CBSE Class 9 Maths Syllabus for Board Exam 2026-27, Download PDF Here

Units

Unit Name

Chapter Name

Marks

I

Number System

• Number System

07

II

Algebra

• Introduction to Polynomials

• Sequences and Progressions

• Exploring Algebraic Identities

• Linear Equations in Two Variables

20

III

Coordinate Geometry

• Coordinate Geometry

04

IV

Geometry

• Introduction to Euclid’s Geometry: Axioms and Postulates

• Lines and Angles

• Triangles – Congruence Theorems

• 4-gons (Quadrilaterals)

• Circles

25

V

Mensuration

• Area and Perimeter

• Surface Area and Volume

14

VI

Statistics and Probability

• Statistics

• Introduction to Probability

10

Total

80

Unit I: Number Systems

1. REAL NUMBERS

• Introduction to rational numbers  
• Representation of rational numbers on the number line  
• Density of rational numbers and its proof  
• Finding rational numbers between any two rational numbers  
• Decimal representation of rational numbers  
• Introduction to irrational numbers  
• Proof of irrationality of √2 and √3  
• The square root spiral 

Unit II: Algebra

1. INTRODUCTION TO POLYNOMIALS

• Algebraic expressions  
• Definition of a polynomial.  
• Degree of a polynomial  
• Introduction to linear polynomials and applications  
• Exploring linear patterns  
• Modelling linear growth and linear decay  
• Linear relationships  
• Visualising linear relationships  
• Slope and y-intercept of a line y = ax + b 

2. SEQUENCES AND PROGRESSIONS

• Introduction to sequences  
• Explicit or general rule of a sequence  
• Recursive rule of a sequence  
• Arithmetic Progressions  (AP): nth term, visualising an AP, and practical contexts leading to Aps  
• Sum of the first n natural numbers  
• Geometric Progressions (GP): nth term, visualising a GP, and practical contexts leading to GPs  
• Applications of GP in fractals  
• Tower of Hanoi puzzle 

3.EXPLORING ALGEBRAIC IDENTITIES

• Revisiting algebraic identities  
• Visualising identities using geometrical models  
• Factorisation of algebraic expressions using identities  
• More identities and their applications  
• Visualising factorisation of quadratic expressions through algebra tiles and without using algebra tiles  
• Finding new identities  
• Simplifying rational expressions 

4. LINEAR EQUATIONS IN TWO VARIABLES

• Introduction to linear equations in two variables through practical examples  
• Solution of linear equation in two variables: graphical representation  
• Slope-intercept form of linear equation in two variables  
• Drawing graphs of linear equations when x and y assume only certain values  
• Pair of linear equations in two variables  
• Graphical method for solving a pair of linear equations in two variables  
• Nature of solutions: consistency and inconsistency  
• Algebraic methods of solving a pair of linear equations: substitution and elimination method 

Unit III: Coordinate Geometry

1. COORDINATE GEOMETRY

• Brief history of coordinate geometry  
• The 2-D Cartesian coordinate system  
• Distance between two points in the 2-D plane  
• Midpoint of the line segment between two points in the 2-D plane 

Unit IV: Geometry

1. Introduction to Euclid’s Geometry: Axioms and Postulates 

• History of geometry  
• Constructing a square with a given side as described in the Baudhayana’s Sulbasutras  
• Discovering Euclid’s definitions  
• Axioms: Axioms of measurement and rules for geometric objects  

2. LINES AND ANGLES

• Rays and angles  Measures of angles  
• Intersecting lines and angles  
• Pairs of angles  
• Theorems and examples on intersecting lines  
• Theorems and examples on parallel lines 

3. TRIANGLES

• Practical applications of triangles  
• Proofs of conditions of congruence of triangles  
• Theorems on triangles  
• Propositions and their converse  
• Problems based on applications of theorems on triangles 

4. QUADRILATERALS

• Properties of parallelograms  
• Important theorems related to parallelograms and their proof  
• Midpoint theorem and its applications  
• Understanding the notion of central symmetry in the context of parallelograms 

5. CIRCLES

• Practical applications and uses of circles  
• Definitions related to a circle — centre, diameter, and radius  
• Chords and the angles they subtend  
• Midpoints and perpendicular bisectors of chords  
• Distance of chords from the centre  
• Subtended angles by an arc  
• Cyclicity of points 

UNIT V: MENSURATION 

1. Mensuration: Area and Perimeter

• Perimeter of shapes  
• Perimeter of a circle: Introduction to Pi and its irrationality  
• Length of an arc Area of shapes: rectangles, parallelograms, and triangles  
• Heron’s formula  
• Squaring a rectangle: Proof from Baudhayana’s Sulbasutras  
• Area of a circle: derivation  
• Area of the sector of a circle  
• Brahmagupta’s formula for area of a cyclic 4-gon  
• Heron’s formula as a special case of Brahmagupta’s formula 

2. Mensuration: Surface Area and Volume

• Surface areas and volumes of spheres (including hemispheres) and right circular cones 

UNIT VI: STATISTICS AND PROBABILITY 

1. Statistics 

• Graphical representation of data  
• Measures of central tendency 

2. Introduction to Probability 

• Concept of probability and randomness  
• The probability scale  
• Empirical probability: analysing statistical data and performing experiments  
• Theoretical probability: sample space and events  
• Representing probability through tree diagrams and tables 

S. No.

Typology of Questions

Total Marks

% Weightage (approx.)

1

Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.

Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas

43

54

2

Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.

19

24

3

Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations

Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.

Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions

18

22

Total

80

100