Maths Class 8 CBSE Board

Ganita Prakash · Grade 8 · Part II 📐 Chapter 7: Area Complete Study Notes — Formulae, Concepts, Examples & Practice Questions 📏 Rectangle & Square 🔺 Triangle ▱ Parallelogram 💎 Rhombus 🪤 Trapezium 🌍 Real-Life Area 📋 Contents What is Area? Rectangle & Square Triangle Area of any Polygon Parallelogram Rhombus Trapezium Areas in […]

Class 8 · Mathematics · Chapter 6 🔢 Algebra Play NCERT Ganita Prakash Part-II · Easy Notes for Exam Prep Think of a Number Tricks Number Pyramids Calendar Magic Divisibility Tricks Largest Product Table of Contents 6.1 Introduction to Algebra Play 6.2 Think of a Number Tricks 6.3 Number Pyramids 6.4 Fun with Grids (Calendar […]

Class 8 · Mathematics · NCERT Chapter 5 — Tales by Dots and Lines A complete, exam-ready guide to Mean, Median, Dot Plots, Line Graphs and Data Interpretation 📊 Mean & Median 📈 Line Graphs 🔢 Frequency Tables 💻 Spreadsheets 🗺️ Infographics 📚 Contents Introduction & Quick Overview 5.1 Mean as a Centre (The Balancing […]

Class 8 · Mathematics · NCERT Chapter 4: Exploring Some Geometric Themes Understand fractals, visualise 3D solids, nets, projections & isometric drawings — all made simple! 🌿 Fractals 📦 3D Solids & Nets 📐 Projections 📏 Isometric Drawing 🐜 Shortest Path 📋 Table of Contents Chapter Overview What are Fractals? Sierpinski Carpet Sierpinski Gasket Koch […]

📐 Mathematics · Class 8 Proportional Reasoning – 2 Chapter 3 · Ganita Prakash (NCERT) · Complete Study Notes Ratio & Proportion Map Scale Pie Charts Inverse Proportion Direct Proportion 📋 Contents 3.1 Proportionality — A Quick Recap 3.2 Ratios in Maps (Representative Fraction) 3.3 Ratios with More than 2 Terms 3.4 Dividing a Whole […]

  Class 8 · Mathematics · Chapter 2 📐 The Baudhāyana-Pythagoras Theorem Complete NCERT notes — easy to understand, exam-ready, and student-friendly! 🏛️ Ancient Indian Maths 📐 Right Triangles 🔢 Pythagoras Theorem ✨ Baudhāyana Triples ∞ Fermat’s Last Theorem 📋 Contents Introduction & Historical Background 2.1 Doubling a Square 2.2 Halving a Square 2.3 Hypotenuse […]

Chapter 1 – Fractions in Disguise Chapter 2 – The Baudhayana-Pythagoras Theorem Chapter 3 – Proportional Reasoning-2 Chapter 4 – Exploring Some Geometric Themes Chapter 5 – Tales by Dots and Lines Chapter 6 – Algebra Play Chapter 7 – Area

Class 8 • Maths • Chapter 1 🎭 Fractions in Disguise Complete study notes on Percentages — from basics to compounding & profit/loss, crafted for NCERT Class 8 students. 📐 Fractions & % 💰 Profit & Loss 🏦 Simple Interest 📈 Compounding 📉 Depreciation 📋 Contents What is a Percentage? Fractions as Percentages Percentage of […]

Notes Maths Ganita Prakash Class 8 – 2025-26 Notes Class 8 Maths Ganita Prakash – I Notes Class 8 Maths Ganita Prakash – II Notes Maths Class 8 Old Book Notes Class 8 Maths

📘 Class 8 · Chapter 7 · Ganita Prakash Proportional Reasoning — 1 Understand Ratios, Proportion, Cross Multiplication, Dividing in a Ratio & Unit Conversions — with real-life examples! ⚖️ Ratios 🔗 Proportion ✖️ Cross Multiplication 🍋 Rule of Three ➗ Dividing in a Ratio 📐 Unit Conversions 📋 Table of Contents Chapter Introduction — […]

📘 Class 8 · Chapter 6 · Ganita Prakash We Distribute, Yet Things Multiply Master Distributive Property, Algebraic Identities, Fast Multiplication Tricks & Pattern Spotting! 🔢 Distributivity 📐 Algebraic Identities ⚡ Fast Multiplication 🔎 Pattern Recognition 📊 Algebraic Expressions 📋 Table of Contents Chapter Introduction 6.1 The Distributive Property of Multiplication Identity 1: (a + […]

