๐ Chapter 1: Real Numbers – Class 10 CBSE Maths Introduction: In this chapter, we learn about the basic building blocks of mathematics – real numbers. These include rational and irrational numbers, their properties, and how to use the Euclidean Division Algorithm. ๐ข What are Real Numbers? Real numbers include: Natural Numbers (1, 2, 3...) Whole Numbers (0, 1, 2...) Integers (...–2, –1, 0, 1, 2...) Rational Numbers (e.g. 2/3, –4, 5.6) Irrational Numbers (e.g. √2, ฯ) Together, all these form the set of Real Numbers . ✅ Properties of Real Numbers Closure Property Rational and irrational numbers are closed under addition, subtraction, and multiplication. Commutative Property a + b = b + a and a × b = b × a Associative Property (a + b) + c = a + (b + c) Distributive Property a × (b + c) = a × b + a × c ๐ Euclid’s Division Lemma If a and b are positive integers (a > b), then: a = bq + r, where 0 ≤ r < b Exampl...
๐ฉ Class 10 Maths Chapter 4 – Quadratic Equations | CBSE Notes with Examples Welcome to Swathi's 10th Maths Notes Hub! This article provides complete, exam-focused notes for Class 10 CBSE Maths Chapter 4 – Quadratic Equations . If you’re a Class 10 student preparing for your board exam, this chapter is very important. Let’s dive into definitions, methods, formulas, and solved examples. ๐ท What is a Quadratic Equation? A quadratic equation is any equation of the form: ax² + bx + c = 0 , where a ≠ 0. Examples: 2x² + 3x – 5 = 0 x² – 4x + 4 = 0 Here, a, b, c are real numbers, and x is the variable. ๐น Standard Form and Key Terms: Quadratic Term : ax² Linear Term : bx Constant Term : c Example: In the equation 3x² – 7x + 2 = 0, a = 3, b = –7, c = 2 ๐ถ Methods to Solve a Quadratic Equation Class 10 CBSE syllabus teaches three main methods : 1. Factorization Method Split the middle term and factor the equation. Example: x² – 7x + 12 = 0 = x² – ...
๐งฎ Class 10 Maths Chapter 5: Arithmetic Progressions (CBSE Notes + Formulas + Examples) Welcome to Swathi’s Class 10 Maths Notes Hub! In this post, you’ll find complete notes for Chapter 5 – Arithmetic Progressions , including all key concepts, formulas, and solved examples. These notes are designed to help CBSE Class 10 students understand the topic easily and prepare effectively for exams. ๐ What is an Arithmetic Progression (A.P.)? An Arithmetic Progression is a number sequence in which the difference between any two consecutive terms is always the same. Examples: 2, 4, 6, 8, 10... (common difference = 2) 7, 3, -1, -5... (common difference = -4) ๐น Key Terms First term (a) : The first number in the sequence. Common difference (d) : The fixed difference between two consecutive terms. nth term (an) : The term at position n in the sequence. ๐ธ Important Formulas General Term (nth term) a n = a + ( n − 1 ) d a_n = a + (n - 1)d a n = a + ( n − 1...
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