CISCE ICSE Class 9 Mathematics Syllabus - Free PDF Download
CISCE Syllabus 2026-27 ICSE Class 9: The CISCE ICSE Class 9 Mathematics Syllabus for the examination year 2026-27 has been released by the Council for the Indian School Certificate Examinations, CISCE. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2026-27 CISCE ICSE Class 9 Mathematics Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new CISCE syllabus to prepare for their annual exam properly.
The detailed CISCE ICSE Class 9 Mathematics Syllabus for 2026-27 is below.
Academic year:
CISCE ICSE Class 9 Mathematics Revised Syllabus
CISCE ICSE Class 9 Mathematics Course Structure 2026-27 With Marking Scheme
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Syllabus
1 Rational and Irrational Numbers
- Rational Numbers
- Properties of Rational Numbers
- Decimal Representation of Rational Numbers
- Irrational Numbers and Proof of Irrationality
- Concept of Real Numbers
- Surds
- Rationalisation of Surds
- Simplifying an Expression by Rationalization of the Denominator
2 Compound Interest [Without Using Formula]
- Calculation of Interest
- Introduction
- Important Terms
- Formula: Simple Interest
- Calculation of Interest
- Examples
- Concept of Compound Interest
3 Compound Interest [Using Formula]
- Concept of Compound Interest
- Inverse Formula
- Miscellaneous Problem
- When the Interest is Compounded Half Yearly
- When the Time is Not an Exact Number of Years and the Interest is Compounded Yearly
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
4 Expansions
- Algebraic Identities
( a + b )2 = a2 + 2ab + b2 .
- Expansion of (a + b)3
- Expansion of Formula
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 ) = x2 + ( a + b ) x + ab
- Special Product
- ( 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
- ( x + a ) ( x + b ) ( x + c ) = x3 + ( a + b + c ) x3 + ( ab + bc + ca ) x + abc
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
5 Factorisation
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation of a Quadratic Trinomial by Splitting the Middle Term
- Method of Factorisation : Difference of Two Squares
- Method of Factorisation : the Sum Or Difference of Two Cubes
6 Simultaneous (Linear) Equations [Including Problems]
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Method of Elimination by Equating Coefficients
- Equations Reducible to Linear Equations
- Simultaneous linear equations
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
- Word Problems on Linear Equations
- Introduction
- Example 1
- Example 2
- Example 3
- Key Points Summary
- Pair of Linear Equations in Two Variables
7 Indices [Exponents]
- Laws of Exponents
- Handling Positive, Fraction, Negative and Zero Indices
- ( a x b )m = am x bm and `(a/b)^m = a^m/b^m`
- If a ≠ 0 and n is a positive integer, then `nsqrta` = a1/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)
- ( a x b )m = am x bm and `(a/b)^m = a^m/b^m`
- Simplification of Expressions
- Solving Exponential Equations
8 Logarithms
- Introduction of Logarithms
- Interchanging Logarithmic and Exponential Forms
- Logarithmic to Exponential
- Exponential to Logarithmic
- Laws of Logarithm
- Product Law
`log_a (mxxn) = log_a (m) + log_a (n)`
- Quotient Law
`log_a (m/n) = log_a (m) - log_a (n)`
- Power Law
`log_a (m)^n = nlog_a (m)`
- Product Law
- Expansion of Expressions with the Help of Laws of Logarithm
- More About Logarithm
9 Triangles [Congruency in Triangles]
- Basic Concepts of Triangles
- Definition:Triangle
- Parts of a Triangle
- Basic Properties of a Triangle
- Key Points Summary
- Relation Between Sides and Angles of Triangle
- 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.
- 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.
- Important Terms of Triangle
- 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.
- Median : The median of a triangle, corresponding to any side, is the line joining the mid-point of that side with the opposite vertex.
- Congruence of Triangles
- Criteria for Congruence of Triangles
10 Isosceles Triangles
- Classification of Triangles based on Sides
- Introduction
- Classification of Triangles based on Sides
- Key Points Summary
- Isosceles Triangles Theorem
- Theorem: If Two Sides of a Triangle Are Equal, the Angles Opposite to Them Are Also Equal.
- Converse of Isosceles Triangle Theorem
- Theorem: If Two Angles of a Triangle Are Equal, the Sides Opposite to Them Are Also Equal.
11 Inequalities
- Inequalities in a Triangle
- If two sides of a triangle are unequal, the greater side has the greater angle opposite to it.
- If Two Angles of a Triangle Are Unequal, the Greater Angle Has the Greater Side Opposite to It.
- Of All the Lines, that Can Be Drawn to a Given Straight Line from a Given Point Outside It, the Perpendicular is the Shortest.
- Corollary 1 : The sum of the lengths of any two sides of a triangle is always greater than the third side.
- Corollary 2 : The difference between the lengths of any two sides of a triangle is always less than the third side.
12 Mid-point and Its Converse [ Including Intercept Theorem]
- Theorem of Midpoints of Two Sides of a Triangle
- Equal Intercept Theorem
- If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
13 Pythagoras Theorem [Proof and Simple Applications with Converse]
- Right-angled Triangles and Pythagoras Property
- Advanced Regular Polygon
- 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
14 Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
- Introduction of Rectilinear Figures
- 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.
