Tamil Nadu Board of Secondary Education Class 9 Mathematics Syllabus - Free PDF Download
Tamil Nadu Board of Secondary Education Syllabus 2025-26 Class 9: The Tamil Nadu Board of Secondary Education Class 9 Mathematics Syllabus for the examination year 2025-26 has been released by the Tamil Nadu Board, Tamil Nadu Board of Secondary Education. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2025-26 Tamil Nadu Board of Secondary Education Class 9 Mathematics Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new Tamil Nadu Board of Secondary Education syllabus to prepare for their annual exam properly.
The detailed Tamil Nadu Board of Secondary Education Class 9 Mathematics Syllabus for 2025-26 is below.
Academic year:
Tamil Nadu Board of Secondary Education Class 9 Mathematics Revised Syllabus
Tamil Nadu Board of Secondary Education Class 9 Mathematics and their Unit wise marks distribution
Tamil Nadu Board of Secondary Education Class 9 Mathematics Course Structure 2025-26 With Marking Scheme
| # | Unit/Topic | Weightage |
|---|---|---|
| 1 | Set Language | |
| 2 | Real Numbers | |
| 3 | Algebra | |
| 4 | Geometry | |
| 5 | Coordinate Geometry | |
| 6 | Trigonometry | |
| 7 | Mensuration | |
| 8 | Statistics | |
| 9 | Probability | |
| Total | - |
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Syllabus
1 Set Language
- Concept of Sets
- Introduction
- Definition: Sets
- Well-defined and Not Well-defined Sets
- Elements of a Set and Notation
- Properties of Sets
- Examples
- Real-Life Applications
- Key Points Summary
- Representation of a Set
- Introduction
- Methods of Set Representation
- Number Sets with Different Methods
- Representing Sets Using Pictures
- Representing Sets Using Brackets
- Key Points Summary
- Types of Sets
- Introduction
- Exploring Different Types of Sets
- Real-Life Applications
- Key Points Summary
- Set Operations
- Complement of a Set
- Union of Two Sets
- Intersection of Two Sets
- Difference of Two Sets
- Symmetric Difference of Sets
- Properties of Set Operations
- Commutative Property
- Associative Property
- Distributive Property
- De Morgan’s Laws
- De Morgan’s Laws for Set Difference
- De Morgan’s Laws for Complementation
- Cardinality of a Set
- Definition: Cardinality
- Examples
- Real-Life Application
- Key Points Summary
2 Real Numbers
- Rational Numbers
- Denseness Property of Rational Numbers
- Concept of Irrational Numbers
- Representation of Irrational Numbers on the Number Line
- Decimal Representation of Rational Numbers
- Period of Decimal
- Conversion of Terminating Decimals into Rational Numbers
- Conversion of Non-terminating and Recurring Decimals into Rational Numbers
- Decimal Representation to Identify Irrational Numbers
- Concept of Real Numbers
- Representing Real Numbers on the Number Line
- Radical Notation
- Fractional Index
- Surds
- Order of a Surd
- Surds of the same order
- Simplest form of a surd
- Pure and Mixed Surds
- Simple and Compound Surds
- Binomial Surd
- Laws of Radicals
- Operations on Surds
- Rationalisation of Surds
- Scientific Notation
- Writing a Decimal Number in Scientific Notation.
