Syllabus for PGT - Mathematics | AWES PGT Mock Test Series 2024 - AWES TGT/PGT PDF Download

 Page 1


Syllabus for the post of PGT -Mathematics 
Sets: 
Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets. Subsets of a set 
of real numbers especially intervals (with notations). Universal set. Venn diagrams. Union and 
Intersection of sets. Difference of sets. Complement of a set. Properties of Complement. 
Relations & Functions: 
Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite 
sets. Cartesian product of the set of reals with itself (upto R x R x R).Definition of relation, pictorial 
diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial 
representation of a function, domain, co-domain and range of a function. Real valued functions, 
domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, 
exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product 
and quotients of functions. 
Trigonometric Functions 
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one 
measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the 
identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of 
trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, 
cosx & cosy and their simple applications. Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and 
tan3x.  
Complex Numbers and Quadratic Equations 
Need for complex numbers, especiallyv-1, to be motivated by inability to solve some of the 
quardratic equations. Algebraic properties of complex numbers. Argand plane  
Linear Inequalities 
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation 
on the number line. 
Permutations and Combinations 
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of 
Formulae for nPr and nCr and their connections, simple applications. 
Binomial Theorem 
Historical perspective, statement and proof of the binomial theorem for positive integral indices. 
Pascal’s triangle, simple applications. 
Sequence and Series 
Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression 
(G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean 
(G.M.), relation between A.M. and G.M. 
Straight Lines 
Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, 
point -slope form, slope-intercept form. Distance of a point from a line. 
Conic Sections 
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of 
intersecting lines as a degenerated case of a conic section. Standard equations and simple properties 
of parabola, ellipse and hyperbola. Standard equation of a circle. 
Subject specific syllabus includes the concepts of NCERT/CBSE syllabus and Text Books (Classes XI 
& XII), however, the questions will be testing the depth of understanding and application of 
these concepts at the level of Post- Graduation. 
4
Page 2


