MATHS 9TH CBSE

Let’s delve into detailed solutions for key example problems from Chapter 6 CBSE: Lines and Angles

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Example 1: Prove Vertical Opposite Angles are Equal Question Given two intersecting lines, prove that vertical opposite angles are equal. Solution Example 2: Prove Corresponding Angles are Equal Question Prove that if a transversal intersects two parallel lines, the corresponding angles are equal. Solution Example 3: Angle Sum Property of a Triangle Question Prove that … Read more

Lines and Angles

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Critical Evaluation 1. Chapter Overview This chapter deals with the fundamental concepts of lines and angles, forming the basis for more advanced geometric concepts. It emphasizes understanding and proving various properties of angles and lines, including: 2. Strengths 3. Challenges 4. Key Concepts Evaluated 5. Recommendations for Improvement 6. Exam-Oriented Focus Would you like detailed … Read more

Let’s explore another problem that is commonly asked in the CBSE Class 9 exam pattern…

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Question The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are reversed. Find the number. Solution Step 1: Define the variables Let the two-digit number be 10x+y10x + y, where: Step 2: Write the given conditions as equations Step 3: Solve the equations From … Read more

“Linear Equations in Two Variables,” is pivotal for understanding mathematical relationships and their graphical representations..

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Strengths of the Chapter Challenges and Criticisms Suggestions for Improvement Higher-Order Questions Conclusion The chapter serves as an essential building block for mathematical reasoning and problem-solving. However, introducing modern tools, real-world applications, and interdisciplinary approaches would make it more engaging and relevant for students. This would not only solidify their understanding but also foster an … Read more

The Fourth Chapter of CBSE Class 9 Maths “Linear Equations in Two Variables”

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Concepts Solved Examples Example 1: Plotting the Graph Problem: Plot the graph of 3x+2y=63x + 2y = 6. Solution:Rewrite as y=−32x+3y = \frac{-3}{2}x + 3.Find solutions by substituting values of xx: xx yy 00 62=3\frac{6}{2} = 3 22 −3(2)2+3=0\frac{-3(2)}{2} + 3 = 0 44 −3(4)2+3=−3\frac{-3(4)}{2} + 3 = -3 Plot points (0,3)(0, 3), (2,0)(2, 0), … Read more

Let’s explore Coordinate Geometry even further with challenging problems, advanced applications, and step-by-step solutions to deepen understanding

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Advanced Problem-Solving in Coordinate Geometry 1. Intersection of Lines Problem: Find the point of intersection of the lines represented by: Solution:To find the intersection, solve the two equations simultaneously. From Equation 2: x=2y−5.x = 2y – 5. Substitute x=2y−5x = 2y – 5 into Equation 1: 2(2y−5)+3y=13.2(2y – 5) + 3y = 13. 4y−10+3y=13.4y – … Read more

“Coordinate Geometry”, which introduces the fundamental concepts of representing and analyzing geometric shapes in a two-dimensional plane using the Cartesian system

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Key Concepts 1. Cartesian System The Cartesian system uses two perpendicular axes: Origin (OO): Intersection point of the axes (0,0)(0, 0).Points are represented as ordered pairs (x,y)(x, y), where: 2. Quadrants The plane is divided into four quadrants: 3. Plotting Points Example: Plot (2,3)(2, 3). 4. Distance Formula The distance between two points (x1,y1)(x_1, y_1) … Read more

Dive deeper into problem-solving techniques in polynomials, We’ll explore…

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1. Factoring Techniques Factoring is crucial for simplifying and solving polynomial equations. Case 1: Common Factor Find the greatest common factor (GCF) and factor it out.Example: Factor 6×3+9x26x^3 + 9x^2. =3×2(2x+3).= 3x^2(2x + 3). Case 2: Grouping Group terms to create common factors.Example: Factor x3+3×2+x+3x^3 + 3x^2 + x + 3. =(x3+3×2)+(x+3).= (x^3 + 3x^2) … Read more