Functions - Types of functions - Algebra of real valued functions, Surds and Logarithms, Mathematical Induction and its applications, Permutations and combinations - Linear and Circular Permutations – Combinations, Binomial Theorem - for a positive integral index - for any rational index - applications - Binomial coefficients - Partial Fractions Exponential and Logarithmic Series - Quadratic Expressions - Quadratic inequations, Theory of Equations - Relations between the roots and coefficients in any equation - Transformation of equations - reciprocal equations - cubic equations - Cardan's solution - Biquadratic equations - Ferrari and Decarte's solutions. Matrices and Determinants - Definition - Types of Matrices - Algebra of Matrices - Properties of determinants of 2X2 and 3X3 order matrices - Simultaneous Linear equations in two and three variables – Rank of matrix. Complex numbers - their properties - Demoivre's Theorem - Applications - Expansions of Trigonometric functions.
Unit 2. Trigonometry
Trigonometric functions - Graphs – Periodicity, trigonometric ratios of compound angles, multiple and sub-multiple angles, Transformations, Trigonometric Equations, Inverse Trigonometric functions, Hyperbolic and inverse hyperbolic functions, Properties of Triangles, Heights and Distances (in two dimensional plane)
Unit 3. Vector Algebra
Scalar Product – Angle between two vectors, properties of scalar product, applications of dot products. Vector Product – Right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors – Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines – Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points, angle between two lines. Skew lines – Shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points. Planes – Equation of a plane, passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere – Equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.
Unit 4. Probability
Addition and multiplication theorems of probability - their applications - conditional probability and Baye's Theorem, . Mean and Variance of a random variable - Binomial and Poisson, normal distributions.
Unit 5. Coordinate Geometry
Locus - Translation and Rotation of Axes, The Straight Line, The Pair of Straight Lines, Coordinate planes in three dimensions - distance between two points - section formula and their applications, Direction cosines and direction ratios of a line - angle between two lines - projection of a line, The plane and its general equation - Equation of the plane in different forms, Circles and system of Circles, Conics - Parabola - Ellipse - Hyperbola - their applications - Equations of Tangent, Normal, Polar and Pole to these conics, Polar Coordinates.
Unit 6. Calculus
Functions - Limits – Continuity, Differentiation - Different Methods, Successive Differentiation including Leibnitz's Theorem, Applications of Differentiation, Partial Differentiation including Euler's Theorem on homogeneous functions, Different methods of Integration, Definite integrals and their applications to areas - reduction formulae. Numerical Integration - Trapezoidal and Simpson's Rules, Differential equations - Formation and solution of first order, first degree differential equations, Second order linear homogenous equations with constant coefficients.