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.