KVS TGT Mathematics Syllabus 2025, Download Official PDF

KVS has announced a big vacancy in the TGT and other posts on its official website. This exam is being conducted by the CBSE and also provides the official syllabus and exam pattern. The TGT mathematics exam is conducted in three stages: one is a prelims exam for each TGT aspirant, 2nd stage contains the subject-specific, and the last and 3rd depends on your subject orientation.

KVS TGT Math Syllabus 2025

Today, we are going to provide the official syllabus of the KVS TGT Mathematics subject. You all know that Maths is the subject that can provide you with 100% marks if you solve the questions smartly. KVS has announced a total vacancy of 413, and for this post, lakhs of aspirants will fight for this post. Read this article properly to get the complete syllabus and exam pattern of the KVS TGT Mathematics subject.

KVS TGT Math Exam Pattern 2025

Before narrating the detailed syllabus topic-wise wise you must know about the latest syllabus and exam pattern. In the exam pattern of the KVS TGT Mathematics, candidates can get all the details of exam types and its number of questions as well as its time duration. You all know there are three stages in the KVS TGT Exam in each subject as below. We have revealed each point in detail.

• Mode of Exam – OMR Offline
• Total No. of Questions – 100 MCQ-based
• Total Marks – 300 marks
• Negative Marking – 1 mark for each incorrect answer
• Exam Duration –  2 hours (120 minutes)

Parts	Subjects	No. of Questions	Total Marks	Duration
Part I	General Reasoning	20	60	2 Hours (120 minutes)
Part II	Numeric Ability	20	60
Part III	Basic Computer Literacy	20	60
Part IV	General Knowledge	20	60
Part V	Language Competency Test (English)	10	30
Part VI	Language Competency Test (One other Modern Indian Language)	10	30
Total		100	300

KVS TGT Tier 2 Exam Pattern 2025

The examination will include questions based on the subjects chosen by the candidates. It will be conducted in two modes: descriptive (pen-and-paper) and objective (OMR-based). In the objective section, each correct answer will carry 1 mark, while 0.25 marks will be deducted for every incorrect response. The total duration of the exam will be 2 hours and 30 minutes, with no separate time allocation for individual sections.

Type	Number of Questions	Marks	Duration
Objective	60	60	2.5 hours
Descriptive	10	40
Total	70	100

KVS TGT Maths Syllabus 2025

Mathematics is an evergreen subject, and number scoring. There is a good demand the mathematics teachers in our country, and students always go away from mathematics subjects. After many demands, we have provided the KVS Mathematics subject syllabus topic-wise. This is the KVS TGT Mathematics syllabus with proper details.

The syllabus is primarily derived from NCERT textbooks of classes 6 to 10; however, candidates are also expected to know about topics up to the graduation level. The list given below provides an outline of the subjects that aspirants should focus on while preparing for the TGT Maths examination.

Real Numbers

• Review of representation of natural numbers, integers, and rational numbers on the number line.
• Rational numbers as recurring/ terminating decimals.
• Operations on real numbers.
• Examples of non-recurring/non-terminating decimals.
• Existence of non-rational numbers (irrational numbers) such as J2, i3, and their representation on the number line.
• Definition of the nth root of a real number.
• Laws of exponents with integral powers. Rational exponents with positive real bases

Polynomials

• Definition of a polynomial in one variable, with examples and counterexamples.
• Coefficients of a polynomial, terms of a polynomial, and the zero polynomial.
• Degree of a polynomial.
• Constant, linear, quadratic, and cubic polynomials.
• Monomials, binomials, trinomials.
• Factors and multiples.
• Zeros of a polynomial.
• Relationship between zeros and coefficients of quadratic polynomials.
• Remainder Theorem with examples, Factor Theorem.

Linear Equations in Two Variables 

• Linear equations in one variable.
• Introduction to the equation in two variables.
• Focus on linear equations of the type axe + by + c=0.
• Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

Pair of Linear Equations in two variables

• Pair of linear equations in two variables and the graphical method of their solution, consistency/inconsistency.
• Algebraic conditions for several solutions.
• Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination.Simple situational problems.

