| 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 vice-versa.
- ● 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
- ● 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 Sub-multiple 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 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.
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