The syllabus consists of five units: (i) Sets and Functions (ii) Algebra (iii) Coordinate Geometry (iv) Calculus (v) Statistics and Probability.
|I.||Sets and Functions||8|
|V.||Statistics and Probability||6|
3. Trigonometric Functions
Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other. Definition of trigonometric functions with the help of unit circle. Truth of the sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sin x, sin y, cos x & cos y and their simple application. Deducing identities like the following:
Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x.
3. Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.
4. Permutations and Combinations
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, formula for nPr and nCr, simple applications.
2. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.
3. Introduction to Three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
Derivative introduced as rate of change both as that of distance function and geometrically. Definition of Derivative, relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Probability of an event, probability of 'not', 'and' and 'or' events.