Mathematics (MATH)
7 units: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability.
Detailed syllabus
Unit 1: Relations and Functions (10 hours, 4 marks)
Reflexive, symmetric, transitive and equivalence relations; one-one and onto functions, composite functions, inverse of a function.
Unit 2: Inverse Trigonometric Functions (10 hours, 3 marks)
Definition, range, domain, principal value branches, graphs and elementary properties of inverse trigonometric functions.
Unit 3: Matrices (15 hours, 6 marks)
Notation, order, equality and types of matrices, transpose, symmetric and skew-symmetric matrices, addition, multiplication and scalar multiplication and their properties, non-commutativity, invertible matrices and uniqueness of the inverse.
Unit 4: Determinants (10 hours, 4 marks)
Determinants up to 3×3, properties, minors, cofactors, area of a triangle, adjoint and inverse of a square matrix, consistency of linear systems, solving systems in two or three variables using the inverse.
Unit 5: Continuity and Differentiability (20 hours, 8 marks)
Continuity and differentiability, chain rule, derivatives of inverse trigonometric, implicit, exponential and logarithmic functions, logarithmic differentiation, parametric forms, second-order derivatives.
Unit 6: Application of Derivatives (18 hours, 7 marks)
Rate of change, increasing and decreasing functions, tangents and normals, maxima and minima (first and second derivative tests), real-life problems.
Unit 7: Probability (17 hours, 8 marks)
Conditional probability, multiplication theorem, independent events, total probability, Bayes' theorem, random variables and probability distributions, mean and variance.
Source: official document