CBSE Class 9 Maths Syllabus 2026-27

CBSE Class 9 Maths Syllabus 2026-27 covers NCERT Ganita Manjari Part I with 8 chapters across coordinates, algebra, numbers, circles, mensuration, probability and sequences.

The syllabus builds reasoning, proof, visualisation and problem-solving through graphs, patterns, identities, diagrams, formulas and exploratory tasks.

CBSE Class 9 Maths Syllabus for 2026-27 is based on Ganita Manjari: Textbook of Mathematics for Grade 9 Part I, the current NCERT Mathematics textbook for the Secondary Stage. The book was first published in April 2026 and marks a major shift from the earlier NCERT Mathematics: Textbook for Class IX. The current textbook has 8 chapters in Part I, from Orienting Yourself: The Use of Coordinates to Predicting What Comes Next: Exploring Sequences and Progressions. The syllabus now places stronger focus on reasoning, representation, proof, exploration, visualisation and mathematical communication.

Key Takeaways

  • New Textbook: The NCERT Class 9 Maths book for 2026-27 is titled Ganita Manjari Part I.
  • Total Chapters: The Class 9 Maths syllabus in Part I has 8 chapters.
  • Main Areas: The syllabus covers coordinates, linear polynomials, numbers, identities, circles, mensuration, probability and sequences.
  • Learning Approach: Ganita Manjari uses pictorial, numerical, algebraic and graphical representations.
  • Enrichment Note: Questions and sections marked with an asterisk are for enrichment and not formal assessment.
  • Previous Book: The earlier NCERT book was titled Mathematics: Textbook for Class IX.
  • Major Change: The current book begins with coordinates instead of number systems.
  • Book Detail: Ganita Manjari Part I was first published in April 2026.

NCERT Class 9 Maths Syllabus 2026-27

NCERT Class 9 Maths Syllabus 2026-27 follows the Ganita Manjari Part I chapter sequence. The book introduces Secondary Stage Mathematics through coordinates, algebraic thinking, number systems, visual identities, circle geometry, measurement, probability and sequences.

The official textbook title is Ganita Manjari: Textbook of Mathematics for Grade 9 Part I. The title combines Ganita, meaning mathematics, with Manjari, meaning a bouquet of flowers in many Indian languages. The book presents mathematics as a set of connected ideas rather than isolated rules.

The textbook uses the Low Threshold–High Ceiling approach. The opening tasks are accessible, while selected asterisk-marked problems offer deeper exploration.

The syllabus develops concepts through four main representations:

  • Pictorial
  • Numerical
  • Algebraic
  • Graphical

These representations make the Class 9 Maths Syllabus concept-led. Chapter 1 uses graphs and coordinates. Chapter 4 explains algebraic identities through visual and geometric models. Chapter 7 introduces probability through outcomes, tables, experiments and tree diagrams.

Representation Where It Appears in Ganita Manjari
Pictorial Algebraic identities, circles, mensuration and visual models
Numerical Numbers, probability, sequences and measurements
Algebraic Linear polynomials, identities and progressions
Graphical Coordinates, linear polynomials, number line and visual patterns

CBSE Class 9 Maths Chapter Wise Syllabus

CBSE Class 9 Maths chapter wise syllabus includes 8 chapters in Ganita Manjari Part I. The chapter order begins with coordinate geometry and then moves into algebra, numbers, identities, geometry, mensuration, probability and sequences.

The updated sequence is different from the earlier NCERT Class 9 Maths textbook. The earlier book began with Number Systems, while Ganita Manjari begins with coordinate-based thinking.

Class 9 Maths Chapters List

Chapter Number Chapter Name Page Number
Chapter 1 Orienting Yourself: The Use of Coordinates 1
Chapter 2 Introduction to Linear Polynomials 16
Chapter 3 The World of Numbers 41
Chapter 4 Exploring Algebraic Identities 68
Chapter 5 I’m Up and Down, and Round and Round 92
Chapter 6 Measuring Space: Perimeter and Area 118
Chapter 7 The Mathematics of Maybe: Introduction to Probability 155
Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions 174
Additional Resource Graph Paper 197

Ganita Manjari Class 9 Maths Syllabus Chapter 1: Orienting Yourself

Chapter 1 introduces the Cartesian plane and the use of coordinates. It shows how location can be described using ordered pairs.

