1. Algebra:
Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation.
Representation of real numbers on a line. Complex numbers  basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and viceversa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications.
2. Matrices and Determinants: Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications  Solution of a system of linear equations in two or three unknowns by Cramer's rule and by Matrix Method.
3. Trigonometry: Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Submultiple angles. Inverse trigonometric functions. Applications  Height and distance, properties of triangles.
4. Analytical Geometry of two and three dimensions: Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic.
Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.
5. Differential Calculus:
Concept of a real valued function  domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits  examples. Continuity of functions  examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical
interpretation of a derivative  applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.
6. Integral Calculus and Differential equations: Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals  determination of areas of plane regions bounded by curves  applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various types  examples. Application in problems of growth and decay.
7. Vector Algebra:
Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of vector, scalar product or dot product of twovectors. Vector product and cross product of two vectors. Applicationswork done by a force and moment of a force, and in geometrical problems.
8. Statistics and Probability:
Statistics: Classification of data, Frequency distribution, cumulative frequency distribution  examples Graphical representation  Histogram, Pie Chart, Frequency Polygon  examples. Measures of Central tendency  mean, median and mode. Variance and standard deviation  determination and comparison. Correlation and regression.
Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability  classical and statistical  examples. Elementary theorems on probability  simple problems. Conditional probability, Bayes' theorem  simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.
