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Class 9 Maths: Ganita Manjari

Browse 14 chapter guides, then practise with worksheets and unit tests.

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14 Chapter Guides
Choose a chapter guide 14 guide pages · Parts 1 & 2
Chapter 01 Unit 3: Coordinate Geometry

The Use of Coordinates

Basic Definitions & Glossary Cartesian Plane & Quadrants Distance & Reflections
Notes
Open chapter notesHistorical Evolution & Prime Meridian Coordinate GridsSettling In: Practical Floor Mapping & Spatial DimensionsThe 2-D Cartesian Coordinate System & QuadrantsDistance Between Two Points & Geometric Reflections
NCERT
Exercise 1-1Exercise 1-2Exercise 1-3Exercise 1-4Exercise 1-5
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 02 Unit 2: Algebra

Introduction to Linear Polynomials

Algebraic Expressions & Variables Linear Equations & Patterns Linear Growth vs Decay General Form: y = ax + b
Notes
Open chapter notesAlgebraic Expressions, Variables & Polynomial DegreesLinear Polynomials, Equations & Input-Output FunctionsExploring Linear Patterns & Generalizing Terms (\( 2n - 1 \))Linear Growth vs. Linear DecayThe Master Equation of Linear Relationships: \( y = ax + b \)Visualising Linear Relationships: Graphing & Slopes
NCERT
Exercise 2-1Exercise 2-2Exercise 2-3Exercise 2-4Exercise 2-5Exercise 2-6End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 03 Unit 1: Number Systems

The World of Numbers

Dawn of Counting & Śūnya Integers, Fortunes & Debts Fractions & Density Proof of √2 Irrationality
Notes
Open chapter notesThe Dawn of Mathematics: The Human Need to CountThe Revolution of Śhūnya: When Nothing Became SomethingIntegers (\( \mathbb{Z} \)): Fortunes (Dhana) & Debts (Ṛiṇa)Fractions, Rational Numbers (\( \mathbb{Q} \)) & DensityIrrational Numbers & Proof of \( √ 2 \) IrrationalityReal Numbers (\( \mathbb{R} \)): Decimals & Cyclic Patterns
NCERT
Exercise 3-1Exercise 3-2Exercise 3-3Exercise 3-4Exercise 3-5End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 04 Unit 2: Algebra

Exploring Algebraic Identities

Consecutive Square Patterns Geometric Proof of (a+b)² Trinomial Square (a+b+c)² Splitting Middle Term & Tiles
Notes
Open chapter notesIntroduction: The Magic of Consecutive Square PatternsVisualising Identities: Geometric Proof of \( (a + b)^2 \)Factorisation & The Identity \( (a - b)^2 \)Trinomial Square \( (a + b + c)^2 \) & Śhrīdharāchārya's MethodFactorisation Using Algebra Tiles & Splitting Middle TermVolumetric Cubes: Binomial Cubes & Sum/Difference of CubesSimplifying Rational Expressions & Real-World Problems
NCERT
Exercise 4-1Exercise 4-2Exercise 4-3Exercise 4-4Exercise 4-5End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 05 Unit 4: Geometry

Circles

Circle & Concept of Locus Reflection & Rotational Symmetry Chords & Subtended Angles Perpendiculars & Baudhāyana Formula
Notes
Open chapter notesDefinitions: Circle & Concept of LocusSymmetries of a Circle: Reflection & RotationHow Many Circles Pass Through Given Points?Chords and the Angles They SubtendPerpendiculars, Chord Distances & Baudhāyana-Pythagoras FormulaAngles Subtended by an Arc (Inscribed Angle Theorem)Concyclicity & Cyclic Quadrilaterals
NCERT
Exercise 5-1Exercise 5-2Exercise 5-3Exercise 5-4Exercise 5-5Exercise 5-6End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 06 Unit 5: Mensuration

Measuring Space: Perimeter and Area

400m Track Mystery & Staggers History of π & Circumference Equal Semicircle Paths Paradox Parallelograms & Median Area Theorem
Notes
Open chapter notesPerimeter of a Shape & The 400m Athletics Track MysteryThe Circumference/Diameter Ratio & The History of \( π \)Length of an Arc & Athletics Track Stagger FormulasPerimeter Paradox: The Equal Semicircle PathsArea of Parallelogram, Triangle & The Median Area TheoremHeron’s Formula & Brahmagupta’s Cyclic 4-Gon FormulaBaudhāyana’s Śulbasūtra: Squaring a Rectangle (800 BCE)Area of a Circle & Sector (Nīlakaṇṭha's Visual Proof)
NCERT
Exercise 6-1Exercise 6-2Exercise 6-3End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 07 Unit 6: Statistics & Probability

Introduction to Probability

Randomness & Probability Scale (0 to 1) Experimental vs Theoretical Law of Large Numbers Sample Spaces & Events
Notes
Open chapter notesWhat is Probability & What is Randomness?The Probability Scale (0 to 1)Measuring Probability Objectively: Experimental & TheoreticalSampling, The Law of Large Numbers & Gambler's FallacyElements of Probability: Sample Spaces & EventsTree Diagrams for Multi-Step Experiments
NCERT
Exercise 7-1Exercise 7-2Exercise 7-3Exercise 7-4End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 08 Unit 2: Algebra

