How to answer a direct proportion question with a square root (v is directly proportional to the square root of h, and v = 8 when h = 36. Find v when h = 18, to 3 s.f.)
1. Write it with k: v ∝ √h → v = k√h
2. Put in the pair you are given and find k: 8 = k√36 = 6k, so k = 8/6 = 4/3 — leave k as a fraction
3. Substitute: h = 18 → v = (4/3)√18 = 5.656… = 5.66 (3 s.f.)
Common trap: rounding k too early. If you write k = 1.33, you get 1.33 × √18 = 5.642… = 5.64 — and lose the accuracy mark. Keep k as 4/3 (or 8/6) until the very end.
Level up: with the same formula v = (4/3)√h, find v when h = 81.
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Road to A* follows the IGCSE 0580 course in order, one concept per episode. This is episode 37.
For: IGCSE 0580 E2.8 Proportion (Extended) · GCSE
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