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ICSE Class 8 Math's Chapter 10 from Selina Publications teaches direct and inverse variations, focusing on how two quantities change in relation to each other. Direct variation describes when two quantities increase or decrease proportionally (y = kx), while inverse variation shows when one quantity increases as the other decreases, maintaining a constant product (xy = k). The chapter covers identifying these relationships, solving related word problems, and applying these concepts to real-world scenarios like fuel consumption, taxi fares, and the cost of items.
Key Concepts
Direct Variation: When two quantities change in the same direction. If one quantity increases, the other increases by the same proportion, and vice versa. The relationship is expressed as y = kx, where 'k' is a constant.
Inverse Variation: When two quantities change in opposite directions. If one quantity increases, the other decreases proportionally, and vice versa. The relationship is expressed as xy = k, where 'k' is a constant.
How to Identify Variations
Analysis: Students learn to analyze tables and word problems to determine whether the variables are in a direct or inverse relationship.
Ratios: For direct variation, the ratio of the two variables (x/y) is constant. For inverse variation, the product of the two variables (x*y) is constant.
Real-World Applications
The chapter uses practical examples to illustrate the concepts, such as:
Distance and Fuel Consumption: A truck's diesel consumption varies directly with the distance it travels.
Cost and Quantity: The cost of items varies directly with the number of items purchased.
Work and Time: The time taken to complete a task can vary inversely with the number of people working on it.
Taxi Fares: Taxi fares vary directly with the distance of the journey.
Learning Outcomes
By studying this chapter, students will be able to:
Identify conditions for direct and inverse proportions.
Solve for missing quantities in both direct and inverse variation problems.
Apply the concepts to solve problems in everyday life

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