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

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

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

is inversely proportional to the square root of .
When , .  
Write  in terms of .  

................................................

is directly proportional to .
When , .  

Find  when .  

.................................................

varies directly with .
When .
Find when .

..............................................

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

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

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

Use your model to calculate the distance from its source if metres.

is directly proportional to the cube root of .
When .  
Find when .  

................................................

varies inversely with the square of .
When , .

Write  in terms of .

= ...................................................

When , find the positive value of .

 = ...................................................

is inversely proportional to the square of .
when .

Find  when .  

= ....................................................