Class 9 Mathematics

Learn about rational and irrational numbers, real numbers, their properties, representation on number line, and operations on real numbers.

Key Topics:

• Introduction to Number Systems
• Irrational Numbers
• Real Numbers and Their Decimal Expansions
• Representing Real Numbers on the Number Line
• Operations on Real Numbers
• Laws of Exponents for Real Numbers
• Rationalization of Denominators

Understand polynomials in one variable, degree of polynomial, zeros of polynomial, remainder theorem, factorization, and algebraic identities.

Key Topics:

• Introduction to Polynomials
• Polynomials in One Variable
• Zeros of a Polynomial
• Remainder Theorem
• Factor Theorem
• Factorization of Polynomials
• Algebraic Identities

Introduction to Cartesian plane, plotting points, coordinates, quadrants, and finding distance between two points.

Key Topics:

• Introduction to Coordinate Geometry
• Cartesian System
• Plotting Points in the Plane
• Coordinates of a Point
• Four Quadrants
• Abscissa and Ordinate
• Origin and Axes

Solving linear equations with two variables, graphical representation of linear equations, and equations of lines parallel to axes.

Key Topics:

• Introduction to Linear Equations
• Linear Equations in Two Variables
• Solution of a Linear Equation
• Graph of a Linear Equation in Two Variables
• Equations of Lines Parallel to x-axis and y-axis

Learn about Euclid's definitions, axioms, postulates, and the axiomatic approach to geometry.

Key Topics:

• Introduction to Euclid's Geometry
• Euclid's Definitions
• Euclid's Axioms
• Euclid's Postulates
• Equivalent Versions of Euclid's Fifth Postulate

Study types of angles, parallel lines, transversals, angle relationships, and theorems on angles.

Key Topics:

• Basic Terms and Definitions
• Intersecting Lines and Non-intersecting Lines
• Pairs of Angles
• Parallel Lines and a Transversal
• Corresponding Angles
• Alternate Interior Angles
• Alternate Exterior Angles
• Interior Angles on the Same Side of Transversal
• Lines Parallel to the Same Line
• Angle Sum Property of a Triangle

Learn about congruence of triangles, criteria for congruence (SSS, SAS, ASA, RHS), properties of triangles, and inequalities in triangles.

Key Topics:

• Introduction to Triangles
• Congruence of Triangles
• Criteria for Congruence of Triangles
• SSS Congruence Rule
• SAS Congruence Rule
• ASA Congruence Rule
• RHS Congruence Rule
• Some Properties of a Triangle
• Inequalities in a Triangle

Study properties of parallelograms, rectangles, rhombus, squares, trapeziums, and the mid-point theorem.

Key Topics:

• Introduction to Quadrilaterals
• Angle Sum Property of a Quadrilateral
• Types of Quadrilaterals
• Properties of a Parallelogram
• Another Condition for a Quadrilateral to be a Parallelogram
• The Mid-point Theorem
• Properties of Rectangle
• Properties of Rhombus
• Properties of Square
• Properties of Trapezium

Learn about areas of parallelograms and triangles on the same base and between the same parallels.

Key Topics:

• Introduction to Areas
• Figures on the Same Base and Between the Same Parallels
• Parallelograms on the Same Base and Between the Same Parallels
• Triangles on the Same Base and Between the Same Parallels
• Relationship Between Area of Parallelogram and Triangle

Study circle properties, chords, arcs, angles subtended by chords, cyclic quadrilaterals, and circle theorems.

Key Topics:

• Introduction to Circles
• Chords of a Circle
• Equal Chords and Their Distances from the Centre
• Angle Subtended by an Arc of a Circle
• Angle Subtended by a Chord at a Point
• Cyclic Quadrilaterals
• Perpendicular from the Centre to a Chord

Learn geometric constructions using compass and ruler - bisecting angles, perpendiculars, and constructing triangles.

Key Topics:

• Introduction to Constructions
• Basic Constructions
• Construction of Bisector of a Line Segment
• Construction of Bisector of an Angle
• Construction of Perpendicular Lines
• Construction of an Angle Equal to a Given Angle
• Some Constructions of Triangles
• Construction of Triangle Given Base, Base Angle and Sum of Other Two Sides
• Construction of Triangle Given Base, Base Angle and Difference of Other Two Sides

Application of Heron's formula to find area of triangles and quadrilaterals when sides are given.

Key Topics:

• Introduction to Heron's Formula
• Area of a Triangle - by Heron's Formula
• Application of Heron's Formula in Finding Areas of Quadrilaterals

Calculate surface area and volume of cubes, cuboids, cylinders, cones, spheres, and hemispheres.

Key Topics:

• Introduction to Surface Areas and Volumes
• Surface Area of a Cuboid and a Cube
• Surface Area of a Right Circular Cylinder
• Surface Area of a Right Circular Cone
• Surface Area of a Sphere
• Volume of a Cuboid
• Volume of a Cylinder
• Volume of a Right Circular Cone
• Volume of a Sphere
• Volume of a Hemisphere

Collection and presentation of data, mean, median, mode, graphical representation of data, and frequency distribution.

Key Topics:

• Introduction to Statistics
• Collection of Data
• Presentation of Data
• Graphical Representation of Data
• Bar Graphs
• Histograms
• Frequency Polygons
• Measures of Central Tendency
• Mean (Arithmetic Mean)
• Median
• Mode

Introduction to probability, experimental and theoretical probability, random experiments, outcomes, and events.

Key Topics:

• Introduction to Probability
• Random Experiments
• Outcomes and Events
• Experimental Probability
• Theoretical Probability
• Probability of an Event
• Equally Likely Outcomes
• Complementary Events