# Mathematics Class 9 ICSE CISCE Topics and Syllabus

## Syllabus

1 Rational and Irrational Numbers
2 Compound Interest [Without Using Formula]
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 )
• 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
• Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
7 Indices [Exponents]
9 Triangles [Congruency in Triangles]
• Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
• 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.
• 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.
• Congruence of Triangles
• Criteria for Congruence of Triangles
11 Inequalities
12 Mid-point and Its Converse [ Including Intercept Theorem]
13 Pythagoras Theorem [Proof and Simple Applications with Converse]
• Pythagoras Theorem
• 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]
15 Construction of Polygons (Using Ruler and Compass Only)
16 Area Theorems [Proof and Use]
• Concept of Area
• 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
18 Statistics
19 Mean and Median (For Ungrouped Data Only)
21 Solids [Surface Area and Volume of 3-d Solids]
22 Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and Their Reciprocals]
23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
24 Solution of Right Triangles [Simple 2-d Problems Involving One Right-angled Triangle]
27 Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
28 Distance Formula
30 Construction of Triangles
31 Changing the Subject of a Formula
32 Similarity
• Similarity
• Similar triangles
• Criteria of Similarity
- AA Criterion of similarity
- SAS Criterion of similarity
- SSS Criterion of similarity
• Construction of similar triangles