Quadratic Equations

• Standard form of a quadratic equation ax² + bx + c = 0, (a 0 0).
• Solutions of quadratic equations (only real roots) by factorisation, and by using the quadratic formula.
• Relationship between discriminant and nature of roots.

Arithmetic Progressions

• Arithmetic Progression, nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

Coordinate Geometry

• The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, and notations.
• Graphs of linear equations.
• Distance formula.
• Section formula (internal division)

Introduction to Euclid’s Geometry

• History – Geometry in India and Euclid’s geometry.
• Euclid’s method of formalising observed phenomena into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems.
• The five postulates of Euclid.

Quadrilaterals

• The diagonal divides a parallelogram into two congruent triangles.
• In a parallelogram, opposite sides are equal, and conversely.
• In a parallelogram, opposite angles are equal, and conversely.
• A quadrilateral is a parallelogram if a pair of opposite sides is parallel and equal.

Circles

• Equal chords of a circle subtend equal angles at the centre, and the converse is also true.
• The perpendicular from the centre of a circle to a chord bisects the chord; conversely, a line through the centre that bisects a chord is perpendicular to it.
• Equal chords of a circle (or of congruent circles) are equidistant from the centre (or respective centres), and the converse holds.
• The angle subtended by an arc at the centre is double that subtended by it at any other point on the remaining part of the circle.
• Angles in the same segment of a circle are equal.
• If a line segment joining two points subtends equal angles at two other points on the same side, all four points lie on a circle.
• The sum of the pair of opposite angles of a cyclic quadrilateral is 180∘180∘, and the converse is true.
• Tangent to a circle at the point of contact.
• The tangent at any point of a circle is perpendicular to the radius at the point of contact.
• The lengths of tangents drawn from an external point to a circle are equal.

Area

• Area of a triangle using Heron’s formula.
• Area of sectors and segments of a circle.
• Problems based on areas and perimeter/circumference of the above-mentioned plane figures.
• While calculating the area of a segment of a circle, problems should only involve central angles of 60∘60∘, 90∘90∘, and 120∘120∘.

Surface Area and Volume

• Surface areas and volumes of spheres (including hemispheres) and right circular cones.
• Surface areas and volumes of combinations involving any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.
• Area of a triangle using Heron’s formula and its application in finding the area of a quadrilateral.

Statistic

• Bar graphs, histograms (with varying base lengths), and frequency polygons.
• Mean, median, and mode of grouped and ungrouped data.
• Infographics and presentation of data.
• Presentation of data in tabular form.

PROBABILITY

• Classical definition of probability.
• Simple problems on finding the probability of an event.
• Elementary probability and basic law.
• Discrete and continuous random variables.

TRIGONOMETRY

• Trigonometric ratios of an acute angle of a right-angled triangle.
• Proof of the existence (well defined) of trigonometric ratios; motivate the ratios defined at 0∘0∘ and 90∘90∘.
• Values of trigonometric ratios for 30∘30∘, 45∘45∘, and 60∘60∘.
• Relationships between the ratios.

TRIGONOMETRIC IDENTITIES

• Proof and applications of the identity sin⁡2A+cos⁡2A=1sin2A+cos2A=1.
• Only simple identities are to be given.

HEIGHTS AND DISTANCES

• Angle of elevation and angle of depression.
• Simple problems on heights and distances (restricted to a maximum of two right triangles).
• Angles of elevation/depression restricted to 30∘30∘, 45∘45∘, and 60∘60∘.

CALCULUS

• Sets, functions, and their graphs: polynomial, sine, cosine, exponential, and logarithmic functions.
• Step function.
• Limits and continuity.
• Differentiation, including methods like the chain rule, product rule, and quotient rule.
• Second-order derivatives of the above functions.
• Integration is the reverse process of differentiation.
• Integrals of the functions introduced above.

Inequalities

• Elementary inequalities
• Absolute value
• Inequality of means
• Cauchy-Schwarz Inequality
• Tchebycheff’s Inequality