Bounds | Upper bound | Lower bound | GCSE

This video is going to show you how to solve maths calculations that are based on using the upper bound and lower bound of a measurement.

This is a core skills video, so I’ll be explaining the basics of bound calculations and I’ll build on this in a later video that will have harder questions needed for higher level study.

But to begin with, let’s look at a standard question requiring the use of bounds.

In this question we’re told that a garden has a length of 20 metres and a width of 6 metres and we’re asked to calculate the upper bound and lower bound for the area of the garden.

To do this I’m going to draw a simple diagram of the garden, where we have the length and the width given, and I want to focus on what it means when the measurements are given to the nearest metre.

All questions about bounds will have this phrase because they are questions based on the accuracy of a measurement and how this affects our calculations.

So, to understand what this means we’re going to think about the accuracy of the length and width measurement of the garden.

If the length is measured to the nearest metre it means that it can only be measured accurately between 19.5 m and 20.5 m. What I’ve done here is added half a metre onto 20, and I’ve subtracted half a metre from 20.

So I’ve divided a metre by 2 and added and subtracted the result in either direction.

If we were told the measurement was to the nearest 10 cm, I would have added 5 cm, and also subtracted 5 cm.

So for questions about bounds you need to consider the range for which the measurement is accurate.

In this case, the upper bound for length is 20.5 m, and the lower bound for length is 19.5 m and this will be crucial for the area calculation.

We can consider the width in a similar way because we were told that it was also measured to the nearest metre, so we add on half a metre to get an upper bound of 6.5 m, and we subtract half a metre to get a lower bound of 5.5 m.

Note that the difference between these values is 1 metre, because that is what we were told about the accuracy of the measurements.
So if we want to calculate the upper bound for the area of the garden, we need to recall that the area of a rectangle is length times width, and so the upper bound will use the highest values and then multiply them together.

We therefore get 20.5 multiplied by 6.5 to give an upper bound area of 133.25 metres squared.

So, for the lower bound for area, we take the lower values above which gives 19.5 multiplied by 5.5 and therefore a lower bound area of 107.25 metres squared.

So what these results mean is that the area of the garden is somewhere between these two values, but we can’t calculate it more accurately that this.

This is because all measurements are not completely precise so there’ll always be a degree of error, and this is the principle behind questions you might be asked about bounds.

Now that you’ve got to the end of the video don’t forget to like, comment and share and subscribe if you what more help with your maths. Thank you.