The syllabus covers axes, origin, quadrants, plotting points, reading coordinates, computing distances and finding midpoints. It connects geometry with algebra through points and positions on a plane.

Chapter 1 Topics

Area Topics Covered
Coordinate Plane Axes, origin, quadrants and ordered pairs
Point Location Plotting points and reading coordinates
Distance Distance between two points on the Cartesian plane
Midpoint Midpoint of a line segment
Representation Graph paper, grids and geometric relationships

Important formulas:

Distance between two points:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Midpoint of two points:

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Ganita Manjari Class 9 Maths Syllabus Chapter 2: Introduction to Linear Polynomials

Chapter 2 develops algebraic thinking through expressions and linear polynomials. It connects patterns, tables, input-output relations and graphs.

The syllabus covers variables, constants, algebraic expressions, linear polynomials and graphical representation. Students see how a changing quantity can be represented by an algebraic rule.

Chapter 2 Topics

Area Topics Covered
Algebraic Expressions Variables, constants and terms
Linear Polynomials Linear form and value of a polynomial
Patterns Writing rules from numerical and visual patterns
Graphs Graphical representation of linear relationships
Connections Algebraic and graphical views of the same relation

Important forms:

Linear polynomial:

p(x) = ax + b

Value of a polynomial at x = k:

p(k) = ak + b

Linear equation from a linear polynomial:

ax + b = c

Ganita Manjari Class 9 Maths Syllabus Chapter 3: The World of Numbers

Chapter 3 extends number understanding from integers and rational numbers to irrational numbers. It builds number sense through number lines, density and visual constructions.

The syllabus covers rational numbers, irrational numbers, real numbers, density of rational numbers, proofs of irrationality and the square root spiral.

Chapter 3 Topics

Area Topics Covered
Rational Numbers Fractions, decimals and number line placement
Irrational Numbers Non-terminating, non-repeating numbers
Density Rational numbers between two rational numbers
Proofs Irrationality proofs
Visualisation Square root spiral and geometric construction

Important ideas:

A rational number can be written as p/q, where q ≠ 0.

An irrational number cannot be written as p/q.

Between any two rational numbers, infinitely many rational numbers exist.

Ganita Manjari Class 9 Maths Syllabus Chapter 4: Exploring Algebraic Identities

Chapter 4 explains algebraic identities through visual and geometric models. It makes expansion, simplification and factorisation more conceptual.

The syllabus covers standard identities, factorisation and simplification of expressions. Visual models help students see where identities come from.

Chapter 4 Topics

Area Topics Covered
Identities Standard algebraic identities
Expansion Expanding expressions using identities
Factorisation Factorising expressions through identities
Visual Models Geometric interpretation of identities
Simplification Reducing expressions using known forms

Important identities:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

(a + b)(a - b) = a² - b²

(x + a)(x + b) = x² + (a + b)x + ab

Ganita Manjari Class 9 Maths Syllabus Chapter 5: I’m Up and Down, and Round and Round

Chapter 5 develops geometry through circles, chords, arcs, angles and cyclic figures. It connects formal reasoning with visual diagrams.

The syllabus covers circle basics, chord relationships, arc relationships, angle properties and cyclic figure reasoning. The chapter builds proof-based geometry through diagrams and arguments.

Chapter 5 Topics

Area Topics Covered
Circle Basics Centre, radius, chord, arc and circumference
Chords and Arcs Relationships between equal chords and arcs
Angles Angles formed by chords and arcs
Cyclic Figures Points and figures related to circles
Reasoning Diagram-based proof and geometric argument

Important ideas:

A circle is the set of all points at a fixed distance from a fixed point.

The fixed point is the centre.

The fixed distance is the radius.

Ganita Manjari Class 9 Maths Syllabus Chapter 6: Measuring Space: Perimeter and Area

Chapter 6 develops mensuration through plane figures and circles. It connects measurement formulas with derivation, visualisation and historical methods.

The syllabus covers perimeter, area, circles and measurement of two-dimensional figures. Formula understanding is built through models, derivations and applications.

Chapter 6 Topics

Area Topics Covered
Perimeter Boundary length of plane figures
Area Surface covered by plane figures
Circles Circumference and area of circles
Formula Derivation Visual and historical ways of deriving formulas
Application Measurement problems from real situations

Important formulas:

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

Area of triangle = 1/2 × base × height

Circumference of circle = 2πr

Area of circle = πr²

Ganita Manjari Class 9 Maths Syllabus Chapter 7: The Mathematics of Maybe

Chapter 7 introduces probability as a way to measure uncertainty. It uses experiments, outcomes, tables and tree diagrams.

