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EMRS TGT Mathematics Syllabus 2026, Exam Pattern
1
EMRS TGT Mathematics Preliminary Exam Tier 1 - Hindi130 questions • 150 mins • 130 marks
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EMRS TGT Mathematics Preliminary Exam Tier 1 - English130 questions • 150 mins • 130 marks
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Emrs TGT Mathematics 2026 Exam Free Online Question Bank
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EMRS TGT Mathematics Combo Packages
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4. 1500 (+) Current Affairs MCQ with Answer PDF in English.
5. 1000 (+) GK MCQ with Answer PDF Book in English.
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Combo - 14 Tier 2 (Hindi)
1. Online Mock Test Series in Hindi = 30 Tests.
2. Question Bank - 1700 Questions with Answer.
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4. 1500 (+) Current Affairs MCQ with Answer PDF in Hindi.
5. 1000 (+) GK MCQ with Answer PDF Book in Hindi.
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4. 1500 (+) Current Affairs MCQ with Answer PDF in English.
5. 1000 (+) GK MCQ with Answer PDF Book in English.
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Combo Package
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Combo - 16 Tier 1 Preliminary (Hindi)
1. Online Mock Test Series in Hindi = 25 Tests.
2. Question Bank - 3000 Questions with Answer.
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4. EBook of EMRS TGT Mathematics (1000 MCQ) PDF Format in Hindi.
5. 1500 (+) Current Affairs MCQ with Answer PDF in Hindi.
6. 1000 (+) GK MCQ with Answer PDF Book in Hindi.
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3. Printed Material 10 Mock Test Papers with OMR Sheet.
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4. EBook of EMRS TGT Mathematics (1000 MCQ) PDF Format in English.
5. 1500 (+) Current Affairs MCQ with Answer PDF in English.
6. 1000 (+) GK MCQ with Answer PDF Book in English.
2. Question Bank - 3000 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
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4. EBook of EMRS TGT Mathematics (1000 MCQ) PDF Format in Hindi.
5. 1500 (+) Current Affairs MCQ with Answer PDF in Hindi.
6. 1000 (+) GK MCQ with Answer PDF Book in Hindi.
2. Question Bank - 1700 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
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Combo Package
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Combo - 19 Tier 2 (English)
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2. Question Bank - 1030 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
4. EBook of EMRS TGT Mathematics (1000 MCQ) PDF Format in English.
5. 1500 (+) Current Affairs MCQ with Answer PDF in English.
6. 1000 (+) GK MCQ with Answer PDF Book in English.
2. Question Bank - 1030 Questions with Answer.
3. Printed Material 10 Mock Test Papers with OMR Sheet.
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EMRS TGT Mathematics Syllabus 2026, Exam Pattern
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EMRS TGT Mathematics Syllabus 2026, Exam Pattern, Exam Date 2026
Detail Information about EMRS has published notification 2026 for the recruitment of TGT 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 TGT Syllabus 2026 – Overview
EMRS TGT Mathematics Syllabus 2026
General 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 Honors
Reasoning 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 Systems
Language 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 Hindi
1. 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 |
(c) Regional Language:
Basic grammar questions like Synonyms, Antonyms, One Word Substitutions, Error Detection, Spelling Error etc. (at Higher Secondary Level) in the following languages:
(1) Assamese (2) Bengali (3) Bodo (4) Dogri (5) English (6) Garo (7) Gujarati (8) Hindi, (9) Kannada (10) Kashmiri (11) Khasi (12) Malayalam (13) Manipuri (14) Marathi (15) Mizo (16) Nepali (17) Odiya (18) Santhali (19) Telugu (20) Urdu
Domain Knowledge :-
(a) Experiential activity-based pedagogy and case study based questions
(i) Experiential Activity-Based Pedagogy in Mathematics:
Constructivist Approach: Understanding that students learn best by actively constructing their own knowledge. This involves designing activities where students discover mathematical principles for themselves, rather than just being told. For example, using paper folding to discover the properties of quadrilaterals.
