EMRS PGT Mathematics Syllabus 2025 Download PDF, Check Exam Pattern
The EMRS PGT Mathematics Syllabus 2025 includes topics like Algebra, Calculus, Trigonometry, Geometry, Probability, and Linear Programming. Effective preparation requires understanding concepts, practicing problems, revising formulas, solving previous papers, and managing time efficiently. Regular practice and mock tests improve accuracy and confidence.
Soumya Tiwari16 Oct, 2025
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EMRS PGT Mathematics Syllabus 2025: EMRS PGT Recruitment 2025 has been announced. The official notification for EMRS PGT Recruitment 2025 was released recently for the recruitment of Post Graduate Teacher (PGT) Mathematics. The selection for the job will be based on a two-tiered written examination that will evaluate general teaching aptitude as well as subject knowledge of the candidate. Candidates must prepare as per the EMRS PGT Mathematics Syllabus 2025 for both the tiers of the written examination.
EMRS PGT Mathematics Syllabus 2025
EMRS PGT Mathematics 2025 paper tests the advanced level mathematics concepts for post-graduate teachers. The Syllabus of Mathematics for EMRS PGT includes the topics from Sets, Relations, Functions, Trigonometry, Complex Numbers, Calculus, Linear Programming, Vector, Probability and Three-dimensional Geometry. The paper emphasizes on the conceptual clarity as well as the problem-solving skills. It also includes the applications of derivatives, integrals, differential equations, matrices. The candidates need to have good analytical and logical reasoning for teaching at higher secondary level.
| EMRS PGT Mathematics Syllabus 2025 | ||
| S.No | Topic | Subtopics / Details |
| 1 | Sets | Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of real numbers, Universal set, Venn diagrams, Union, Intersection, Difference, Complement, Properties of Complement |
| 2 | Relations & Functions | Ordered pairs, Cartesian product, Number of elements in Cartesian product, Definition of relation, domain, co-domain, range, Function as a special relation, pictorial representation, Real valued functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic, greatest integer; Sum, difference, product, quotient of functions |
| 3 | Trigonometric Functions | Positive and negative angles, radians and degrees conversion, Definition using unit circle, sin²x + cos²x = 1, signs of trigonometric functions, Domain, range, graphs, sum and difference formulas, multiple angle identities |
| 4 | Complex Numbers & Quadratic Equations | Need for complex numbers, algebraic properties, Argand plane representation |
| 5 | Linear Inequalities | Linear inequalities in one variable, algebraic solutions, representation on number line |
| 6 | Permutations & Combinations | Fundamental principle of counting, factorial, nPr, nCr, simple applications |
| 7 | Binomial Theorem | Historical perspective, proof for positive integral indices, Pascal's triangle, applications |
| 8 | Sequence & Series | Arithmetic progression, Geometric progression, general terms, sums, infinite series, Arithmetic mean (A.M.), Geometric mean (G.M.), relation between A.M. and G.M. |
| 9 | Straight Lines | Slope, angle between lines, equation forms, distance of a point from a line |
| 10 | Conic Sections | Circles, ellipse, parabola, hyperbola, degenerate cases, Standard equations, simple properties |
| 11 | Introduction to Three-dimensional Geometry | Coordinate axes and planes, coordinates of points, distance between points |
| 12 | Limits & Derivatives | Derivative as rate of change, intuitive limits, Limits of polynomials, rational, trigonometric, exponential, logarithmic functions, Derivative of sum, difference, product, quotient, derivatives of polynomials and trigonometric functions |
| 13 | Statistics | Measures of dispersion: Range, Mean deviation, variance, standard deviation (ungrouped/grouped data) |
| 14 | Probability | Random experiments, outcomes, sample spaces, Events: occurrence, ‘not’, ‘and’, ‘or’, exhaustive, mutually exclusive, Set-theoretic probability, axiomatic approach, connections with earlier probability concepts |
| 15 | Inverse Trigonometric Functions | Definition, range, domain, principal value, graphs |
| 16 | Matrices | Concept, order, equality, types, zero/identity matrix, transpose, symmetric/skew-symmetric matrices, Operations: addition, multiplication, scalar multiplication, invertible matrices |
| 17 | Determinants | Determinants (up to 3×3), minors, co-factors, Applications: area of a triangle, adjoint and inverse, solving linear equations |
