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 a:b = 3:4 and b:c = 5:6, what is a:c?

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

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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If x^2 - 5x + 6 = 0, what are the roots?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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If 8x = 512, what is the value of x?

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If the sum of three consecutive integers is 96, what are the integers?

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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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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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