Topic Details (Notes format)

How to Solve Direct and Inverse Variation Problems

Subject: Mathematics

Book: Maths Mastery

Direct variation follows y = kx, where y changes proportionally with x (e.g., doubling x doubles y). Inverse variation follows y = k/x, implying that multiplying x by a factor divides y by the same factor. For instance, if y ∝ x, you might have y = 3x; doubling x from 2 to 4 changes y from 6 to 12. Conversely, if y ∝ 1/x, and x changes from 2 to 4, y becomes half. Variation problems are integral in physics (Ohm’s Law), chemistry (pressure-volume relationships), and everyday concepts like speed-time relationships. Mastering them helps you interpret how one quantity shifts in response to another.

Practice Questions

If 2x - 3 = 7, what is the value of x?

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What is the square root of 144?

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What is the sum of the first 20 odd numbers?

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If 3x = 81, what is the value of x?

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What is the sum of the first 50 positive integers?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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