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 and y = 4, what is the value of x^2 + y^2?

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The LCM of 12 and 15 is:

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The probability of getting an even number when rolling a die is:

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What is the sum of all even numbers between 1 and 50?

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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 perimeter of a square is 36 cm, what is the length of its diagonal?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If the radius of a circle is 7 cm, what is its circumference?

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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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