Mathematics (MATH)
7 units: Principle of Mathematical Induction, Binomial Theorem, Sequence and Series, Straight Lines, Conic Sections.
Detailed syllabus
Unit 1: Principle of Mathematical Induction (7 hours, 3 marks)
Process of proof by induction, natural numbers as the least inductive subset of reals, the principle and simple applications.
Unit 2: Binomial Theorem (13 hours, 6 marks)
Statement and proof for positive integral indices, Pascal's triangle, general and middle terms, simple applications.
Unit 3: Sequence and Series (15 hours, 6 marks)
Arithmetic and geometric progressions, A.M. and G.M. and their relation, arithmetico-geometric series, infinite G.P. and its sum, sums of n terms of Σn, Σn² and Σn³.
Unit 4: Straight Lines (10 hours, 5 marks)
Slope of a line, angle between two lines, forms of the equation of a line (parallel to an axis, point-slope, slope-intercept, two-point, intercept), distance of a point from a line.
Unit 5: Conic Sections (20 hours, 10 marks)
Sections of a cone: circle, ellipse, parabola, hyperbola and degenerate cases; standard and general equation of a circle; standard equations and simple properties of parabola, ellipse and hyperbola.
Unit 6: Statistics (5 hours, 3 marks)
Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped and grouped data.
Unit 7: Probability (10 hours, 7 marks)
Random experiments, outcomes, sample spaces, events (not, and, or), exhaustive and mutually exclusive events, axiomatic probability, probability of an event and of not/and/or events.
Source: official document