Case Study 1: Exponents and Divisibility Himanshu prepared a project on real numbers, where he explained exponential laws and divisibility rules. Questions: Case Study 2: Representation of Irrational Numbers Ravi used the Pythagoras theorem to represent √2 and √3 on a number line. Questions: Case Study 3: Decimal Expansions Students got decimals: 3.142857142857… and 0.1010010001… […]
📘 Class 9 Mathematics – Important Questions / Assignments Number Systems Polynomials Coordinate Geometry Linear Equations Euclid’s Geometry Lines & Angles Triangles Quadrilaterals Circles Heron’s Formula Surface Areas and Volumes Statistics
Class 9 Mathematics – NCERT Solutions Class 9 Mathematics – NCERT Solutions Number Systems Polynomials Coordinate Geometry Linear Equations in Two Variables Euclid’s Geometry Lines & Angles Triangles Quadrilaterals Circles Heron’s Formula Surface Areas and Volumes Statistics
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Statistics Statistics is the study of collection, organization, analysis and interpretation of data. Data A distinct piece of information in the form of fact or figures collected or represented for any specific purpose is called Data. In Latin, it is known as the Datum. Collection of Data Data are generally of two types Primary Data Data collected
Plane figure The figures which we can draw on a piece of paper or which lie on a plane are called Plane Figures. Example – Circle, Square, Rectangle etc. Solid figures The 3D shapes which occupy some space are called Solid Figures. Example – Cube, Cuboid, Sphere etc. Volume Space occupied by any solid shape is the capacity or volume of that
Perimeter It is the outside boundary of any closed shape. To find the perimeter we need to add all the sides of the given shape. The perimeter of a rectangle is the sum of its all sides. Its unit is same as of its length. Perimeter = 3 + 7 + 3 + 7 cm
Introduction to Circles There are lot many objects in our life which are round in shape. Few examples are the clock, dart board, cartwheel, ring, Vehicle wheel, Coins, etc. Circles Interior and Exterior of a Circle In a flat surface, the interior of a circle is the line whose distance from the centre is less than the radius. The exterior
Quadrilateral Any closed polygon with four sides, four angles and four vertices are called Quadrilateral. It could be regular or irregular. Angle Sum Property of a Quadrilateral The sum of the four angles of a quadrilateral is 360° If we draw a diagonal in the quadrilateral, it divides it into two triangles. And we know the
Triangle A closed figure with three sides is called a Triangle. It has three vertex, sides and Angles. Types of Triangle 1. There are three types of triangles on the basis of the length of the sides. Name of Triangle Property Image Scalene Length of all sides are different Isosceles Length of two sides are equal
Basic terms and Definitions 1. Point – A Point is that which has no component. It is represented by a dot. 2. Line – When we join two distinct points then we get a line. A line has no endpoints it can be extended infinitely. 3. Line Segment – It is the part of the line which has
Introduction Euclid was a teacher of mathematics at Alexandria in Egypt, popularly known as ‘Father of Geometry”. He introduced the method of proving mathematical results by using deductive logical reasoning and the previously proved result. He collected all his work in a book called “Elements”. This book is divided into thirteen chapters and each chapter is
Linear Equations The equation of a straight line is the linear equation. It could be in one variable or two variables. Linear Equation in One Variable The equation with one variable in it is known as a Linear Equation in One Variable. The general form is px + q = s, where p, q and s
Cartesian System If we take two number lines, one horizontal and one vertical, and then combine them in such a way that they intersect each other at their zeroes, and then they form a Cartesian Plane. Quadrants of the Cartesian Plane The Cartesian plane is dividing into four quadrants named as Quadrant I, II, III, and IV anticlockwise