Use of Manipulatives and Teaching Aids: You should know how and when to use tools to explain concepts.
Examples: Using algebra tiles to model polynomials, geoboards to explore geometric shapes and area, Cuisenaire rods for fractions, or even simple items like beads and blocks for number theory.
Problem-Based Learning (PBL): Designing lessons around a single, complex real-world problem. For instance, a lesson on percentages and budgeting could start with the problem: "Plan a hypothetical class trip for 50 students with a budget of ₹20,000."
Inquiry-Based Learning: Encouraging students to ask questions and investigate mathematical ideas. For example, instead of giving the formula for the area of a circle ($A = pi r^2$), you might ask students to measure the circumference and diameter of various circular objects, find their ratio, and discover the concept of $pi$ themselves.
Gamification in Math: Using games and puzzles to teach mathematical skills and logic. This could include board games, logic puzzles, or digital math games that make practice more engaging.
Connecting Math to Real Life: Demonstrating the practical application of mathematical concepts, such as using ratios and proportions in cooking, applying geometry in art and architecture, or using statistics to analyze sports data.
(ii) Case Study Based Questions in Mathematics:
Diagnosing Student Misconceptions: Can you identify the specific error in a student's thinking? For example, a student consistently solves $3(x+2)$ as $3x+2$. The case study would test if you can pinpoint this distributive property error.
Differentiated Instruction: Proposing strategies to support both struggling students and challenge high-achievers within the same classroom. How would you handle a class where some students don't understand fractions while others are ready for decimals?
Classroom Management: How would you manage a hands-on activity to ensure all students are engaged and learning, not just playing or getting off-task?
Assessment for Learning: Using student responses (right or wrong) to guide your next teaching steps. If many students make the same mistake on a quiz, what does that tell you, and what would you do next?
Application of Pedagogical Theories: Applying theories of learning (like those from Piaget or Vygotsky) to justify your teaching choices in a given scenario.
(b) National Education Policy (NEP)- 2020
Key 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: (Mathematics) :
Real Number:
Representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification.
Rational numbers as recurring / terminating decimals. Examples of non-recurring /non-terminating decimals. Existence of non-rational numbers (irrational numbers) and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.
Laws of exponents with integral powers. Rational exponents with positive real bases. Rationalization of real numbers. Euclid’s division lemma, Fundamental Theorem of Arithmetic. Expansions of rational numbers in terms of terminating / non-terminating recurring decimals.
Elementary Number Theory:
Peano’s Axioms, Principle of Induction; First Principal, Second Principle, Third Principle, Basis Representation Theorem, Greatest Integer Function, Test of Divisibility, Euclid’s algorithm, The Unique Factorization Theorem, Congruence, Chinese Remainder Theorem, Sum of divisors of a number. Euler’s totient function, Theorems of Fermat and Wilson.
Matrices:
R, R2, R3 as vector spaces over R and concept of Rn. Standard basis for each of them. Linear Independence and examples of different bases. Subspaces of R2, R3. Translation, Dilation, Rotation, Reflection in a point, line and plane. Matrix form of basic geometric transformations. Interpretation of eigenvalues and eigenvectors for such transformations and eigenspaces as invariant subspaces. Matrices in diagonal form. Reduction to diagonal form upto matrices of order 3. Computation of matrix inverses using elementary row operations. Rank of matrix, Solutions of a system of linear equations using matrices.
Polynomials:
Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial, Constant, linear, quadratic, cubic polynomials;
monomials, binomials, trinomials. Factors and multiples. Zeros / roots of a polynomial / equation. Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization of quadratic and of cubic polynomials using the Factor Theorem. Algebraic expressions and identities and their use in factorization of polynomials. Simple expressions reducible to these polynomials.
Linear Equations in two variables:
Introduction to the equation in two variables. Proof that a linear equation in two variables as infinitely many solutions and justify their being written as ordered pairs of real numbers, Algebraic and graphical solutions.
