How to write maths answers in the Class 10 board exam: one answer, marked line by line

A student can get a maths answer right and still lose marks, because what went missing were the lines in between. This guide takes one familiar five-mark question and shows which line would earn which mark under a step-by-step marking scheme.

The question

This is a quadratic-equations word problem written for this guide, with fresh numbers, so it is not one you have already seen in a textbook. It is a good test because it has every kind of line an examiner looks for: a variable, an equation, algebra, and a decision at the end. The question is shown at the top of this page.

The answer, marked line by line

Below is a full-marks answer, with an illustrative split of the 5 marks in the style of a CBSE marking scheme. Tap any line to remove it from the answer and watch what happens to the total.

Notice what the figure shows. In this split, the boxed answer, “50 km/h”, sits on a line worth one mark. A student who solves it in their head and writes only the answer has done the hardest thinking and thrown away most of the marks for it.

The full solution, as it should look on the page

Let the uniform speed of the van be $x$ km/h. Then:

Speed cannot be negative, so $x = -60$ is rejected. The speed of the van is 50 km/h.

A quick check costs ten seconds: at 50 km/h the trip takes 4.8 hours; at 60 km/h it takes 4 hours. That is 0.8 hours, which is 48 minutes less, as the question says.

Six habits that protect your marks

These come straight from how step marking works. None needs extra knowledge. All of them need practice, because under exam pressure the hand skips whatever the brain thinks is obvious.

1. Name the unknown, with its unit. “Let the speed be $x$ km/h” is the line that starts a word problem, and the easiest one to skip.
2. Write the equation before you touch it. The equation is the method. If you simplify in your head and write only the result, the examiner cannot see the method, and cannot give method marks.
3. One step per line, with the equals signs lined up. This makes your work easy to follow and easy to mark. It also makes your own slips easier to spot.
4. Name the theorem or property you use. “By BPT”, “tangents from an external point are equal”, “the radius is perpendicular to the tangent at the point of contact”. In geometry the reason is part of the answer; see why triangle proofs lose marks.
5. Reject roots with a reason. Speed, length, age and number of people cannot be negative or fractional when the story forbids it. Write the reason in words, then cross the root out.
6. Box the final answer, with its unit. km/h, $\text{cm}^2$, ₹, years. This is good practice rather than a written CBSE rule: a bare number does not say what was found.

What changes for each type of question

One-mark multiple-choice questions

A multiple-choice question is marked on the choice you make, so working does not earn marks there. It still helps: do a short working in the rough-work space, because a sign slip made in the head can cost a one-mark question.

Geometry proofs

Draw the figure and label it. Then write Given, To prove, Construction (if any) and Proof, with a reason beside every statement. A clear, labelled figure also makes your own reasoning easier to follow.

Heights and distances

The diagram is half the answer. Mark the angle of elevation or depression at the correct point, label the heights and distances, then write each trigonometric ratio from a named right triangle, such as $\text{In } \triangle ABC, \; \tan 30^\circ = \frac{AB}{BC}$.

Case studies

A case study gives one situation and then asks several parts, usually labelled (i), (ii), (iii) and so on. Treat each part as its own small question: name the quantity, write the formula, substitute, and answer with the unit. If part (iii) needs a value from part (i), write that value down again at the start of part (iii) and show where it came from. Then a slip in part (i) does not have to spoil the working you show for part (iii).

How to practise this (it takes ten minutes a day)

• Each day, write out one long answer in full as if for the board, even if you could do it in your head.
• Swap it with a friend, or check it against an official CBSE marking scheme, and mark it step by step.
• For every mark you would lose, note which of the six habits was missing.

CBSE publishes a sample paper and its marking scheme every year on its academic website. Reading one marking scheme slowly, step by step, teaches more about board answers than any list of tips.