- Classification of Polygons
- Regular Polygon
- Irregular Polygon
- Convex Polygon
- Concave Polygon
- Simple Polygon
- Complex Polygon
- Diagonal Properties of Different Kinds of Parallelograms
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of Rectangle
- Properties of a Square
15 Construction of Polygons (Using Ruler and Compass Only)
- Constructing a Quadrilateral
- 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.
- Construction of Parallelograms
- Construction of Trapezium
- To construct a trapezium ABCD, whose four sides are given.
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Square: Properties and Construction
- To Construct a Regular Hexagon
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°`
16 Area Theorems [Proof and Use]
- Concept of Area
- Introduction
- Formula: Area
- The Standard Unit of Area
- Example
- Figures Between the Same Parallels
- 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.
- Triangles with the Same Vertex and Bases Along the Same Line
17 Circle
- Basic Concept of Circle
- Introduction
- Definition: Circle
- Definition: Radius
- Definition: Diameter
- Definition: Chord
- Example
- Real-Life Applications
- Key Points Summary
- Chord
- Arc of the Circle
- Introduction
- Formation of Arcs
- Minor Arc
- Major Arc
- Key Points Summary
- Theorems on Angles in a Circle
- Segment of a Circle
- Introduction
- Types of Segments
- Key Points Summary
- Sector of a Circle
- Introduction
- Types of Sectors
- The Quadrant
- Key Points Summary
18 Statistics
- Concepts of Statistics
- Constants and Variables in Mathematics
- Definition: Constants
- Definition: Variables
- Identifying Terms
- Real-Life Application
- Key Points Summary
- Tabulation of Data
- Frequency
- Frequency Distribution Table
- Ungrouped Frequency Distribution Table
- Grouped Frequency Distribution Table
- Class Intervals and Class Limits
- Cumulative Frequency and Cumulative Frequency Table
- Frequency Distribution and Its Applications
- Introduction
- Frequency Distribution & Data Arrangement
- Structure of a Frequency Distribution Table
- Example
- Real-life Applications
- Key Points Summary
- Graphical Representation of Continuous Frequency Distribution
- Histogram
- Frequency Polygon
19 Mean and Median (For Ungrouped Data Only)
- Mean of Grouped Data
- Properties of Mean
20 Area and Perimeter of Plane Figures
- Concept of Perimeter
- Introduction
- Formula: Perimeter
- Units of Perimeter
- Example 1
- Example 2
- Key Points Summary
- Perimeter of Triangle
- Some Special Types of Triangles - Equilateral and Isosceles Triangles
- Area of a General Quadrilateral
- Circumference of a Circle
- Area of Circle
21 Solids [Surface Area and Volume of 3-d Solids]
- Solid Figures
- Surface Area of a Cuboid
- Surface Area of a Cube
- Mensuration of Cylinder
- Definition: Cylinder
- Properties of a Cylinder
- Activity 1
- Activity 2
- Cost of an Article
- Cost = Rate x Quantity
- Cross Section of Solid Shapes
- Volume = Area of cross - section x length
- Surface area ( excluding cross - section ) = Perimeter of cross - section x length
- Flow of Water ( or any other liquid )
- The volume of water that flows in unit time = Area of cross-section x speed of flow of water.
22 Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and Their Reciprocals]
- Concept of Perpendicular, Base, and Hypotenuse in a Right Triangle
- Notation of Angles
- Trigonometric Ratios
- Relation Among Trigonometric Ratios
23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
- Trigonometric Ratios of Specific Angles
- Trigonometric Equation Problem and Solution
24 Solution of Right Triangles [Simple 2-d Problems Involving One Right-angled Triangle]
- Solution of Right Triangles
25 Complementary Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometrical Ratios of Complementary Angles
- Complimentary Angles for Tangent ( Tan ) and Contangency ( Cot )
- Complimentary Angles for Secant ( Sec ) and Cosecant ( Cosec )
26 Co-ordinate Geometry
- Dependent and Independent Variables
- Ordered Pair
- Cartesian Coordinate System
- Co-ordinate Geometry
- Co-ordinate Axes
- Coordinates of a Point
- Important Results
- Quadrants and Sign Convention
- Plotting of Points
- Concept of Graph
- Definition: Graph
- Graph Paper
- X-axis and Y-axis
- Use of Scale
- Graphs of Linear Equations
- Equally Inclined lines
- Slope of a Straight line
- Slopes of parallel lines
- Slopes of perpendicular lines
- Forms of the Equation of a Straight Line
- y = mx+c
27 Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
28 Distance Formula
- Distance Formula
- Circumcircle of a Triangle
- Introduction
- Definition: Circumcircle
- Definition: Circumcenter
- Definition: Circumradius
- Step-by-Step Construction
- Position of Circumcenter in Different Triangles
- Key Points Summary
29 Profit , Loss and Discount
- Concept of Discount
- To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given
- To Find S.P., When C.P. and Gain (Or Loss) Percent Are Given
- Profit or Loss as a Percentage
- Profit Percentage
- Loss Percentage
- Formula
- Understanding Profit or Loss Percentage with Example
- Overhead Expenses
30 Construction of Triangles
- Construction of Triangles
- 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
- Construct Isosceles Triangle
31 Changing the Subject of a Formula
- Changing the Subject of a Formula
32 Similarity
- Similarity of Triangles (Corresponding Sides & Angles)
- Corresponding Sides
- Corresponding Angles
