Answer Writing Guide | Ishu (My Wife)

Rule 1: Start with "To Find" / "Given"

ALWAYS start every answer with "Given:" listing what's given, then "To Find:" or "To Prove:" what you need. This alone = 1 mark in many questions!

Rule 2: Box Your Final Answer

Draw a box around the final answer. Or underline it with a double line. CBSE checker looks for this first if no box, marks may be cut.

Rule 3: Write "Hence Proved" / ""

For every proof question, END with "Hence Proved" or "". Missing this = direct mark cut! It signals you completed the proof.

Rule 4: Always Write +C

EVERY indefinite integral must end with "+C". Missing +C = automatic mark cut. No exceptions. Train yourself to write it every single time.

Rule 5: Write Units

Areas must end with "sq. units". Lengths with "units". Cost with "". Volume with "cubic units". No units = last step mark deducted.

Rule 6: Quote Theorems

When using a theorem, NAME it! Write "By Bayes' Theorem", "By Rolle's Theorem", "By LMVT", "By Corner Point Theorem". Naming = extra mark!

Rule 7: Show All Steps

NEVER skip intermediate steps. Even if you can do it in your head write every line. Skipped steps = skipped marks. Each step = marks.

Rule 8: Verify Your Answer

After finding max/min do the 2nd derivative test. After finding x,y,z substitute back. Write "Verification:" shows confidence + gets marks.

Rule 9: Neat & Legible Writing

CBSE checkers check 40+ copies/day. Neat handwriting = positive impression = benefit of doubt on borderline marks. Never write in pencil (answers).

Poku's Secret Tip: Before writing ANY answer, spend 20 seconds planning: "What's given? What do I need? Which formula? How many steps?" This planning time saves 5 the time later and prevents silly mistakes!

1M

1-Mark Questions

MCQ / VSA: Just write the answer. For VSA one formula or one line. No explanation needed.

2M

2-Mark Questions

Show formula + substitution + answer. 2 steps minimum. Box final answer.

3M

3-Mark Questions

3-4 steps. Show working clearly. Each logical step = 1 mark. Conclusion line mandatory.

5M

5-Mark Questions

6-8 steps. Full working. Sub-parts if applicable. Verify answer. Box result. "Hence Proved" if proof.

Important

How CBSE Actually Awards Marks

CBSE follows "step marking" every logical step has a weightage. Here's how:

Writing correct formula = mark to 1 mark
Correct substitution = mark
Correct computation = to 1 mark
Correct conclusion / final answer = 1 mark
Even if your final answer is WRONG, you get marks for correct steps!
So NEVER leave a question blank attempt every step you know

Marks Reserved for Presentation

Where Presentation Marks Live

Proof questions: "Hence Proved" at end = 0.5 mark
Integration: +C = 0.5 mark
Area: "sq. units" in answer = 0.5 mark
LPP: Corner point table = 1 mark
Determinants: Verifying |A|0 = 0.5 mark
Max/Min: 2nd derivative test = 0.5 mark
Probability: Defining events at start = 0.5 mark

Total possible "free" marks = 4-6 marks just from these writing habits!

How to Start Each Question Type

Wrong Way

f(x) = f(x)
2x = 2x
x = x
Done.

Right Way (CBSE)

Let f: RR, f(x)=2x+3

One-One:
Let f(x) = f(x) ...(i)
2x+3 = 2x+3
2x = 2x
x = x
f is One-One.

Integration: The Perfect Format

Incomplete

xe^x dx
= xe^x - e^x

Full Marks Format

I = xe^x dx
Using integration by parts
(ILATE: u=x, dv=e^xdx)
= xe^x - 1e^x dx
= xe^x - e^x
= e^x(x-1) + C MUST!

Proof Questions: Must-Use Structure

Start: "LHS = [write LHS as given]"
Work step by step, equal sign at each step
End with: "= RHS" on the last line
Final line: "Hence, LHS = RHS. Proved. "
Never write "= = = " (multiple equals) in one line
Write each transformation on a new line for clarity

Continuity Questions: Exact Format

CBSE Perfect Format

For continuity at x = a,
we need: LHL = RHL = f(a) ...(condition)

LHL = lim(xa) f(x) = [compute] = A
RHL = lim(xa) f(x) = [compute] = B
f(a) = [compute] = C

Since LHL = RHL = f(a) = [value],
f is continuous at x = a.

