Detail Information about EMRS has published notification 2026 for the recruitment of PGT Mathematics vacancies. Those Candidates who are Interested to the following vacancy and completed all Eligibility Criteria can read the Notification & Apply Online. In this page we provide the Complete Syllabus of this Recruitment with Latest Update Exam Pattern and the Exam Date also.EMRS PGT Mathematics Highlights 2026 - Overview
| Department Name |
Eklavya Model Residential School |
| Post Name |
PGT Mathematics |
| Total Posts |
Notified Soon |
| Application Mode |
Online |
| Selection Process |
Tier -I : Preliminary (Qualifying) Examination
Tier -II : Subject Knowledge Examination |
| Location |
All Over India |
| Category |
Syllabus and Exam Pattern |
| Official Website |
https://recruitment.nta.nic.in |
EMRS PGT Mathematics Syllabus 2026General Knowledge & Current affairs :
1. General Politics
2. Culture
3. Indian Constitution
4. Books
5. Current events
6. Economic
7. Geography
8. History
9. Sports and Games
10. Awards and HonorsReasoning Ability :
1. Puzzles & Seating arrangement
2. Data sufficiency
3. Statement based questions (Verbal. reasoning)
4. Inequality, Blood relations
5. Sequences and Series
6. Direction Test
7. Assertion and Reason
8. Venn Diagrams
Knowledge of ICT :
1. Fundamentals of Computer System
2. Basics of Operating System
3. MS Office
4. Keyboard
5. Shortcuts and their uses
6. Important Computer Terms and Abbreviations
7. Computer Networks
8. Cyber Security, and Internet
Teaching Aptitude :
1. Teaching-Nature
2. Characteristics
3. Objectives and Basic requirements
4. Learner's characteristics
5. Factors affecting teaching
6. Methods of Teaching
7. Teaching Aids and Evaluation SystemsLanguage Competency :(a) General English :1. Verb
2. Tenses
3. Voice
4. Subject-Verb Agreement
5. Articles
6. Comprehension
7. Fill in the Blanks
8. Adverb
9. Error Correction
10. Sentence Rearrangement
11. Unseen Passages
12. Vocabulary
13. Antonyms/Synonyms
14. Grammar
15. Idioms & Phrases(b) General Hindi1. संधि
2. समास
3. विलोम शब्द
4. पर्यायवाची शब्द
5. सामान्य अमुद्धियाँ
6. वाक्यांशों के लिए एक शब्द
7. मुहावरे लोकोक्तिया
8. अपठित गद्यांश पर आधारित प्रश्न |Domin Knowledge :-
(a) Experiential activity-based pedagogy and case study based questions(b)National Education Policy (NEP)- 2020Key Principles and Vision:-
Fundamental Pillars: Understand the five foundational pillars of NEP 2020: Access, Equity, Quality, Affordability, and Accountability.
Holistic Development: The goal of developing students who possess critical thinking, creativity, ethical values, and empathy, moving away from rote learning.
Multidisciplinarity: The breakdown of rigid subject silos between arts and sciences, and curricular and extracurricular activities.
Structural and Curricular Reforms:-
New Schooling Structure: Know the details of the 5+3+3+4 curricular structure, replacing the old 10+2 system.
Foundational Stage (Ages 3-8): Focus on Early Childhood Care and Education (ECCE), and play-based, activity-based learning.
Preparatory Stage (Ages 8-11): Introduction of subjects and formal classroom teaching.
Middle Stage (Ages 11-14): Introduction of more abstract concepts in science, math, social sciences, arts, and humanities.
Secondary Stage (Ages 14-18): Focus on multidisciplinary study, critical thinking, and flexibility in subject choice.
Foundational Literacy and Numeracy (FLN): The policy's high priority on achieving universal FLN by Grade 3. Be aware of the National Mission on Foundational Literacy and Numeracy (NIPUN Bharat).
Vocational Education: Integration of vocational education from Grade 6 onwards, including internships.
Teacher Education and Professional Development:-
Teacher Recruitment and Standards: The policy's vision for a robust, merit-based teacher recruitment process. Be familiar with the proposed National Professional Standards for Teachers (NPST).
Teacher Training: The new 4-year integrated B.Ed. as a minimum degree for teaching by 2030. The importance of continuous professional development (CPD) for teachers.
National Mission for Mentoring (NMM): The establishment of a large pool of mentors to support teachers.
Assessment and Technology:-
Assessment Reforms: A shift from summative, rote-based exams to regular, formative, and competency-based assessments.
PARAKH (Performance Assessment, Review, and Analysis of Knowledge for Holistic Development): The establishment of this national assessment center to set norms, standards, and guidelines.
Holistic Progress Card: The new report card system designed to provide a comprehensive view of a student's development.
Technology Integration: The creation of the National Educational Technology Forum (NETF) to promote the use of technology in education, including digital resources and virtual labs.Subject Knowledge Test: 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, especially√−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane
Linear Inequalities :
Linear inequalities, Algebraic solutions of linear inequalities in one variable and their representationon 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.
Introduction to Three-dimensional Geometry :
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance betweentwo 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 logarithmicfunctions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient offunctions. 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 uniquenessof 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).
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. d𝑥/ d𝑦 + px = q, where p and q are functions ofy 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 ofvectors.
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.
EMRS PGT Mathematics Exam Pattern 2026Tier -I -Preliminary (Qualifying) Examination in OMR (Objective)Duration : 150 MinutesNegative Marking : 0.33
| S.No |
Subject |
No.of Question |
Marks |
| Part I |
General Awareness |
10 |
10 |
| Part II |
Reasoning Ability |
15 |
15 |
| Part III |
Knowledge of ICT |
15 |
15 |
| Part IV |
Teaching Aptitude |
30 |
30 |
| Part V |
Domain Knowledge:
a) Experiential activity-based pedagogy and case study-based questions. (20 Question)
b) NEP-2020 (10 Question)
|
30
[20+10]
|
30 |
| |
Total |
100 |
100 |
| Part VI |
Language Competency Test (General Hindi, General English-10 mark each subject). |
20 |
20 |
Tier -II (Only for Candidates who will be shortlisted in the ratio of 1:10 against the notified vacancies
on the basis of Tier I Preliminary examination)- Subject Knowledge Examination
Negative Marking : 0.33
| Component of the test |
Number of questions |
Total marks |
Duration of the test |
| Objective |
Descriptive |
Objective |
Descriptive |
|
| Subject Knowledge Test |
40 |
15 |
40 |
60 |
3 Hours |
| Total |
55 |
100 |
3 Hours |
Preparation of merit list: Merit list for the post of Hostel Warden will be prepared on the basis of performance in the Tier II examination only.
EMRS PGT Tier - II Exam Date : Notified Soon
