On this page
In Class 10 board maths, the final answer is only part of the marks. CBSE's marking schemes give marks for steps, figures and reasoning, and they show where students lose marks even when their method was mostly right. This post uses the official 2026-27 Mathematics Standard sample paper and its marking scheme to show where those marks are.
How the paper is built
The sample paper has 38 compulsory questions in five sections, for 80 marks in 3 hours:
Section A: 18 multiple-choice and 2 assertion-reason questions, 1 mark each
Section B: 5 very short answer questions, 2 marks each
Section C: 6 short answer questions, 3 marks each
Section D: 4 long answer questions, 5 marks each
Section E: 3 case-study questions, 4 marks each
The instructions ask you to draw neat and clean figures where needed, to take π as 22/7 unless stated otherwise, and say calculators are not allowed. The marking scheme states that the Section A multiple-choice questions carry no part marks. Everywhere else, marks are split across steps.
Where the marks sit: three examples from the marking scheme
These splits come from the official marking scheme.
A 2-mark probability question (Q25). Two dice are thrown and you need the probability that the product is prime. The scheme gives ½ mark for writing the total outcomes (36), ½ mark for listing the favourable outcomes, and 1 mark for the final probability (1/6). If you write only a final answer and it is wrong, there is nothing to award. With the first two steps written, you would still have 1 of the 2 marks.
A 3-mark arithmetic progression question (Q28 A). The exterior angles of a polygon form an AP and you must find the number of sides. The scheme gives 1 mark for setting up the sum equation, 1 mark for reducing and factorising the quadratic, ½ mark for writing both roots (n = −15 or 12), and ½ mark for rejecting −15 and stating n = 12. One sentence of reasoning is worth half a mark.
A 5-mark heights and distances question (Q35). In both alternatives, the scheme gives 1 full mark for a correct figure before any trigonometry starts. The proof question (Q33) also gives 1 mark for the figure, "given", "to prove" and construction together.
The common mistakes, and what to write instead
Jumping to the answer. Write each step on its own line, as the marking scheme does.
Not rejecting impossible values. In the swimming-pool question (Q32), the quadratic gives x = 8 or x = 37. The scheme rejects 37 because the pool's length and breadth would come out negative. Always add the line "Rejecting ... because ...".
Answering x instead of the question. The same question asks for the pool's length and breadth, not x. The scheme gives separate marks for 34 m and 24 m. Underline what is asked, and finish with a sentence that answers it.
Missing figures. In heights and distances, a figure earns its own mark. Label every point the question names.
Proofs without structure. For theorem questions, write "Given", "To prove", "Construction" and "Proof" as headings. They are marked.
Dropping units. The scheme writes answers like 154 cm², 770 m² and 50√2 m. Keep units in the final line, and square or cube them correctly for area and volume.
Sign slips in coordinate geometry and quadratics. Put brackets around negative numbers when you substitute, for example (−3)² rather than −3².
A worked layout you can copy
Take the alternative Q28 (B): find the sum of integers between 1 and 400 that are multiples of both 4 and 5. A clean answer looks like this:
Turn the words into an AP: multiples of 20, so 20, 40, ..., 380, with a = 20 and d = 20.
State the formula you use: aₙ = a + (n − 1)d.
Substitute and solve: 20 + (n − 1) × 20 = 380, so n = 19.
Use the result: S₁₉ = (19/2)(20 + 380) = 3800.
Answer in words, with units if any.
The marking scheme spreads its 3 marks across writing the AP, finding n and finding the sum, so each line above earns something.
A two-week practice routine
Do one sample paper section a day and mark it with the official scheme, half-mark by half-mark. Tally the marks lost to each mistake type above. After two weeks, fix your two most expensive habits first.
If a step keeps going wrong and you can't see why, compare your method with a full worked solution. The Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
For more on layout, read how neat working reduces errors in maths and physics. For exam day, see how to check your answers in the last 10 minutes. And to turn every lost half-mark into a lesson, read why making mistakes helps you learn.
Print the marking scheme today and mark one section of your own work against it.