- Converting Scientific Notation to Decimal Form
- Arithmetic of Numbers in Scientific Notation
3 Algebra
- Algebraic Expressions
- Introduction
- Types of Expressions
- Rules for Separating Terms
- Framing Algebraic Expressions and Formulas
- Real-Life Applications
- Key Points Summary
- Polynomial and its Degree
- Introduction
- Definition: Polynomial in One Variable
- Definition: Degree
- Definition: Polynomials of Two or More Variables
- Real-Life Application
- Key Points Summary
- Standard Form of a Polynomial
- Degree of Polynomial
- Polynomial in one variable
- Polynomial in more than one variable
- Types of Polynomials
- Types of polynomials (based on number of terms):
- Monomial
- Binomial
- Trinomial
- Types of the polynomial (based on the degree):
- Linear polynomial
- Quadratic polynomial
- Cubic polynomial
- Arithmetic of Polynomials
- Addition of Polynomials
- Introduction
- Row Method
- Column Method
- Example 1
- Example 2
- Example 3
- Key Points Summary
- Subtraction of Polynomials
- Introduction
- Row Method
- Column Method
- Example 1
- Example 2
- Example 3
- Example 4
- Key Points Summary
- Multiplication of Two Polynomials
- Value of a Polynomial
- Roots of a Polynomial Equation
- Remainder Theorem
- Factor Theorem
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Expansion of (x + a)(x + b)
- Expansion of (a + b + c)2
- Expansion of (x + a)(x + b)(x + c)
- Expansion of (a + b)3
- Expansion of (a - b)3
- Factorisation Using Identities
- Factorisation Using Identity a2 + 2ab + b2 = (a + b)2
- Factorisation Using Identity a2 - 2ab + b2 = (a - b)2
- Factorisation Using Identity a2 - b2 = (a + b)(a - b)
- Factorisation using Identity a2 + b2 + c2 + 2ab + 2bc + 2ac = (a + b + c)2
- Factorisation using Identity a3 + b3 = (a + b)(a2 - ab + b2)
- Factorisation using Identity a3 - b3 = (a - b)(a2 + ab + b2)
- Factorisation using Identity a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
- Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.
- Division Algorithm for Polynomials
- Synthetic Division
- Highest Common Factor (HCF)
- Definition: HCF
- Steps to Find HCF
- Example 1
- Example 2
- Key Points Summary
- General Form of Linear Equation in Two Variables
- Graph of a Linear Equation in Two Variables
- Methods of solving linear equations in two variables
- Simultaneous method
- Comparing the Ratios of Coefficients of a Linear Equation
- Methods of Solving Simultaneous Linear Equations by Substitution
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
- Consistency and Inconsistency of Linear Equations in Two Variables
- Zeroes of a Polynomial
4 Geometry
- Angles and Their Measurement in Higher Mathematics
- Definition: Angle
- Properties of Angle
- Types of Angles
- Introduction
- Types of Angles
- Activity: Exploring a Straight Angle Using Paper Folding
- Key Rotational Benchmarks
- Concept for Angle Sum Property
- Related Angles
- Concept of Pairs of Angles
- Introduction
- Adjacent Angles
- Vertically Opposite Angles
- Congruent Angles
- Complementary Angles
- Supplementary Angles
- Example 1
- Example 2
- Key Points Summary
- Concept of Transversal Lines
- Introduction
- Angles Formed by Two Lines and Their Transversal
- When Two Parallel Lines Are Cut by a Transversal
- Example 1
- Basic Concepts of Triangles
- Definition:Triangle
- Parts of a Triangle
- Basic Properties of a Triangle
- Key Points Summary
- Criteria for Congruence of Triangles
- Types of Quadrilaterals
- Introduction
- Trapezium
- Isosceles Trapezium
- Parallelogram
- Rectangle
- Rhombus
- Square
- Example 1
- Example 2
- Example 3
- Key Points Summary
- Properties of a Square
- Properties of Rectangle
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of Trapezium
- Properties of Isosceles Trapezium
- Properties of Kite
- Theorem: In a Parallelogram, Opposite Sides Are Equal.
- Angle Subtended by Chord at the Centre
- Theorem: Parallelograms on the Same Base and Between the Same Parallels.
- Corollary: Triangles on the same base and between the same parallels are equal in area.
- Corollary: A rectangle and a parallelogram on the same base and between the same parallels are equal in area.
- Basic Concept of Circle
- Introduction
- Definition: Circle
- Definition: Radius
- Definition: Diameter
- Definition: Chord
- Example
- Real-Life Applications
- Key Points Summary
- Congruence of Circles
- Circles Passing Through One, Two, Three Points
- Infinite circles pass through one point.
