Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 7

Jack is searching for treasure on an island. He has the following map of the island and has marked his location on it. a) In which direction should Jack walk to get to the shipwreck? Circle your answer. [A] Southwest [B] Southeast [C] Northwest [D] Northeast? b) Circle the bearing of Dead Man’s Cave from the Abandoned Fort. [A] 090° [B] 180° [C] 270° [D] 360° c) Find the distance, in metres, from Jack’s location to Skull Rock. d) Jack thinks that from Skull Rock, he just has to walk 1600 m to get to the Abandoned Fort. Why might he be incorrect?

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Video Transcript

Jack is searching for treasure on an island. He has the following map of the island and has marked his location on it. Part a) In which direction should Jack walk to get to the shipwreck? Circle your answer. Is it southwest, southeast, northwest, or northeast?

There are also parts b), c), and d) to this question, which we will look at later. We are told in the question that north is pointing vertically upwards, which is usually the case when given a map. The compass point south points vertically downwards. West points to the left. And east points to the right horizontally. The four main points on a compass going clockwise from north are north, east, south, and west. One acronym that is used to remember this is “Never Eat Shredded Wheat.”

The four answers in this part of the question, southwest, southeast, northwest, and northeast, split these four points. The compass point halfway between north and east is northeast. Likewise, the compass point halfway between south and east is southeast. We can find the compass points southwest and northwest in the same way. We are told in this question that Jack wants to walk to the shipwreck. The shipwreck is diagonally down and to the left from Jack’s location. This corresponds to the compass point southwest. The direction that Jack needs to walk to get to the shipwreck is southwest. The second part of the question says the following.

b) Circle the bearing of Dead Man’s Cave from the Abandoned Fort. Is it 90 degrees, 180 degrees, 270 degrees, or 360 degrees?

Before starting this question, it is important that we remember how we measure bearings. Bearings must always have three figures. This is why there is a zero in front of the 90 degrees. They are also measured clockwise from north. We must use our protractor or knowledge of compass points to measure in a clockwise direction from north. As we start to measure from north, this compass point has the bearing 000 degrees. When we return to this compass point having moved in a clockwise direction, we have completed a full circle. Therefore, this is also equal to 360 degrees.

The angle between the north and east points on a compass is a right angle. As a right angle is equal to 90 degrees, the bearing when walking in an easterly direction is 090 degrees. The compass point south has a bearing of 180 degrees. This is because north and south are on a straight line. And angles on a straight line add up to 180 degrees. Adding another 90 degrees to this gives us 270 degrees. Therefore, when walking in a westerly direction, we are travelling on a bearing of 270 degrees.

In this part of the question, we want to calculate the bearing of Dead Man’s Cave from the Abandoned Fort. This means that we’re starting at the Abandoned Fort and walking towards Dead Man’s Cave. Walking from the Abandoned Fort to Dead Man’s Cave means we’re walking in a westerly direction. We know that when travelling west, we’re travelling on a bearing of 270 degrees. This means that the correct answer of the bearing of Dead Man’s Cave from the Abandoned Fort is 270 degrees.

We can show this on the map by firstly drawing a north line at the Abandoned Fort as this is the point we are starting from. We measure in a clockwise direction until we hit the line that joins the Abandoned Fort and Dead Man’s Cave. This angle is equal to 270 degrees, confirming that our answer is correct. A couple of common mistakes or misconceptions here are that the angle would be 180 degrees as we’re walking in a straight line. However, this is incorrect. We must always measure our bearings from the compass point north in a clockwise direction. The third part of the question says the following.

c) Find the distance, in metres, from Jack’s location to Skull Rock.

When dealing with any question like this on a map, it is important to note that we are finding the straight line distance. This is sometimes called as the crow flies. In reality, the distance that Jack would have to travel might be greater as he might not be able to travel in a straight line. And the ground might not be flat. We are told underneath the map that the scale is one centimetre to 400 metres. This means that one centimetre on the map is equal to 400 metres on the island.

Our first step is to measure the distance on the map between Jack’s location and Skull Rock. If we are printing the map, it is important that we print it at full size. Otherwise, our answer when we measure this distance will be different. It is also important that we measure as accurately as possible although there will be a small margin for error in most exams.

The distance on the map is equal to 7.2 centimetres. To get from one to 7.2, we multiply by 7.2. This means that we need to multiply 400 by 7.2 to calculate the distance in metres. This is equal to 2880 metres. The straight line distance in metres from Jack’s location to Skull Rock is 2880 metres.

If we didn’t have a calculator, we could still work out this calculation, 400 multiplied by 7.2. We could do this by splitting 400 into four multiplied by 100. We could then firstly multiply 100 by 7.2. This is equal to 720 as multiplying any number by two moves all the digits two places to the left. Four multiplied by 72 is equal to 288. Therefore, four multiplied by 720 is equal to 2880. This is the same answer as we got on the calculator. The final part of the question says the following.

d) Jack thinks that from Skull Rock, he just has to walk 1600 metres to get to the Abandoned Fort. Why might he be incorrect?

The distance on the map between Skull Rock and the Abandoned Fort is four centimetres. We know that the scale on the map is one centimetre to 400 metres. This means that four centimetres on the map would indeed be equal to 1600 metres. Multiplying one by four gives us four. And multiplying 400 by four gives us 1600. This initially suggests that Jack is correct. He does have to walk 1600 metres to get to the Abandoned Fort. However, we are looking for a reason why he might be incorrect.

As mentioned in part c), we don’t know whether he’s able to walk in a straight line from Skull Rock to the Abandoned Fort. We also don’t know whether the land or ground is flat. One reason why he might be incorrect is that we don’t know the elevation of the island. The distance between the two places would only be 1600 metres if it was completely flat. If the ground wasn’t completely flat, the distance between the two points would be greater.

A different answer that would also be correct is that we don’t know if he can walk in a straight line. This is the straight line distance between Skull Rock and the Abandoned Fort. Once again, if he can’t walk in a straight line, then Jack would walk a distance greater than 1600 metres.

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