AP EAPCET Mathematics Syllabus 2023- Check List of Chapters & Important Topics for EAMCET Exam

Algebra

• Mathematical Induction: Principle of Mathematical Induction & Theorems - Applications of Mathematical Induction - Problems on divisibility
• Matrices: Types of matrices - Scalar multiple of a matrix and multiplication of matrices - Transpose of a matrix - Determinants - Adjoint and Inverse of a matrix - Consistency and inconsistency of Equations- Rank of a matrix - Solution of simultaneous linear equations
• Functions: Types of functions – Definitions - Inverse functions and Theorems - Domain, Range, Inverse of real valued functions
• 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 equations
• 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
• Permutations and Combinations: Fundamental Principle of counting – linear and circular permutationsPermutations of ‘n’ dissimilar things taken ‘r’ at a time - Permutations when repetitions allowed - Circular permutations - Permutations with constraint repetitions - Combinations-definitions, certain theorems, and their applications
• 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, the occurrence of complex roots in conjugate pairs and its consequences - Transformation of equations - ReciprocalEquations
• 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 Equations: General Solution of Trigonometric Equations - Simple Trigonometric Equations – Solutions
• Trigonometric Ratios up to 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 – Incircle and Excircle of a triangle
• Inverse Trigonometric Functions: To reduce a Trigonometric Function into a bijection - Graphs of Inverse Trigonometric Functions - Properties of Inverse TrigonometricFunctions

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 the dot product in i, j, k system - Angle between two vectors - Geometrical Vector methods - Vector equations of the plane in normal form - Angle between two planes - Vector product of two vectors and properties - Vector product in i, j, k system - Vector Areas - Scalar Triple Product - Vector equations of plane in different forms, skew lines, shortest distance and their Cartesian equivalents. Plane through the line of intersection of two planes, condition for coplanarity of two lines, perpendicular distance of a point from a plane, the angle between line and a plane. Cartesian equivalents of all these results - Vector Triple Product –Results

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 variances
• Random Variables and Probability Distributions: Random Variables - Theoretical discrete distributions – Binomial and Poisson distributions
• 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 and applications

COORDINATE GEOMETRY

• Locus: Definition of locus – Illustrations - To find equations of locus - Problems connected to it
• Transformation of Axes: Transformation of axes - Rules, Derivations, and Illustrations - Rotation of axes - Derivations – Illustrations
• 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 a 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 - Pair of lines - second degree general equation - Conditions for parallel lines - distance between them, Point of the 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-center and radius equation of a circle with a given line segment as diameter & equation of a circle through three noncollinear 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 a 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 in term of its midpoint - 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 - Radical axis of two circles- properties- Common chord and common tangent of two circles – radical centre
• Direction Cosines and Direction Ratios: Direction Cosines - DirectionRatios
• 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
• 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 a tangent-Asymptotes. j) Three Dimensional Coordinates: Coordinates - Section formulae - Centroid of a triangle and tetrahedron
• 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
• Plane: Cartesian equation of Plane - SimpleIllustrations

CALCULUS

• Applications of Derivatives: Errors and approximations - Geometrical Interpretation of a derivative - Equations of tangents and normals - Lengths of tangent, normal, sub tangent and sub normal - Angles between two curves and condition for orthogonality of curves - Derivative as Rate of change - Rolle’s Theorem and Lagrange’s Mean value theorem without proofs and their geometrical interpretation - Increasing and decreasing functions - Maxima and Minima
• Limits and Continuity: Intervals and neighbourhoods – Limits - Standard Limits –Continuity
• Differentiation: Derivative of a function - Elementary Properties - Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function – Derivatives - Methods of Differentiation - SecondOrder Derivatives
• Definite Integrals: Definite Integral as the limit of the sum - Interpretation of Definite Integral as an area - Fundamental theorem of Integral Calculus (without proof) – 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
• 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

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