True or False? To find the average speed for a journey made in two parts, add the two speeds and halve the result.

False. You can only average the two speeds when each part of the journey takes the same length of time , which is unusual. Otherwise the longer part of the journey counts for more.

Define a compound measure .

A compound measure is a quantity worked out from more than one other measurement. Compound measures are used to describe rates , which say how much one quantity changes for each unit of another.

A quantity is measured in units written in the form a/b . What does that tell you about its formula?

The formula is whatever a measures divided by whatever b measures. For example a rate of pay in dollars per hour is an amount of money divided by a time , because dollars measure money and hours measure time.

How do you use a formula triangle ?

Cover up the quantity you want to find. If it sat on the top of the triangle, multiply the two beneath it; if it sat on the bottom , divide the top one by the other.

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Compound Measures & Speed (Cambridge (CIE) IGCSE International Maths: Extended): Flashcards

Exam code: 0607

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Complete the formula for average speed.
$speed = \frac{______}{______}$

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Cards in this collection (14)

Complete the formula for average speed.
$speed = \frac{______}{______}$
The completed formula is:
$speed = \frac{distance}{time}$
The word "speed" here always means average speed across the whole journey, not the speed at a single moment.
True or False?
To find the average speed for a journey made in two parts, add the two speeds and halve the result.
False.
You can only average the two speeds when each part of the journey takes the same length of time, which is unusual.
Otherwise the longer part of the journey counts for more.
A runner covers 10 km in three quarters of an hour. What is their average speed in metres per second, to 3 significant figures?
Convert both quantities first, since 10 km is 10 000 m and three quarters of an hour is 2700 s.
Dividing gives $10000 \div 2700 = 3.7037 \dots$ which rounds to 3.70 m/s as the answer.
True or False?
A speed in $km/h$ can be used directly with a time measured in minutes.
False.
The units have to match before you multiply or divide, so either change the time into hours or change the speed into kilometres per minute.
Using hours and minutes together makes the answer wrong by a factor of 60.
How far does a car travelling at a steady $60 km/h$ go in 2.5 hours?
The car travels 150 km, because $60 \times 2.5 = 150$ when the speed is multiplied by the time.
No conversion is needed here, because the speed is in kilometres per hour and the time is already in hours.
A sprinter runs 100 m at an average speed of $8.85 m/s$ throughout. How long does the run take, to the nearest hundredth of a second?
Rearranging gives $time = \frac{100}{8.85}$ which works out as $11.29943 \dots$ seconds.
Rounded to the nearest hundredth of a second that gives 11.30 s as the answer.
True or False?
A speed of $1 m/s$ is the same as a speed of $3.6 km/h$ exactly.
True.
In one hour an object moving at 1 metre per second covers $1 \times 3600 = 3600$ metres.
That is 3.6 kilometres, so the two speeds are the same.
Define a compound measure.
A compound measure is a quantity worked out from more than one other measurement.
Compound measures are used to describe rates, which say how much one quantity changes for each unit of another.
A quantity is measured in units written in the form a/b. What does that tell you about its formula?
The formula is whatever a measures divided by whatever b measures.
For example a rate of pay in dollars per hour is an amount of money divided by a time, because dollars measure money and hours measure time.
Complete these two compound measure formulas.
$density = \frac{______}{volume}$
$pressure = \frac{force}{______}$
The completed formulas are:
$density = \frac{mass}{volume}$
$pressure = \frac{force}{area}$
Both follow the units, since a density in ${kg/m}^{3}$ is a mass over a volume and a pressure in ${N/m}^{2}$ is a force over an area.
What does population density measure, and what are its units?
Population density is the number of people per unit of area, so it is a population divided by an area.
It is usually given in people per square kilometre, written as ${people/km}^{2}$ in units form.
True or False?
Fuel consumption always means the volume of fuel used divided by the distance travelled.
False.
It depends on the units: a fuel consumption in $km/litre$ is a distance divided by a volume, while one in $litres/km$ is the other way round.
Read the units first, then decide which quantity goes on top.
How do you use a formula triangle?
Cover up the quantity you want to find.
If it sat on the top of the triangle, multiply the two beneath it; if it sat on the bottom, divide the top one by the other.
A pump has a flow rate of 720 litres per minute. How many litres does it deliver in 3.1 seconds?
Change the rate into litres per second first, since $720 \div 60 = 12$ litres pass each second.
Then multiply by the time, giving $12 \times 3.1 = 37.2$ litres altogether.

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