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

What is the area of a circle with a diameter of 14 cm?

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

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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If the probability of an event is 1/4, what is the probability of its complement?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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A cube has a side length of 4 cm. What is its volume?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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