Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 16

GCSE Mathematics Foundation Tier Pack 2 • Paper 3 • Question 16


Video Transcript

Lara has drawn the following scale drawing for her garden. She has marked the corner of the shed and the centre of the pond with a cross. a) Work out the real distance between the marked corner of the shed and the centre of the pond. And b) find the bearing from the centre of the pond to the marked corner of the shed.

It’s worth mentioning that because this is a scale drawing question, when you print the question out on your printer, make sure the setting say that it’s 100 percent size. Don’t scale to fit the size of page. So we need to know where the crosses are on our drawing. And we need to know the scale of this drawing.

We’re going to need to accurately measure this distance with our ruler and then use the scale to work out what the real distance is. Then, in part b of the question, we’re going to be measuring this angle round here accurately with our protractor. And that will give us the bearing off the corner of the shed from this point on the scale drawing.

One more thing, make sure that you look directly down on top of your ruler when taking measurements. Because your ruler has a certain thickness, if you look at this from an angle, you may read off the wrong measurement. Okay, let’s get on and do our measuring.

Take a moment to carefully lay down the ruler on the page. Make sure that the zero mark lines up exactly with one of the crosses and then read off exactly where the other cross meets. This is a centimetre ruler. And in between each centimetre, there are a 10 little markings. So this is 8.5 centimetres.

Now, the scale tells us that one centimetre on the drawing represents six metres in real life. But we don’t have one centimetre, we have 8.5 centimetres. That’s 8.5 times as big as one centimetre. So it’s going to represent 8.5 times as many metres. So to work out how many metres that represents, we’re gonna have to do six times 8.5.

Now, six times five is 30, so zero units and carry the three tens. Then, six times eight is 48. But we got the three to carry from before. So 48 plus three is 51. Now, there was one decimal place in the calculation, 8.5. So this is gonna be one decimal place in our answer. So the answer is 51.0.

And as a quick mental check, we can think two times 8.5, well, two times eight is 16 and two times 0.5 is one. So two times 8.5 is 17. And three times 17, well, three times 10 is 30. Three times seven is 21. If we add those two together, we get 51.

The answer to part a then is the real distance is 51 metres.

And in part b, we need to find the bearing from the centre of the pond to the marked corner of the shed. So the way we do that is we stand at the centre of the pond, we face directly north, and then we work out how many degrees do we have to turn clockwise to facing the direction that we want to face.

So the first thing to do is to draw in this line between the two crosses. Now, most protractors only measure up to 180 degrees. This angle here that we’re trying to measure is greater than 180 degrees. So we’re gonna have to use a little trick. We know that a full circle is 360 degrees. So if we measure this angle here and subtract that from 360, we can work out the measure of the angle that we want.

First, carefully line up the baseline of the protractor that between the zeros on the base here with the north arrow. Then, make sure that the centre of the crosshairs here matches the centre of the cross. Finally, find the scale that begins at zero and use that to measure up to your angle. In that case, it’s between 30 and 40 degrees.

Now, there are 10 little ticks between 30 and 40 degrees. So each one of those little ticks represents one degree. The line that we’re looking for is on the eighth one of those. So that tells us that the angle is 38 degrees.

So this angle here is 38 degrees. But we’re looking for the other angle. So the calculation is 360 degrees minus 38 degrees which is 322 degrees. Remember when we’re giving bearings, we must give three digits. And in fact, 322 is three digits. So our answer is the bearing is 322 degrees. But if the bearing we were looking for was only 38 degrees, we would need to have put a leading zero in front of it. So we would have to give our answer as 038 degrees.

Finally, it’s worth mentioning that because these are measurements, you get as bit of leeway with your answers. That means you’d still get some marks if in the first part your measurement was between 8.3 centimetres and 8.7 centimetres and therefore your real distance was between 49.8 and 52.2 or in part b your bearing was between 320 degrees and 324 degrees.

But generally speaking, with these questions, it’s worth taking your time and being as accurate as you can to maximize the marks that you get.

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