The syllabus covers randomness, empirical probability, theoretical probability and simple representations of chance events. It helps students compare experimental results with theoretical possibilities.

Chapter 7 Topics

Area Topics Covered
Randomness Chance events and uncertain outcomes
Outcomes Listing and organising possible results
Empirical Probability Probability based on experiments
Theoretical Probability Probability based on equally likely outcomes
Representations Outcome tables and tree diagrams

Important formula:

P(E) = Number of favourable outcomes / Total number of outcomes

Probability range:

0 ≤ P(E) ≤ 1

Ganita Manjari Class 9 Maths Syllabus Chapter 8: Predicting What Comes Next

Chapter 8 explores patterns, sequences and progressions. It connects algebraic rules with visual models and recursive thinking.

The syllabus covers arithmetic progressions, geometric progressions, recursive rules and pattern prediction. Visual patterns and fractals support the shift from observation to algebraic generalisation.

Chapter 8 Topics

Area Topics Covered
Sequences Pattern recognition and term listing
Arithmetic Progression Constant difference between consecutive terms
Geometric Progression Constant ratio between consecutive terms
Recursive Rules Rules based on previous terms
Visual Patterns Fractals and model-based sequence thinking

Important forms:

Arithmetic progression:

a, a + d, a + 2d, a + 3d, ...

nth term of an AP:

an = a + (n - 1)d

Geometric progression:

a, ar, ar², ar³, ...

nth term of a GP:

an = arⁿ⁻¹

Class 9 Maths New Syllabus 2026-27: What Has Changed

Class 9 Maths new syllabus 2026-27 is based on Ganita Manjari: Textbook of Mathematics for Grade 9 Part I. The previous NCERT textbook was titled Mathematics: Textbook for Class IX. It was first published in February 2006 and followed a 15-chapter structure.

The earlier textbook began with Number Systems, followed by Polynomials, Coordinate Geometry, Linear Equations in Two Variables, Introduction to Euclid’s Geometry, Lines and Angles, Triangles and Quadrilaterals. It also had separate chapters on Constructions, Heron’s Formula, Surface Areas and Volumes, Statistics and Probability.

Ganita Manjari Part I changes both the title and the learning sequence. It begins with coordinates, then moves into linear polynomials, numbers, algebraic identities, circles, perimeter and area, probability, and sequences. The updated book uses visualisation, reasoning, proof, representations and exploratory tasks more strongly.

Previous NCERT Book: Mathematics Textbook for Class IX Current NCERT Book: Ganita Manjari Part I
Started with Number Systems Starts with Orienting Yourself: The Use of Coordinates
Had 15 chapters Has 8 chapters in Part I
Had Polynomials as a broader algebra chapter Introduces Linear Polynomials in Chapter 2
Had Linear Equations in Two Variables as a separate chapter Builds linear equations through linear polynomial work
Had Euclid’s Geometry, Lines and Angles, Triangles and Quadrilaterals Uses circle geometry and proof-based reasoning in Chapter 5
Had Constructions as a separate chapter No separate constructions chapter in Part I
Had Heron’s Formula and Surface Areas and Volumes Uses Measuring Space: Perimeter and Area for 2D measurement
Had Statistics as Chapter 14 Statistics does not appear as a separate chapter in Part I
Had Probability as Chapter 15 Probability appears as Chapter 7
Did not have a separate sequences chapter Chapter 8 covers sequences and progressions

Class 9 Maths Syllabus with Chapters and Topics

Class 9 Maths syllabus with chapters is organised through eight areas in Ganita Manjari Part I. Each chapter combines concepts, representations and problem-solving.

Chapter Mathematical Area Main Topic Focus
Chapter 1 Coordinate Geometry Coordinates, distance, midpoint and graph paper
Chapter 2 Algebra Linear polynomials, patterns and graphs
Chapter 3 Numbers Rational numbers, irrational numbers and number line
Chapter 4 Algebraic Reasoning Identities, expansion, simplification and factorisation
Chapter 5 Geometry Circles, chords, arcs, angles and cyclic figures
Chapter 6 Mensuration Perimeter, area, circles and formula derivation
Chapter 7 Probability Chance, outcomes, empirical and theoretical probability
Chapter 8 Sequences AP, GP, recursive rules and visual patterns

This mapping gives a topic view without repeating the chapter list. It also shows the mathematical area behind each chapter.

