I. Algebra:
a) Functions – Types of functions – Algebra of real valued functions. b) Mathematical induction and applications. c) Permutations and Combinations – linear and circular permutations – combinations. d) Binomial theorem – for a positive integral index – for any rational index – applications – Binomial Coefficients. e) Partial fractions. f) Exponential and logarithmic series. g) Quadratic expressions, equations and inequations in one variable. h) Theory of equations – Relations between the roots and Coefficients in any equation – Transformation of equations – reciprocal equations. i) Matrices and determinants – Types of matrices – Algebra of matrices – Properties of determinants – simultaneous linear equations in two and three variables – Consistency and inconsistency of simultaneous equations. j) Complex numbers and their properties – De Moivre’s theorem – Applications – expansions of trigonometric functions.
II. Trigonometry
a) Trigonometric functions – Graphs – periodicity. b) Trigonometric ratios of compound angles, multiple and sub-multiple angles. c) Transformations. d) Trigonometric equations. e) Inverse trigonometric functions. f) Hyperbolic and inverse hyperbolic functions. g) Properties of Triangles. h) Heights and distances (in two-dimensional plane)
III. Vector Algebra
a) Algebra of vectors – angle between two non-zero vectors – linear combinations of vectors – vector equation of line and plane. b) Scalar and vector product of two vectors and their applications. c) Scalar and vector triple products – Scalar and vector products of four vectors
IV. Probability
a) Random experiments – Sample space – events – probability of an event – addition and multiplication theorems of probability – Baye’s theorem. b) Random variables – Mean and variance of a random variable – Binomial and Poisson distributions
V. Coordinate Geometry
a) Locus – Translation and rotation of axes. b) Straight line. c) Pair of straight lines. d) Circles and system of circles. e) Conics – Parabola – Ellipse – Hyperbola – Equations of tangent, normal and polar at any point of these conics. f) Polar Coordinates. g) Coordinates in three – dimensions – distances between two points in the space – Section formula and their applications. h) Direction Cosines and direction ratios of a line – angle between two lines. i) Cartesian equation of a plane in (i) general form (ii) normal form and (iii) intercept form – angle between two planes. j) Sphere – Cartesian equation – Centre and radius
VI. Calculus
a) Functions – limits – Continuity. b) Differentiation – Methods of differentiation. c) Successive differentiation – Leibnitz’s theorem and its applications. d) Applications of differentiation. e) Partial differentiation including Euler’s theorem on homogeneous functions. f) Integration – methods of integration. g) Definite integrals and their applications to areas – reduction formulae. h) Numerical integration – Trapezoidal and Simpson’s rules. i) Differential equations – order and degree – Formation of differential equation – Solution of differential equation by variable separable method – Solving homogeneous and linear differential equations of first order and first degree.