iGCSE Mathematics (0580) :E1.11 Demonstrate an understanding of ratio and proportion. iGCSE Style Questions Paper 2

Question

$y$ is inversely proportional to $\sqrt{x}$ and $x$ is directly proportional to $w^2$.
When $w = 12$, $y = 12$.

Find $y$ in terms of $w$.

▶️ Answer/Explanation

Solution

$y = \frac{144}{w}$

1. First relationship: $y = \frac{k}{\sqrt{x}}$

2. Second relationship: $x = mw^2$

3. Combine: $y = \frac{k}{\sqrt{mw^2}} = \frac{k}{\sqrt{m}w}$

4. Substitute w=12, y=12 to find k/√m = 144

Question

$w$ is proportional to the square root of $y$.
$y$ is inversely proportional to $x$.
When $x = 4$, $y = 16$ and $w = 8$.

Find $w$ in terms of $x$.

▶️ Answer/Explanation

Solution

Ans: $\frac{16}{\sqrt{x}}$

First find $y = \frac{k}{x}$ → $16 = \frac{k}{4}$ → $k = 64$, so $y = \frac{64}{x}$.

Then $w = m\sqrt{y}$ → $8 = m\sqrt{16}$ → $m = 2$.

Substitute: $w = 2\sqrt{\frac{64}{x}} = \frac{16}{\sqrt{x}}$.

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