EAMCET
EAMCET Mathematics Syllabus
Engineering Entrance , EAMCET (Engg)
EAMCET Mathematics Syllabus:
Unit 1. 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.
Unit 2. Trigonometry
1. Trigonometric functions  Graphs  Periodicity
2. Trigonometric ratios of compound angles, multiple and submultiple 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)
Unit 3. 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
Unit 4. 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.
Unit 5. 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.
Unit 6. 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.
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