# Maths skills for science

## Jump to

## 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. **

True.

## Equations in science and how to rearrange them

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

## Calculating the mean

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) ÷ 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.

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.

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

The mean.

## 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 ÷ Area**

### Calculate the pressure

**A pair of snowshoes have an area of 2 m² and a force acting on them of 700 N. Calculate the pressure underneath the snowshoes.**

**Working out:**

Pressure = | ? |

Force = | 700 N |

Area = | 2 m² |

**Answer:**

Pressure = | Force ÷ Area |

Force = | 700 N |

Area = | 2 m² |

### 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 ÷ Pressure.**

**Calculate the force acting on a door when a hand with area 0.02 m² applies a pressure of 250 N/m².**

Force = | Pressure x Area |

Force = | 250 x 0.02 |

Force = | 0.5 N |

**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/m².**

Area = | Force ÷ Pressure |

Area = | 720 ÷ 2200 |

Area = | 0.33 m² |

### 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.

- 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 ÷ time

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

Speed = | distance ÷ time |

Distance = | speed x time |

Time = | distance ÷ speed |

There is more information on Forces and movement.

## Standard units

are used in nearly every country in the world.

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

Quantity | Unit name | Symbol |
---|---|---|

time | second | s |

length | metre | m |

energy | Joule | J |

mass | kilogram | kg |

pressure | Pascal | Pa |

force | Newton | N (1 Pa = 1 N/m²) |

area | metre squared | m² |

speed | metres per second | m/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.

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.

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 ÷ time = 101000 ÷ 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? **

Seconds.

**What are the standard units for speed in science? **

Metres per second (m/s).

## Test your knowledge

### Quiz - Maths skills for science

## Did you know?

Using different units can have very serious consequences in the real world. NASA’s 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.

### Why knowing units is important

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.