KVS TGT Mathematics Syllabus 2025 PDF, Check Exam Pattern

Kendriya Vidyalaya Sangathan has released the official KVS TGT Mathematics Syllabus 2025 and KVS Notification 2025. Now that KVS TGT Recruitment 2025 is officially launched, students appearing for the Mathematics post will get an insight into the Tier-II syllabus. The exam pattern and topics they need to revise are all structured in the official Mathematics syllabus. The KVS TGT Math Syllabus 2025 is curated to test a candidate’s conceptual clarity and the ability to teach the subject at school-level Mathematics classes. 

KVS TGT Mathematics Syllabus 2025

The KVS TGT Mathematics Syllabus 2025 contains all the important topics that are taught in secondary and senior secondary classes of the Mathematics curriculum. The areas of Mathematics included are algebra, geometry, calculus, trigonometry, statistics, mathematical reasoning and much more. Candidates can download the official KVS TGT Mathematics Syllabus PDF for a quick revision, keep all the topics in one place and study the same. The complete KVS TGT Mathematics syllabus is divided into major units that cover all essential concepts taught in secondary and senior secondary classes. Below is the detailed, chapter-wise official syllabus.

REAL NUMBERS

This unit begins with a review of natural numbers, integers, irrational numbers, rational numbers, and their representation on a number line. Students must understand recurring and terminating decimals, operations on real numbers, and examples of non-terminating decimals. The syllabus includes the existence of irrational numbers like √2 and √3, including how they are plotted on the number line. Candidates must know the definition of the nth root of a real number, rules of rationalisation, and combinations of surds involving integers and natural numbers. The syllabus includes laws of exponents, rational exponents with positive real bases, and the Fundamental Theorem of Arithmetic. Additional topics include number theory, sequences, patterns, triangular numbers, hexagonal numbers, cube numbers, palindromic patterns, Kaprekar constant, clock and calendar numbers, Collatz conjecture, and Brahmagupta’s methods of computation.

POLYNOMIALS

This section covers the definition of a polynomial, examples and non-examples, coefficients, zero polynomials, degree of polynomials, and types like monomials, binomials, and trinomials. Candidates must understand zeros of a polynomial along with the relationship between zeros and coefficients for quadratic polynomials. The Remainder Theorem and Factor Theorem are included, along with factorisation of ax² + bx + c and cubic polynomials. Algebraic expressions and identities must be verified and used in factorisation.

MATRICES

This part includes concepts of R, R², and R³ as vector spaces and their standard bases. Students must understand linear independence, different bases, and subspaces of R² and R³. The curriculum covers geometric transformations such as translation, dilation, rotation, and reflection, along with their matrix representation. Eigen values, eigen vectors, and eigen spaces of these transformations are included. Candidates need to know diagonal matrices, reduction to diagonal form (up to order 3), matrix inverses using elementary row operations, matrix rank, and solving linear equations using matrices.

LINEAR EQUATIONS IN TWO VARIABLES

This unit includes linear equations in one and two variables. Students will learn about equations of the form ax + by + c = 0, representation of solutions as ordered pairs, plotting on a graph, and understanding that a linear equation has infinitely many solutions.

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Students must understand graphical and algebraic solutions of two linear equations, including substitution and elimination methods. The concept of consistency and inconsistency and simple real-life problems based on the equations are included.

QUADRATIC EQUATIONS

The syllabus includes standard form ax² + bx + c = 0, methods of solving quadratic equations through factorisation and quadratic formula, and understanding the discriminant to determine the nature of roots.

ARITHMETIC PROGRESSIONS

This section covers nth term, sum of n terms, and applications of A.P. in daily life.

COORDINATE GEOMETRY

Candidates must understand the Cartesian plane, coordinates of points, graphs of linear equations, the distance formula, section formula (internal division), and area of a triangle using coordinates.

INTRODUCTION TO EUCLID'S GEOMETRY

This includes the history of geometry in India and Euclid’s system, Euclid’s postulates, axioms, and theorems. Students must understand relationships between axioms and theorems, such as proving that two lines cannot share more than one common point.

LINES AND ANGLES

Topics include adjacent angle properties, vertically opposite angles, and fundamentals of parallel lines.

TRIANGLES

The syllabus includes congruence criteria like SAS, ASA, SSS, and RHS. Students must know properties of sides and angles of triangles, proportionality rules, and conditions for similarity of triangles.

QUADRILATERALS

This unit covers properties of parallelograms, conditions for identifying parallelograms, diagonals bisecting, and mid-point theorem in triangles.

CIRCLES

The syllabus includes equal chords, perpendicular bisectors from the centre, angles subtended by arcs, cyclic quadrilaterals, tangents, tangent–radius properties, and equal tangents from an external point.

AREAS

Students must understand Heron’s formula, areas of sectors and segments of a circle, and problems involving perimeter and circumference. Only basic angles (60°, 90°, 120°) are included for segments.

SURFACE AREAS AND VOLUMES

The unit includes surface areas and volumes of spheres, hemispheres, cones, cubes, cuboids, cylinders, and combinations of two shapes. Heron's formula is also used for areas of quadrilaterals.

STATISTICS

Candidates must learn bar graphs, histograms with varying base lengths, frequency polygons, mean, median, mode, infographics, data tables, and data presentation.

PROBABILITY

This includes the classical definition of probability, basic laws, discrete and continuous random variables, and simple events.

TRIGONOMETRY

Students must know trigonometric ratios of acute angles, existence of ratios, trigonometric values for 30°, 45°, 60°, and relationships among ratios.

TRIGONOMETRIC IDENTITIES

Proof and application of the identity sin²A + cos²A = 1 and related simple identities.

HEIGHTS AND DISTANCES

Simple problems involving angles of elevation and depression, restricted to 30°, 45°, and 60°, using at most two right triangles.

CALCULUS

This unit includes sets, functions and graphs (polynomials, trigonometric, exponential, logarithmic), step functions, limits, continuity, differentiation (product, quotient, chain rule), second order derivatives, basic integration, and integrals of elementary functions.

INEQUALITIES

This part includes elementary inequalities, absolute values, inequality of means, the Cauchy–Schwarz inequality, and Tchebychef’s inequality.

KVS TGT Mathematics Syllabus PDF 2025

Students who are preparing for the Mathematics exam should download the KVS TGT Mathematics Syllabus PDF for a quick revision. The Mathematics syllabus PDF will help candidates keep all the topics in one place and study as per the official curriculum without missing out on any chapter. It can be downloaded from the KVS website from the KVS TGT Recruitment 2025 section or through the link given below. .

Download KVS TGT Mathematics Syllabus 2025 PDF

KVS TGT Mathematics Exam Pattern 2025

The KVS TGT Mathematics Exam Pattern helps students understand how the question paper is designed. The Tier-II exam includes both objective and descriptive questions based on the mathematics syllabus.

• Objective Questions: Based on Mathematics and other general sections.

• Descriptive Section: Includes questions testing conceptual clarity and explanation skills.

• The exam checks mathematical knowledge and teaching capability.