Bayes' Theorem: 4-Step Format (5 marks)

Must Write Exactly This

Most Expensive Mistakes (Cost You Most Marks)

Forgetting +C in indefinite integrals mark cut guaranteed
Not writing "sq. units" after area mark cut
cos(-x) written as -cos(x) WRONG concept, full marks cut
Not verifying max/min with 2nd derivative test 1 mark cut
Not making corner-point table in LPP 1-2 marks cut
Not stating "f is continuous" or "f is bijective" in conclusion mark cut
Skipping sign in cofactor: forgetting (-1)^(i+j) wrong answer
Not checking |A|0 before finding inverse step mark lost
Not defining events in Probability (E,E,A) 1 mark cut
Integration by parts: wrong ILATE order creates messy unsolvable integral
Each of these is worth 0.5-1 mark collectively 6-8 marks lost!

Quick Win Habits Do These ALWAYS

Write question number clearly before every answer
Leave 2-3 lines between sub-parts (a), (b), (c)
Draw a rough sketch for geometry and AOI questions
Write = sign at start of each new continuation line (=, , )
For multipart questions, label clearly: Part (a), Part (b)
IF you get stuck, write the formula/theorem partial credit given
Review last 10 mins: check +C, units, boxed answers, "Hence Proved"

Ch 1-2: Relations & ITF

Equivalence: Prove ALL 3 properties separately, never together
Bijective: One-One first, then Onto separate headings
ITF: Check xy < 1 before tan addition formula
cos(-x) = π - cos(x) write this identity explicitly

Ch 3-4: Matrices & Determinants

Matrix decomposition: always verify P=Pᵀ and Q=-Qᵀ
System solving: write AX=B fully, then find |A|, adj(A), A
Cofactors: write each C, C... separately with (-1)^(i+j)
NEVER skip |A|0 verification step

Ch 5-6: Calculus

Continuity: Write "LHL = RHL = f(c)" as first line of every Q
Differentiation: Show every chain-rule step explicitly
Optimization: Set f'(x)=0, solve, THEN verify with f''(x)
Write conclusion: " f is maximum/minimum at x = __"

Ch 7-8: Integrals & Area

By Parts: Write "Using ILATE, u=__, dv=__" before applying
King Property: Write "Let I = ...(i)", apply property "(ii)", add
ALWAYS write limits when changing variable in substitution
Area: Always state "by symmetry" if using it, and sketch!

Ch 9: Differential Equations

Identify type first: Variable Separable / Homogeneous / Linear
Linear DE: Write P=___, Q=___, I.F.=___ explicitly
Write "Integrating both sides" before integration step
Always write "General Solution:" or "Particular Solution:"

Ch 10-11: Vectors & 3D

Vector form first, then Cartesian show both if asked
Cross product: expand 33 determinant fully showing each step
Distance formula: write formula, substitute, simplify 3 lines
Angle: always use |dot product| for angle between lines (not planes)

Ch 12-13: LPP & Probability

LPP: Corner-point table is MANDATORY make it every time
LPP: Shade feasible region in graph. State conclusion formally
Probability: Define events E,E,A at very start
Bayes: Show Total Probability step before applying Bayes'

3 Hour Time Strategy for 80 Marks Paper

0-15

Read the ENTIRE paper

Identify easy vs hard questions. Plan your attack order.

15-45

Section A: MCQ + VSA (1M + 2M)

20 questions. ~1 min each. Don't overthink MCQs.

45-90

Section B: 3-Mark Questions

6 questions ~7 mins each. Show all steps.

90-150

Section C: 5-Mark + Case Studies

45M + 2 case studies. ~10 mins per 5M. Case study = 8 mins.

150-170

Any skipped / Difficult questions

Go back to anything you left. Attempt partially if stuck.

170-180

Final Review The Marks Audit

Check: +C everywhere? sq. units? Boxes? "Hence Proved"? Question numbers?

The Last 10 Minutes Checklist

All indefinite integrals have +C
All area answers have "sq. units"
All final answers are boxed or underlined
All proof questions end with "Hence Proved" or ""
All question numbers are written (don't miss any!)
LPP has corner-point table
Continuity questions have "LHL=RHL=f(c)" line
Probability has events defined
Even 2 minutes of checking typically recovers 2-3 marks!