KVS PGT Maths Syllabus: Download Syllabus PDF

KVS PGT Maths Syllabus

If you are preparing for KVS PGT, can read or download KVS PGT Maths Syllabus here. We have discussed topic-wise complete  syllabus.


Syllabus and Scheme for Limited Departmental Examination

Post – PGT Maths in Central Schools (Kendriya Vidyalaya)

Job Description –

    1. To teach particular subject 
    2. To assist the principal/vice principal 
    3. To help children for holistic development

Kendriya Vidyalaya PGT Maths Pattern & Syllabus (KVS PGT Maths)


S.No. PGT (Post Graduate Teachers)
No. Questions Maximum Marks
1 Subject Competency 80 80
2 Academics 20 20
3 General Aptitude

(i) General Knowledge (18 Questions)
(ii) Reasoning Aptitude (12 Questions)
(iii) Quantitative Aptitude (06 Questions)
(iv) General Hindi & General English (14)

50 50
Total (Duration of LDE: 2 Hours 30 Minutes 150 150

KVS PGT Maths Syllabus in Detail

You can analyze complete syllabus that is given below. General aptitude is also given in detail.

Topics Details Number of Questions
General Knowledge
That Do no require subject specialization
A. Current Affairs/events of national and international importance
B. History of India and Indian National Movements.
C. Indian and World Geography- Physical, Social, Economic geography and of India and the world etc.
D. Indian Polity and Governance – Constitution, Political System, Panchayati Raj, Public Issues, Articles, Rights etc.
E. Economic and Social Development – Sustainable development, poverty, Inclusion, Demographics, Social sectors initiatives etc.
F. General issues on Environment, Ecology, Bio-diversity, Climate Change, General Science, General Computer & Computer Literacy.
Reasoning Aptitude A. General Mental/ Analytical Ability
B. Verbal/Logical Reasoning, Relations & Hierarchies
C. Analogies, Assertion, Truth Statements.
D. Coding and Decoding, Situational Reasoning.
E. Series and Patterns involving words and alphabets.
Hindi & English Knowledge A. Proficiency related to the language, Elements of Language, Pedagogy of language development,
Communication and Comprehension abilities, Speaking, Listening, Reading and Writing proficiencies etc.
Quantitative Aptitude A. Two and Three dimensional/Venn diagrams based questions
B. Number Patterns, Series, Sequences, Basic Numeracy
C. Arithmetic aptitude, Data interpretation (Charts, Graphs or tables, Data sufficiency etc.)
D. Direction sense, Analysis and interpretation in various contexts.
General Aptitude Total Marks 50


Knowledge/Areas/Skill to be tested

A. Subject Competency- (80 Marks)

(As per annexure)

B. Academics: (20 Marks)

  • Pedagogy
  • Teaching methodology
  • Basics of ICT and Educational psychology
  • Instructional leadership assessment & other related issues.
  • Admission Guidelines Code of Conduct of teachers and students
  • Rules for Examination and Promotion & Scheme of Studies and Syllabus.
  • Academic supervision
  • Health Services in schools.

C. General Aptitude: – 50 Marks

(i) General Knowledge.
(ii) Reasoning Aptitude,
(iii) Quantitative Aptitude,
(iv) General Hindi & General English


Syllabus for Limited Departmental Exam. for the post of PGT (MATHEMATICS).

1 – 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), Power set. Universal set, Venn diagrams, Union and Intersection of
sets, Difference of sets, Complernent of a set, Properties of Complement Sets.

2 – 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 RXRxR). 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.

3 – 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. Signs of trigonometric functions.
Expressing sin (x+y) and cos (x+y) in terins of sinx, siny, cosx&cosy and their simple applications.

4 – Principle of Mathematical Induction:
Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

5 – Complex Numbers and Quadratic Equations
Need for complex numbers, especially, to be motivated by inability to solve some of the quadratic equations.
Algebraic properties of complex numbers. Solution of quadratic equations (with real coefficients) in the complex
number system. Square root of a complex number.

6 – Permutations and Combinations
Fundamental principle of counting. Factorial n(n!) ,Permutations and combinations, derivation of formulae for np. and Cy and their connections, simple applications.

7 – Binomial Theorem History, statement and proof of the binomial theorem for positive integral indices.Pascal’s
triangle, General and middle term in binomial expansion, simple applications.

8 – 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 first iterms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between
A.M. and G.M.

9 – Straight Lines
Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between
two lines. Various forms of equations of a line: parallel to axis, point-slope form, slopeintercept form, two-point
form, intercept form and normal form. General equation of a line.Equation of family of lines passing through the
point of intersection of two lines. Distance of a point from a line.
10 – Introduction to Three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

11 – 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.

12. Probability
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘nor’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability connections with other theories studied in earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or events.

13 – Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions,
composite functions, inverse of a function. Binary operations.

14 – Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties
of inverse trigonometric functions.

15 – 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. Non commutativity of multiplication of
matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order
2).Concept of elementary row and column operations. invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

16 – Determinants
Determinant of a square matrix (up to 3 x 3 matrices). properties of deterininants, 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.

17 – Continuity and Differentiability
Continuity and differentiability, derivative of composite functions, chain rule, derivatives 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. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

18 – 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.

19 – 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, scalar triple product of vectors.

20 – Three-dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line,
coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of  plane. Angle between (i) Two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

21 – Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes?
theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated
independent (Bernoulli) trials and Binomial distriburion.


Reference Books : Text Books published by NCERT for classes XI & XI.


Candidates can download syllabus PDF from here. – Click Here

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