Mathematics

TS EAMCET Mathematics Syllabus – Engineering 

Candidates appearing for TS EAMCET or Telangana State Engineering, Agriculture, and Medical Common Entrance Test in Engineering stream should refer the below mentioned Mathematics syllabus:

1. Algebra 

a. Partial Fractions: 

• Partial fractions of f(x)/g(x) when g(x) contains irreducible factors only
• Partial fractions of f(x)/g(x) when g(x) contains non – repeated linear factors
• Partial fractions of f(x)/g(x) when g(x) contains repeated and/or non-repeated linear factors

b. Permutations and Combinations: 

• Fundamental Principle of counting 
• Combinations – definitions, certain theorems  
• Linear and circular permutations
• Permutations of ‘n’ dissimilar things taken ‘r’ at a time

c. Binomial Theorem: 

• Binomial theorem for rational Index (without proof)
• Binomial theorem for positive integral index 

d. Theory of Equations: 

• The relation between the roots and coefficients in an equation 
• Equation with real coefficients, the occurrence of complex roots in conjugate pairs and its consequences 
• Transformation of equations 
• Reciprocal Equations 
• Solving the equations when two or more roots of it are connected by certain relation.

e. Quadratic Expressions: 

• Quadratic expressions, equations in one variable 
• Change in signs 
• Sign of quadratic expressions 
• Maximum and minimum values

f. De Moivre’s Theorem: 

• De Moivre’s theorem- Integral and Rational indices  
• Geometrical Interpretations 
• nth roots of unity
• Illustrations.

g. Complex Numbers: 

• Complex number as an ordered pair of real numbers 
• Representation of complex numbers in the form 𝑎 + 𝑖𝑏 
• Fundamental Operations 

h. Matrices: 

• Types of matrices  
• Scalar multiple of a matrix and multiplication of matrices 
• Transpose of a matrix – Adjoint and Inverse of a matrix 
• Determinants
• Consistency and inconsistency of Equations
• Solution of simultaneous linear equations 
• Rank of a matrix

i. Functions: 

• Types of functions 
• Inverse functions and Theorems 
• Definitions
• Range
• Domain
• The inverse of real-valued functions

j. Mathematical Induction: 

• Principle of Mathematical Induction & Theorems 
• Problems on divisibility 
• Applications of Mathematical Induction

2. Trigonometry

a. Inverse Trigonometric Functions:

• To reduce a Trigonometric Function into a bijection 
• Properties of Inverse Trigonometric Functions 
• Graphs of Inverse Trigonometric Functions

b. Trigonometric Equations: 

• General Solution of Trigonometric Equations 
• Solutions 
• Simple Trigonometric Equations

c. 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 

d. Hyperbolic Functions: 

• Definition of Hyperbolic Function 
• Graphs 
• Definition of Inverse Hyperbolic Functions 
• Graphs – Addition formulae of Hyperbolic Functions

e. Trigonometric Ratios up to Transformations: 

• Graphs and Periodicity of Trigonometric functions 
• Sum and Product rules 
• Trigonometric ratios and Compound angles 
• Transformations 
• Trigonometric ratios of multiple and sub-multiple angles

3. Vector Algebra

a. Product of Vectors: Scalar Product – 

• Geometrical Interpretations 
• Properties of the dot product 
• Expression of the dot product in 𝑖,𝑗, 𝑘 system
• Orthogonal Projections  
• Geometrical Vector methods 
• Vector equations of a plane in normal form
• The angle between two planes  
• Vector product in 𝑖,𝑗, 𝑘 system  
• Vector product of two vectors and properties 
• Vector Areas 
• Vector equations of a plane in different forms, skew lines, shortest distance and their Cartesian equivalents
• A 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 the line and a plane. Cartesian equivalents of all these results 
• Scalar Triple Product 
• Vector Triple Product  
• Results -Angle between two vectors

b. Addition of Vectors: 

• Vectors as a triad of real numbers 
• Addition of vectors 
• Classification of vectors 
• The angle between two nonzero vectors  
• Scalar multiplication 
• Component of a vector in three dimensions 
• Linear combination of vectors 
• Vector equations of line and plane including their Cartesian equivalent forms

4. Probability

a. Random Variables and Probability Distributions: 

• Random Variables 
• Theoretical discrete distributions 
• Binomial and Poisson Distributions 

b. Measures of Dispersion: 

• Range 
• Mean deviation for ungrouped data

c. Probability: 

• Random experiments and events  
• Independent and dependent events 
• The classical definition of probability 
• Axiomatic approach and addition theorem of probability 
• Multiplication Theorem
• Conditional Probability

5. Coordinate Geometry

a. The Straight Line:

• Revision of fundamental results 
• Family of straight lines 
• Straight line 
• Straight line – Illustrations 
• Straight line – Reduction into various forms 
• Condition for Concurrent lines 
• Concurrent lines –  Angle between two lines 
• Length of the perpendicular from a point to a Line 
• Normal form 
• Symmetric form 
• Concurrent lines – Distance between two parallel lines 
• Properties related to a triangle 
• Intersection of two Straight Lines.

b. 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 Intersection Of Pair Of Lines 
• Homogenising A Second Degree Equation With A First Degree Equation In 𝑥 And 𝑦

c. Locus: 

