CBSE Class 12 Maths Sample Paper 2026–27: Official PDF, Pattern and Marking Plan

Open the two official CBSE documents

Download both the Mathematics Sample Question Paper and the matching Marking Scheme from CBSE Academic. Confirm that the page heading says Class XII and 2026–27 and that the subject is Mathematics, code 041. Applied Mathematics is a different subject and has its own paper.

Separate a method error from a calculation slip

Keep three things beside each missed question: the condition you needed, the first valid equation and the first incorrect line. A long answer with the wrong starting condition needs a different repair from a correct method with a sign error. Use the official scheme for marks; these original illustrations explain how to choose the next task.

For f(x) = x³ − 3x, f′(x) = 3x² − 3 vanishes at x = −1 and x = 1. These are stationary points, not automatically maxima. The derivative signs are positive, negative, positive across the three intervals. Therefore x = −1 gives a local maximum and x = 1 a local minimum. If an answer labels both as maxima, the missing step is the sign test; copying the derivative again will not repair it.

A short retest that changes the demand

Try g(x) = x³ − 12x without notes. Its derivative is 3x² − 12, so the stationary values are −2 and 2. The sign changes identify a local maximum at −2 and a local minimum at 2. Now restrict the same function to [0, 3]: compare g(0) = 0, g(2) = −16 and g(3) = −9. The absolute maximum on that interval is 0 at x = 0, while the minimum is −16 at x = 2. This checks whether you can adapt the method when the domain changes.

Record what you could do alone, not how familiar the solution felt. If the error returns, bring both attempts to the teacher. If it does not, move on to a different unit while keeping a later mixed check. One successful exercise is evidence about that skill, not a forecast of your board score.

Understand the 2026–27 paper design

The official curriculum specifies an 80-mark, three-hour theory paper plus 20 marks of internal assessment. It allocates 55% of theory marks to remembering and understanding, 25% to applying, and 20% to analysing, evaluating and creating. There is no overall choice, while internal choice is provided within sections. Always use the actual SQP instructions for the exact section and question structure.

Attempt the paper like a board examination

• Choose a quiet three-hour window and keep only permitted stationery on the desk.
• Read the official instructions before starting and record the actual start and finish time.
• Show complete mathematical steps; do not award yourself method marks for work that is only in your head.
• Mark questions that consumed too much time, even if the final answer was correct.
• Do not open the marking scheme until the timed attempt has ended.

Mark by step, not by final answer

Use the official marking scheme to compare the method and the credited steps. Record lost marks under concept, interpretation, setup, algebra or arithmetic, incomplete working, and time. A wrong final value caused by one arithmetic slip needs a different response from a solution that began with the wrong model.

Use a 72-hour repair cycle

Use the correction interval to repair and retest errors before deciding whether another full paper is useful. The suggested sequence also includes a Day 7 transfer check; it does not guarantee a score gain.

• Day 0: attempt and mark the paper; select the three error patterns costing the most marks.
• Day 1: rebuild the relevant idea and solve a small focused set without time pressure.
• Day 3: reattempt the missed questions with no solution visible.
• Day 7: test the same skills through different questions, then update the study plan.

A parent review that does not add pressure

Ask the student to show the error categories and the dated reattempts. Avoid treating one mock score as a prediction. The better questions are whether repeated errors are falling, whether all units are represented, and whether the student can finish with enough time to check.

• Was the attempt genuinely timed and uninterrupted?
• Did the student use the official marking scheme?
• Which three patterns cost the most marks?
• When will those skills be retested?
• Is the next full paper scheduled after the repair work?

Turn a paper mistake into focused practice

Choose the skill where your written method first went wrong. Each original lesson includes hints, worked corrections and an independent retest; none is an official paper or a prediction of the next exam.