Representations in Class 9 Maths Syllabus

Ganita Manjari uses multiple representations to build mathematical understanding. This is a major feature of the Class 9 Maths latest syllabus.

Representation Chapters Where It Is Central
Graphical Coordinates, linear polynomials and number line
Algebraic Linear polynomials, identities and progressions
Numerical Numbers, probability, sequences and measurements
Geometric Circles, area, identities and coordinate geometry
Tabular Probability, patterns and sequences
Visual Square root spiral, algebraic identities, circles and fractals

This representation-based design connects ideas across chapters. A sequence can be studied numerically, algebraically and visually.

Class 9 Maths Learning Outcomes

Class 9 Maths learning outcomes in Ganita Manjari connect with reasoning, proof, representation, problem-solving and mathematical communication. The textbook develops these outcomes through examples, exercises, exploration tasks and “Think and Reflect” questions.

Learning Goal Ganita Manjari Syllabus Connection
Mathematical Reasoning Proofs, justifications and argument-based questions
Representation Fluency Pictorial, numerical, algebraic and graphical models
Problem-Solving Practice exercises, end-of-chapter exercises and application tasks
Visualisation Coordinates, square root spiral, identities, circles and mensuration
Algebraic Thinking Linear polynomials, identities and progressions
Geometric Reasoning Circles, chords, arcs, angles and cyclic figures
Quantifying Uncertainty Empirical and theoretical probability
Mathematical Communication Explaining steps, reasoning and patterns in written form

Asterisk Questions in Ganita Manjari Class 9 Maths

Asterisk-marked questions in Ganita Manjari are enrichment questions. They require higher-order thinking and deeper reasoning.

The textbook states that questions and sections marked with an asterisk are not part of formal assessment. They are included for deeper exploration.

Marking Meaning
* Question Enrichment question requiring deeper reasoning
* Section Extended inquiry or project-based exploration
Assessment Status Not included in formal examinations
Learning Value Higher-order thinking, curiosity and independent inquiry

Class 9 Maths Term Wise Syllabus

Class 9 Maths term wise syllabus can follow the order of Ganita Manjari Part I. A balanced split places Chapters 1 to 4 in Term 1 and Chapters 5 to 8 in Term 2.

Term Chapters Covered
Term 1 Orienting Yourself: The Use of Coordinates, Introduction to Linear Polynomials, The World of Numbers, Exploring Algebraic Identities
Term 2 I’m Up and Down, and Round and Round, Measuring Space: Perimeter and Area, The Mathematics of Maybe, Predicting What Comes Next

This split keeps coordinate geometry, algebra and numbers in the first half. Geometry, mensuration, probability and sequences form the second half.

Class 9 Maths Deleted Syllabus

The Class 9 Maths deleted syllabus for 2026-27 is best understood through the current NCERT textbook. Ganita Manjari Part I has 8 chapters, so preparation follows this updated chapter list.

Several chapters from the earlier NCERT Class 9 Maths textbook do not appear as separate chapters in Part I. These include Introduction to Euclid’s Geometry, Lines and Angles, Triangles, Quadrilaterals, Constructions, Heron’s Formula, Surface Areas and Volumes and Statistics.

Some ideas may still appear indirectly through diagrams, reasoning or measurement work. The current textbook sequence is the final reference for the 2026-27 syllabus.

Earlier Chapter Name Current 2026-27 Position
Introduction to Euclid’s Geometry Not a separate chapter in Part I
Lines and Angles Not a separate chapter in Part I
Triangles Not a separate chapter in Part I
Quadrilaterals Not a separate chapter in Part I
Constructions Not a separate chapter in Part I
Heron’s Formula Not a separate chapter in Part I
Surface Areas and Volumes Not a separate chapter in Part I
Statistics Not a separate chapter in Part I
Probability Included as Chapter 7
Sequences and Progressions Included as Chapter 8

NCERT Class 9 Maths Book 2026

The NCERT Class 9 Maths book 2026 is Ganita Manjari: Textbook of Mathematics for Grade 9 Part I. It was first published in April 2026.