📚 Mathematics • Class 8 • NCERT Ganita Prakash 🔢 Chapter 5: Number Play Explore the magical world of numbers — patterns, divisibility, digital roots, and more! 📌 Parity ➗ Divisibility Rules 🔍 Remainders 🌱 Digital Roots 🔐 Cryptarithms 🧮 Algebra 📋 Contents Introduction to Number Play Sums of Consecutive Numbers Parity — Even & […]

  Class 8  ·  Mathematics  ·  NCERT Ganita Prakash Chapter 4: Quadrilaterals Complete study notes covering definitions, properties, proofs, key results, and exam-ready practice questions. Rectangle Square Parallelogram Rhombus Kite Trapezium Angle Sum = 360° Congruence Proofs 📚 Table of Contents Introduction to Quadrilaterals Rectangle Square Angles in a Quadrilateral Parallelogram Rhombus Kite Trapezium Quick […]

Class 8 Mathematics · NCERT Ganita Prakash Chapter 3 · A Story of Numbers Complete Study Notes — History, Evolution & Key Concepts of Number Systems Number Systems Place Value Base-n Systems Roman Numerals Hindu Numerals Zero & Its Importance 📚 Table of Contents Origins of Counting & Hindu Numerals Mechanism of Counting Early Number […]

Class 8 · Ganita Prakash · Chapter 2 ⚡ Power Play Exponents, Exponential Growth, Scientific Notation & Large Numbers 📖 Complete Notes 🧮 Exam-Ready ✅ NCERT Based 📋 Contents at a Glance Exponential Growth — Paper Folding Activity Exponential Notation — Basics Laws of Exponents The Other Side — Zero & Negative Exponents Powers of […]

Chapter 1 – A Square and A Cube Chapter 2 – Power Play Chapter 3 – A Story of Numbers Chapter 4 – Quadrilaterals Chapter 5 – Number Play Chapter 6 – We Distribute, Yet Things Multiply Chapter 7 – Proportional Reasoning-1

📚 Class 8 Mathematics · NCERT Chapter 1: A Square and a Cube Complete Study Notes · Ganita Prakash · Grade 8 ✔ Square Numbers ✔ Square Roots ✔ Cube Numbers ✔ Cube Roots ✔ Exam Questions 📋 Contents The Locker Puzzle – Chapter Introduction 1.1 Square Numbers (Perfect Squares) Properties of Perfect Squares Square […]

Short Questions 1. What is the simplest form of the ratio 18 : 24? Solution:HCF of 18 and 24 = 6Divide both terms by 618 ÷ 6 : 24 ÷ 6 = 3 : 4 2. Are 4 : 6 and 8 : 12 proportional? Solution:4 : 6 = 2 : 38 : 12 = […]

Short Questions 1. What is the distributive property of multiplication over addition? Answer: a(b+c)=ab+ac Multiply a with each term inside the bracket. 2. Expand (a+1)(b+1). Answer: ab+a+b+1 (a+1)(b+1)=ab+a+b+1 3. Expand (a−b)2 Answer: a2−2ab+b2a^2-2ab+b^2 (a−b)(a−b)=a2−ab−ab+b2=a2−2ab+b2(a-b)(a-b)=a^2-ab-ab+b^2=a^2-2ab+b^2 4. Expand (a+b)2(a+b)^2. Answer: a2+2ab+b2a^2+2ab+b^2 (a+b)(a+b)=a2+ab+ab+b2 5. Expand  (a+b)(a−b)(a+b)(a-b). Answer: a2−b2 (a+b)(a−b)=a2−ab+ab−b2=a2−b2 6. Find 46246^2. Solution:462=(40+6)2=402+2(40)(6)+62 =1600+480+36=2116 7. Find 91291^2. Solution:912=(100−9)2=10000−1800+81=8281 […]

Short Questions Q1. Write 10 as a sum of consecutive numbers. Answer:10 = 1 + 2 + 3 + 4Step 1: Start from 1Step 2: Keep adding consecutive numbers1 + 2 + 3 + 4 = 10 Q2. Express 12 as sum of consecutive numbers. Answer:12 = 3 + 4 + 5Step 1: Try middle […]

SHORT QUESTIONS 1. What is a quadrilateral? Answer: A quadrilateral is a figure with four sides because “quadri” means four and “latus” means sides. 2. What is the sum of angles in a quadrilateral? Answer: A quadrilateral can be divided into 2 triangles → each triangle has 180° → 180° + 180° = 360°. 3. What […]

