Examiner Insights · CBSE Class 12 Maths

Where CBSE Class 12 Maths students lose marks — and exactly what to do about it

Q: What are the most common mistakes in CBSE Class 12 Maths?

The most repeated points are: Integration; Partial fractions for repeated or quadratic factors; Area questions without a diagram. Each one on this page has the fix and, where free, a worked example showing the wrong and right method.

Q: Which CBSE Class 12 Maths topics come up most?

In the material we analysed, the biggest areas were Calculus (35 marks), Vectors and 3D geometry (14 marks), Algebra (matrices, determinants) (10 marks).

Q: Is this a prediction of the 2027 board exams paper?

No one outside the exam board knows what will be on the next paper. The "focus" list is an informed prediction from how often topics appeared and how weakly they were answered; it is not a guarantee, so revise the whole specification.

CBSE does not publish examiner reports. This page uses CBSE's official unit weights and marking-scheme conventions, plus public analyses of common errors (each linked). The mistakes are well documented but not ranked by CBSE itself.

7sources checked
6syllabus topics weighted
10mistakes catalogued
6focus areas for 2027 board exams

What to focus on for 2027 board exams Top 10 mistakes Get the one-page PDF

Summaries are in our own words with links to the originals. Predictions are informed guesses, not a guarantee. You'll meet these notes as you revise too: under practice questions, inside mark schemes and in “What to do next”.

Ranked for 2027 board exams

What to focus on for 2027 board exams

Based on the 2025-26 curriculum weights; check the 2026-27 curriculum when CBSE publishes it. Ranked by us from the official marks per unit and how often each error comes up in the sources below; CBSE publishes no ranking of its own.

Informed prediction, not a guarantee: any topic on the specification can be examined.

1
Calculus: integrals, applications, differential equations
35 of 80 marks — nearly half the paper — and the most error-prone area in public analyses.
High confidenceCBSE unit weights 2025-26Secondary analyses
Learn Practise Class 12 chapters Mistake: Integration Mistake: Area questions without a diagram Mistake: Maxima and minima Mistake: Linear differential equations
2
Vectors and three-dimensional geometry
14 marks.
High confidenceCBSE unit weights
Learn Practise Class 12 chapters
3
Matrices and determinants
10 marks; cofactor signs.
High confidenceCBSE unit weights
Learn Practise Class 12 chapters Mistake: Matrices
4
Probability and Bayes' theorem
8 marks; conditional set-up.
High confidenceCBSE unit weights
Learn Practise Class 12 chapters Mistake: Probability
5
Relations, functions and inverse trig
8 marks.
High confidenceCBSE unit weights
Learn Practise Class 12 chapters Mistake: Relations and functions Mistake: Inverse trigonometric functions
6
Linear programming
5 marks; usually a full-marks question if corner points are checked.
Medium confidenceCBSE unit weights
Learn Practise Class 12 chapters

Mistakes library

The 10 mistakes that cost the most marks

Ordered by how often and how widely they were reported. The first 5 are free in full; Pro unlocks the fix and a worked example for every other one.

#1Integration: + C forgotten and substitution signs

What goes wrong: Named in public analyses as the most common and costly integration slip, together with sign errors during substitution.

Fix: Write + C on every indefinite integral; show the substitution and dt line.

Worked example (our own): Evaluate ∫ 2x/(x² + 1) dx.

Loses marks

ln(x² + 1)

Earns the marks

Let t = x² + 1, dt = 2x dx
∫ dt/t = ln|t| + C = ln(x² + 1) + C

Why: Every indefinite integral needs + C. Show the substitution line.

Sources: Physics Wallah — Common mistakes to avoid in CBSE Class 12 Maths; Physics Wallah — Silly calculation mistakes in CBSE Class 12 Maths

Learn: Calculus Practise this

#2Partial fractions for repeated or quadratic factors

What goes wrong: The partial-fraction form is set up incorrectly for repeated factors or irreducible quadratics.

Fix: Repeated (x − a)² needs A/(x − a) + B/(x − a)²; an irreducible quadratic needs (Bx + C)/(x² + …).

Worked example (our own): Write the form of the partial fractions for 1/((x − 1)²(x + 2)).

Loses marks

A/(x − 1)² + B/(x + 2)

Earns the marks

A/(x − 1) + B/(x − 1)² + C/(x + 2)

Why: A repeated factor (x − 1)² needs a term for each power: (x − 1) and (x − 1)².

Sources: Physics Wallah — Common mistakes to avoid in CBSE Class 12 Maths

Learn: Calculus Practise this

#3Area questions without a diagram

What goes wrong: Students who skip the sketch in area problems usually set up the wrong limits or subtract the wrong way.

Fix: Sketch the region, find intersection points, and integrate (top − bottom) between them.

Worked example (our own): Find the area enclosed between y = x² and y = x.

Loses marks

∫₀² (x² − x) dx = 2/3

Earns the marks

Sketch: the curves meet where x² = x ⇒ x = 0 or 1
On 0 ≤ x ≤ 1 the line is above the parabola
Area = ∫₀¹ (x − x²) dx = ½ − ⅓ = 1/6 square units

Why: Draw the diagram first: it gives the limits and which curve is on top.

Sources: Physics Wallah — Common mistakes to avoid in CBSE Class 12 Maths

Learn: Calculus Practise this

#4Maxima and minima: missing a root or the test

What goes wrong: Misreading the optimisation question, keeping only one critical point, or not justifying max/min.

Fix: Solve f′(x) = 0 fully, then apply the second-derivative test to each point; answer the question in context.

Worked example (our own): Find the local maximum and minimum values of f(x) = x³ − 3x.

Loses marks

f′(x) = 3x² − 3 = 0 ⇒ x = 1 ⇒ minimum value −2

Earns the marks

f′(x) = 3x² − 3 = 0 ⇒ x = ±1
f″(x) = 6x: f″(1) = 6 > 0 ⇒ local minimum f(1) = −2
f″(−1) = −6 < 0 ⇒ local maximum f(−1) = 2

Why: Take both roots, and use the second-derivative (or first-derivative) test for each before naming max or min.

Sources: Physics Wallah — Common mistakes to avoid in CBSE Class 12 Maths

Learn: Calculus Practise this

#5Probability: conditional probability and Bayes' theorem set up wrongly

What goes wrong: Probability questions are "scoring and direct" but misreading which event is given leads to the wrong conditional probability.

Fix: Define events in words, write P(A|B) with the given event after the bar, and show the total-probability line.

Worked example (our own): 2% of a population has a condition. A test is positive for 95% of people with it and 10% of people without it. A person tests positive. Find the probability they have the condition.

Loses marks

0.95

Earns the marks

P(D) = 0.02, P(+|D) = 0.95, P(+|D′) = 0.10
P(+) = 0.02 × 0.95 + 0.98 × 0.10 = 0.019 + 0.098 = 0.117
P(D|+) = 0.019 / 0.117 ≈ 0.162

Why: Bayes' theorem: define the events, write the total probability of the evidence, then divide.

Sources: Physics Wallah — Common mistakes to avoid in CBSE Class 12 Maths

Learn: Probability Practise this