CBSE Class 9 Mathematics: chapter-wise study guide

Orienting Yourself: The Use of Coordinates

• The Cartesian Plane: Quadrants, Axes and Reflections
• Distance Formula, Midpoint and Collinear Points

Introduction to Linear Polynomials

• Finding Linear Relationships y = ax + b and Their Graphs
• Polynomials in One Variable, Degree and Value

The World of Numbers

• Decimal Expansions and Converting Recurring Decimals to p/q
• Irrational Numbers, Proofs and the Square Root Spiral

Exploring Algebraic Identities

• Cubic Identities and the Sum of Three Cubes
• Factorising Using Algebraic Identities

I'm Up and Down, and Round and Round

• Angles in a Circle and Cyclic Quadrilaterals
• Chord Theorems and Distance from the Centre

The chapter on circles; CBSE calls it 'Circles'.

Measuring Space: Perimeter and Area

• Circumference, Arc Length, Sector and Segment
• Heron's Formula and Areas of Quadrilaterals

The Mathematics of Maybe: Introduction to Probability

• Experimental and Theoretical Probability
• Sample Space, Events and Tree Diagrams

Predicting What Comes Next: Exploring Sequences and Progressions

• Arithmetic Progressions: nth Term and Sum of Terms
• Geometric Progressions, Recursive Rules and Fractal Patterns

Propositions and their Converses

• If-Then Statements, Converses and Counterexamples
• Isosceles Triangles and the Converse of the Pythagoras Theorem

Covers the 'propositions and their converse' part of CBSE's 'Triangles – Congruence Theorems'.

How Quantities Combine: Understanding Data

• Combined Mean and Weighted Mean
• Mixtures, Concentration and Percentage Shares

The World of Algorithms

• Column Addition, Lists and the Efficiency of Algorithms
• Computing the GCD: Definition, Euclid's Subtraction and Āryabhaṭa's Division

Not in the annual exam

Not in CBSE's Class IX course structure (which was released before Part II); ask the school whether it is examined. Its ideas support the computational-thinking competencies (CG-9).

Quadrilaterals

• The Midpoint Theorem, Its Converse and Varignon's Parallelogram
• Properties of a Parallelogram and Tests for Special Quadrilaterals

Two Variables, One Line

• Linear Equations in Two Variables: Solutions, Slope and Graph
• Solving Pairs of Linear Equations: Substitution, Elimination and Graphs

Math of Space: Surface Area and Volume

• Cones, Spheres, Hemispheres and Recasting Solids
• Cuboids, Cubes and Cylinders: Surface Area and Volume

Introduction to Euclid's Geometry: Axioms and Postulates

• Euclid's Definitions and Axioms (Common Notions)
• Euclid's Postulates, the Fifth Postulate and Playfair's Axiom

In the CBSE syllabus but not a chapter of Ganita Manjari.

Lines and Angles

• Linear Pairs, Vertically Opposite Angles and Angles at a Point
• Parallel Lines, Transversals and the Angle Sum of a Triangle

In the CBSE syllabus but not a chapter of Ganita Manjari.

Triangles: Congruence Theorems

• SAS, ASA and AAS Congruence with CPCT
• SSS and RHS Congruence, Equidistant Points and Failed Tests

In the CBSE syllabus; only its 'propositions and converses' part has an NCERT chapter (Chapter 9).