Unit I: Relations and Functions (08 Marks)

Chapter 1: Relations

Topics: Ordered pairs, Cartesian products, types of relations: reflexive, symmetric, transitive, and equivalence relations.

Chapter 2: Functions

Topics: One-one and onto functions, composition of functions, invertible functions, binary operations.

Chapter 3: Inverse Trigonometric Functions

Topics: Domains, ranges, principal value branches, graphs, and properties of inverse trigonometric functions.

Unit II: Algebra (10 Marks)

Chapter 4: Matrices

Topics: Types of matrices, operations, properties, transpose, symmetric and skew-symmetric matrices, invertible matrices.

Chapter 5: Determinants

Topics: Determinants up to order 3, properties, minors, cofactors, applications, adjoint and inverse, solving systems of equations.

Unit III: Calculus (35 Marks)

Chapter 6: Continuity and Differentiability

Topics: Continuity, differentiability, derivatives of composite, implicit, inverse trig functions, second-order derivatives, MVT and Rolle’s Theorem.

Chapter 7: Applications of Derivatives

Topics: Increasing/decreasing functions, tangents and normals, maxima and minima, real-life applications.

Chapter 8: Integrals

Topics: Indefinite and definite integrals, properties, basic integration techniques, substitution, parts, partial fractions.

Chapter 9: Applications of Integrals

Topics: Area under curves (lines, parabolas, circles), area between two curves.

Chapter 10: Differential Equations

Topics: Formation, order, degree, general/particular solutions, variable separable method, linear equations.

Unit IV: Vectors and Three-Dimensional Geometry (14 Marks)

Chapter 11: Vectors

Topics: Magnitude, direction, types of vectors, operations, dot and cross product, geometric interpretation.

Chapter 12: Three-Dimensional Geometry

Topics: Direction cosines and ratios, equations of lines and planes, coplanarity, angles, shortest distance.

Unit V: Linear Programming (05 Marks)

Chapter 13: Linear Programming

Topics: Formulation, feasible and infeasible regions, graphical method, optimization of objective function.

Unit VI: Probability (08 Marks)

Chapter 14: Probability

Topics: Conditional probability, Bayes’ theorem, random variables, probability distributions, Bernoulli trials, binomial distribution.