Mathematics SSLC (English Medium) Class 10 Tamil Nadu Board of Secondary Education Syllabus 2025-26

• Definition of Relation
• Domain
• Co-domain and Range of a Relation

• Ways of Representing Functions

1. Tabular Representation of a Function
2. Graphical Representation of a Function
3. Analytical Representation of a Function

• Some Elementary Functions
• Types of Functions
• Operations on Functions
• Inverse of a Function
• Algebra of Functions
• Some Special Functions

• Vertical line test

• Types of Function based on Elements:
  1) One One Function (or injective)
  2) Many One Function
  3) Onto Function (or surjective)
  4) One One and Onto Function (or bijective)
  5) Into Function
  6) Constant Function
• Types of Function based on Equation:
  1) Identity Function
  2) Linear Function
  3) Quadratic Function
  4) Cubic Function
  5) Polynomial Functions
• Types of Function based on the Range:
  1) Modulus Function
  2) Rational Function
  3) Signum Function
  4) Even and Odd Functions
  5) Periodic Functions
  6) Greatest Integer Function
  7) Inverse Function
  8) Composite Functions
• Types of Function based on the Domain:
  1) Algebraic Functions
  2) Trigonometric Functions
  3) Logarithmic Functions
• Explicit and Implicit Functions
• Value of a Function
• Equal Functions

1. Constant function
2. Identity function
3. Real valued function

• Composition of three functions

• Linear Function
• Modulus or Absolute valued Function
• Quadratic Function
• Cubic Function
• Reciprocal Function
• Constant Function

• Significance of the Fundamental Theorem of Arithmetic

• Congruence Modulo
• Connecting Euclid’s Division lemma and Modular Arithmetic
• Modulo operations

• N^th Term of Geometric Progression (G.P.)
• General Term of a Geometric Progression (G.P.)
• Sum of First N Terms of a Geometric Progression (G.P.)
• Sum of infinite terms of a G.P.
• Geometric Mean (G.M.)

• Sum to infinite terms of a G.P.

• Sum of first n natural numbers
• Sum of first n odd natural numbers
• Sum of squares of first n natural numbers
• Sum of cubes of first n natural numbers

• System of Linear Equations in Three Variables

• Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of Polynomials
• Least Common Multiple (LCM) of Polynomials
• Relationship between LCM and GCD

• Reduction of Rational Expression
• Excluded Value
• Operations of Rational Expressions
  - Multiplication of Rational Expressions
  - Division of Rational Expressions
  - Addition and Subtraction of Rational Expressions
  Addition and Subtraction of Rational Expressions with Like Denominators
  - Addition and Subtraction of Rational Expressions with unlike Denominators

• Find the Square Root by Factorization Method
• Finding the Square Root of a Polynomial by Division Method

• Definition: Quadratic Equation
• Definition: Roots of a Quadratic Equation
• Types of Quadratic Equations
• Definition: Solution Set
• Examples

• Variables
• Constants
• Two types of variation: Direct variation, Indirect variation

• Finding the Nature of Solution of Quadratic Equations Graphically
• Solving quadratic equations through the intersection of lines

• Matrices
• Determinants
• Cramer’s Rule
• Application in Economics

• Introduction
• Fundamental Geometrical Concepts

• Corresponding Sides
• Corresponding Angles

• Basic Proportionality Theorem (BPT) or Thales theorem Statement
• Converse of Basic Proportionality Theorem
• Angle Bisector Theorem
• Converse of Angle Bisector Theorem
• Construction of triangle
  - Construction of a segment of a circle on a given line segment containing an angle θ.
  - Construction of a triangle when its base, the vertical angle, and the median from the vertex of the base are given.
  - Construct a triangle when its base, the vertical angle, and the altitude from the vertex to the base are given.
  - Construct a triangle when its base, the vertical angle, and the point on the base where the bisector of the vertical angle meets the base.

In a triangle if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right angled triangle. 

• Introduction
• Definition: Secant
• Definition: Tangent
• Key Points Summary

• Special cevians 
• Ceva’s Theorem
• Menelaus Theorem

• Co-ordinate Axes
• Coordinates of a Point
• Important Results

• Collinearity of three points

• Slope of a Straight line
• Slopes of parallel lines
• Slopes of perpendicular lines

• y = mx+c

• Inclination of a line
• Slope of a line
• Perpendicular Lines
• Angle between intersecting lines
• Different Forms of an equation of a straight line
• General form to other forms

• Definition:  Line of Sight
• Definition: Angles of Elevation
• Definition: Angle of Depression

• Definition: Cylinder
• Properties of a Cylinder
• Activity 1
• Activity 2

• Definition: Cone
• Types of Cones
• Properties of a Cone
• Activity

• Surface area of a sphere
• Hemisphere
• Hollow Hemisphere