成人快手

Key points

  • Scientific equations or formulae are used to work things out.
  • The is a useful average for analysing data.
  • An equation may need rearranging to help work out a different part of the equation.
  • Using standard units means that scientists around the world can work together more easily.

True or false?

Seconds, hours and years are all units for time.

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Equations in science and how to rearrange them

Watch this video that shows skills learnt in maths that are used in science as well.

While you are watching, look out for how units can often relate to the equation

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Calculating the mean

Two students watch as a car rolls down a ramp.

The mean is a type of . To find the mean, add up all the results and divide by the number of results.

For example, an experiment into how the angle of a ramp affects the time for a toy car to travel a certain distance. Three readings were taken at the first angle, giving results of 5.2, 5.6 and 5.7 seconds.

To find the mean:

(5.2 + 5.6 + 5.7) 梅 3 = 5.5 seconds.

Tip: Calculate the numbers in brackets first. If using a calculator, press enter afterwards, before moving onto the rest of the calculation.

Two students watch as a car rolls down a ramp.
A photo of green apples - There is one red apple in the middle of the green apples.

When collecting data, take to make sure they are correct. A reading that is very different to the others is called an outlier.

When an outlier is spotted in a set of results, take the reading again. An outlier is like spotting a red apple in a crate full of green apples.

For example, in the ramp and toy car experiment, if the readings were 5.2 s, 5.6 s and 8.7 s, the third result of 8.7 s is an outlier should be repeated.

Tip: If a repeat reading of an outlier is closer to the other readings, then the outlier is ignored. It would not be used in the calculation of the mean.

A photo of green apples - There is one red apple in the middle of the green apples.

What does adding all results together and dividing by the number of results calculate?

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Rearranging an equation

In science, scientific equations or formulae are used to work things out.

Here is an example:

  • Pressure is a measure of how much force is acting on an area.
  • To find the pressure, the force acting and the area over which it is acting, need to be known.
  • Pressure is calculated by dividing the force by the area: Pressure = Force 梅 Area

Calculate the pressure

A photo of a person wearing snowshoes, walking on snow.
Image caption,
The snowshoe spreads the weight of the body out over a larger area. This reduces the pressure, which avoids sinking into the snow.
An image a a pair of crosses legs. On one foot is a red high heel on the other foot is a grey and white trainer.
Image caption,
The high-heeled shoe would be more likely to sink into a soft surface than the trainer, due to greater pressure on the area.
A photo of four pieces of yellow paper attached to a corkboard with different coloured pushpins.
Image caption,
You can push a drawing pin in a board because of the increased pressure on its point.

A pair of snowshoes have an area of 2 尘虏 and a force acting on them of 700 N. Calculate the pressure underneath the snowshoes.

Rearrange the equation

The pressure equation can be rearranged to find either the force or the area.

  • To find the force acting on an object: Force = Pressure x Area.
  • To find the area that a force is acting on: Area = Force 梅 Pressure.

Calculate the force acting on a door when a hand with area 0.02 尘虏 applies a pressure of 250 N/尘虏.

Calculate the area that is having a force applied when a person standing on one leg applies a force of 720 N with a pressure of 2200 N/尘虏.

How to use a formula triangle

Another way to work out the equation is by using this formula triangle.

It relates (P), (F) and (A). Put the three letters in the right place and work out two of them in order to find the third.

Here are the steps to use any formula triangle:

  • Cover up the letter with the missing information and use the letters that have information.
  • Look where the divide and multiply symbols are on the triangle to find out how to rearrange the formula.
A triangle that has an F at the top and a P and A at the bottom. A divide symbol separate the F from the P and the A and a multiply symbol separates the P and the A
  • To work out force (F), it is pressure (P) multiplied by area (A).
  • To work out pressure (P), it is force (F) divided by area (A).
  • To work out area (A), it is force (F) divided by pressure (P).

Here is another equation that can be rearranged using a formula triangle:

Speed = distance 梅 time

See if you can rearrange this. Click the show answer button to see if you are right.

There is more information on Forces and movement.

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Standard units

are used in nearly every country in the world.

The table below shows some of the standard units in the SI system.

QuantityUnit nameSymbol
timeseconds
lengthmetrem
energyJouleJ
masskilogramkg
pressurePascalPa
forceNewtonN (1 Pa = 1 N/尘虏)
areametre squared尘虏
speedmetres per secondm/s

Units can give a clue about which equation can be used to work out the answer. For example, speed has units of metres per second. This means that metres - the units for length or distance - divided by seconds - the units for time - gives speed with units of metres per second, m/s.

An image from above of a car travelling on a long and winding road surrounded by fields

First change the data to the correct standard units otherwise the answers will be wrong.

For example, when calculating the average speed of a car that took 2 hours to travel 101 km, both quantities need to be changed to standard units.

An image from above of a car travelling on a long and winding road surrounded by fields
  • The standard unit for time is seconds: 2 hours = 120 minutes = 7200 seconds

  • The standard unit for length or distance is metres: 101 km = 101000 m

  • Speed = distance 梅 time = 101000 梅 7200 = 14 m/s

If the data was not converted into standard units and number were just put into the equation, 101 divided by 2 gives a speed of 50.5 m/s, which is incorrect.

What is the standard unit for time?

What are the standard units for speed in science?

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Test your knowledge

Quiz - Maths skills for science

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Did you know?

A diagram of what NASA鈥檚 Mars Climate Orbiter would look like on Mars

Using different units can have very serious consequences in the real world. NASA鈥檚 Mars Climate Orbiter launched in 1998 and is thought to have burnt and broken up in the atmosphere of Mars. This was partly because units had not been converted by some engineers, meaning the craft travelled too close to the atmosphere.

A diagram of what NASA鈥檚 Mars Climate Orbiter would look like on Mars

Why knowing units is important

A photo of a road lined with trees, at the side of the road is a speed sign that says 80.

In some countries this sign would mean 80 miles per hour, in others it would mean 80 kilometres per hour. Here on this French road, it shows an 80 kilometres per hour limit.

A photo of a road lined with trees, at the side of the road is a speed sign that says 80.
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Play the Atomic Labs game! game

Try out practical experiments in this KS3 science game.

Play the Atomic Labs game!
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More on Working scientifically

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