Mathematics — Notes, PYQs & Video Lectures

Unit 1: Sets (15 hours, 4 marks)

Sets and their representations, empty, finite, infinite and equal sets, subsets, intervals, power set, universal set, Venn diagrams, union, intersection, difference and complement of sets and their properties.

Unit 2: Relations and Functions (15 hours, 4 marks)

Ordered pairs, Cartesian product of sets, relations, domain, co-domain and range; functions and their graphs: constant, identity, polynomial, rational, modulus, exponential, logarithmic, signum and greatest integer functions; sum, difference, product and quotient of functions.

Unit 3: Trigonometric Functions (15 hours, 7 marks)

Positive and negative angles, radian and degree measure, trigonometric functions via the unit circle, sin²x + cos²x = 1, signs, domain, range and graphs; compound-angle formulae, sum-to-product identities, identities for 2x and 3x, general solutions of sin θ = sin α, cos θ = cos α and tan θ = tan α.

Unit 4: Complex Numbers and Quadratic Equations (13 hours, 6 marks)

Need for complex numbers, algebraic properties, Argand plane, polar representation, modulus and argument, solution of quadratic equations in the complex number system.

Unit 5: Linear Inequalities (5 hours, 4 marks)

Linear inequalities in one variable and with the modulus function on the number line; graphical solution of linear inequalities in two variables.

Unit 6: Permutations and Combinations (12 hours, 5 marks)

Fundamental principle of counting, factorial, permutations and combinations, formulae for nPr and nCr and their connection, simple applications.

Unit 7: Limits and Derivatives (25 hours, 10 marks)

Intuitive idea of limit; limits of polynomial, rational, trigonometric, exponential and logarithmic functions; derivative as rate of change and as slope of a tangent; derivative of sum, difference, product and quotient; derivatives of polynomial and trigonometric functions.

Source: official document