The textbook includes 8 chapters and graph paper. It uses real-life contexts, worked examples, practice exercises, end-of-chapter exercises, “Think and Reflect” prompts, enrichment questions and QR-linked resources.

Book Publication Detail Main Contents
Ganita Manjari Part I First Edition April 2026 Class 9 Mathematics textbook
Chapters 8 chapters Coordinates, algebra, numbers, circles, mensuration, probability and sequences
Graph Paper Page 197 Coordinate and graph-based practice
Enrichment Asterisk-marked questions and sections Higher-order thinking and deeper reasoning

MATHEMATICS (IX-X) (CODE NO. 041)

Session 2022-23

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to meet the emerging needs of all categories of students. For motivating the teacher to relate the topics to real life problems and other subject areas, greater emphasis has been laid on applications of various concepts.

The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distances. Carrying out experiments with numbers and forms of geometry, framing hypothesis and verifying these with further observations form inherent part of Mathematics learning at this stage. The proposed curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc.

The teaching of Mathematics should be imparted through activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments.

Objectives

The broad objectives of teaching of Mathematics at secondary stage are to help the learners to:

  • consolidate the Mathematical knowledge and skills acquired at the upper primary stage;
  • acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles and symbols and underlying processes and skills;
  • develop mastery of basic algebraic skills;
  • develop drawing skills;
  • feel the flow of reason while proving a result or solving a problem;
  • apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method;
  • to develop ability to think, analyze and articulate logically;
  • to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases;
  • to develop necessary skills to work with modern technological devices and mathematical software’s.
  • to develop interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns,
  • to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;
  • to develop interest in the subject by participating in related competitions;
  • to acquaint students with different aspects of Mathematics used in daily life;
  • to develop an interest in students to study Mathematics as a

COURSE STRUCTURE CLASS –IX

Units Unit Name Marks
I NUMBER SYSTEMS 10
II ALGEBRA 20
III COORDINATE GEOMETRY 04
IV GEOMETRY 27
V MENSURATION 13
VI STATISTICS & PROBABILITY 06
Total 80

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18) Periods

  1. Review of representation of natural numbers, integers, and rational numbers on the number Rational numbers as recurring/ terminating decimals. Operations on real numbers.
  1. Examples of non-recurring/non-terminating Existence of non-rational numbers (irrational numbers) such as, and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
  2. Definition of nth root of a real
  3. Rationalization (with precise meaning) of real numbers of the type

and (and their combinations) where x and y are natural number and a and b are integers.

  1. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general )

UNIT II: ALGEBRA

  1. POLYNOMIALS (26) Periods

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.

Recall of algebraic expressions and identities. Verification of identities:

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16) Periods

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + 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.

UNIT III: COORDINATE GEOMETRY

COORDINATE GEOMETRY (7) Periods

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.
UNIT IV: GEOMETRY
1. INTRODUCTION TO EUCLID’S GEOMETRY (7) Periods

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example:

(Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

  1. LINES AND ANGLES (15) Periods
  1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the
  2. (Prove) If two lines intersect, vertically opposite angles are
  1. (Motivate) Lines which are parallel to a given line are

TRIANGLES (22) Periods

  1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
  2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
  3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
  4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other (RHS Congruence)
  5. (Prove) The angles opposite to equal sides of a triangle are
  6. (Motivate) The sides opposite to equal angles of a triangle are

4. QUADRILATERALS (13) Periods

  1. (Prove) The diagonal divides a parallelogram into two congruent
  2. (Motivate) In a parallelogram opposite sides are equal, and
  3. (Motivate) In a parallelogram opposite angles are equal, and
  4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and
  5. (Motivate) In a parallelogram, the diagonals bisect each other and
  6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

CIRCLES (17) Periods

1.(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2.(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

  1. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4.(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

5.(Motivate) Angles in the same segment of a circle are equal.

6.(Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

7.(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION

  1. AREAS (5) Periods

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17) Periods

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

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15) Periods

Bar graphs, histograms (with varying base lengths), and frequency polygons.