Pair of Linear Equations in two variables:
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions / inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication.
Quadratic Equations:
Standard form of a quadratic equation. Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e., by using quadratic formula. Relationship between
discriminant and nature of roots. Relation between roots and coefficients, Symmetric functions of the roots of an equation. Common roots.
Arithmetic Progressions:
Derivation of standard results of finding the nth term and sum of first n terms.
Inequalities:
Elementary Inequalities, Absolute value, Inequality of means, Cauchy – Schwarz Inequality, Chebyshev's Inequality.
Combinatorics:
Principle of Inclusion and Exclusion, Pigeon Hole Principle, Recurrence Relations, Binomial Coefficients.
Calculus:
Sets. Functions and their graphs: polynomial, sine, cosine, exponential and logarithmic functions. Step function, Limits and continuity. Differentiation, Methods of differentiation like Chain rule, Product rule and Quotient rule. Second order derivatives of above functions. Integration as reverse process of differentiation. Integrals of the functions introduced above.
Euclidean Geometry:
Axioms / postulates and theorems. The five postulates and Euclid. Equivalent versions of the fifth postulate. Relationship between axiom and theorem. Theorems and lines and angles, triangles and quadrilaterals, Theorems on areas of parallelograms and triangles, Circles, theorems on circles, Similar triangles, Theorem on similar triangles. Constructions.
Ceva’s Theorem, Menelaus's Theorem, Nine Point Circle, Simson’s Line, Centres of Similitude of Two Circles, Lehmus Steiner Theorem, Ptolemy’s Theorem.
Coordinate Geometry:
The Cartesian plane, coordinates of a point, Distance between two points and section formula, Area of a triangle.
Areas and Volumes:
Area of a triangle using Heron’s formula and its application in finding the area of a quadrilateral.
Surface areas and volumes of cubes, cuboids, spheres (Including hemispheres) and right circular cylinders/cones. Frustum of a cone.
Area of a circle: area of sectors and segments of a circle.
Trigonometry:
Trigonometric ratios of an acute angle of a right – angled triangle. Relationships between the rations.
Trigonometric identities. Trigonometric ratios of complementary angles. Heights and distances.
Statistics:
Introduction to Statistics: Collection of data, presentation of data, tabular form, ungrouped /grouped, bar graphs, histograms, frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data. Mean, median and mode of grouped data. Cumulative frequency graph.
Probability:
Elementary Probability and basic laws. Discrete and Continuous Random variable, Mathematical Expectation, Mean and Variance of Binomial, Poisson and Normal distribution. Sample mean and Sampling Variance. Hypothesis testing using standard normal variate. Curve Fitting. Correlation and Regression.
EMRS TGT Mathematics Exam Pattern 2026
Tier -I -Preliminary (Qualifying) Examination in OMR (Objective)
Duration : 150 Minutes
Negative Marking : 0.33
EMRS TGT Syllabus 2026 – Overview
| Organization Name | National Education Society for Tribal Students (NESTS) |
| School Name | Eklavya Model Residential Schools (EMRSs) |
| Post Names | TGT Mathematics |
| No.of Posts | Notified Soon |
| Mode of Application | Online |
| Selection Process | Tier -I : Preliminary (Qualifying) Examination Tier -II : Subject Knowledge Examination |
| Category | Syllabus and Exam Pattern |
| Job Location | Across India |
| Official Website | emrs.tribal.gov.in |
EMRS TGT Mathematics Syllabus 2026
General 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 Honors
Reasoning 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 Systems
Language 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 Hindi
1. 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 |
(c) Regional Language:
Basic grammar questions like Synonyms, Antonyms, One Word Substitutions, Error Detection, Spelling Error etc. (at Higher Secondary Level) in the following languages:
(1) Assamese (2) Bengali (3) Bodo (4) Dogri (5) English (6) Garo (7) Gujarati (8) Hindi, (9) Kannada (10) Kashmiri (11) Khasi (12) Malayalam (13) Manipuri (14) Marathi (15) Mizo (16) Nepali (17) Odiya (18) Santhali (19) Telugu (20) Urdu
Domain Knowledge :-
(a) Experiential activity-based pedagogy and case study based questions
(i) Experiential Activity-Based Pedagogy in Mathematics:
Constructivist Approach: Understanding that students learn best by actively constructing their own knowledge. This involves designing activities where students discover mathematical principles for themselves, rather than just being told. For example, using paper folding to discover the properties of quadrilaterals.
