CBSE Class IX Mathematics Syllabus 2026 – 27

Unit 1: Number System

No. of periods : 12

Key Concepts

• 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

Relevant CGs

CG-1, C-1.1, CG-9

The student will be able to:

• Understand the concept of a rational number.
• Represent rational numbers on the number line.
• Understand the properties of rational numbers.
• Explain the concept of density of rational numbers.
• Compute decimal representation of rational numbers.
• Understand the concept of irrational numbers.
• Prove the irrationality.
• Construct the square root spiral.
• Apply computational thinking to represent rational and irrational numbers through algorithms and visual models, generate decimal expansions systematically, and reason about numbers using step-by-step logical procedures.

UNIT II: ALGEBRA

No. of periods : 66

Key Concepts

• 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

Relevant CGs

CG-3, C-3.2, CG-9

The student will be able to:

• Understand the meaning of an algebraic expression.
• Define a polynomial.
• Identify the degree, terms and coefficients of terms in a polynomial.
• Model linear growth and decay using linear polynomials.
• Explain and identify patterns in linear relationships.
• Identify the slope and y-intercept of a linear equation in two variables.
• Graph a linear equation in two variables.
• Use computational thinking to identify patterns, construct linear expressions, and systematically represent and analyse linear relationships using equations and graphs.

Key Concepts

• 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

Relevant CGs

CG-11, C-8.1, CG-9

The student will be able to:

• Understand the concept of a sequence of numbers.
• Identify the pattern in a sequence and predict the next few terms.
• Determine the recursive and explicit rules for different sequences.
• Obtain the terms of sequence given its recursive and explicit rule.
• Identify Arithmetic Progressions (AP).
• Determine the nth term of an AP.
• Visualise an AP graphically.
• Identify Geometric Progressions (GP).
• Determine the nth term of a GP.
• Visualise a GP graphically.
• Analyse attributes of fractals using GP.
• Solve the Tower of Hanoi puzzle.
• Use computational thinking to identify patterns, write step-by-step rules, and model patterns in sequences and progressions.

Key Concepts

• 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

Relevant CGs

CG-7, C-7.2, CG-9

The student will be able to:

• Visualise algebraic identities using geometric models.
• Determine the factors of algebraic expressions using identities.
• Interpret factors of quadratic expressions through geometric models.
• Find simplified versions of rational expressions.
• Use computational thinking strategies, such as decomposition and step-by-step procedures to visualise algebraic identities, factor expressions, and simplify rational expressions.

Key Concepts

• 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

Relevant CGs

CG-3, C-3.2, C-8.1, CG-9

The student will be able to:

• Understand the concept of a linear equation in two variables.
• Graph a pair of linear equations.
• Solve a pair of linear equations graphically.
• Solve a pair of linear equations through the methods of substitution and elimination.
• Determine the nature of solutions of a pair of linear equations.
• Model and solve contextualised problems using a pair of linear equations and draw conclusions.
• Model daily-life phenomena using representations, such as graphs, tables, and equations.
• Use computational thinking to systematically represent, solve, and interpret pairs of linear equations through graphs, tables, and step-by-step procedures.

UNIT III: COORDINATE GEOMETRY

No. of periods : 6

Key Concepts

• 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

Relevant CGs

CG-4, C-4.5, CG-9

The student will be able to:

• Specify locations and the position of one point relative to another point using coordinates.
• Represent a floor plan on a grid using coordinates.
• Compute the distance between two points using coordinates.
• Determine whether three points lie in a straight line using coordinates.
• Compute the position of the midpoint of a line segment using coordinates.
• Check whether a triangle is right-angled using coordinates.
• Apply computational thinking to model situations on the coordinate plane and verify geometric properties through systematic reasoning.

UNIT IV: GEOMETRY

No. of periods : 69

Key Concepts

• 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

Relevant CGs

CG-7, C-7.1, C-7.3

The student will be able to:

• Describe how geometry grew from the practical needs ancient civilisations.
• Describe contributions of India, Egypt and Greece to the development of geometric ideas.
• Understand the role of definitions, axioms, and postulates.
• Explain that there are elements of plane geometry (point, line, surface) for which we have an intuitive sense.
• State the 5 postulates of Euclidean geometry.
• Define parallelism of straight lines.
• Explain the construction of a square as given in the Sulbasutras.
• Justify simple constructions using the axioms.

