Swathi’s Class 10 Maths Notes Hub

  🟩 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. 🔷 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. 🔹 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 🔶 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 – ...

  Chapter 3: Pair of Linear Equations in Two Variables – Class 10 CBSE Maths In this chapter, we learn how to form and solve two linear equations in two variables. It is an important chapter for Class 10 Board Exams and helps build the foundation for Algebra in higher studies. ✏️ What is a Linear Equation in Two Variables? An equation of the form ax + by + c = 0 , where a , b , and c are real numbers, and x and y are variables, is called a linear equation in two variables. Example: 2x + 3y = 6 x − y = 4 📈 Graphical Method to Solve Equations Plot both equations on the graph. The point of intersection is the solution. If the lines intersect → One solution If the lines are parallel → No solution If the lines overlap → Infinite solutions ✍️ Algebraic Methods of Solving Equations 🔁 Substitution Method ➖ Elimination Method ✳️ Cross Multiplication Method 🔢 Important Formulas ✅ General Form: ax + by + c = 0 ✅ Cross Multiplication Formula: x ...

  Understanding polynomials is a key part of Class 10 Mathematics. This chapter lays the foundation for many algebraic concepts used in higher classes. In this post, you will find easy explanations, formulas, and a PDF download link of notes that will help you prepare well for your exams. ✍️ What is a Polynomial? A polynomial is an algebraic expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Examples of polynomials: x 2 + 2 x + 3 x^2 + 2x + 3 x 2 + 2 x + 3 5 y 3 − 4 y + 7 5y^3 - 4y + 7 5 y 3 − 4 y + 7 3 a 2 + 2 a b + b 2 3a^2 + 2ab + b^2 3 a 2 + 2 ab + b 2 But expressions like 1 x \frac{1}{x} x 1 ​ or x \sqrt{x} x ​ are not polynomials. 🧠 Types of Polynomials Based on Degree Degree Example Type 0 5 Constant 1 x + 1 x + 1 x + 1 Linear Polynomial 2 x 2 + 3 x + 2 x^2 + 3x + 2 x 2 + 3 x + 2 Quadratic Polynomial 3 x 3 − 1 x^3 - 1 x 3 − 1 Cubic Polyno...

  📘 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. 🔢 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, π) 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 🔁 Euclid’s Division Lemma If a and b are positive integers (a > b), then: a = bq + r, where 0 ≤ r < b Exampl...