Use of Manipulatives and Teaching Aids: You should know how and when to use tools to explain concepts.
Examples: Using algebra tiles to model polynomials, geoboards to explore geometric shapes and area, Cuisenaire rods for fractions, or even simple items like beads and blocks for number theory.
Problem-Based Learning (PBL): Designing lessons around a single, complex real-world problem. For instance, a lesson on percentages and budgeting could start with the problem: "Plan a hypothetical class trip for 50 students with a budget of ₹20,000."
Inquiry-Based Learning: Encouraging students to ask questions and investigate mathematical ideas. For example, instead of giving the formula for the area of a circle ($A = pi r^2$), you might ask students to measure the circumference and diameter of various circular objects, find their ratio, and discover the concept of $pi$ themselves.
Gamification in Math: Using games and puzzles to teach mathematical skills and logic. This could include board games, logic puzzles, or digital math games that make practice more engaging.
Connecting Math to Real Life: Demonstrating the practical application of mathematical concepts, such as using ratios and proportions in cooking, applying geometry in art and architecture, or using statistics to analyze sports data.
(ii) Case Study Based Questions in Mathematics:
Diagnosing Student Misconceptions: Can you identify the specific error in a student's thinking? For example, a student consistently solves $3(x+2)$ as $3x+2$. The case study would test if you can pinpoint this distributive property error.
Differentiated Instruction: Proposing strategies to support both struggling students and challenge high-achievers within the same classroom. How would you handle a class where some students don't understand fractions while others are ready for decimals?
Classroom Management: How would you manage a hands-on activity to ensure all students are engaged and learning, not just playing or getting off-task?
Assessment for Learning: Using student responses (right or wrong) to guide your next teaching steps. If many students make the same mistake on a quiz, what does that tell you, and what would you do next?
Application of Pedagogical Theories: Applying theories of learning (like those from Piaget or Vygotsky) to justify your teaching choices in a given scenario.
(b) National Education Policy (NEP)- 2020
Key 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: (Mathematics) :
Real Number:
Representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification.
Rational numbers as recurring / terminating decimals. Examples of non-recurring /non-terminating decimals. Existence of non-rational numbers (irrational numbers) and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.
Laws of exponents with integral powers. Rational exponents with positive real bases. Rationalization of real numbers. Euclid’s division lemma, Fundamental Theorem of Arithmetic. Expansions of rational numbers in terms of terminating / non-terminating recurring decimals.
Elementary Number Theory:
Peano’s Axioms, Principle of Induction; First Principal, Second Principle, Third Principle, Basis Representation Theorem, Greatest Integer Function, Test of Divisibility, Euclid’s algorithm, The Unique Factorization Theorem, Congruence, Chinese Remainder Theorem, Sum of divisors of a number. Euler’s totient function, Theorems of Fermat and Wilson.
Matrices:
R, R2, R3 as vector spaces over R and concept of Rn. Standard basis for each of them. Linear Independence and examples of different bases. Subspaces of R2, R3. Translation, Dilation, Rotation, Reflection in a point, line and plane. Matrix form of basic geometric transformations. Interpretation of eigenvalues and eigenvectors for such transformations and eigenspaces as invariant subspaces. Matrices in diagonal form. Reduction to diagonal form upto matrices of order 3. Computation of matrix inverses using elementary row operations. Rank of matrix, Solutions of a system of linear equations using matrices.
