Scale drawings — Paper 1 · IGCSE Mathematics 0580

6 The scale on a map is 1:250 000. For A road is 4.6 centimetres long on the map. Examiner's Use Calculate the actual length of the road in kilometres. Answer km [2]

2 marks

Mark scheme: 6 11.5 2 M1 for 4.6 × figs 25 or W1 for figs 115

This question in 0580/11 Oct/Nov 2008

13 The diagram shows an accurate drawing of a triangular field. 1 centimetre represents 15 metres. Florentina walks along a straight path from A to the side BC. The path is always the same distance from AB and AC. C A B (a) Using a straight edge and compasses only, construct the line of the path. You must show your construction arcs clearly. [2] (b) The path meets BC at D. How far, in metres, is Florentina from B when she reaches D? Answer(b) m [1]

3 marks

Mark scheme: 13 (a) Correct ruled line with correct arcs and W2 W1 for correct ruled line, 30° to 34° to AB at 30° to 34° to the line AB. (i) with correct arcs but short of BC or (ii) reaching BC with wrong or absent arcs. (b) 105(m) to 112.5(m) 1ft 15 × their DB (±2mm)

This question in 0580/11 May/June 2009

20 A running track has a boundary that is always 40 metres from a straight line, AB. Examiner's AB = 70 m. Use The scale drawing below shows the line AB. 1 centimetre represents 10 metres. A 70 m B (a) Complete the scale drawing accurately to show the boundary of the running track. [2] (b) Calculate, in metres, the total length of the actual boundary. Answer(b) m [3]

5 marks

Mark scheme: 20 (a) Two parallel straight lines 2 W1 for 2 correct lines or 2 semicircles. 7 cm long and 4 cm from AB and two semicircular ends 4 cm from A and from B. (b) 391 or 3 M1 for 2 × 70 soi 391.3 to 391.4 cao and M1 ind for 2 × π × 40 SC2 for answer of 39.1 or 39.13 to 39.14

This question in 0580/12 May/June 2010

7 The scale on a map is 1 : 20 000. Calculate the actual distance between two points which are 2.7 cm apart on the map. Give your answer in kilometres. Answer km [2]

2 marks

Mark scheme: 7.2 × 20000 7 0.54 2 M1 for oe 100000 or SC1 for figs 54 in answer

This question in 0580/11 May/June 2011

17 The scale of a map is 1 : 500 000. For On the map the centres of two cities are 26 cm apart. Examiner's Use Calculate the actual distance, in kilometres, between the centres of the two cities. Answer km [2]

2 marks

Mark scheme: 17 130 2 M1 for 26 × 500 000 or 1 cm represents 5 km oe IGCSE – October/November 2011 0580 13 1 1

This question in 0580/13 Oct/Nov 2011

13 (a) The scale drawing shows the positions of two villages, A and B. The scale is 1 centimetre represents 200 metres. North B North A Scale: 1 cm to 200 m (i) Measure the bearing of B from A. Answer(a)(i) … [1] (ii) Work out the actual distance from A to B. Answer(a)(ii) … m [1] (b) The post box in Village A has a volume of 84 000 cm3. The post box in Village B has a volume of 0.1 m3. Which post box has the greater volume? Show how you decide. Answer(b) Post box in Village … [1] __________________________________________________________________________________________

3 marks

Mark scheme: 13 (a) (i) 326 – 330 1 (a) (ii) 1100 – 1140 1 (b) B 1 dep on 100 000 or [0].084 seen www scores 0

This question in 0580/12 May/June 2014

24 The scale drawing shows the positions in a town of the Police station, P, and the Fire station, F. The scale is 1 centimetre represents 40 metres. North F North Scale: 1 cm to 40 m P (a) Measure the bearing of P from F. Answer(a) … [1] (b) Find the actual distance from F to P. Answer(b) … m [2] (c) The Ambulance station, A, is on a bearing of 236° from F. Work out the bearing of F from A. Answer(c) … [2]

5 marks

Mark scheme: 24 (a) 111 to 115 1 (b) 304 to 320 2 B1 for 7.6 to 8.0 (c) [0]56 cao 2 M1 for 236−180 oe

This question in 0580/12 Oct/Nov 2015

18 This scale drawing shows the positions of two towns, A and B, on a map. North A B (a) Measure the bearing of town B from town A. Answer(a) … [1] (b) On the map, town C is 8 cm from town A on a bearing of 155°. Mark the position of town C on the scale drawing. [2] __________________________________________________________________________________________

