GCSE Compound measures Practice Questions

Write down the formula

Speed is the distance divided by the time.

Substitute the values and divide

Dividing $120$ by $2$ gives $60$.

State the answer with its units

The speed is $60\,\mathrm{km/h}$.

Recall what pressure measures

Pressure measures how much force is pressing on each unit of area.

Think about the units

The unit newtons per square metre is a force divided by an area, and the unit tells you the formula.

Select the correct formula

So pressure = force divided by area. For example, $180\,\mathrm{N}$ on $9$ square metres gives $20\,\mathrm{N}$ per square metre.

Write down the formula

Density is mass divided by volume.

Multiply both sides by the volume

This clears the fraction and gives the mass.

Divide both sides by the density

So the volume is the mass divided by the density.

Test the rearrangement with numbers

A mass of $84\,\mathrm{g}$ and a density of $7\,\mathrm{g}$ per cubic centimetre give a volume of $12$ cubic centimetres, and $7$ times $12$ is indeed $84$.

Check the answer by working backwards

Density times volume returns the mass, so the rearrangement is consistent.

State the final answer

The final answer is volume = mass divided by density.

Write down the rule for average speed

The rest counts as part of the total time, even though no distance is covered during it.

Work out the time for the first ride

Twenty-four km at $16\,\mathrm{km/h}$ takes one and a half hours.

Convert the rest into hours

Fifteen minutes is a quarter of an hour.

Work out the time for the second ride

Eighteen km at $24\,\mathrm{km/h}$ takes three quarters of an hour.

Add the distances and the times

The cyclist covers $42\,\mathrm{km}$ in a total of $2.5$ hours from start to finish.

Divide the total distance by the total time

The average speed for the whole journey is $16.8\,\mathrm{km/h}$.

Check the answer by working backwards

Riding at $16.8\,\mathrm{km/h}$ for $2.5$ hours covers $42\,\mathrm{km}$, which matches the real total distance.

Avoid the common error

The mean of the two riding speeds is $20\,\mathrm{km/h}$. That ignores the rest and ignores the different times spent riding, so it is wrong.

Check the units

Kilometres divided by hours gives km/h.

State the final answer

The final answer is $16.8\,\mathrm{km/h}$.

Decide on a common unit

Speeds can only be compared once they are all written in the same unit.

Convert $20\,\mathrm{m/s}$

Multiplying metres per second by $3.6$ gives kilometres per hour, because there are $3600$ seconds in an hour and $1000$ metres in a kilometre.

Leave $70\,\mathrm{km/h}$ as it is

This speed is already in the chosen unit.

Convert $1.1\,\mathrm{km}$ per minute

There are $60$ minutes in an hour, so multiply by $60$.

Convert $19\,\mathrm{m/s}$

Nineteen metres per second is $68.4$ kilometres per hour.

Convert $1150$ metres per minute

In an hour this covers $69\,000$ metres, which is $69\,\mathrm{km}$.

Put the five speeds in order

Once every speed is in km/h the comparison is straightforward.

Identify the greatest

The greatest speed is $20\,\mathrm{m/s}$, which is $72\,\mathrm{km/h}$.

Check the answer by working backwards

Converting back gives $20\,\mathrm{m/s}$, so the conversion was right.

Avoid the common error

Comparing the bare numbers $20$ and $70$ without converting would wrongly pick $70\,\mathrm{km/h}$. The units must match first.

Check the units

The factor $3.6$ comes from multiplying by $3600$ seconds and dividing by $1000$ metres.

Sanity-check the size of the answer

Seventy-two km/h is roughly $45\,\mathrm{mph}$, a fast road speed, which is a sensible answer for the greatest of the five.

Note how the formula rearranges

No rearrangement is needed here; the work is entirely in the units.

Reflect on the method

Comparing compound measures always starts by writing them all in one unit.

State the final answer

The final answer is $20\,\mathrm{m/s}$, which is $72\,\mathrm{km/h}$.