| 18 | Continuity & Differentiability | Continuity and differentiability, composite functions, chain rule, implicit differentiation, Derivatives of exponential and logarithmic functions, parametric forms, second order derivatives |
| 19 | Applications of Derivatives | Rate of change, increasing/decreasing functions, maxima and minima, real-life applications |
| 20 | Integrals | Integration as inverse of differentiation, methods: substitution, partial fractions, by parts, Definite integrals, fundamental theorem of calculus, Applications: area under curves (lines, circles, parabolas, ellipses) |
| 21 | Differential Equations | Order and degree, general/particular solutions, Methods: separation of variables, homogeneous equations, linear differential equations |
| 22 | Vectors | Scalars and vectors, magnitude, direction, types, addition, scalar multiplication, Dot and cross product, geometrical interpretation, properties, applications |
| 23 | Three-dimensional Geometry (Advanced) | Direction cosines/ratios of lines, Cartesian/vector equation of a line, Skew lines, shortest distance between lines, angle between lines |
| 24 | Linear Programming | Introduction, terminology: constraints, objective function, optimization, Graphical solution for two-variable problems, feasible/infeasible regions, optimal solutions |
| 25 | Probability (Advanced) | Conditional probability, multiplication theorem, independent events, total probability, Bayes’ theorem, Random variables and probability distributions, mean of random variable |
EMRS PGT Mathematics Syllabus 2025 PDF
EMRS PGT Mathematics Syllabus 2025 is out. The official syllabus for the EMRS PGT Mathematics can be downloaded from the National Education Society for Tribal Students (NESTS) website or from the link given below.
EMRS PGT Mathematics Exam Pattern
The EMRS PGT Mathematics 2025 exam comprises two tiers. Tier 1 is a qualifying preliminary objective exam based on general awareness, reasoning, ICT, teaching aptitude, and domain knowledge. This tier also has a Language competency test. Tier 2 is a subject knowledge exam with both objective and descriptive components, designed to assess the candidates' knowledge of Mathematics.
| EMRS PGT Mathematics Exam Pattern | |||||
| Exam Tier | Section | Number of Questions | Marks | Duration | Remarks |
| Tier 1 | General Awareness | 10 | 10 | 2 hours 30 minutes | Objective |
| Reasoning Ability | 15 | 15 | Objective | ||
| Knowledge of ICT | 15 | 15 | Objective | ||
| Teaching Aptitude | 30 | 30 | Objective | ||
| Domain Knowledge | 30 | 30 | Objective | ||
| Language Competency Test | - | 20 | Qualifying (English & Hindi) | ||
| Tier 2 | Subject Knowledge (Objective) | 40 | 40 | 3 hours | Includes Mathematics topics |
| Subject Knowledge (Descriptive) | 15 | 60 | |||
EMRS PGT Mathematics Syllabus 2025
Preparation of EMRS PGT Mathematics Syllabus 2025 demands a well-thought strategy, concept clarity, and consistent practice. Put in dedicated efforts to study the theory as well as solve questions. Make a revision of the important formulas and previous year questions.
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Read Syllabus: Break it into major topics and determine your strong and weak areas.
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Plan your Studies: Schedule time monthly for each topic, revision, and mock tests.
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Study Concepts: Focus on definitions, formulas, and important problem-solving techniques.
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Practice Questions: Solve numerical and conceptual questions from standard books and previous years' question papers.
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Prepare Short Notes: Keep formula sheets and quick revision notes for all major topics.
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Take Mock Tests: Enhance your speed and accuracy, and identify weak areas.
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Time Management: Allocate time for both theory and practice, prioritizing high-weightage topics.
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Application-Based: Understand and apply concepts to solve real-life problems, especially in calculus, vectors, and probability.
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Clarify Doubts: Clear your doubts as soon as possible with the help of teachers, friends, or online resources.
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Stay Consistent: Follow daily study schedules and maintain a positive attitude throughout your preparation
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