Proportion (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

The table below shows the population of bacteria cells, $p$, in a petri dish $x$ hours after their first introduction.

By finding and testing both a quadratic and a cubic variation model for $p$ in terms of $x$, decide which would be a closer fit for the data.

$y$ is inversely proportional to the square root of $x$.
When $y=7$, $x=2.25$.  
Write $y$ in terms of $x$.  

$y=$................................................

$p$ is directly proportional to ${\left(q+2\right)}^2$.
When $q=1$, $p=1$.  

Find $p$ when $q=10$.  

$p=$ .................................................

$y$ varies directly with ${(x-1)}^2$ .
When $x=5,y=4$.
Find $y$ when $x=7$.

$y=$ ..............................................

The intensity of a magnetic field, $I$, measured in Teslas, T, varies inversely as the cube of the distance from its source, $d$ metres.

If the intensity of the magnetic field is $0.1$T at a distance of 2 metres, find an equation for the relationship between $I$ and $d$.

Complete the following table showing the intensity, $I$ Teslas, at certain distances, $d$ metres.

Use your model to calculate the distance from its source if $I=0.0512$ metres.

$y$ is directly proportional to the cube root of $\left(x+3\right)$.
When $x=5,y=\frac{2}{3}$.  
Find $y$ when $x=24$.  

$y=$................................................

$t$ varies inversely with the square of $(x+1)$.
When $x=2$, $t=5$.

Write $t$ in terms of $x$.

$t$ = ...................................................

When $t=1.8$, find the positive value of $x$.

$x$ = ...................................................

$y$ is inversely proportional to the square of $(x+1)$.
$y=0.875$ when $x=1$.

Find $y$ when $x=4$.  

$y$ = ....................................................