Short Questions Question 1: What is one-to-one mapping in counting? Answer: One-to-one mapping means matching each object with exactly one object (like one stick for one cow), ensuring accurate counting without missing or repeating items. Question 2: What is a number system? Answer: A number system is a standard sequence of symbols or names arranged […]

SHORT QUESTIONS Question 1. What is the thickness after 3 folds if initial thickness is 0.001 cm? Solution:Thickness doubles each time= 0.001 × 2³= 0.001 × 8= 0.008 cm Answer: 0.008 cm Question 2. Express 2 × 2 × 2 × 2 × 2 in exponential form. Solution:2 multiplied 5 times = 2⁵ Answer: 2⁵ […]

Chapter 1 – A Square and A Cube Chapter 2 – Power Play Chapter 3 – A Story of Numbers Chapter 4 – Quadrilaterals Chapter 5 – Number Play Chapter 6 – We Distribute, Yet Things Multiply Chapter 7 – Proportional Reasoning-1

Short Questions 1. What is a perfect square? Answer: A number obtained by multiplying a number by itself.Solution:Example: 4=2×24 = 2 \times 2, 9=3×39 = 3 \times 3 2. Which numbers remain open in the locker problem? Answer: Square numbersSolution:Only numbers with odd number of factors remain open → perfect squares like 1, 4, 9, […]

Short Questions Q1. Find the area of a rectangle of length 8 cm and width 5 cm. Solution:Area = length × width = 8 × 5 = 40 cm²Answer: 40 cm² Q2. Find the area of a triangle with base 10 cm and height 6 cm. Area of triangle=12×base×height\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}Area of triangle=21​×base×height […]

Short Questions Q1. Think of a number, double it, add 8, divide by 2, subtract the original number. Solution: Let the number = x Step 1: Double it → 2xStep 2: Add 8 → 2x + 8Step 3: Divide by 2 → (2x + 8) ÷ 2 = x + 4Step 4: Subtract original number […]

Short Questions Q1. Find the mean of 5, 10, 15. Step 1: Add all numbers 5 + 10 + 15 = 30 Step 2: Count numbers = 3 Step 3: Mean = Total ÷ Number = 30 ÷ 3 = 10 Q2. Find the median of 2, 4, 6, 8, 10. Step 1: Arrange numbers […]

Short Questions Q1. What is a fractal? Answer: A fractal is a shape that shows the same pattern repeatedly at smaller scales. Q2. What is the value of  RnR_n ​ in Sierpinski Carpet? Solution: Each step produces 8 times the previous squares: Rn+1=8RnR_{n+1} = 8R_n ​, so Rn=8nR_n = 8^n . Q3. What is H1H_1 […]

Short Questions Question: What is meant by a proportional relationship? Answer: A proportional relationship is one in which two or more quantities change by the same factor. Question: Define a ratio. Answer: A ratio is a comparison of two quantities written in the form a : b. Question: What condition must be satisfied for two […]

Short Practical Questions Question: Map scale = 1 : 60,00,000. Distance on map = 1 cm. Find real distance. Steps: 1 cm = 60,00,000 cm Convert → 60 km Answer: 60 km Question: Scale 1 : 50. Drawing length = 3 cm. Find actual length. Steps: Actual = 3 × 50 = 150 cm Answer: […]

Short Questions Q1. Find the diagonal of a square of side 6 cm. Solution:We know: diagonal = side × √2= 6√2 cm Answer: 6√2 cm Q2. Find the hypotenuse of an isosceles right triangle with equal sides 5 cm. c2=2a2c^2 = 2a^2 c2=2a2 Solution:c² = 2 × 5² = 2 × 25 = 50c = […]

Short Theoretical Questions 1. What is meant by percentage? Answer: Percentage means a fraction out of 100. It is written using the symbol (%). 2. Why is the denominator 100 used in percentages? Answer: Because “per cent” means “per hundred”, so all percentages are expressed out of 100. 3. How are fractions and percentages related? […]

Important Questions Maths Ganita Prakash Class 8 – 2025-26 Important Questions Class 8 Maths Ganita Prakash – I Important Questions Class 8 Maths Ganita Prakash – II Important Questions Maths Class 8 Old Book Important Questions Class 8 Maths

Chapter 1 – Fractions in Disguise (Practical Questions) Chapter 1 – Fractions in Disguise (Theory Questions) Chapter 2 – The Baudhayana-Pythagoras Theorem (Practical Questions) Chapter 3 – Proportional Reasoning-2 (Practical Questions) Chapter 3 – Proportional Reasoning-2 (Theory Questions) Chapter 4 – Exploring Some Geometric Themes Chapter 5 – Tales by Dots and Lines Chapter 6 – […]