Mathematics (English Medium) ICSE Class 9 CISCE Syllabus 2026-27

• Introduction
• Important Terms
• Formula: Simple Interest 
• Calculation of Interest
• Examples

( a + b )² = a² + 2ab + b² .

1.  Expansion of ( x + a ) ( x + b ) :   

• ( x + a ) ( x + b ) = x² + ( a + b ) x + ab
  
  
• ( x + a ) ( x - b ) = x² + ( a - b ) x - ab
  
  
• ( x - a ) ( x + b ) = x² - ( a - b ) x - ab
  
  
• ( x - a ) ( x - b ) = x² - ( a + b ) x + ab

2. Expansion of ( a + b + c )² :

• ( a + b + c )² = a² + b² + c² + 2 ( ab + bc + ca )
  
  
• ( a + b - c )² = a² + b² + c² + 2 ( ab - bc - ca )
  
  
• ( a - b + c )² = a² + b² + c² - 2 ( ab + bc - ca )
  
  
• ( a - b - c )² = a² + b² + c² - 2 ( ab - bc + ca )

• ( x + a ) ( x + b ) ( x + c ) = x³ + ( a + b + c ) x³ + ( ab + bc + ca ) x + abc 
  
  
• ( a + b ) ( a² - ab + b² ) = a³ + b³
  
  
• ( a - b ) ( a² + ab + b² ) = a³ - b³
  
  
• ( a + b + c ) ( a² + b2 + c² - ab - bc - ca ) = a³ + b³ + c³ - 3abc

• Introduction
• Example 1
• Example 2
• Example 3
• Key Points Summary

• ( a x b )^m = a^m x b^m and `(a/b)^m = a^m/b^m`
  
  
• If a ≠ 0 and n is a positive integer, then `nsqrta` = a^1/n 
  
  
• `a^(m/n) = nsqrt (a^m) ; Where a ≠ 0. `
  
  
• For any non - zero number a,
  
  `a^n = 1/( a^-n ) and a^(-n) = 1/(a^n)`  
  
  
• Any non - zero number raised to the power zero is always equal to unity ( i.e., 1)

• Definition:Triangle
• Parts of a Triangle
• Basic Properties of a Triangle
• Key Points Summary

• If all the sides of a triangle are of  different lengths, its angles are also of different measures in such a way that, the greater side has greater angle opposite to it.
  
  
• If all the angles of a triangle have different measures, its sides are also of different lengths in such a way that, the greater angle has greater side opposite to it.
  
  
• If any two sides of a triangle are equal, the angles opposite to them are also equal. Conversely, if any two angles of a triangle are equal, the sides opposite to them are also equal.
  
  
• If all the sides of a triangle are equal, all its angles are also equal. Conversely, if all the angles of a triangle are equal, all its sides are also equal.

• Median : The median of a triangle, corresponding to any side, is the line joining the mid-point of that side with the opposite vertex.
  
  
• Centroid : The point of intersection of the medians is called the centroid of the triangle.
  
  
• Altitude : An altitude of a triangle, corresponding to any side, is the length of the perpendicular drawn from the opposite vertex to that side.
  
  
• Orthocentre : The point of intersection of the altitudes of a triangle is called the orthocentre.
  
  
• Corollary 1 : If one side of a triangle is produced, the exterior angle so formed is greater than each of the interior opposite angles.
  
  
• Corollary 2 : A triangle cannot have more than one right angle.
  
  
• Corollary 3 : A triangle cannot have more than one obtuse angle.
  
  
• Corollary 4 : In a right angled triangle, the sum of the other two angles ( acute angles ) is 90°.
  
  
• Corollary 5 : In every triangle, at least two angles are acute.
  
  
• Corollary 6 : If two angles of a traingle are equal to two angles of any other triangle, each to each, then the third angles of both the triangles are also equal. 

• Introduction
• Classification of Triangles based on Sides
• Key Points Summary

• Theorem: If Two Sides of a Triangle Are Equal, the Angles Opposite to Them Are Also Equal.

• Theorem: If Two Angles of a Triangle Are Equal, the Sides Opposite to Them Are Also Equal.

• If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.