Key Concepts

• 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

Relevant CGs

CG-7, C-7.1, C-7.3, CG-9

The student will be able to:

• Explain the notion of an angle.
• Explain the notion of a ray.
• Explain that angles are formed between two rays with a common starting point.
• State that a straight angle equals two right angles and measures 180° while a right angle measures 90°.
• Classify angles as acute, right, obtuse, or reflex.
• Define parallelism.
• State and apply the linear pair theorem and its converse.
• Follow proof by contradiction in geometry.
• Prove that vertically opposite angles are equal.
• Identify corresponding, alternate, and interior angles.
• Explain transitivity of parallelism.
• Explain why a triangle must have at least two acute angles; why it cannot have two obtuse angles, or all three angles less than 60°
• Apply computational thinking to analyse geometric ideas by breaking constructions into ordered steps, using axioms and postulates as rules, and justifying geometric results through logical step-by-step reasoning.

Key Concepts

• 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

Relevant CGs

CG-4, C 4.1, C-7.3

The student will be able to:

• Explain that a triangle is rigid, unlike a quadrilateral.
• Identify uses of triangle rigidity.
• Explain why triangles give strength and stability to structures.
• Describe what it means for two triangles to be congruent.
• Identify correspondence between the vertices, sides, and angles of two congruent triangles.
• Use the SAS congruence axiom.
• Use the SSS congruence condition.
• Use the ASA congruence condition.
• Use the RHS congruence condition.
• Use the AAS congruence condition.
• Prove the basic properties of isosceles triangles.
• Explain the notion of a proposition.
• Explain the notion of converse of a proposition.
• Identify the converse of a given proposition.
• Explain that not all converses are true; use counter examples to show that some converses are false.
• Explain why SSA is not, in general, a valid congruence condition.
• Identify the situations where SSA is a valid congruence condition.
• Justify the role of diagram accuracy.

Key Concepts

• 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

Relevant CGs

CG-4, C-4.2, C-7.3

The student will be able to:

• Frame a precise definition of a 4-gon.
• Prove various characterisations of a parallelogram.
• Prove the midpoint theorem.
• Prove a converse of the midpoint theorem.
• Prove that the medians of a triangle are concurrent and each median is divided in the ratio 2:1 at the point of concurrence.
• Prove that the 4-gon formed by joining the midpoints of a given 4-gon is a parallelogram.
• Find the coordinates of the midpoint of a line segment given its end points and find the coordinates of the fourth vertex of a parallelogram given the other three.
• Understand reflection and rotation symmetries of 4-gons.
• Understand how any 4-gon can tile a plane.
• Practice forming logical converses of statements and asking questions guided by converses of theorems.
• Engage in drawing, measurement and paper manipulation activities to discover geometric patterns involving triangles and 4-gons.

Key Concepts

• 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

Relevant CGs

CG-4, C-7.3, CG-9

The student will be able to:

