How to Write the Paper: The 3-Hour Plan

The 15 minutes of reading time

You cannot write from 10:15 to 10:30, but you can do a lot of thinking.

By 10:30 you already know your choices and which questions to start with.

The 3-hour plan

A useful rule: about 2 minutes a mark, less in Section A, more in Section D, and 25 minutes kept for checking.

If you are behind at 11:50, do not rush Section D. Cut time from checking instead; a 5-mark answer with clean steps is worth more than a quick look over 1-mark answers.

The order to attempt questions

1. Go section by section, A to E. Start each section on a fresh page and keep its answers together. The examiner marks faster and misses nothing.
2. In Section A, give each MCQ about 1½ minutes. If one needs more than 2 minutes, mark it on the question paper, leave a line in the answer book and move on. Come back at the end.
3. In B, C and D, do the questions you are sure of first, leaving space for the others. Write each one's number in the margin so the order does not matter.
4. Never leave a question blank. In the last 25 minutes, go back to anything skipped and write whatever steps you can: the formula, the figure, the first equation. Each can earn marks.

If case studies feel easier to you, doing Section E before Section D is fine, as long as each section's answers stay together and the numbers are correct.

Presentation that earns marks

• One step per line. Write the formula first, then put in the values. The formula line often carries ½ mark by itself.
• Units in the final answer: cm, cm², m³, ₹. A volume written in cm² looks like a wrong answer.
• Figures in pencil, labelled. In heights and distances mark the angles, the heights and the unknown. In theorem proofs write Given, To prove, Construction, Proof as headings; together with the figure they carry 1 mark.
• Box or underline the final answer. End proofs with a clear line: "Hence proved" or "Hence ABCD is a rhombus."
• Reasons in geometry: write the reason in brackets beside each step, such as (alternate angles) or (tangents from an external point are equal).
• Rough work goes in a margin column on the same page, marked "Rough work", not on scraps.
• Space: leave a line between parts (i), (ii) and (iii) and between questions. A cramped page hides steps.

Common ways students lose marks

1. Keeping an impossible root. A width comes out as $x = 8$ or $x = -15$. Write "$x = -15$ is rejected, as a width cannot be negative" and then use $x = 8$.
2. Gaps in the irrationality proof. Not saying that $a$ and $b$ are co-prime integers with $b \neq 0$, or not writing the contradiction at the end. Both lines carry marks.
3. Wrong axis in the section formula. A point on the x-axis has $y = 0$; a point on the y-axis has $x = 0$. Students often swap these.
4. No figure in heights and distances. That is 1 mark lost before the working starts. Using $\sin$ when the two sides in the triangle are opposite and adjacent (use $\tan$) is the next most common slip.
5. Mode formula mix-ups. $f_1$ is the frequency of the modal class, $f_0$ the class before and $f_2$ the class after. Taking the class with the highest cumulative frequency as the modal class is also a common error.
6. Wrong total in probability. Two dice give 36 outcomes, not 12. If some cards are removed from a pack, the total is no longer 52.
7. Arc length and sector area confused. Arc length is $\frac{\theta}{360} \times 2\pi r$; sector area is $\frac{\theta}{360} \times \pi r^2$. Check the unit: cm for length, cm² for area.
8. Hidden faces counted in combined solids. When a cone sits on a cylinder, the joined circle is not part of the surface. Add only the curved surfaces you can see and any base still showing.
9. Moving terms across "=" in a trig identity. Transposing terms or cross-multiplying across the "=" sign assumes what you have to prove, and loses marks. Start from one side, usually the harder one, and reach the other; or simplify the LHS and the RHS separately until both give the same expression, which is also accepted.
10. Copying a number wrongly from the question. It happens in the 5-markers most. Check the data once when you finish each question.
11. MCQ answers written as a letter only. Write the letter and the answer, for example (b) 26. If you mislabel the option, the value shows what you meant.

Case-based questions and OR choices

Case studies (Section E, 4 marks each)

• Read the case once and underline the numbers and what each letter stands for.
• Parts (i) and (ii) are 1 mark each and usually one step. Write the formula and the answer in two or three lines; don't write a page.
• Part (iii) is 2 marks and has the OR. It usually builds on (i) and (ii): if (i) and (ii) ask you to form two equations, (iii) asks you to solve them. Choose the OR option that reuses what you have already found.
• If you are unsure of (i), still attempt (iii). Its marks are given for method too.
• Label clearly: 36 (i), 36 (ii), 36 (iii) (a).

OR choices in Sections B, C and D

• Decide during the reading time, not while writing.
• Choose the option where you can see the whole method in 30 seconds, not the one that "looks shorter". A familiar proof is often safer than a calculation with awkward numbers.
• If you change your mind halfway, cross out the abandoned attempt with a single line and write the new option's label clearly.