Syllabus for the post of PGT -Mathematics 
Sets: 
Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets. Subsets of a set 
of real numbers especially intervals (with notations). Universal set. Venn diagrams. Union and 
Intersection of sets. Difference of sets. Complement of a set. Properties of Complement. 
Relations & Functions: 
Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite 
sets. Cartesian product of the set of reals with itself (upto R x R x R).Definition of relation, pictorial 
diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial 
representation of a function, domain, co-domain and range of a function. Real valued functions, 
domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, 
exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product 
and quotients of functions. 
Trigonometric Functions 
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one 
measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the 
identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of 
trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, 
cosx & cosy and their simple applications. Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and 
tan3x.  
Complex Numbers and Quadratic Equations 
Need for complex numbers, especiallyv-1, to be motivated by inability to solve some of the 
quardratic equations. Algebraic properties of complex numbers. Argand plane  
Linear Inequalities 
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation 
on the number line. 
Permutations and Combinations 
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of 
Formulae for nPr and nCr and their connections, simple applications. 
Binomial Theorem 
Historical perspective, statement and proof of the binomial theorem for positive integral indices. 
Pascal’s triangle, simple applications. 
Sequence and Series 
Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression 
(G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean 
(G.M.), relation between A.M. and G.M. 
Straight Lines 
Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, 
point -slope form, slope-intercept form. Distance of a point from a line. 
Conic Sections 
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of 
intersecting lines as a degenerated case of a conic section. Standard equations and simple properties 
of parabola, ellipse and hyperbola. Standard equation of a circle. 
Subject specific syllabus includes the concepts of NCERT/CBSE syllabus and Text Books (Classes XI 
& XII), however, the questions will be testing the depth of understanding and application of 
these concepts at the level of Post- Graduation. 
4
Introduction to Three-dimensional Geometry 
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between 
two points. 
Limits and Derivatives 
Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive 
idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic 
functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, 
difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions. 
Statistics 
Measures of Dispersion: Range, Mean deviation, variance and standard deviation of 
ungrouped/grouped data.  
Probability 
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 
‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) 
probability, connections with other theories of earlier classes. Probability of an event, probability of 
‘not’, ‘and’ and ‘or’ events. 
Relations and Functions 
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto 
functions. 
Inverse Trigonometric Functions 
Definition, range, domain, principal value branch.  Graphs of inverse trigonometric functions.
Matrices 
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, 
symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and 
multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. 
On commutativity of multiplication of matrices and existence of non-zero matrices whose product is 
the zero matrix (restrict to square matrices of order 2).Invertible matrices and proof of the uniqueness 
of inverse, if it exists; (Here all matrices will have real entries). 
Determinants 
Determinant of a square matrix (up to 3 x 3 matrices),  minors, co-factors and applications of 
determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, 
inconsistency and number of solutions of system of linear equations by examples, solving system of 
linear equations in two or three variables (having unique solution) using inverse of a matrix. 
Continuity and Differentiability 
Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse 
trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic 
functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, 
derivative of functions expressed in parametric forms. Second order derivatives.  
Applications of Derivatives 
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and 
minima (first derivative test motivated geometrically and second derivative test given as a provable 
tool). Simple problems (that illustrate basic principles and understanding of the subject as well as 
real-life situations). 
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Syllabus for the post of PGT -Mathematics 
Sets: 
Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets. Subsets of a set 
of real numbers especially intervals (with notations). Universal set. Venn diagrams. Union and 
Intersection of sets. Difference of sets. Complement of a set. Properties of Complement. 
Relations & Functions: 
Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite 
sets. Cartesian product of the set of reals with itself (upto R x R x R).Definition of relation, pictorial 
diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial 
representation of a function, domain, co-domain and range of a function. Real valued functions, 
domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, 
exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product 
and quotients of functions. 
Trigonometric Functions 
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one 
measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the 
identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of 
trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, 
cosx & cosy and their simple applications. Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and 
tan3x.  
Complex Numbers and Quadratic Equations 
Need for complex numbers, especiallyv-1, to be motivated by inability to solve some of the 
quardratic equations. Algebraic properties of complex numbers. Argand plane  
Linear Inequalities 
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation 
on the number line. 
Permutations and Combinations 
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of 
Formulae for nPr and nCr and their connections, simple applications. 
Binomial Theorem 
Historical perspective, statement and proof of the binomial theorem for positive integral indices. 
Pascal’s triangle, simple applications. 
Sequence and Series 
Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression 
(G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean 
(G.M.), relation between A.M. and G.M. 
Straight Lines 
Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, 
point -slope form, slope-intercept form. Distance of a point from a line. 
Conic Sections 
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of 
intersecting lines as a degenerated case of a conic section. Standard equations and simple properties 
of parabola, ellipse and hyperbola. Standard equation of a circle. 
Subject specific syllabus includes the concepts of NCERT/CBSE syllabus and Text Books (Classes XI 
& XII), however, the questions will be testing the depth of understanding and application of 
these concepts at the level of Post- Graduation. 
4
Introduction to Three-dimensional Geometry 
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between 
two points. 
Limits and Derivatives 
Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive 
idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic 
functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, 
difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions. 
Statistics 
Measures of Dispersion: Range, Mean deviation, variance and standard deviation of 
ungrouped/grouped data.  
Probability 
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 
‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) 
probability, connections with other theories of earlier classes. Probability of an event, probability of 
‘not’, ‘and’ and ‘or’ events. 
Relations and Functions 
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto 
functions. 
Inverse Trigonometric Functions 
Definition, range, domain, principal value branch.  Graphs of inverse trigonometric functions.
Matrices 
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, 
symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and 
multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. 
On commutativity of multiplication of matrices and existence of non-zero matrices whose product is 
the zero matrix (restrict to square matrices of order 2).Invertible matrices and proof of the uniqueness 
of inverse, if it exists; (Here all matrices will have real entries). 
Determinants 
Determinant of a square matrix (up to 3 x 3 matrices),  minors, co-factors and applications of 
determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, 
inconsistency and number of solutions of system of linear equations by examples, solving system of 
linear equations in two or three variables (having unique solution) using inverse of a matrix. 
Continuity and Differentiability 
Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse 
trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic 
functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, 
derivative of functions expressed in parametric forms. Second order derivatives.  
Applications of Derivatives 
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and 
minima (first derivative test motivated geometrically and second derivative test given as a provable 
tool). Simple problems (that illustrate basic principles and understanding of the subject as well as 
real-life situations). 
5
Integrals 
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, 
by partial fractions and by parts, Evaluation of simple integrals of the following types and problems 
based on them. 
Fundamental Theorem of Calculus. Basic Properties of definite integrals and evaluation of definite 
integrals;  
Applications of the Integrals 
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in 
standard form only) 
Differential Equations 
Definition, order and degree, general and particular solutions of a differential equation. Solution of 
differential equations by method of separation of variables, solutions of homogeneous differential 
equations of first order and first degree. Solutions of linear differential equation of the type: dy /dx + 
py = q, where p and q are functions of x or constants. d ?? / d ?? + px = q, where p and q are functions of 
y or constants. 
Vectors 
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a 
vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, 
negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, 
position vector of a point dividing a line segment in a given ratio. Definition, Geometrical 
Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of 
vectors. 
Three - dimensional Geometry 
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector 
equation of a line, skew lines, shortest distance between two lines. Angle between two lines. 
Linear Programming 
Introduction, related terminology such as constraints, objective function, optimization, graphical 
method of solution for problems in two variables, feasible and infeasible regions (bounded or 
unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial 
constraints). 
Probability 
Conditional probability, multiplication theorem on probability, independent events, total probability, 
Bayes’ theorem, Random variable and its probability distribution, mean of random variable.  
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