EMRS PGT Mathematics Syllabus Exam Date 14th December 2025

 

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