CBSE Class 9 Sample Papers, Syllabus, Test Papers & NCERT Solutions

Chapter 1 Number Systems Class 9 Notes Chapter 2 Polynomials Class 9 Notes Chapter 3 Introduction to Euclid’s Geometry Class 9 Notes Chapter 4 Lines and Angles Class 9 Notes Chapter 5 Triangles Class 9 Notes Chapter 6 Coordinate Geometry Class 9 Notes Chapter 7 Heron’s Formula Class 9 Notes Chapter 8 Linear Equations in Two Variables Class 9 Notes Chapter 9 Quadrilaterals Class […]

1. Some Basic Definitions (i) Trial: A single performance of a random experiment is known as a trial. (ii) Sample space: The set consisting of all possible outcomes of a random experiment is known as sample space. (lii) Event: A subset of the sample space of a random experiment is called an event. 2. Probability: Let n be the total number of trials and […]

1. Primary and Secondary Data: When the information was collected by the investigator herself or himself with a definite objective in her or his mind, the data obtained is called primary data. When the information was gathered from a source which already had the information stored, the data obtained is called secondary data. 2. Raw Data: Let us consider […]

1. Cuboid: A figure which is surrounded by six rectangular surfaces is called cuboid. The opposite surface of a cuboid is equal and parallel. A cuboid has 12 edges and 8 corners. Each corner of a cuboid is called the vertex of a cuboid. The line segment joining the opposite vertices is called the diagonal of a […]

1. Need of Accurate Figures: Sometimes one needs an accurate figure, for example, to draw a map of a building to be constructed, to design tools and various parts of a machine, to draw road maps, etc. To draw such figures some basic geometrical instruments are needed. 2. Geometry Box: A geometry box contains the following basic geometrical instruments […]

1. Circle: The collection of all points in a plane which are at a fixed distance from a fixed point in the plane is called a circle. The following examples of the circle are 2. Basic Definition Chord: Suppose, we take any two points on a circle, then the line segment PQ is called the chord of the […]

1. Congruent Figures: Two figures are called congruent if they have the same shape and same size. If two figures X and Y are congruent (see adjoining figure), then using a tracing paper we can superpose one figure over the other such that it will cover the other completely. So, if two figures X and Y are […]

1. Quadrilateral: A plane figure bounded by four lines segment AB, BC, CD and DA is called a quadrilateral. The sum of the angles of a quadrilateral is 360°. 2. Various Types of Quadrilaterals (i) Parallelogram: A quadrilateral in which opposite sides are parallel is called parallelogram and it is written as Parallelogram. (ii) Rectangle: A parallelogram each of whose angle […]

Linear Equations: Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers and a and b are not both zero is called a linear equation in two variables. The solution of a linear equation is not affected when the same number is […]

1. Triangle: A plane figure bounded by three line segments is called a triangle. In ΔABC has (i) three vertices, namely A, B and C. (ii) three sides, namely AB, BC and CA. (iii) three angles, namely ∠A, ∠B and ∠C. 2. Types of Triangle on the Basis of Sides (i) Equilateral triangle: A triangle having all sides equal […]

1. Cartesian System: The system used to describe the position of a point in a plane is called the cartesian system. In a cartesian system, there are two perpendicular lines and a point is located by referring them. The horizontal line XX’ is called X-axis and vertical line YY’ is called Y-axis. The point where these lines […]

1. Triangle: A closed figure formed by three intersecting lines is called a triangle (‘Tri’ means ‘three’). A triangle has three sides, three angles and three vertices. e.g., In triangle ABC, denoted as ∆ABC. AB, BC, CA are the three sides, ∠A, ∠B, ∠C are the three angles and A, B, C are three vertices. 2. Congruence of […]

1. Basic Terms and Definitions (i) Line segment: A part of a line with two endpoints is called a line segment. Line segment AB is denoted by . (ii) Ray: A part of a line with one endpoint is called a ray. The ray AB is denoted by . (iii) Collinear points and non-collinear points: If three or more than […]

1. Axioms or Postulates: Axioms or postulates are the assumptions which are obvious universal truths. They are not proved. Mainly postulates are used for especially geometry and axioms are used for especially algebra. 2. Theorems: Theorems are statements which are proved using ‘ definitions, axioms, previously proved statements and deductive reasoning. 3. Euclid’s Definitions, Axioms or Postulates A point is […]

1. Polynomial: A polynomial in one variable x is an algebraic expression of the form 2. Terms: The several parts of a polynomial separated by ‘+’ or ‘-‘ operations are called the terms of the expression. 3. Types of Polynomial (i) Constant polynomial: A polynomial containing one term only, consisting of a constant is called a constant polynomial. […]

1. Natural Numbers: Numbers which start from one (1) are known as natural numbers. The collection of all natural numbers is denoted by N. N = {1, 2, 3, 4, …….} 2. Whole Numbers: Numbers which start from zero (0) are known as whole numbers. The collection of all whole numbers is denoted by W. or If ‘0’ […]

Chapter 1 – Number Systems Formulas Chapter 2 – Polynomials Formulas Chapter 3 – Coordinate Geometry Formulas Chapter 4 – Linear Equations in Two Variables Formulas Chapter 5 – Introduction to Euclids Geometry Formulas Chapter 6 – Lines and Angles Formulas Chapter 7 – Triangles Formulas Chapter 8 – Quadrilaterals Formulas Chapter 9 – Areas of Parallelograms and Triangles Formulas Chapter 10 – Circles Formulas […]