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

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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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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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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

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What is the value of x if 3x + 7 = 16?

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What is the cube of 4?

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What is the sum of all odd numbers from 1 to 99?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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