learn its proof whole.
• Q35: 1 of the 5 marks is for a correct figure, in both the kite and the lighthouse options.
• Q32: the quadratic gives two widths. Throwing out the one that would make the pool's sides negative, and stating the width that is left, is worth a full mark.

Worked, our own (the Q32 type). A rectangular field is 30 m by 24 m. A path of the same width, x m, runs along the inside of all four sides, and the grass left in the middle covers 432 m². Find x.

• The grass is a rectangle (30 − 2x) m by (24 − 2x) m, so (30 − 2x)(24 − 2x) = 432.
• Multiply out: 720 − 108x + 4x² = 432, so 4x² − 108x + 288 = 0. Divide by 4: x² − 27x + 72 = 0.
• Factorise: (x − 3)(x − 24) = 0, so x = 3 or x = 24.
• Reject 24: the grass would be 30 − 48 = −18 m long, which is impossible. So x = 3 m, and the grass is 24 m by 18 m. Check: 24 × 18 = 432.

Section E: 3 case studies, 4 marks each (Q36 to Q38)

What it tests: reading a real situation and turning it into maths. Each case has three parts worth 1, 1 and 2 marks, and the choice is only in the 2-mark part. In 2026-27 the cases are a company's sanitiser sales (a pair of linear equations, Q36), tangents to a circular garden (Circles, Q37) and a class's test marks (Statistics: the modal class, the median class, then the mean or the mode, Q38).

Tip: the short parts often set up the long one. In Q36, the June equation you write for part (i) is one of the two equations you solve in part (iii)(A); the other comes from the 1000 bottles sold that month.

A way to split the 3 hours

CBSE does not set a time for each section. Here is one way to use the 180 minutes (our suggestion, not CBSE's):

That is a little over 2 minutes a mark, with less time for 1-mark questions and more for proofs and long problems. Sit the CBSE paper once with a clock, then adjust these numbers to your own speed.

Three things that trip students up

1. Writing only the answer. From Section B on, the marking scheme hands out marks ½ or 1 at a time for steps. Each correct step you write can earn its share; a bare final answer cannot show them.
2. Skipping the figure. In Q35 a correct figure is worth 1 mark, and in Q33 the figure with given, to prove and construction is another 1.
3. Picking (A) in every assertion-reason question where both statements are true. Check whether R really explains A.

Self-check: 6 questions with answers

Try them on paper first. Answers are below.

1. How many questions are in the paper, and how many must you answer?
2. In a Section E case study, which part has a choice, and how many marks is it worth?
3. Which unit carries the most marks in 2026-27, and how many?
4. Assertion: the point (0, 0) is the same distance from (3, 4) and from (−4, 3). Reason: the distance of a point (x, y) from the origin is √(x² + y²). Which option, (A), (B), (C) or (D)?
5. Two positive whole numbers that follow each other multiply to 56. Write a quadratic equation, solve it, and say which root you reject.
6. Some data has mean 20 and median 18. Use the empirical relation to estimate the mode.

Answers: 1) 38 questions, and all of them must be answered (the only choices are the "OR" options). 2) Part (iii), worth 2 marks. 3) Algebra, 20 of the 80 marks. 4) (A). Both distances are √(9 + 16) = √25 = 5, and R is the rule that gives them. 5) x(x + 1) = 56, so x² + x − 56 = 0, which factorises as (x + 8)(x − 7) = 0. So x = 7 or x = −8. Reject −8 because the numbers are positive. The numbers are 7 and 8. 6) Mode = 3 × median − 2 × mean = 3 × 18 − 2 × 20 = 54 − 40 = 14.

How to check an AI's answer for this paper

Plenty of sites and chatbots offer "solutions" to the sample paper. Before you learn from one, take a minute to check it:

• Check the year. Ask which paper it is solving. The 2026-27 Standard paper is headed "CLASS - X (2026 - 27)", and its Q1 is the largest-number question with remainders 4 and 6. If the AI's Q1 is something else, it is using another year's paper.
• Compare with CBSE's marking scheme, not with the AI. The scheme gives the right option for every multiple-choice question (Q1 is (B), 26) and the step marks for every other question.
• Check the letter and the value together. An answer such as "(C) 26" cannot be right when 26 is option (B). Both must point to the same choice.
• Put the answer back into the question. If an AI says Q36(iii)(A) is 450 small and 550 large bottles, check: 450 + 550 = 1000 bottles, and 10 × 450 + 15 × 550 = 4500 + 8250 = 12,750 rupees. Both match the question, so the answer stands.
• Be wary of "the pattern has changed". The General Instructions on page 1 are the authority on the format, and every page of the 2026-27 paper says the design is unchanged. If a chatbot or a video says otherwise, check the PDF.

More on using AI well: how to use ChatGPT for homework without cheating yourself.

Practise for this paper

• Timed: our free Class 10 revision papers run against a clock and are laid out in 1, 2, 3 and 5-mark sections, marked in your browser. They mark the final answer only and have no case-study section, so use CBSE's own paper to practise Section E and step marking.
• By chapter, marked instantly: the practice page has Class 10 board practice topics in English, Hindi and Marathi.
• Unit I in depth: NCERT Class 10 Maths Chapter 1, Real Numbers, explained simply covers Q1, Q21 and Q26 of this paper, with the marking-scheme split for Q26.
• Planning the run-up: Class 10 boards, a 60-day revision plan.
• Practice questions with answers, chapter by chapter: Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions, Triangles and Coordinate Geometry.

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 checked on 20 October 2026.

• CBSE, Class X Mathematics Standard (041) sample question paper, 2026-27 (General Instructions; Q1 to Q38): cbseacademic.nic.in/web_material/SQP/ClassX_2026_27/MathsStandard-SQP.pdf
• CBSE, Class X Mathematics Standard (041) marking scheme, 2026-27 (Section A rule; Q1, Q21, Q28, Q32, Q33, Q35, Q36): cbseacademic.nic.in/web_material/SQP/ClassX_2026_27/MathsStandard-MS.pdf
• CBSE, Class X Mathematics Basic (241) sample question paper, 2026-27 (General Instructions): cbseacademic.nic.in/web_material/SQP/ClassX_2026_27/MathsBasic-SQP.pdf
• CBSE, Mathematics curriculum, Class X, 2026-27 (course structure, question paper design for Standard and Basic, internal assessment): cbseacademic.nic.in/web_material/CurriculumMain27/SecPart1/Maths_SecP1X_2026-27.pdf
• CBSE, sample question papers, Class X, 2026-27 (list of papers): cbseacademic.nic.in/SQP_CLASSX_2026-27.html
• CBSE, Class X Mathematics Standard (041) sample question paper, 2025-26 (compared for repeated questions): cbseacademic.nic.in/web_material/SQP/ClassX_2025_26/MathsStandard-SQP.pdf

The structure, marks and marking rules are from the documents above. The chapter matching, the time plan, the explanations, worked examples and self-check questions on this page are our own; every number was checked by calculation.

Practise this class: Class 10 worksheets, chapter by chapter · free practice, marked instantly · timed revision papers