PORTION FOR EAMCET MATHS

MathematicsI. ALGEBRA:
1. Functions - Types of functions - Algebra of real valued functions 2. Surds and Logarithms 3. Mathematical Induction and its applications 4. Permutations and combinations - Linear and Circular Permutations - Combinations 5. Binomial Theorem - for a positive integral index - for any rational index - applications - Binomial coefficients 6. Partial Fractions 7. Exponential and Logarithmic Series 8. Quadratic Expressions - Quadratic inequations 9. 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. 10. 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. 11. Complex numbers - their properties - Demoivre's Theorem - Applications - Expansions of Trigonometric functions.
II. TRIGONOMETRY:
1. Trigonometric functions - Graphs - Periodicity 2. Trigonometric ratios of compound angles, multiple and sub-multiple angles 3. Transformations 4. Trigonometric Equations 5. Inverse Trigonometric functions 6. Hyperbolic and inverse hyperbolic functions 7. Properties of Triangles 8. Heights and Distances (in two dimensional plane)
III. VECTOR ALGEBRA:
1. Algebra of Vectors 2. Scalar and Vector Products of Two vectors and their applications 3. Scalar and Vector triple products - Scalar and Vector products of four vectors
IV. PROBABILITY:
1. Addition and multiplication theorems of probability - their applications - conditional probability and Baye's Theorem 2. Mean and Variance of a random variable - Binomial and Poisson distributions.
V. COORDINATE GEOMETRY:
1. Locus - Translation and Rotation of Axes 2. The Straight Line 3. The Pair of Straight Lines 4. Coordinate planes in three dimensions - distance between two points - section formula and their applications 5. Direction cosines and direction ratios of a line - angle between two lines - projection of a line 6. The plane and its general equation - Equation of the plane in different forms 7. Circles and system of Circles 8. Conics - Parabola - Ellipse - Hyperbola - their applications - Equations of Tangent, Normal, Polar and Pole to these conics. 9. Polar Coordinates.
VI. CALCULUS:
1. Functions - Limits - Continuity 2. Differentiation - Different Methods 3. Successive Differentiation including Leibnitz's Theorem 4. Applications of Differentiation 5. Partial Differentiation including Euler's Theorem on homogeneous functions 6. Different methods of Integration 7. Definite integrals and their applications to areas - reduction formulae. 8. Numerical Integration - Trapezoidal and Simpson's Rules 9. Differential equations - Formation and solution of first order, first degree differential equations.