Proportion

$y$ varies inversely with $x$. If $x=9$, then $y=8$.

Feb/March 2018

y varies inversely with $x^2$. If $x = 3$, then $y = 2$.

Feb/March 2023

Since $y$ varies directly with $(x+2)^2$, when $x=8$ the value of $y$ is $250$.

May/June 2016

$y$ varies inversely as the square of $(x + 1)$. $y = 0.875$ when $x = 1$.

May/June 2019

Between two magnets, the attractive force $F$ Newtons varies inversely with the square of the distance $d$, cm, separating the magnets. If $d = 1.5$, then $F = 48$.

May/June 2021

The variable $z$ is inversely proportional to the square of $(y - 2)$. For $y = 5$, the value of $z$ is $9$.

May/June 2021

The quantity $w$ varies as the square root of $y$, and $y$ varies inversely with $x$. If $x = 4$, then $y = 16$ and $w = 8$.

May/June 2022

Find the value of $y$ when $x = 7$.

May/June 2024

$m$ varies inversely with the square root of $(t+2)$. When $t = 23$, $m = 0.5$.

May/June 2025

The quantity $d$ varies inversely as $(w + 1)^2$. When $w = 4$, $d = 3.2$.

Oct/Nov 2016

The quantity y is inversely proportional to $x^3$. At $x = 2$, the value of $y$ is $0.5$.

Oct/Nov 2018

$y$ varies inversely with $\sqrt{x}$, and $x$ varies directly with $w^2$. If $w = 12$, then $y = 12$.

Oct/Nov 2022

$x$ varies inversely with the square root of $w$. If $w = 16$, then $x = 3$.

Oct/Nov 2023

The relationship is $y\propto \frac{1}{\sqrt{x+1}}$. If $x=8$, then $y=3$.

Oct/Nov 2025

y varies inversely with $(x+2)^2$. w varies directly with x. If y = 8, then x = 3.5. If w = 15, then x = 90.

Oct/Nov 2025