Mathematics Introduction Class | Syllabus Discussion | Study Plan, Strategy & Blueprint

This syllabus is designed as per the latest CBSE curriculum for the academic session 2025–2026. It covers all units, topics, and subtopics in a clear sequence, ensuring complete concept clarity and effective practice for board exams and entrance tests like JEE.

🗂️ Unit-Wise Detailed Syllabus

✅ UNIT 1: Relations and Functions

Types of Relations: Reflexive, Symmetric, Transitive, Equivalence Relations
Types of Functions: One-One, Onto, Bijective Functions
Composition of Functions and Invertible Functions
Binary Operations
Inverse Trigonometric Functions
- Basic concepts
- Properties and principal value branches

✅ UNIT 2: Algebra

Matrices:

Concept, notation, order, equality, types of matrices
Zero and Identity matrix
Operations: Addition, Multiplication, Scalar Multiplication
Properties of matrix operations
Transpose of a matrix
Symmetric and Skew-Symmetric matrices
Elementary row and column operations
Invertible matrices

Determinants:

Determinant of a square matrix (up to 3×3 matrices)
Properties of determinants
Minors, Cofactors, Adjoint
Applications: Solving system of linear equations in two or three variables using Cramer’s Rule, Matrix Method, and Inverse Method

✅ UNIT 3: Calculus

Continuity and Differentiability:

Continuity of functions
Differentiability, Chain Rule
Derivatives of implicit functions
Exponential and logarithmic functions
Logarithmic differentiation
Second-order derivatives
Mean Value Theorems (Rolle’s and Lagrange’s)

Applications of Derivatives:

Rate of change
Increasing and decreasing functions
Tangents and Normals
Approximation
Maxima and Minima (one variable)
Simple problems based on real-life situations

Integrals:

Indefinite integrals as antiderivatives
Basic integration formulas
Integration by substitution, by parts, and by partial fractions
Definite integrals: Properties, evaluation, and applications
Fundamental Theorem of Calculus

Applications of Integrals:

Area under simple curves
Area between two curves (lines, parabolas, circles)

Differential Equations:

Definition, order, and degree
General and particular solutions
Formation of differential equations
Solution of differential equations by separation of variables, homogeneous differential equations, and linear differential equations

✅ UNIT 4: Vectors and Three-Dimensional Geometry

Vector Algebra:

Vectors and scalars, types of vectors
Addition, scalar multiplication
Position vector of a point
Section formula, distance between two points
Dot product, cross product, scalar triple product

Three-Dimensional Geometry:

Direction cosines and ratios
Equation of a line in space (vector and cartesian forms)
Angle between two lines
Shortest distance between two lines
Plane: Equation of plane, Angle between two planes
Distance of a point from a plane
Angle between a line and a plane

✅ UNIT 5: Linear Programming

Introduction and related terminology
Mathematical formulation of linear programming problems (LPP)
Graphical method of solving LPPs
Feasible and infeasible regions
Optimal solutions

✅ UNIT 6: Probability

Conditional Probability
Independent events
Bayes’ Theorem
Random Variables and Probability Distributions (discrete)
Mean and Variance of random variables
Binomial Distribution

📖 Key Focus in Online Classes

✔️ NCERT and NCERT Exemplar questions
✔️ Previous Year Board Questions (PYQs)
✔️ HOTS (Higher Order Thinking Skills) Questions
✔️ Practice Assignments and Chapter Tests
✔️ Formula Sheets and Concept Notes
✔️ Doubt Solving & Revision Sessions
✔️ CBSE Board Pattern Sample Papers & Mock Exams

🎯 Goal

✨ Develop strong conceptual clarity
✨ Master step-by-step solutions for full marks
✨ Apply concepts to real-life and competitive exams (JEE, CUET)
✨ Build confidence for scoring 100/100 in Maths!

📚 This Class 12th Mathematics Online Class Syllabus (CBSE Board Session 2025–2026) ensures that you stay exam-ready with structured learning, practice, and expert guidance.

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