Variation

Variation describes how one quantity changes when another changes. You will learn direct variation, inverse variation, joint variation, and partial variation for O-Level. We use y = kx for direct, y = k/x for inverse.

  • Direct variation
  • Inverse variation
  • Joint variation
  • Partial variation

Lessons for Variation

Direct Variation

Definitiony varies directly as x means y = kx, where k is the constant of variation.As x increases, y increases …

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Inverse Variation

Definitiony varies inversely as x means y = k/x, where k is the constant.As x increases, y decreases so that …

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Joint Variation

Definitiony varies jointly as x and z means y = kxz.You can mix direct and inverse: y ∝ x/z means …

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Partial Variation

Definitiony is partly constant and partly varies with x. So y = kx + c.We need two pairs of values …

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Exercises for Variation

Direct variation problems

Solve:y ∝ x. When x = 5, y = 20. Find y when x = 8.p ∝ q2. When q …

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Inverse variation problems

Solve:y ∝ 1/x. When x = 4, y = 5. Find y when x = 10.t ∝ 1/v2. When v …

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Joint variation problems

Solve:y varies jointly as x and z. When x = 2, z = 5, y = 30. Find y when …

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Partial variation problems

Solve:C is partly constant and partly varies as d. When d = 2, C = 10. When d = 5, …

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