JAMB 2014 Mathematics · Question 5

y varies directly as w2. When y = 8, w = 2. Find y when w = 3

Options

A.18
B.12
C.9
D.6

Answer: A. 18

Explanation written with AI and checked against the answer key

Analyze the question: "y varies directly as w²" means y is proportional to the square of w. We need to find the constant of proportionality first, then use it to find y at the new value of w. Concept: Direct variation: y ∝ w² → y = kw², where k is a constant. Solution: Step 1: Find k using y = 8 when w = 2. 8 = k(2)² 8 = 4k k = 2 Step 2: Write the formula. y = 2w² Step 3: Find y when w = 3. y = 2(3)² y = 2(9) y = 18 Check (alternative method): y₁/w₁² = y₂/w₂² 8/4 = y/9, so 2 = y/9, and y = 18 ✔ Answer: A (18) Exam tip: For variation questions, always follow these steps: (1) write the relationship with k, (2) find k, (3) rewrite the formula, (4) substitute. Watch out for the square: a common mistake is to use w instead of w² (that would give 12, option B, a trap!). Always square the value before multiplying by k.

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