3 marks

Mark scheme: 18 (a) 230 1 (b) C marked in correct position 2 B1 for correct distance 8 cm or correct bearing 155°

This question in 0580/13 Oct/Nov 2015

21 The scale drawing shows a park ABCD. The scale is 1 centimetre represents 20 metres. North D C B Scale: 1 cm to 20 m A (a) Find the actual distance AD. … m [2] (b) Measure the bearing of B from A. … [1] (c) There is a path across the park that is equidistant from CB and CD. Using a straight edge and compasses only, construct the position of the path. Show your construction arcs. [2] Question 22 is printed on the next page.

5 marks

Mark scheme: 21(a) 168 2 B1 for 8.4 seen 21(b) [0]74 1 21(c) Correct angle bisector with correct arcs 2 B1 for correct bisector with wrong / no arcs meeting AB

This question in 0580/13 Oct/Nov 2017

21 (a) Change 568 000 cm into metres. … m [1] (b) The scale drawing shows the positions of two towns, A and B. The scale is 1 centimetre represents 5 kilometres. North B North A Scale : 1 cm to 5 km (i) Measure the bearing of town B from town A. … [1] (ii) Find the actual distance, in kilometres, from town A to town B. … km [2]

4 marks

Mark scheme: 21(a) 5680 1 21(b)(i) [0]68 1 21(b)(ii) 46 2 B1 for 9.2 [cm]

This question in 0580/13 May/June 2018

10 The scale drawing shows the positions of town A and town B. The scale is 1 centimetre represents 12 kilometres. North B North Scale: 1 cm to 12 km A (a) Work out the actual distance from town A to town B. … km [2] (b) Measure the bearing of town B from town A. … [1]

3 marks

Mark scheme: 10(a) 102 2 B1 for 8.3 to 8.7 10(b) [0]64[°] 1

This question in 0580/12 Oct/Nov 2018

20 (a) Change 3670 centimetres to metres. … m [1] (b) The scale drawing shows the positions of town S and town T. The scale is 1 centimetre represents 15 kilometres. North S North T Scale: 1 cm to 15 km (i) Find the actual distance between these two towns. … km [2] (ii) Measure the bearing of town T from town S. … [1]

4 marks

Mark scheme: 20(a) 36.7[0] 1 20(b)(i) 117 2 B1 for 7.8 20(b)(ii) 137 1

This question in 0580/11 May/June 2019

13 The scale drawing shows a rock, R. The scale is 1 centimetre represents 30 metres. A lighthouse, L, is 210 m from R, on a bearing of 125°. On the diagram, mark the position of L. North R Scale : 1 cm to 30 m [2]

2 marks

Mark scheme: 13 L correctly marked 2 B1 for 6.8 cm to 7.2 cm B1 for 123˚ to 127˚

This question in 0580/13 May/June 2019

8 The scale drawing shows the positions of town A and town B. The scale is 1 cm represents 12 kilometres. A B Scale: 1 cm to 12 km (a) Find the actual distance between town A and town B. … km [2] (b) Town C is 72 km from town A and 96 km from town B. On the scale drawing, construct the position of town C. [3]

5 marks

Mark scheme: 8(a) 108 2 B1 for 9 cm 8(b) Accurate position of town C with arcs 3 B2 for accurate position of town C without arcs or two arcs, one accurate or B1 for 6 and 8 soi

This question in 0580/12 May/June 2020

10 (a) A circular garden has diameter 11.4 m. Draw the garden accurately, using a scale of 1 cm represents 1.5 m. Scale: 1 cm to 1.5 m [2] (b) On a map, the distance between two towns is 9.6 cm. The scale of the map is 1 : 50 000. Work out the actual distance between the two towns in kilometres. … km [2]

4 marks

Mark scheme: 10(a) Circle with 3.8 cm radius drawn 2 M1 for 11.4 ÷ 1.5 or 5.7 ÷ 1.5 10(b) 4.8 2 9.6 × 50000 M1 for or answer figs 48 100 × 1000

This question in 0580/13 May/June 2020

8 A field, ABC, is in the shape of a triangle. AC = 500 m and BC = 650 m. Using a ruler and compasses only, complete the scale drawing of the field ABC. Leave in your construction arcs. Use a scale of 1 cm to represent 100 m. The side AB has been drawn for you. A B Scale: 1 cm to 100 m [3]

