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Every year CBSE publishes a sample question paper (SQP) with its marking scheme, and it is the closest preview you will get of the real board paper. Many students solve it once and move on. Used properly, it tells you how marks are split, which steps earn credit and where careless answers lose marks. This post goes through the 2026-27 Mathematics sample paper section by section, works two of its questions, and ends with a six-week plan.
What does the 2026-27 sample paper look like?
The paper is 3 hours long and carries 80 marks. It has 38 compulsory questions in five sections:
Section A: 18 multiple-choice questions and 2 assertion-reason questions, 1 mark each (20 marks).
Section B: 5 very short answer questions, 2 marks each (10 marks).
Section C: 6 short answer questions, 3 marks each (18 marks).
Section D: 4 long answer questions, 5 marks each (20 marks).
Section E: 3 case-study questions, 4 marks each (12 marks).
There is no overall choice, but there is internal choice in 2 questions of Section B, 3 of Section C, 2 of Section D and one sub-part each of 2 questions in Section E. Calculators are not allowed. Every page carries the note that there is "no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27". The other 20 marks of your total come from internal assessment, which the CBSE curriculum for 2026-27 splits into periodic tests (10) and mathematics activities (10).
Which units carry the most marks?
The same curriculum document gives unit-wise marks for the theory paper: Relations and Functions 8, Algebra 10, Calculus 35, Vectors and Three-Dimensional Geometry 14, Linear Programming 5, and Probability 8. Calculus alone is 35 of 80 marks, a little under 44 per cent. That covers continuity and differentiability, applications of derivatives, integrals, applications of integrals and differential equations.
The curriculum also says there is "no chapter wise weightage" and that care should be taken to cover all chapters. So the unit marks tell you where to spend most of your time, not what you can skip. A five-mark linear programming question is quick marks if you have practised it.
How do you avoid losing marks in Section A?
Twenty one-mark questions reward accuracy more than speed. Most lost marks here come from domain and range slips in inverse trigonometry, sign errors and reading too fast.
Assertion-reason questions need a fixed routine: decide whether the assertion is true, then whether the reason is true, and only then whether the reason explains the assertion. Question 19 of the sample paper is a good test. The assertion says the integral of |x − 2| from −1 to 1 equals 4. On that interval x − 2 is negative, so |x − 2| = 2 − x, and the integral is [2x − x²/2] from −1 to 1 = (2 − 0.5) − (−2 − 0.5) = 1.5 + 2.5 = 4. True. The reason states the rule for integrating an even function over [−a, a], which is also true. But |x − 2| is not an even function, so the reason does not explain the assertion. The marking scheme gives option (B): both true, reason not the correct explanation.
Worked example: a five-mark Bayes' theorem question
Question 35 is about a fitness app. 45% of users have Alpha smartwatches, 30% Beta, 15% Gamma and 10% Delta. The chances of a false heart-rate alert from each are 0.01, 0.02, 0.05 and 0.01. Find (i) the probability that a randomly chosen user gets a false alert, and (ii) the probability that a false alert came from a Beta watch.
Define events. E₁ to E₄ are "user has Alpha / Beta / Gamma / Delta". A is "user gets a false alert". State that E₁ to E₄ form a partition of the sample space.
Write the given probabilities. P(E₁) = 0.45, P(E₂) = 0.3, P(E₃) = 0.15, P(E₄) = 0.1, and P(A|E₁) = 0.01, P(A|E₂) = 0.02, P(A|E₃) = 0.05, P(A|E₄) = 0.01.
Total probability. P(A) = 0.45 × 0.01 + 0.3 × 0.02 + 0.15 × 0.05 + 0.1 × 0.01 = 0.0045 + 0.006 + 0.0075 + 0.001 = 0.019.
Bayes' theorem. P(E₂|A) = (0.3 × 0.02) / 0.019 = 0.006 / 0.019 = 6/19.
The marking scheme gives 1 mark for the P(Eᵢ) values, 1 for the conditional probabilities, 1½ for part (i) and 1½ for part (ii). Two of the five marks come before any calculation, for setting the problem up. Students who jump straight to the formula throw those away.
What do case-study questions in Section E test?
Case studies wrap a standard calculation in a story. In Question 37, a water quality index is W(x) = 35 + 1.6x − 0.02x², where x is investment in crores. W′(x) = 1.6 − 0.04x = 0 gives x = 40. W″(x) = −0.04 < 0, so this is a maximum, and W(40) = 35 + 64 − 32 = 67. At x = 35, W = 35 + 56 − 24.5 = 66.5, so it falls 0.5 short of the maximum. The maths is a one-variable maxima problem. The skill being tested is reading the passage and pulling out the function.
A six-week plan for the board paper
Weeks 1 and 2: Calculus, a little each day. Ten derivative and integral questions in the Section B and C format, with full working. Our integration practice plan has a structure you can reuse.
Week 3: Vectors and 3D geometry, plus linear programming. Draw every feasible region neatly and label the corner points.
Week 4: Relations and functions, matrices and determinants, probability.
Week 5: Mixed sets. Shuffle questions from all units. In an experiment by Rohrer and Taylor (2007), students who practised mixed maths problems scored 63% on a test a week later, against 20% for students who practised one problem type at a time.
Week 6: Two full papers under timed conditions, including the sample paper. Mark them with the marking scheme, not just the answer key.
When you check your work and cannot see where a step went wrong, the Fermi Problem Library has a step-by-step solver that explains the reasoning, so you can compare your line of working with a full solution. For the wider revision timetable, see our CBSE Class 12 revision plan for the final 8 weeks.
This week, download the sample paper and its marking scheme, solve Section D in 50 minutes, and mark yourself step by step.