Polynomial Polynomial is an algebraic expression which includes constants, variables and exponents. It is the expression in which the variables have only positive integral powers. Example 1. 4×3 + 3×2 + x +3 is a polynomial in variable x. 2. 4×2 + 3x-1 – 4 is not a polynomial as it has negative power. 3. 3×3/2 + 2x – 3 is
Mathematics Number System Chapter 1 (Open) Polynomials Chapter 2 (Open) Coordinate Geormetry Chapter 3 (Open) Linear Equation in two Variables Chapter 4 (Open) Introduction to Euclid’s Geometry Chapter 5 (Open) Lines and Angles Chapter 6 (Open) Triangles Chapter 7 (Open) Quadrilaterals Chapter 8 (Open) Circles Chapter 9 (Open) Heron’s Formula Chapter 10 (Open) Surface Areas
🔶 Meaning of Accounting: Accounting is the art of recording, classifying, summarising, and interpreting financial transactions to provide useful financial information for decision-making. 🔶 Features of Accounting: 🔶 Objectives of Accounting: 🔶 Advantages of Accounting: 🔶 Limitations of Accounting: 🔶 Basic Terms in Accounting: Term Meaning Transaction An economic activity between two parties measurable in
🔷 1. गति की परिभाषा (Definition of Motion) जब कोई वस्तु समय के साथ अपनी स्थिति में परिवर्तन करती है, तो कहा जाता है कि वह गति में है। 📌 परिभाषा:गति वह स्थिति है जब कोई वस्तु समय के साथ अपनी स्थिति को बदलती है। उदाहरण: चलती गाड़ी, उड़ता पक्षी, बहता पानी। 🔶 2. गति
🔷 1. भूमिका (Introduction) 📌 परिभाषा:ऊतक: समान संरचना और कार्य वाली कोशिकाओं का समूह। 🔹 2. ऊतकों के प्रकार (Types of Tissues) दो प्रमुख वर्ग: 🌿 3. पादप ऊतक (Plant Tissues) पादप ऊतक दो प्रकार के होते हैं: 🟢 A. मेरिस्टीमैटिक ऊतक (Meristematic Tissue) 📌 यह कोशिकाएँ लगातार विभाजित होती रहती हैं।📌 ये ऊतक वृद्धि
🔷 1. भूमिका (Introduction) 🔹 2. कोशिका की खोज और इतिहास वैज्ञानिक योगदान रॉबर्ट हुक (1665) कॉर्क (पेड़ की छाल) की पतली स्लाइस का परीक्षण करते हुए ‘सेल’ शब्द का पहली बार प्रयोग किया। लीuwenhoek पहली बार जीवित कोशिकाएँ देखीं। श्लाइडेन (1838) सभी पौधे कोशिकाओं से बने होते हैं। श्वान (1839) सभी जानवरों की संरचना
🔷 1. भूमिका (Introduction) 🔹 2. डाल्टन का परमाणु सिद्धांत (Dalton’s Atomic Theory) ✍🏻 मुख्य बिंदु: 📌 सीमाएँ: बाद में हुए अनुसंधानों से यह सिद्ध हुआ कि परमाणु को और भी छोटे कणों (इलेक्ट्रॉन, प्रोटॉन, न्यूट्रॉन) में विभाजित किया जा सकता है। 🔹 3. तत्व, यौगिक और मिश्रण ✅ तत्व (Element): 📘 उदाहरण: ✅ यौगिक
🔷 1. प्रस्तावना (Introduction) हम जानते हैं कि पदार्थ अणुओं और परमाणुओं से बना होता है। लेकिन एक परमाणु अंदर से कैसा दिखता है? उसमें कौन-कौन से कण होते हैं? – यही इस अध्याय में पढ़ते हैं। 🔹 2. परमाणु का इतिहास (History of Atomic Models) (A) डाल्टन का परमाणु सिद्धांत (John Dalton – 1808)
🔷 परिचय (Introduction) हमारे आस-पास के पदार्थ दो प्रकार के होते हैं: यह अध्याय समझाता है कि कौन-से पदार्थ शुद्ध हैं, कौन-से मिश्रण हैं और उन्हें कैसे पहचाना और अलग किया जा सकता है। 🧊 1. शुद्ध पदार्थ क्या है? 📌 परिभाषा: वह पदार्थ जिसमें केवल एक ही प्रकार के कण (atoms या molecules) होते
परिचय (Introduction) हमारे चारों ओर बहुत सारी चीजें हैं — हवा, पानी, किताब, कुर्सी, मोबाइल, भोजन आदि। इन सभी को हम पदार्थ (Matter) कहते हैं। विज्ञान में पदार्थ को इस प्रकार परिभाषित किया गया है: “पदार्थ वह है जिसकी कोई द्रव्यमान (mass) और स्थान (volume) होता है और जो हमारी इंद्रियों से अनुभव किया जा
English Medium Section Title Theme No. Theme Title Marks Reading of World History Introduction of World History I EARLY SOCIETIES Introduction Timeline I (6 MYA TO 1 BCE) 1. Writing and City Life 10 II EMPIRES Introduction Timeline II (C. 100 BCE TO 1300 CE) 2. An Empire Across
Unit Name Chapter Name India and the Contemporary World – II The Rise of Nationalism in Europe Nationalism in India The Making of a Global World The Age of Industrialization Print Culture and the Modern World Contemporary India – II Resources and Development Forest and Wildlife Water Resources Agriculture Minerals and Energy Resources Manufacturing Industries
