Standard & Compound Units Practice Questions

Write $2.4$ tonnes in kilograms.

Write $0.75\text{ m}^2$ in $\text{cm}^2$.

Write $4500\text{ cm}^3$ in litres.

A packing crate stands on a horizontal floor. The base of the crate is a rectangle measuring $1.2$ m by $0.5$ m. The crate exerts a force of $1560$ newtons on the floor.

Work out the pressure, in $\text{N/m}^2$, that the crate exerts on the floor.

A different crate exerts a pressure of $4000\text{ N/m}^2$ on the floor. The base of this crate has an area of $0.35\text{ m}^2$.

Work out the force this crate exerts on the floor.

How many minutes does Bus B take to travel from Hartwell to Cromer Park?

Sara lives in Hartwell. She must arrive at Cromer Park by 09:30.

Write down the time of the latest bus she can catch from Hartwell.

The distance from Hartwell to Cromer Park is $24$ km.

Work out the average speed of Bus B for this journey. Give your answer in km/h.

The density of ice is $0.92\text{ g/cm}^3$.

Change $0.92\text{ g/cm}^3$ into $\text{kg/m}^3$.

A conveyor belt in a factory moves at a constant speed of $1.4$ m/s.

Work out this speed in km/h.

Priya went for a bike ride.

She cycled the first $18$ km at an average speed of $24$ km/h.
She then rested for $15$ minutes.
She then cycled a further $12$ km at an average speed of $18$ km/h.

Work out Priya's average speed for the whole bike ride, including the rest.

A rectangular lawn measures $1250$ cm by $840$ cm.

Fertiliser is spread on lawns at a rate of $35$ grams per square metre.

Work out the mass of fertiliser needed for this lawn. Give your answer in kilograms.

Work out Kelvin's basic rate of pay in pence per minute.

Last week Kelvin was paid a total of £$467.40$.

Work out the number of overtime hours he worked last week.

Work out the mass of the cylinder. Give your answer in kilograms, correct to 3 significant figures.

A trolley can safely carry a total mass of at most $50$ kg.

Work out the greatest number of these cylinders that can be carried safely on the trolley at the same time.

An alloy is made by melting together two metals.

$400$ g of metal A, of density $8.9\text{ g/cm}^3$, is mixed with $250$ g of metal B, of density $7.1\text{ g/cm}^3$.

The volume of the alloy is equal to the total volume of the two metals.

Work out the density of the alloy. Give your answer correct to 2 decimal places.

Show that the average speed of the car for the whole journey is $\dfrac{2uv}{u+v}$ km/h.

Aisha drives $30$ km at an average speed of $45$ km/h and then a further $30$ km at an average speed of $30$ km/h.

Use the result in part (a) to work out her average speed for the whole journey.

A swimming pool is in the shape of a cuboid. The pool is $25$ m long and $10$ m wide, with a uniform depth of $1.6$ m.

The pool is filled completely using two pipes. Water flows through each pipe at a rate of $450$ litres per minute.

Work out how long it takes to fill the empty pool. Give your answer in hours and minutes, correct to the nearest minute.

($1\text{ m}^3=1000$ litres)

Tom drives to work each morning.

He drives the first $12$ km through town at an average speed of $36$ km/h.
He then drives $30$ km on the motorway at an average speed of $90$ km/h.

Tom says,

"My average speed for the whole journey to work is $63$ km/h, because $63$ is the mean of $36$ and $90$."

Is Tom correct? You must show how you get your answer.