ELEMENTARY MATHEMATICS 
1). ALGEBRA
 ● Concept of set
 ● Operations on sets
 ● Venn diagrams
 ● De Morgan laws
 ● Cartesian product
 ● Relation
 ● Equivalence relation
 ● 19 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 applications. Logarithms and their applications.
2). MATRICES AND DETERMINANTS
 ● Types of matrices
 ● Operations on matrices
 ● Determinant of a matrix
 ● Basic properties of determinants
 ● Adjoint and inverse of a square matrix
 ● ApplicationsSolution 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
 ● ApplicationsHeight 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 threedimensional space, distance between two points
 ● Direction Cosines and direction ratios. Equation 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 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 to 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 equations, 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 a vector, scalar product or dot product of two vectors.
 ● Vector product or cross product of two vectors. Applications—work 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 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.