3 marks

Mark scheme: 8 Correct triangle constructed with 3 B2 for correct triangle with no/incorrect AC= 5 cm and BC = 6.5 cm and arcs intersecting arcs or SC2 for accurate triangle with arcs but sides interchanged or B1 for 6.5 [cm] or 5 [cm] soi

This question in 0580/11 Oct/Nov 2020

9 The scale drawing shows the positions of two towns, P and Q. The scale is 1 cm represents 4 km. North Q North P Scale: 1 cm to 4 km (a) Find the actual distance between town P and town Q. … km [2] (b) Measure the bearing of town Q from town P. … [1] (c) Town X is 28 km from town P on a bearing of 140°. On the scale drawing, mark the position of town X. [2]

5 marks

Mark scheme: 9(a) 32.8 2 M1 for 8 [cm] to 8.4 [cm] seen or for their measurement [in cm] multiplied by 4 9(b) 065 1 9(c) X correctly placed 2 M1 for X on bearing of 140° from P 7 cm from P on a bearing of 140° or for X 7 cm from P If 0 scored, SC1 for X on bearing of 140 from Q and 7 cm from Q

This question in 0580/11 Oct/Nov 2021

4 The scale drawing shows the positions of town A and town B. The scale is 1 cm represents 15 km. North North B A Scale: 1 cm to 15 km (a) Find the actual distance between town A and town B. … km [2] (b) Measure the bearing of town B from town A. … [1]

3 marks

Mark scheme: 4(a) 111 [km] 2 M1 for 7.2[cm] to7.6[cm] seen or for their measurement [in cm] multiplied by 15 evaluated 4(b) [0]71 1

This question in 0580/11 May/June 2022

9 The scale drawing shows the positions of town A and town B. North A B Measure the bearing of town B from town A. … [1]

1 marks

Mark scheme: 9 135 1

This question in 0580/12 May/June 2023

11 The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B. … km [2]

2 marks

Mark scheme: 11 8.75 2 3.5  250000 M1 for oe 100  1000 or B1 for figs 875 or 1 cm : 2.5 km

This question in 0580/12 May/June 2023

14 The scale of a map is 1 : 40 000. On the map the distance between two villages is 37 cm. Calculate the actual distance between the two villages. Give your answer in kilometres. … km [2]

2 marks

Mark scheme: 14 14.8 2 M1 for 1 cm represents 0.4 km soi or B1 for figs 148 as answer

This question in 0580/13 May/June 2024

12 The scale drawing shows the positions of two ships, A and B. The scale is 1 cm represents 6 km. North A Scale : 1 cm to 6 km B (a) Measure the bearing of ship B from ship A. … [1] (b) Find the actual distance between the two ships. … km [2]

3 marks

Mark scheme: 12(a) 143 1 12(b) 39 2 B1 for 6.5 or M1 for their 6.5 × 6

This question in 0580/12 Oct/Nov 2024

9 The scale drawing shows the positions of town K and town L. The scale is 1 cm represents 10 km. North L North K Scale : 1 cm to 10 km (a) Find the actual distance between town K and town L. … km [2] (b) Measure the bearing of town L from town K. … [1] (c) Town M is 40 km from town L on a bearing of 140°. On the scale drawing, mark the position of town M. [2]

5 marks

Mark scheme: 9(a) 85 2 B1 for 8.5 or M1 for their 8.5 × 10 9(b) 065 1 9(c) M in correct position 2 B1 for a correct length, 4cm or B1 for a correct bearing, 140º

This question in 0580/13 Oct/Nov 2024

13 The scale drawing shows the positions of town A and town B. The scale is 1 centimetre represents 10 kilometres. North B North A Scale: 1 cm to 10 km (a) Work out the actual distance from town A to town B. … km [2] (b) Measure the bearing of town B from town A. … [1] (c) Town C is 45 km from town A on a bearing of 310°. On the scale drawing, mark the position of town C. [2]

5 marks

Mark scheme: 13(a) 80 2 B1 for 8 or M1 for their 8 × 10 13(b) 032 1 13(c) Point correctly plotted 2 B1 for distance 4.3 to 4.7 cm from A or B1 for bearing 308º to 312º from A

This question in 0580/11 Oct/Nov 2025