• If all the sides and all the angles of a polygon are equal, it is called a regular polygon.
• Sum of interior angles of an 'n' sided polygon ( whether it is regular or not) = ( 2n - 4 )rt. angles and sum of its exterior angles = 4 right angles = 360°
• At each vertex of every polygon, Exterior angle + Interior angle = 180°.
• Each interior angle of a regular polygon = `[( 2n - 4 ) "rt. angles"]/[n] = [( 2n - 4 ) xx 90°]/n`
• Each exterior

• Rectilinear means along a straight line or in a straight line or forming a straight line.
• A plane figure bounded by straight lines is called a rectilinear figure.
• A closed plane figure, bounded by at least three line segments, is called a polygon.

• Regular Polygon
• Irregular Polygon
• Convex Polygon
• Concave Polygon
• Simple Polygon
• Complex Polygon

• To construct a quadrilateral, whose four sides and one angle are given.
• To construct a quadrilateral, whose three sides and two consecutive angles are given.
• To construct a quadrilateral, whose four sides and one diagonal are given.
• To construct a quadrilateral, whose three sides and two diagonals are given.
• To construct a quadrilateral if two adjacent sides and any three angle are given.

1. To construct a trapezium ABCD, whose four sides are given.

Method 1 : Each interior angle of a regular hexagon is 120° and its opposite sides are parallel.

Method 2 : The length of the side of a regular hexagon is equal to the radius of its circumcircle.

Method 3 : The angle subtended by each side of a regular hexagon at the centre of its circumcircle is `(360°)/6 = 60°`

• Introduction
• Formula: Area
• The Standard Unit of Area
• Example

• Parallelograms on the same base and between the same parallels are equal in area.
• Corollary : The area of a parallelogram is equal to the area of a rectangle on the same base and between the same parallels.
• The area of a triangle is half that of a parallelogram on the same base and between the same parallels.
• Triangles on the same base and between the same parallels are equal in area.
• Corollaries : 
  1. Parallelograms on equal bases and between the same parallels are equal in area.
  2. Area of a triangle is half the area of the parallelogram if both are on equal bases and between the same parallels.
  3. Two triangles are equal in area if they are on the equal bases and between the same parallels.

• Introduction
• Definition: Circle
• Definition: Radius
• Definition: Diameter
• Definition: Chord
• Example
• Real-Life Applications
• Key Points Summary

• Introduction
• Formation of Arcs
• Minor Arc
• Major Arc
• Key Points Summary

• Introduction
• Types of Segments
• Key Points Summary

• Introduction
• Types of Sectors
• The Quadrant
• Key Points Summary

• Definition: Constants
• Definition: Variables
• Identifying Terms
• Real-Life Application
• Key Points Summary

• Ungrouped Frequency Distribution Table
• Grouped Frequency Distribution Table

• Introduction
• Frequency Distribution & Data Arrangement
• Structure of a Frequency Distribution Table
• Example
• Real-life Applications
• Key Points Summary

1. Histogram
2. Frequency Polygon

• Introduction
• Formula: Perimeter
• Units of Perimeter
• Example 1
• Example 2
• Key Points Summary

• Definition: Cylinder
• Properties of a Cylinder
• Activity 1
• Activity 2

• Cost = Rate x Quantity

• Volume = Area of cross - section x length
• Surface area ( excluding cross - section ) = Perimeter of cross - section x length

• The volume of water that flows in unit time = Area of cross-section x speed of flow of water.

• Co-ordinate Axes
• Coordinates of a Point
• Important Results

• Definition: Graph
• Graph Paper
• X-axis and Y-axis
• Use of Scale

• Slope of a Straight line
• Slopes of parallel lines
• Slopes of perpendicular lines

• y = mx+c

• Introduction
• Definition: Circumcircle
• Definition: Circumcenter
• Definition: Circumradius
• Step-by-Step Construction
• Position of Circumcenter in Different Triangles
• Key Points Summary

• Profit Percentage
• Loss Percentage
• Formula
• Understanding Profit or Loss Percentage with Example

• Introduction
• Construction 1: Three Sides Given (SSS)
• Construction 2: Two Sides and Included Angle Given (SAS)
• Construction 3: Two Angles and the Included Side Given (ASA)
• Key Points Summary

• Corresponding Sides
• Corresponding Angles