mathematics

target	495+/500
author	Senior Sibling
name	mathematics
description	Master framework for CBSE 12th Math. Calculus, Vectors, 3D, and Probability.
stream	shared

Mathematics — CBSE Grade 12 (2026-27)

Syllabus Coverage

Unit	Chapters	Theory Marks	Internal Marks
I	Relations & Functions	8	20
II	Algebra (Matrices/Det)	10
III	Calculus (Ch 5-9)	35
IV	Vectors & 3D	14
V	Linear Programming	5
VI	Probability	8

Chapter-by-Chapter Deep Dive

• Calculus: Integration (Partial Fractions, By Parts), Differential Equations, Maxima/Minima.
• 3D Geometry: Skew lines, Shortest distance, Plane equations.
• Probability: Bayes' Theorem, Bernoulli Trials.

High-Yield Topics (490+ Strategy)

• Maxima & Minima Word Problems (5M).
• Integration by Partial Fractions (3M/5M).
• Bayes' Theorem (Sure shot 4M/5M).

Derivation/Proof Bank

1. Proof of Continuity/Differentiability.
2. Property proofs of Definite Integrals.
3. Shortest distance between two skew lines.

Formula Bank

• Integrals: $\int \sqrt{a^2-x^2} dx = ...$
• 3D: $d = |(a_2-a_1) \cdot (b_1 \times b_2)| / |b_1 \times b_2|$

Diagram Bank

• LPP feasible region graphs.
• Area under curves sketches.

CBSE Question Patterns (12th specific)

• 1M: Matrix order/identity MCQs.
• 2M: Simple differentiation.
• 5M: LA on Calculus applications or 3D Geometry.

NEET/JEE Alignment

• JEE: Focus on Indefinite Integration tricks and Coordinate Geometry depth.

Practical Component

• Activity: Verification of relations (Equivalence).
• Viva: What is an onto function? Define a singular matrix.

Common Mistakes (12th specific)

• Forgetting $+C$ in indefinite integrals.
• Sign errors in 3D direction cosines.

Internal Assessment Strategy (20 marks)

• Submit the 10 Math Activities in the record file.
• High performance in Periodic Tests.

Answer Writing for 12th

• State the specific identity/theorem used.
• Show clear algebraic substitution.