- Infinite circles pass through two distinct points.
- There is a unique circle passing through three non-collinear points.
- No circle can pass through 3 collinear points.
- Perpendicular from the Centre to a Chord
- Properties of Chord
- Theorem: a Perpendicular Drawn from the Centre of a Circle on Its Chord Bisects the Chord.
- Converse: The Line Joining the Centre of the Circle and the Midpoint of a Chord is Perpendicular to the Chord.
- Theorem: Equal chords of a circle subtend equal angles at the centre.
- Converse: If the angles subtended by two chords at the centre of a circle are equal, then the chords are equal.
- Properties of Congruent Chords
- Angle Subtended by an Arc of a Circle
- Angle at the Centre and the Circumference
- Theorem: The angle subtended by an arc of the circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- Theorem: Angles in the Same Segment of a Circle Are Equal.
- Cyclic Quadrilateral
- Theorem: Opposite angles of a cyclic quadrilateral are supplementary.
Theorem: Opposite angles of a cyclic quadrilateral are supplementry.
- Converse: If a Pair of Opposite Angles of a Quadrilateral is Supplementary, Then the Quadrilateral is Cyclic.
- If a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is cyclic.
- Exterior Angle of a Cyclic Quadrilateral
- Theorem: If One Side of a Cyclic Quadrilateral is Produced Then the Exterior Angle is Equal to the Interior Opposite Angle.
- Construction of the Centroid of a Triangle.
- Construction of Orthocentre of a Triangle
- Construction of the Circumcentre of a Triangle
- Incircle of a Triangle
- Introduction
- Definition: In-Circle
- Definition: Incenter
- Definition: Inradius
- Step-by-Step Construction
- Key Points Summary
5 Coordinate Geometry
- Concept for Mapping the Space Around Approximately Through Visual Estimation.
- Plotting a Point in the Plane If Its Coordinates Are Given.
- Cartesian Coordinate System
- Co-ordinates of Points and Distance
- The Mid-point of a Line Segment (Mid-point Formula)
- Points of Trisection of a Line Segment (Mid-point Formula)
- Section Formula
- The Coordinates of the Centroid
6 Trigonometry
- Trigonometry
- Trigonometric Ratios of Complementary Angles
- Trigonometric Ratios and Its Reciprocal
- Reciprocal Relation Between Trigonometric Ratios
- Trigonometric Ratios of Some Special Angles
- Trigonometric Table
7 Mensuration
- Area of a Triangle by Heron's Formula
- Collinearity of three points
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Surface Area of a Cuboid
- Surface Area of a Cube
- Volume of a Cuboid
- Volume of Cube
- Geometric Interpretation of the Area of a Triangle
8 Statistics
- Frequency Distribution Table
- Ungrouped Frequency Distribution Table
- Grouped Frequency Distribution Table
- Measures of Central Tendency for Different Data Types
- Introduction
- Measures
- Arithmetic Mean - Raw Data
- Mean of Grouped Data
- Mean of Ungrouped Data
- Method of Finding Mean for Grouped Data: Direct Method
- Method of Finding Mean for Grouped Data: Deviation Or Assumed Mean Method
- Method of Finding Mean for Grouped Data: the Step Deviation Method
- A Special Property of the Arithmetic Mean
- Concept of Median
- Definition: Median
- Formula: Odd Number of Observations
- Formula: Even Number of Observations
- Example 1
- Example 2
- Example 3
- Key Points Summary
- Median of Grouped Data
- Median of Ungrouped Data
- Concept of Mode
- Mode of Grouped Data
- Mode of Ungrouped Data
- Empirical Relationship Between the Three Measures of Central Tendency
9 Probability
- Probability
- Tree diagram
- Probability of an Event
- Basic Ideas of Probability
- Event and Its Types
- Theoretical Probability Or Classical Probability
- Experimental Or Empirical Probabilities
