Syllabus For Mathematics
I. ALGEBRA:
- 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.
- Complex numbers - their properties - Demoivre's Theorem - Applications - Expansions of Trigonometric functions.
II. 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)
III. VECTOR ALGEBRA:
- Algebra of Vectors
- Scalar and Vector Products of Two vectors and their applications
- Scalar and Vector triple products - Scalar and Vector products of four vectors
IV. 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 distributions.
V. 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.
VI. 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.
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