MATHEMATICS QUESTION PAPER DESIGN

CLASS – IX (2022-23)

Time: 3 Hrs. Max. Marks: 80

 

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
INTERNAL ASSESSMENT 20 MARKS
Pen Paper Test and Multiple Assessment (5+5) 10 Marks
Portfolio 05 Marks
Lab Practical (Lab activities to be done from the prescribed books) 05 Marks

COURSE STRUCTURE CLASS –X

Units Unit Name Marks
I NUMBER SYSTEMS 06
II ALGEBRA 20
III COORDINATE GEOMETRY 06
IV GEOMETRY 15
V TRIGONOMETRY 12
VI MENSURATION 10
VII STATISTICS & PROBABILTY 11
Total 80

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER (15) Periods

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of

UNIT II: ALGEBRA

  1. POLYNOMIALS (8) Periods

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

  1. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.

  1. QUADRATIC EQUATIONS (15) Periods

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

Situational problems based on quadratic equations related to day to day activities to be incorporated.

  1. ARITHMETIC PROGRESSIONS (10) Periods

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY

Coordinate Geometry (15) Periods

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

UNIT IV: GEOMETRY

  1. TRIANGLES (15) Periods

Definitions, examples, counter examples of similar triangles.

  1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same
  2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
  3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are
  4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
  5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are
  6. CIRCLES (10) Periods

Tangent to a circle at, point of contact

  1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
  2. (Prove) The lengths of tangents drawn from an external point to a circle are

UNIT V: TRIGONOMETRY

  1. INTRODUCTION TO TRIGONOMETRY (10) Periods

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.

  1. TRIGONOMETRIC IDENTITIES (15) Periods

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

UNIT VI: MENSURATION

  1. AREAS RELATED TO CIRCLES (12) Periods

Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.

  1. SURFACE AREAS AND VOLUMES (12) Periods

Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

1. STATISTICS (18) Periods
Mean, median and mode of grouped data (bimodal situation to be avoided).
  1. PROBABILITY (10) Periods

Classical definition of probability. Simple problems on finding the probability of an event.

MATHEMATICS-Standard QUESTION PAPER DESIGN CLASS – X (2022-23)

Time: 3 Hours Max. Marks: 80

 

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
INTERNAL ASSESSMENT 20 MARKS
Pen Paper Test and Multiple Assessment (5+5) 10 Marks
Portfolio 05 Marks
Lab Practical (Lab activities to be done from the prescribed books) 05 Marks

MATHEMATICS-Basic QUESTION PAPER DESIGN CLASS – X (2022-23)

Time: 3Hours Max. Marks: 80

 

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

  

 

60

  

 

75
 

2

  

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

  

12

  

15
 

 

 

 

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

  

 

 

 

8

  

 

 

 

10
Total 80 100
INTERNAL ASSESSMENT 20 MARKS
Pen Paper Test and Multiple Assessment (5+5) 10 Marks
Portfolio 05 Marks
Lab Practical (Lab activities to be done from the prescribed books) 05 Marks

PRESCRIBED BOOKS:

  1. Mathematics – Textbook for class IX – NCERT Publication
  2. Mathematics – Textbook for class X – NCERT Publication
  3. Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication
  4. Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication
  5. Laboratory Manual – Mathematics, secondary stage – NCERT Publication
  6. Mathematics exemplar problems for class IX, NCERT
  7. Mathematics exemplar problems for class X, NCERT

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CBSE Class 9 Syllabus

CBSE Class 9 Science Syllabus

CBSE Class 9 Hindi Syllabus

CBSE Class 9 English Syllabus

CBSE Class 9 Social Science Syllabus

FAQs (Frequently Asked Questions)

CBSE Class 9 Maths Syllabus 2026-27 includes 8 chapters from NCERT Ganita Manjari Part I. The chapters cover coordinates, linear polynomials, numbers, algebraic identities, circles, perimeter and area, probability and sequences.

  • The new NCERT Class 9 Maths book is called Ganita Manjari: Textbook of Mathematics for Grade 9 Part I. It was first published in April 2026.

The previous NCERT Class 9 Maths book was titled Mathematics: Textbook for Class IX. It had a 15-chapter structure and began with Number Systems.

Class 9 Maths Ganita Manjari Part I has 8 chapters. The book starts with coordinates and ends with sequences and progressions.

No. Asterisk-marked questions and sections in Ganita Manjari are enrichment material. The textbook states that they are not for formal assessment.

The new syllabus follows Ganita Manjari Part I instead of the earlier Mathematics: Textbook for Class IX. It has a new title, 8 chapters in Part I, stronger visual reasoning and a new chapter on sequences and progressions.