WAEC 2019 Mathematics · Question 38

H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.

Options

A.H = $\frac{p}{4y^2}$
B.H = $\frac{2p}{y^2}$
C.H = $\frac{p}{2y^2}$
D.H = $\frac{p}{y^2}$

Answer: C. H = $\frac{p}{2y^2}$

Explanation written with AI and checked against the answer key

Analyze the question: H varies directly as p and inversely as y². We need to find the constant of variation and write H in terms of p and y.

Concept:

Direct variation: H ∝ p
Inverse variation: H ∝ 1/y²
Combined: H = kp/y², where k is a constant.

Solution:

Write the relationship: H = kp/y²

Substitute H = 1, p = 8, y = 2: 1 = k(8)/(2²) 1 = 8k/4 1 = 2k k = 1/2

Put k back into the formula: H = (1/2)(p/y²) = p/(2y²)

Check: p = 8, y = 2 gives H = 8/(2×4) = 8/8 = 1 ✓

Answer: Option C, H = p/(2y²).

Tip: For "varies directly as A and inversely as B," always start with y = kA/B. Find k with the given values first, then rewrite the formula. Always plug the values back in to check your answer quickly.

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H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.

Options

Answer: C. H = p2y2\frac{p}{2y^2}2y2p​

Answer: C. H = $\frac{p}{2y^2}$