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

$y$ varies inversely as the square root of $(x+1)$.

When $x=8,y=5$.

Find $y$ in terms of $x$.

$y$ is directly proportional to $(x-4)$.
When $x=16$, $y=3$.  

Find $y$ in terms of $x$.  

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

$y$ is inversely proportional to $x^3$.
When $x=2$, $y=0.5$.  

Find $y$ in terms of $x$.  

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

$y$ is directly proportional to ${(x-1)}^2$.
When $x=3,y=24$.

Find $y$ when $x=6$.

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

The table below shows the time, $t$ hours, it takes a car to travel a certain distance at different speeds, $s$ miles per hour.

State what type of variation model would be suitable for this data.

Find an equation for $t$ in terms of $s$.

Find the value of $a$.

State the total distance that the car has driven.

Use the model to calculate the speed if a car takes 30 minutes to complete the journey.

Give a reason why using the model to answer part (e) is not suitable.

$m$ varies inversely with the square of $\left(p-1\right)$.
When $p=4,m=5.$
Find $m$ when $p=6$.

$m=$ ..................................................

$y$ is inversely proportional to the square root of $(x+1)$.
When $x=8,y=2$.

Find $y$ when $x=99$.  

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

$y$ is inversely proportional to ${\left(x+3\right)}^2$
When $x=2$, $y=8$.

Find $y$ when $x=7$.  

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

$y$ varies inversely with the square of $(x+2)$.
When $x=3$, $y=2$.

Find $y$ when $x=8$.

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