Mathematics Class 9 English Medium CBSE Topics and Syllabus

• Introduction of Real Number 
• Concept of 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 

• Polynomials 
• Polynomials in One Variable 
• Zeroes of a Polynomial 
• Remainder Theorem 
• Factorisation of Polynomials 
• Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0. 
• Algebraic Identities 

  ( a + b )² = a² + 2ab + b² .

• Linear Equation in Two Variables 
• Linear Equation in One Variable 
• Solution of a Linear Equation 
• Graph of a Linear Equation in Two Variables 
• Equations of Lines Parallel to the X-axis and Y-axis 

• Algebraic Expressions 
  • Variable
  • Constant
  • Algebraic Expressions
  • Value of Expression
  • Number line and an expression

• Algebraic Identities 

  ( a + b )² = a² + 2ab + b² .

• Concept for Euclid’S Geometry 
• Euclid’S Definitions, Axioms and Postulates 
• Equivalent Versions of Euclid’S Fifth Postulate 

• Introduction to Lines and Angles 
• Basic Terms and Definitions 
• Intersecting Lines and Non-intersecting Lines 
• Parallel Lines 
• Pairs of Angles 
• Parallel Lines and a Transversal 
• Lines Parallel to the Same Line 
• Angle Sum Property of a Triangle 

• Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle 
• Congruence of Triangles 
• Criteria for Congruence of Triangles 
• Properties of a Triangle 
  • The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
• Some More Criteria for Congruence of Triangles 
• Inequalities in a Triangle 

• Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles 
• Angle Sum Property of a Quadrilateral 
• Types of Quadrilaterals 
• Another Condition for a Quadrilateral to Be a Parallelogram 
• Theorem of Midpoints of Two Sides of a Triangle 
• Properties of a Parallelogram 
  • Property: The Opposite Sides of a Parallelogram Are of Equal Length. 
  • Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles. 
  • Property: The Opposite Angles of a Parallelogram Are of Equal Measure. 
  • Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection) 
• Tests for Parallelogram 
  • Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram. 
  • Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram. 
  • Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram 

• Concept of Area 
• Corollary: A rectangle and a parallelogram on the same base and between the same parallels are equal in area. 
• Theorem: Parallelograms on the Same Base and Between the Same Parallels. 
• Corollary: Triangles on the same base and between the same parallels are equal in area. 

• Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles 
• Angle Subtended by a Chord at a Point 
• Perpendicular from the Centre to a Chord 
• Circles Passing Through One, Two, Three Points 
  • Infinite circles pass through one point.
  • Infinite circles pass through two distinct points.
  • There is a unique circle passing through three non-collinear points.
  • No circle can pass through 3 collinear points.
• Equal Chords and Their Distances from the Centre 
• Angle Subtended by an Arc of a Circle 
• Cyclic Quadrilateral 

• Introduction of Constructions 
• Basic Constructions 
• Some Constructions of Triangles 

• Area of a Triangle 
• Area of a Triangle by Heron's Formula 
  • Collinearity of three points
• Application of Heron’s Formula in Finding Areas of Quadrilaterals 

Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.

• Surface Area of a Cuboid 
• Surface Area of a Cube 
• Surface Area of Cylinder 
  • Right Circular Cylinder
  • Hollow Cylinder
• Surface Area of a Right Circular Cone 
• Surface Area of a Sphere 
  • Surface area of a sphere
  • Hemisphere
  • Hollow Hemisphere
• Volume of a Cuboid 
• Volume of a Cylinder 
• Volume of a Right Circular Cone 
• Volume of a Sphere 

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

• Concepts of Statistics 
• Collecting Data 
• Presentation of Data 
• Graphical Representation of Data 
  • Bar graph
  • Pie graph
  • Histogram
• Measures of Central Tendency 
  • Mean , Median , Mode
  • Quartile , Inter quartile

• Probability - an Experimental Approach