Polynomials:
Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial, Constant, linear, quadratic, cubic polynomials;
monomials, binomials, trinomials. Factors and multiples. Zeros / roots of a polynomial / equation. Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization of quadratic and of cubic polynomials using the Factor Theorem. Algebraic expressions and identities and their use in factorization of polynomials. Simple expressions reducible to these polynomials.
Linear Equations in two variables:
Introduction to the equation in two variables. Proof that a linear equation in two variables as infinitely many solutions and justify their being written as ordered pairs of real numbers, Algebraic and graphical solutions.
Pair of Linear Equations in two variables:
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions / inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication.
Quadratic Equations:
Standard form of a quadratic equation. Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e., by using quadratic formula. Relationship between
discriminant and nature of roots. Relation between roots and coefficients, Symmetric functions of the roots of an equation. Common roots.
Arithmetic Progressions:
Derivation of standard results of finding the nth term and sum of first n terms.
Inequalities:
Elementary Inequalities, Absolute value, Inequality of means, Cauchy – Schwarz Inequality, Chebyshev's Inequality.
Combinatorics:
Principle of Inclusion and Exclusion, Pigeon Hole Principle, Recurrence Relations, Binomial Coefficients.
Calculus:
Sets. Functions and their graphs: polynomial, sine, cosine, exponential and logarithmic functions. Step function, Limits and continuity. Differentiation, Methods of differentiation like Chain rule, Product rule and Quotient rule. Second order derivatives of above functions. Integration as reverse process of differentiation. Integrals of the functions introduced above.
Euclidean Geometry:
Axioms / postulates and theorems. The five postulates and Euclid. Equivalent versions of the fifth postulate. Relationship between axiom and theorem. Theorems and lines and angles, triangles and quadrilaterals, Theorems on areas of parallelograms and triangles, Circles, theorems on circles, Similar triangles, Theorem on similar triangles. Constructions.
Ceva’s Theorem, Menelaus's Theorem, Nine Point Circle, Simson’s Line, Centres of Similitude of Two Circles, Lehmus Steiner Theorem, Ptolemy’s Theorem.
Coordinate Geometry:
The Cartesian plane, coordinates of a point, Distance between two points and section formula, Area of a triangle.
Areas and Volumes:
Area of a triangle using Heron’s formula and its application in finding the area of a quadrilateral.
Surface areas and volumes of cubes, cuboids, spheres (Including hemispheres) and right circular cylinders/cones. Frustum of a cone.
Area of a circle: area of sectors and segments of a circle.
Trigonometry:
Trigonometric ratios of an acute angle of a right – angled triangle. Relationships between the rations.
Trigonometric identities. Trigonometric ratios of complementary angles. Heights and distances.
Statistics:
Introduction to Statistics: Collection of data, presentation of data, tabular form, ungrouped /grouped, bar graphs, histograms, frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data. Mean, median and mode of grouped data. Cumulative frequency graph.
Probability:
Elementary Probability and basic laws. Discrete and Continuous Random variable, Mathematical Expectation, Mean and Variance of Binomial, Poisson and Normal distribution. Sample mean and Sampling Variance. Hypothesis testing using standard normal variate. Curve Fitting. Correlation and Regression.
EMRS TGT Mathematics Exam Pattern 2026
Tier -I -Preliminary (Qualifying) Examination in OMR (Objective)
Duration : 150 Minutes
Negative 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 and Regional Language-10 mark each subject). This part is qualifying in nature only with minimum 40% marks in each language. Part-I to V of the candidate will not be evaluated, if he/she fails to attain qualifying marks in Part-VI
|
30 | 30 |
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
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.
Tier-II Exam Date 2026 : Notified Soon
Starting Date of Application Form : Notified Soon
Last Date of Application Form : Notified Soon
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.
Tier-II Exam Date 2026 : Notified Soon
Starting Date of Application Form : Notified Soon
Last Date of Application Form : Notified Soon
FAQs
Emrs TGT Mathematics 2026 Exam Syllabus Frequently Asked Questions (FAQ's)
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