Sequences and Progressions

Patterns & Number Sequences Explicit & Recursive Rules Arithmetic Progressions (AP) Geometric Progressions (GP)
Notes
Open chapter notesWhat is a Sequence? Patterns in NumbersExplicit vs. Recursive Rules & The Virahānka–Fibonacci SequenceArithmetic Progressions (AP): Linear GrowthSum of the First n Natural Numbers (Āryabhaṭa, 499 CE)Geometric Progressions (GP): Exponential GrowthFun with Fractals: The Sierpiński Triangle & Bouncing Balls
NCERT
Exercise 8-1Exercise 8-2Exercise 8-3End-of-chapter exercise
Sheets
FoundationPracticeChallenge
Practice
Interactive practicePractice worksheet
Chapter 09 Unit 4: Geometry · Proof

Propositions and Their Converses

If–Then Statements Converses Proofs & Counterexamples Necessary & Sufficient Conditions
Notes
Open chapter notes
Exercises
Exercise Set 9.1
Sheets
FoundationPracticeChallenge
Mini Test
Mini test
Chapter 10 Unit 6: Statistics & Probability

How Quantities Combine: Understanding Data

Weighted Averages Mixtures & Percentages Frequency Tables Charts & Data Interpretation
Notes
Open chapter notes
Exercises
Exercise 10-1Exercise 10-2Exercise 10-3Exercise 10-4Exercise 10-5End-of-chapter exercises
Sheets
FoundationPracticeChallenge
Mini Test
Mini test
Chapter 11 Cross-Unit Computational Thinking

The World of Algorithms

Step-by-Step Procedures Euclid’s Algorithm GCD & LCM Primes & Factorisation
Notes
Open chapter notes
Exercises
Exercise 11-1Exercise 11-2Exercise 11-3End-of-chapter exercises
Sheets
FoundationPracticeChallenge
Mini Test
Mini test
Chapter 12 Geometry

Quadrilaterals

Parallelograms & Proofs Midpoint Theorem Centroid & Symmetry Tiling & Polygons
Notes
Open chapter notes
Exercises
Exercise 12-1Exercise 12-2Exercise 12-3Exercise 12-4End-of-chapter exercises
Sheets
FoundationPracticeChallenge
Mini Test
Mini test
Chapter 13 Algebra

Two Variables, One Line

Linear Equations & Graphs Slope & Intercepts Substitution & Elimination Nature of Solutions
Notes
Open chapter notes
Exercises
Exercise 13-1Exercise 13-2Exercise 13-3Exercise 13-4Exercise 13-5End-of-chapter exercises
Sheets
FoundationPracticeChallenge
Mini Test
Mini test
Chapter 14 Mensuration

Math of Space: Surface Area and Volume

Cubes & Cuboids Cylinders & Cones Spheres & Hemispheres Capacity & Estimation
Notes
Open chapter notes
Exercises
Exercise 14-1Exercise 14-2Exercise 14-3Exercise 14-4End-of-chapter exercises
Sheets
FoundationPracticeChallenge
Mini Test
Mini test
Unit Mastery

Unit-Wise Practice Tests

Two practice papers for each of the six units in the 2026–27 CBSE syllabus. Period counts are teaching time, not exam weightage.

Unit 01 12 Periods

Number System

Rational numbers and density, decimal expansions, irrationality of √2 and √3, number-line constructions and the square root spiral.

Test 1 Test 2
Unit 02 66 Periods

Algebra

Linear polynomials and graphs, identities and factorisation, AP/GP, fractals and Hanoi, and paired linear equations with graphical, substitution and elimination methods.

Test 1 Test 2
Unit 03 6 Periods

Coordinate Geometry

Cartesian coordinates, grid floor plans, distance and midpoint formulas, collinearity and right-triangle checks.

Test 1 Test 2
Unit 04 69 Periods

Geometry

Euclid and constructions, lines and angles, triangle congruence and converses, quadrilateral proofs and symmetry, tiling and circle theorems.

Test 1 Test 2
Unit 05 27 Periods

Mensuration

Perimeter, arcs, sectors and segments, Heron and Brahmagupta, squaring a rectangle, and surface areas and volumes including pyramids.

Test 1 Test 2
Unit 06 24 Periods

Statistics & Probability

Investigative data, weighted averages, stacked bar graphs, mean/median/mode, empirical and theoretical probability, trees, tables and simulation.

Test 1 Test 2

View unit scopes and papers · Earlier-edition unit papers

Annual Exam Simulation

Previous-Syllabus Full-Length Mock Papers

Complete 80-mark, 3-hour annual examination question papers with detailed answer explanations.

Annual Model Test - 01

Complete annual syllabus test paper with MCQs, short answers, and long answer proofs.

80 Marks 3 Hours 38 Questions
Start Model Test 1

Annual Model Test - 02

Standard difficulty annual examination test with case studies and geometry problems.

80 Marks 3 Hours 38 Questions
Start Model Test 2

Full Mock Test - 01

Comprehensive test paper for final practice with timed interactive answering.

80 Marks 3 Hours 38 Questions
Start Full Mock 1

Frequently Asked Questions

What study materials are available for Class 9 Maths?

The hub links to 14 chapter guides, worksheets, worked examples, exercise solutions and 12 unit tests. Geometry foundations and earlier-edition practice are listed separately.

Are the Class 9 Maths NCERT solutions free?

Yes. Class 9 notes and exercise solutions on SJMaths are free to access.

How can I practice for Class 9 Maths exams?

Read a guide, try its worked examples, then practise with exercises, worksheets and unit tests. Use the geometry worksheet for Euclid, angles and triangle congruence.