Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 2 • Question 18

Here is a map showing the library, 𝐿, and the school, 𝑆, in a village. (a) Work out the actual distance between the school and the library. (b) The bakery, 𝐵, is 150 metres due north of the school. Mark 𝐵 on the map.

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Video Transcript

Here is a map showing the library, 𝐿, and the school, 𝑆, in a village. Part a) Work out the actual distance between the school and the library. Part b) The bakery, 𝐵, is 150 metres due north of the school. Mark 𝐵 on the map.

So the first thing we need to do to solve part a and work out the actual distance between the school and the library is measure the distance between the school and the library on the map. And when we measure it, we measured that it’s 5.5 centimetres. And the reason I’ve chosen to measure it in centimetres not millimetres is because our scale talked about one centimetre representing 50 metres. So this will make the next step easier.

So as I mentioned already, there’s a scale on the map. And this tells us that one centimetre on the map is equal to 50 metres in real life. So therefore to work out what the actual distance between the school and the library is, we’re gonna multiply 5.5 because that was the number of centimetres on our map between the school and the library by 50. And that’s cause we know that one centimetre is equal to 50 metres. And when we do that, we get an answer of 275 metres.

Now we can do that on the calculator. But if you want to be using a mental method, I’ll just show you one now. So first of all, we can do five times 50. Well, five multiplied by five is 25. And then we just multiply that by 10. So we get 250 and then we have 0.5 times 50. Well, what this means is half of 50 or half of 50 is 25. And then if we add 250 and 25, we’re gonna get 275 which is the answer we’re looking for.

Okay, great, now we can move on to part b. In part b, we’re asked to mark where the bakery 𝐵 is. And we’re told that the bakery 𝐵 is 150 metres due north of the school. Well, if we take a look on the map, we know that due north is pointing up the page. And that’s because we’ve got an arrow here telling us which way north is.

So we know what direction we’re gonna mark 𝐵 on the map. It’s gonna be directly north of 𝑆, so directly straight up the page from 𝑆. However, we don’t know how far. And to work that out, we’re gonna use the scale again. We know that one centimetre is equal to 50 metres and the bakery is 150 metres north of the school.

So therefore, to work out how far it’s gonna be on the map, what we’re going to do is divide the real distance, so the actual distance which is 150, by the 50 from our scale factor and that’s because we know that every centimetre is worth 50 metres.

So we want to see how many 50 metres go into the 150. Well, the answer to this is going to be three. And that’s because 150 divided by 50 is three or we can make it easier by dividing the numerator and denominator by 10. So we get 15 divided by five which is three. So therefore, we know that 𝐵 is going to be three centimetres directly above 𝑆. So therefore, we measure a three-centimetre line directly straight above 𝑆.

And at the end of this, we’re gonna mark 𝐵 because this is where 𝐵 is gonna be on the map because we’ve worked out that it’s gonna be three centimetres away from 𝑆 because that’s 150 metres and it’s also due north. So we’ve answered part a and part b.

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