GCSE. Maths. Measures and Construction Maps and Scale Drawings

Transcription

1 GCSE Maths Measures and Construction Maps and Scale Drawings

2 Information A plan or drawing cannot be drawn life-size, therefore they are drawn to scale. This means that everything is measured and made smaller in the same way. A scale can be written in different ways. It can be written as a ratio using the same units or as a statement using different units. 1 cm : cm or 1 : cm : 500 m If you are using different units of measurement, then you need to state the units being used. Maps use different scales and are generally less detailed. They are often on a scale like this: Use a ruler to measure the length of the line that represents for example 30 kilometres, and then use this scale to measure the distance on the map. It is important that you check the scale very carefully before working out measurements or distances. Example Scale 1 cm : 30 m Map Measurement Actual Measurement Fenwick Street Med Street 4.5 cm 135 m 2.2 cm 66 m 2

3 Exercise 1 Show how you have worked out your answer. Write each of these statements as a ratio in the form 1 : x a) 1 centimetre : 1 metre b) 1 centimetre : 50 kilometres c) 1 millimetre : 5 kilometres 3

4 Exercise 2 This is the ground floor of a house. Scale: 1 cm : 1.2 m Kitchen Dining Area Table Hall Width Lounge 4

5 Exercise 2 A ruler is necessary for this exercise. Show how you have worked out your answer. a) Using the scale, what is the actual internal width of the Lounge? b) A bookcase bought for the Lounge is 80 cm wide. How long would this be on the plan? c) What is the actual length and width of the Dining Table? d) What is the actual internal length of the Hall? 5

6 Exercise 3 This is a plan of the outdoor area of the Ladybird Play Centre. Scale: 1 :

7 Exercise 3 A ruler is necessary for this exercise. Show how you have worked out your answer. Work out the actual: a) width of the sandpit. b) length of the grassed area. c) length of the apparatus area. d) width of the entire outdoor area. 7

8 Exercise 4 This is a plan of the outdoor area of the Ladybird Play Centre. Scale: 1 :

9 Exercise 4 A ruler is necessary for this exercise. Show you have worked out your answer. Jenny is thinking about ordering apparatus which cover a floor space measuring 9.25 metres by 8 metres. Will the actual apparatus fit on the allotted area according to the plan? 9

10 Exercise 5 Plans and Elevations This is a net plan of a garden shed without a roof. Fill in the missing dimensions marked, on the 2D plan. Using the scale, as stated, calculate the actual: width of the door width of the windows 7 cm cm cm cm Back Front SCALE 2 : 100 (2 cm = 1 m in this drawing.) 10

11 Exercise 5 A ruler is necessary for this exercise. Show how you have worked out your answer.

12 Exercise 6 Scale: Metres

13 Exercise 6 A ruler is necessary for this exercise. Show how you have worked out your answer. Complete the table below by measuring the shortest distance by road on the map and then work out the actual distances. From To Approximate Kilometres (to 1 d.p.) Port Riley (North) Middleton Lighthouse Highcliffe Port Riley (South) Horseshoe Bay Nortown Celtic Cross Celtic Cross Highcliffe

14 Exercise 7 Scale: Metres

15 Exercise 7 A ruler is necessary for this exercise. Clearly show how you have worked out your answer. Sam lives at Port Riley (North) and has to visit the lighthouse to make urgent repairs. There are major road works in Middleton, indicated on the map as closed roads. The only roads that are open are the Celtic Cross and Port Riley (South) roads. The speed limit for cars on the island is 20 km/h. Sam also has the use of a boat which can travel at 18 km/h. The boat is at Port Riley jetty. There is also a jetty at the lighthouse. The boat can only be moored at a jetty. The boat must sail in the channel which runs directly from each jetty to the closest marker buoy. The direct line between the buoys marks the safe distance from the shore in which the boat can sail. Do not include the walking times to and from the jetty or the end of the road in your calculations. Would he be quicker going by boat or car?