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Direct and Inverse Variation (H)

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Direct and Inverse Variation (H)

Tackle direct and inverse variation in GCSE Higher Maths. Use proportion, constants of variation, and graphs to model real situations and solve equations.

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Fascinating Fact:

In rideshare, fare varies directly with distance. If £12 for 8 km, fare = kx gives k = 12/8 = 1.5, so 15 km costs £22.50.

In GCSE Maths (Higher), direct variation means y ∝ x so y = kx, and inverse variation means y ∝ 1/x so y = k/x. You’ll find k from data, interpret gradients and curves, and check units to model real problems confidently.

Key Terms

Direct variation: y ∝ x, so y = kx. The ratio y/x is constant.
Inverse variation: y ∝ 1/x, so xy = k. The product xy is constant.
Constant of variation (k): The fixed number linking variables. Find it by substitution; include correct units.

Frequently Asked Questions (Click to see answers)

How do I find k for direct proportion?

Use a known pair (x, y) and compute k = y/x. Then model with y = kx to predict or check other values.

What is the graph difference between direct and inverse variation?

Direct variation is a straight line through the origin with gradient k. Inverse variation is a curve y = k/x that never crosses the axes.

How do units work in variation problems?

k carries units from y and x. For fare (£) and distance (km), k is £ per km. Keep units consistent before substituting.

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You can find more about this topic by visiting BBC Bitesize - Direct and inverse proportion

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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