Proportion (Cambridge International IGCSE Maths): Exam Questions

The following table of data represents the length, $x$ and area, $y$ of some irregular shapes.

Given that $y$ is proportional to the square of $x$, find the values of $a$and $b$.

$y\propto\frac{1}{\sqrt{x}}$

When $y=8,x=4.$ Find $y$when $x=49$.

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

$y$ varies directly with the square root of $x$. When $x=9$, $y=6$.

Find $y$ when $x=25$.

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

$y$ is inversely proportional to $x$. When $x=9$, $y=8$.

Find $y$ when $x=6$.

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

$y$ 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.

Extract:

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

| s | 30 | 40 | 50 | 60 | | t | 4 | 3 | a | 2 |

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

Extract:

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

| ![s] | 30 | 40 | 50 | 60 | | ![t] | 4 | 3 | ![a] | 2 |

Find an equation for ![t] in terms of ![s].

Find the value of $a$.

Extract:

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

| s | 30 | 40 | 50 | 60 | | t | 4 | 3 | a | 2 |

State the total distance that the car has driven.

Extract:

Find an equation for t in terms of s. 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.

Extract:

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 $( p - 1 )$. 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 $( x + 3 )^{2}$ 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 $x=8$.

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