EAMCET / EAPCET Mathematics

The question paper consists of a total of 40 questions in Mathematics from both First and Second Years.

ALEGBRA
Functions	Types of functions – Definitions - Domain, Range.
Matrices	Types of matrices - Scalar multiple of a matrix and multiplication of matrices - Transpose of a matrix – Determinants (excluding properties of determinants) - Adjoint and Inverse of a matrix - Rank of a matrix - Solution of simultaneous linear equations (Excluding Gauss Jordan Method).
Complex Numbers	Complex number as an ordered pair of real numbers- fundamental operations - Representation of complex numbers in the form a+ib - Modulus and amplitude of complex numbers–Illustrations - Geometrical and Polar Representation of complex numbers in Argand plane-Argand diagram.
De Moivre’s Theorem	De Moivre’s theorem- Integral and Rational indices - nth roots of unity- Geometrical Interpretations–Illustrations.
Quadratic Expressions	Quadratic expressions, equations in one variable - Sign of quadratic expressions – Change in signs – Maximum and minimum values, Quadratic Inequations.
Theory of Equations	The relation between the roots and coefficients in an equation - Solving the equations when two or more roots of it are connected by certain relation - Equation with real coefficients, occurrence of complex roots in conjugate pairs and its consequences, Transformation of equations- Reciprocal equations.
Permutations and Combinations	Fundamental Principle of counting – linear and circular permutations- Permutations of ‘n’ dissimilar things taken ‘r’ at a time - Permutations when repetitions allowed - Circular permutations - Permutations with constraint repetitions - Combinations-definitions, certain theorems.
Binomial Theorem	Binomial theorem for positive integral index, Binomial theorem for rational Index (without proof). Approximations using Binomial theorem.
Partial fractions	Partial fractions of f(x)/g(x) when g(x) contains non –repeated linear factors - Partial fractions of f(x)/g(x) where both f(x) and g(x) are polynomials and when g(x) contains repeated and/or non-repeated linear factors - Partial fractions of f(x)/g(x) when g(x) contains irreducible factors.
TRIGONOMETRY
Trigonometric Ratios upto Transformations	Graphs and Periodicity of Trigonometric functions - Trigonometric ratios and Compound angles - Trigonometric ratios of multiple and sub- multiple angles - Transformations - Sum and Product rules.
Hyperbolic Functions	Definition of Hyperbolic Function – Graphs - Definition of Inverse Hyperbolic Functions – Graphs - Addition formulae of Hyperbolic Functions.
Properties of Triangles	Relation between sides and angles of a Triangle - Sine, Cosine, Tangent and Projection rules- Half angle formulae and areas of a triangle–In-circle and Ex-circle of a Triangle (excluding problems related to heights and distances).
VECTOR ALGEBRA
Addition of Vectors	Vectors as a triad of real numbers - Classification of vectors - Addition of vectors - Scalar multiplication - Angle between two non-zero vectors - Linear combination of vectors - Component of a vector in three dimensions - Vector equations of line and plane including their Cartesian equivalent forms.
Product of Vectors	Scalar Product - Geometrical Interpretations - orthogonal projections - Properties of dot product - Expression of dot product in i, j, k system - Angle between two vectors - Geometrical Vector methods – Vector equations of plane in normal form-Angle between two planes- Vector product of two vectors and properties- Vector product in i, j, k system- Vector Areas.
MEASURES OF DISPERSION AND PROBABILITY
Measures of Dispersion	Range - Mean deviation - Variance and standard deviation of ungrouped/grouped data, coefficient of variation and analysis of frequency distribution with equal means but different variancies.
Probability	Random experiments and events - Classical definition of probability, Axiomatic approach and addition theorem of probability - Independent and dependent events - conditional probability- multiplication theorem and Baye’s theorem
Random Variables and Probability Distributions	Random Variables - Theoretical discrete distributions – Binomial and Poisson Distributions.
COORDINATEGEOMETRY
Locus	Definition of locus –Illustrations-To find equations of locus-Problems connected toit.
The Straight Line	Revision of fundamental results - Straight line - Normal form – Illustrations - Straight line - Symmetric form - Straight line - Reduction into various forms - Intersection of two Straight Lines - Family of straight lines - Concurrent lines - Condition for Concurrent lines - Angle between two lines - Length of perpendicular from a point to a Line - Distance between two parallel lines - Concurrent lines - properties related to a triangle.
Pair of Straight lines	Equations of pair of lines passing through origin - angle between a pair of lines - Condition for perpendicular and coincident lines, bisectors of angles - Pair of bisectors of angles (excluding proofs of all the theorems only) - Pair of lines - second degree general equation - Conditions for parallel lines - distance between them, Point of intersection of pair of lines - Homogenizing a second degree equation with a first degree equation in x and y.
Circle	Equation of circle -standard form-centre and radius equation of a circle with a given line segment as diameter & equation of circle through three non collinear points - parametric equations of a circle - Position of a point in the plane of a circle – power of a point-definition of tangent-length of tangent - Position of a straight line in the plane of a circle-conditions for a line to be tangent – chord joining two points on a circle – equation of the tangent at a point on the circle- point of contact-equation of normal-Chord of contact pole and polar-conjugate points and conjugate lines- equation of chord with given middle point, Relative position of two circles- circles touching each other externally, internally common tangents –centers of similitude- equation of pair of tangents from an external point.
System of circles	Angle between two intersecting circles –condition for orthogonality - Radical axis of two circles- properties- Common chord and common tangent of two circles –radical centre - Intersection of a line and a Circle.
Parabola	Conic sections –Parabola- equation of parabola in standard form-different forms of parabola- parametric equations, Equations of tangent and normal at a point on the parabola (Cartesian and Parametric)- conditions for straight line to be a tangent.
Ellipse	Equation of ellipse in standard form- Parametric equations, Equation of tangent and normal at a point on the ellipse (Cartesian and parametric)- condition for a straight line to be a tangent
Hyperbola	Equation of hyperbola in standard form- Parametric equations - Equations of tangent and normal at a point on the hyperbola (Cartesian and parametric) - conditions for a straight line to be tangent-Asymptotes.
Three Dimensional Coordinates	Coordinates - Section formulae - Centroid of a triangle and tetrahedron.
Direction Cosines and Direction Ratios	Direction Cosines –Direction Ratios (Excluding angle between two lines).
Plane	Cartesian equation of Plane –Simple Illustrations (Excluding angle between two planes).
CALCULUS
Limits and Continuity	Intervals and neighborhoods – Limits - Standard Limits–Continuity.
Differentiation	Derivative of a function - Elementary Properties - Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function – Derivatives - Methods of Differentiation – Second Order Derivatives.
Applications of Derivatives	Geometrical Interpretation of a derivative - Equations of tangents and normals - Angles between two curves and condition for orthogonality of curves - Increasing and decreasing functions - Maxima and Minima.
Integration	Integration as the inverse process of differentiation- Standard forms -properties of integrals - Method of substitution- integration of Algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions - Integration by parts – Integration by partial fractions method – Reduction formulae.
Definite Integrals	Definite Integral as the limit of sum, Interpretation of Definite Integral as an area. Fundamental theorem of Integral Calculus. Properties, Reduction formulae, Application of Definite integral to areas.
Differential equations	Formation of differential equation-Degree and order of an ordinary differential equation - Solving differential equation by i) Variables separable method, ii) Homogeneous differential equation, iii) Non Homogeneous differential equation iv) Linear differential equations.