• Definition of locus 
• Illustrations 
• To find equations of locus  Problems connected to it 

d. Circle: 

Equation of circle – 

• s parametric equations of a circle  
• Position of a point in the plane of a circle 
• length of a tangent  
• Position of a straight line in the plane of a circle
• conditions for a line to be tangent  
• Chord of contact  
• standard form-centre and radius of a circle with a given line segment as diameter & equation of a circle through three non-collinear points  
• power of a point definition of a tangent 
• chord joining two points on a circle 
• equation of the tangent at a point on the circle- 
• point of contact
• equation of normal  
• conjugate points and conjugate lines  
• equation of chord with given middle point  
• centres of similitude 
• common tangents 
• Relative position of two circles 
• pole and polar  
• circles touching each other externally, internally 
• equation of pair of tangents from an external point  

e. Parabola: 

• Conic sections 
• Parabola – equation of the parabola in standard form 
• different forms of a parabola 
• parametric equations

f. System of circles: 

• Angle between two intersecting circles 
• radical centre 
• Radical axis of two circles properties 
• Common chord and common tangent of two circles 
• Intersection of a line and a Circle

g. Ellipse: 

• Equation of ellipse in standard form 
• Parametric equations  

h. Three Dimensional Coordinates: 

• Coordinates 
• Section formulae 
• Centroid of a triangle and tetrahedron  

i. Hyperbola:

• Equation of hyperbola in standard form 
• Parametric equations

j. Plane: 

• Cartesian equation of Plane 
• Simple Illustrations  

k. Direction Cosines and Direction Ratios: 

• Direction Cosines  
• Direction Ratios

l. Transformation of Axes:

• Transformation of axes – Rules, Derivations and Illustrations
• Rotation of axes
• Derivations
• Illustrations

6. Calculus

a. Integration: 

• Integration as the inverse process of differentiation
• Standard forms 
• properties of integrals 
• Method of substitution 
• integration of Algebraic 
• Exponential trigonometric functions 
• Logarithmic  trigonometric functions 
• trigonometric trigonometric functions
• inverse trigonometric functions

b. Differential equations: 

• Formation of the differential equation
• Degree and order of an ordinary differential equation 
• Solving differential equation by Variables separable method

c. Limits and Continuity: 

• Intervals and neighbourhoods 
• Limits 
• Standard Limits 
• Continuity

d. Differentiation: 

• Derivative of a function
• Trigonometric 
• Inverse Trigonometric
• Hyperbolic 
• Inverse Hyperbolic Function 
• Elementary Properties 
• Methods of Differentiation  
• Derivatives 
• Second-Order Derivatives 

e. Definite Integrals:  

• Interpretation of Definite Integral as an area  
• Fundamental theorem of Integral Calculus  
• Definite Integral as the limit of the sum – Properties

f. Applications of Derivatives: 

• Errors and approximations 
• Equations of tangents and normals  
• Lengths of a tangent, normal, subtangent and subnormal
• Angles between two curves and condition for orthogonality of curves 
• Increasing and decreasing functions 
• Geometrical Interpretation of a derivative  
• Rolle’s Theorem  
• Lagrange’s Mean value theorem without proofs and their geometrical interpretation  
• Derivative as Rate of change 
• Maxima and Minima  

Note: 

The following topics are deleted for the Academic Year 2020-21 by the TSBIE for the TS EAMCET-2021 Examination, as per the Telugu Academy Text Book, in the Mathematics Paper II-A

1. Complex Numbers

• Modulus and amplitudes of complex number-illustrations
• Geometrical and polar representation of a complex number in argand plane – argand
• diagram

2. Demovier’s Theorem

• Exercise 2(b) section II and section III

3. Quadratic expressions

• Quadratic inequalities

4. Permutations and Combinations

• Circular permutations
• Exercise 5(e) Section III 
• Permutations with constraint repetitions
• Permutations when repetitions are allowed

5. Binomial Theorem

• Exercise 6(c)
• Exercise 6(b) Section II and related examples
• Exercise 6(a) Section II 5th problem onwards and related examples

6. Partial Fractions

• Exercise 7(d)

7. Measures of Dispersion

• Coefficient of Variation and analysis of frequency distributions with equal means but
• different variances
• Exercise 8(a) Section I Problem 3 onwards
• Mean Deviation for grouped data
• Variance and standard deviation of ungrouped / grouped data

8. Probability

• Bayes’ Theorem and problems on Bayes’ theorem

Note: The following topics are deleted for the Academic Year 2020-21 by the TSBIE for the TS EAMCET-2021 Examination, as per the Telugu Academy Text Book, in the Mathematics Paper II-B

9. Parabola

• Equation of tangent and normal at a point on the parabola
• Ellipse

• Equation of tangent and normal at a point on the ellipse

10. Hyperbola

• Equation of tangent and normal at a point on the hyperbola Exercise 5(a) Section

II onwards and related examples

11. Integration

• Reduction formulae 
• Integration-partial fraction method
• Integration by parts – Integration of exponential, logarithmic and inverse
• trigonometric functions

12. Definite Integrals

• Reduction formula
• Exercise-7(b) Section II (8 to 15)
• Application of definite integrals to areas

13. Differential Equations

• Linear Differential Equations
• Non-Homogeneous Differential Equations
• Homogeneous Differential Equation