? Mathematics Course Syllabus

Senior Secondary (Class 11 & 12)

Course Objective

• Develop deep conceptual understanding

• Build problem solving ability

• Prepare for Board Exams + Competitive Exams

• Strengthen logical and analytical thinking

CLASS 11 MATHEMATICS

Module 1: Sets & Relations

Topics:

• Sets and representation

• Types of sets

• Subsets & power set

• Venn diagrams

• Union, intersection, difference

• Complement of a set

• Relations

• Types of relations

Assessment:

• Concept MCQs

• Venn diagram reasoning problems

Module 2: Functions

Topics:

• Definition of function

• Domain & range

• Types of functions

  • One-one

  • Onto

  • Into

• Composite functions

• Inverse functions

Assessment:

• Domain-range puzzles

• Graph interpretation

Module 3: Trigonometry

Topics:

• Trigonometric ratios

• Trigonometric identities

• Compound angle formulas

• Transformation formulas

• Trigonometric equations

• Graphs of trigonometric functions

Assessment:

• Identity proof questions

• Equation solving

Module 4: Complex Numbers

Topics:

• Imaginary numbers

• Algebra of complex numbers

• Argand plane

• Modulus and argument

• Polar form

• Square roots of complex numbers

Assessment:

• Algebraic manipulation

• Geometric interpretation

Module 5: Quadratic Equations

Topics:

• Standard form

• Nature of roots

• Relationship between roots and coefficients

• Formation of quadratic equations

• Inequalities

Assessment:

• Root based reasoning

• Parameter based problems

Module 6: Sequences & Series

Topics:

• Arithmetic progression

• Geometric progression

• Sum of series

• Infinite GP

• Special series

Assessment:

• Word problems

• Pattern recognition

Module 7: Permutations & Combinations

Topics:

• Factorial notation

• Permutations

• Circular permutations

• Combinations

• Selection problems

Assessment:

• Logical counting problems

Module 8: Binomial Theorem

Topics:

• Binomial expansion

• General term

• Middle term

• Greatest term

• Properties of binomial coefficients

Assessment:

• Expansion based problems

• Term identification

Module 9: Coordinate Geometry

Topics:

• Distance formula

• Section formula

• Area of triangle

• Straight line equations

• Slope concept

• Angle between lines

Assessment:

• Coordinate proofs

• Geometry reasoning

Module 10: Limits & Introduction to Calculus

Topics:

• Intuitive idea of limits

• Standard limits

• Continuity concept

Assessment:

• Limit evaluation

Module 11: Statistics

Topics:

• Measures of central tendency

• Mean

• Median

• Mode

Module 12: Probability

Topics:

• Random experiments

• Events

• Probability rules

• Conditional probability

CLASS 12 MATHEMATICS

Module 1: Relations & Functions

Topics:

• Types of relations

• Equivalence relations

• Functions classification

• Composite functions

• Inverse trigonometric functions

Module 2: Matrices

Topics:

• Types of matrices

• Matrix operations

• Transpose

• Symmetric and skew symmetric matrices

Assessment:

• Matrix algebra

Module 3: Determinants

Topics:

• Determinant expansion

• Properties of determinants

• Cofactors

• Adjoint of matrix

• Inverse of matrix

• Solving linear equations

Assessment:

• Determinant simplification

Module 4: Continuity & Differentiability

Topics:

• Continuity

• Differentiation

• Derivatives of functions

• Chain rule

• Implicit differentiation

• Logarithmic differentiation

Assessment:

• Differentiation techniques

Module 5: Applications of Derivatives

Topics:

• Increasing and decreasing functions

• Maxima and minima

• Tangent and normal

• Rate of change

Assessment:

• Real life optimization problems

Module 6: Integrals

Topics:

• Indefinite integrals

• Substitution method

• Partial fractions

• Definite integrals

• Properties of definite integrals

Assessment:

• Integration techniques

Module 7: Applications of Integrals

Topics:

• Area under curves

• Area between curves

Module 8: Differential Equations

Topics:

• Formation of differential equations

• Variable separable equations

• Homogeneous equations

Module 9: Vector Algebra

Topics:

• Vector basics

• Dot product

• Cross product

• Projection of vectors

Module 10: 3D Geometry

Topics:

• Direction cosines

• Equation of line in space

• Shortest distance

• Angle between lines

Module 11: Linear Programming

Topics:

• Formulation of LPP

• Graphical method

• Feasible region

• Optimization

Module 12: Probability

Topics:

• Conditional probability

• Bayes theorem

• Random variables

• Probability distributions

Teaching Methodology (For Academy Structure)

1?? Concept Building
2?? Illustrative Problems
3?? Guided Practice
4?? Assignment Sheet
5?? Weekly Assessment
6?? Monthly Concept Test
7?? Olympiad/JEE Level Problems