• State the definition of a circle.
• Explain the meanings of the terms ‘chord’, ‘diameter’, ‘radius’, ‘arc’, ‘segment’, and ‘sector’.
• Explain why there exists a unique circle through three non-collinear points.
• Construct the circumcircle and circumcentre of a triangle.
• Describe the location of the circumcentre for acute, obtuse, and right-angled triangles.
• Explain what ‘angle subtended by an arc at the centre’ means.
• Explain why ‘equal chords subtend equal angles at the centre’.
• Explain why ‘chords that subtend equal angles at the centre are equal’.
• Explain why ‘the line from the centre of a circle to the midpoint of a chord is perpendicular to the chord’.
• Explain why ‘a perpendicular from the centre to a chord bisects the chord’.
• State the relationship between length of a chord and its distance from the centre of the circle.
• Explain why ‘equal chords are equidistant from the centre (and conversely)’.
• Explain why ‘among unequal chords, the longer chord is closer to the centre’.
• Explain why ‘the diameter is the longest chord’.
• Explain why ‘the angle subtended by an arc at the centre is double the angle subtended by the arc at any point on the remaining part of the circle’.
• Explain why ‘angles in the same segment of a circle are equal’.
• Explain why ‘the angle in a semicircle is a right angle’.
• Determine when four given points are concyclic.
• Explain why ‘a quadrilateral with supplementary opposite angles is cyclic, and conversely’.
• Explain how circular wheels have influenced transport, farming, building, and technology.
• Identify cultural motifs involving circles, for example, the Dharmachakra, Ashoka Chakra, Sudarshan Chakra.
• Use computational thinking to break down circle-related problems, apply geometric rules step-by-step, and verify properties of figures, such as chords, angles, and cyclic quadrilaterals through systematic reasoning.

UNIT V: MENSURATION

No. of periods : 27

Key Concepts

• 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

Relevant CGs

CG-5, C-5.1, CG-9

The student will be able to:

• Define perimeter as the length around the boundary of any shape.
• Explain that the circumference-to-diameter ratio is constant for all circles.
• List historical approximations to π (from Archimedes, Aryabhata, and Zu Chongzhi).
• Compute the circumference of a circle and the length of an arc.
• Apply ideas of circle perimeter and arc-length to real-world contexts.
• Explain why a median of a triangle divides it into two triangles of equal area.
• Use Heron’s formula to compute the area of a triangle from its sides.
• Explain the classical problem of ‘squaring’ a given shape.
• Explain how ancient civilisations approximated the area of a circle.
• Compute the area of a circle using the formula.
• Explain and use the formula for area of a sector of a circle.
• Solve problems on areas of sectors and segments of circles.
• State Brahmagupta’s formula for the area of a cyclic quadrilateral in terms of its sides.
• Explain why Heron’s formula is a ‘special case’ of Brahmagupta’s formula.
• Explain the notion of ‘special case’ and ‘generalisation’ in mathematics.
• Use computational thinking to break down shapes, apply step-by-step methods to calculate perimeter and area, recognise patterns across formulae, and understand generalisation and special cases in geometry.

Key Concepts

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

Relevant CGs

CG-5, C-5.1, CG-9

The student will be able to:

• Recognise cuboids and cubes in real-life situations.
• Compute the surface area and volume of a cuboid.
• Explain how a cube is a ‘special case’ of a cuboid.
• Describe a right circular cylinder using its radius and height.
• Compute the surface area and volume of a cylinder.
• Recognise cones in daily life, and describe them using radius and height.
• Compute the surface area and volume of a cone.
• Recognise a pyramid, and identify its base and apex.
• Compute the surface area and volume of a pyramid.
• Recognise spheres in real-life situations.
• Compute the surface area and volume of a sphere.
• Use computational thinking to systematically calculate, and compare surface areas and volumes of 3-D shapes by varying dimensions and analysing patterns.

UNIT VI: STATISTICS AND PROBABILITY

No. of periods : 24

Key Concepts

• Graphical representation of data
• Measures of central tendency

Relevant CGs

CG-6, C-6.1, CG–9

The student will be able to:

• Collect, organise, visualise and interpret data to answer a statistical investigative question.
• Compute and apply weighted average in different settings.
• Read and interpret stacked bar graphs and 100% stacked bar graphs.
• Apply computational thinking strategies to analyse real-life data, create appropriate graphical representations, and interpret mean, median and mode for decision-making.

Key Concepts

• 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

Relevant CGs

CG-6, C-6.2, CG-9

The student will be able to:

• Understand the concept of randomness.
• Describe the likelihood of an event using the probability scale.
• Estimate the empirical probability of the occurrence of an event by analysing statistical data.
• Define theoretical probability of an event.
• Apply the definition of theoretical probability to compute the probability of an event.
• Compute probability of events with the help of tree diagrams and tables.
• Use computational thinking strategies, such as pattern recognition and simulation, to model random experiments and estimate probabilities.