While this may seem to be more difficult, the process is almost the same as the last section. If you follow the method precisely, you will have no difficulties.
Questions using more complex forms of proportionality require us to think carefully about what is going on before starting to calculate. The phrases to look out for are:
The cost of a circular badge is directly proportional to the square of its radius. The cost of a badge with radius of $2\text{ cm}$ is $\text{£}0.68$. Find:
As with all of these questions, if you set it up correctly each time, you will start to see the similarities between questions, more than you see the differences.
This time the proportionality is to square of $r$ or $r^2$. After that the working is very similar to all the others we have done in the past two topics.
The mass $M \text{ kg}$, of a solid cube made from lead is proportional to the cube of the length, $L \text{ cm}$, of an edge. When $L = 0.2$, $M = 90$,
As before, the cube is different, but the rest of the method is identical.
$y$ is directly proportional to the square root of $x$. When $x=30$, $y=36$. Find
The force of attraction, $F$ newtons, between two spheres is inversely proportional to the square of the distance, $d \text{ m}$, between the centres of the spheres. When $d = 2$, $F = 0.006$,
The temperature, in degrees Celsius, of sea water varies inversely with the depth (in kilometres) where the measurement was taken. When a reading was taken at a depth of $8 \text{km}$, the temperature was found to be $3^\circ \text{C}$
The time, in seconds, taken to boil a pan of water on a gas hob is inversely proportional to the setting number of the gas ring. When the gas ring is set at $4$, the time taken for the water to boil is $120 \text{ s}$.
This answer is one of any number of correct answers in part a. Other letters can be used. $t$ and $s$ are just my choices.
The kinetic energy of an engine, $\text{E Joules}$ varies as the square of the speed, $v \text{ m/s}$ at which the engine is running. When the speed is $15 \text{ m/s}$, the kinetic energy is $540 \text{ Joules}$.
The tension in an elastic string ($\text{T Newtons}$) is directly proportional to the extension
($x \text{ m}$) of the string. When the tension is $40\text{N}$, the length of the extension is $5 \text{ m}$.
$\text{E}$ is inversely proportional to $\text{G}$.
When $\text{E} = 9$, $\text{G}=25$.
Find the value of $\text{E}$ and $\text{G}$ when $\text{E}=\text{G}$.
The mass $m \text{ kg}$ of a brick is directly proportional to the cube of the length $d\text{ m}$ of the brick.
If a larger similar brick is made, with a length double that of the original, how many times greater is its mass?
In a company development department, it is found that the length of time (in days) to complete a project is inversely proportional to the number of workers employed on the project. It is observed that $6$ workers will take $7$ days to complete a project.
$x$ is proportional to the square root of $y$. Calculate the percentage increase in $x$, when $y$ is increased by $35\%$. Give your answer correct to $2$ significant figures.
The percentage increase in $x$ is $16\%$
$\text{Z}$ is directly proportional to the square root of $\text{Y}$.
$\text{Y}$ is inversely proportional to the square of $\text{X}$.
When $\text{Z} = 15$, $\text{Y} = 9$
When $\text{Y} = 16$, $\text{X} = 3$
Find the value of $\text{Z}$, when $\text{X} = 2$
Match up the numbered proportionality statements with graph which could be a representation of the statements.
