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 x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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What is the square root of 144?

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The LCM of 12 and 15 is:

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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If 2x = 16, what is the value of x?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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