Scale drawings — Paper 2 · IGCSE Mathematics 0580

19 A model of a car is made to a scale of 1 : 40. The volume of the model is 45 cm3. Calculate the volume of the car. Give your answer in m3. Answer m3 [3]

3 marks

Mark scheme: 19 2.88 3 M1 403 oe seen A1 2 880 000 B1ft their 2 880 000 ÷ 1003 or B1 0.000045 M1 403 A1 cao or M1 0.43 M1 45 × 0.43 A1 4

This question in 0580/23 Oct/Nov 2010

13 The scale on a map is 1: 20 000. ForFor Examiner'sExaminer's (a) Calculate the actual distance between two points which are 2.7 cm apart on the map. UseUse Give your answer in kilometres. Answer(a) km [2] (b) A field has an area of 64 400 m2 . Calculate the area of the field on the map in cm2 . Answer(b) cm2 [2]

4 marks

Mark scheme: 7.2 × 20 000 13 (a) 0.54 2 M1 for oe 10 0000 or SC1 for figs 54 in answer (b) 1.61 2 SC1 for figs 161 or M1 2002 or 20 0002 seen IGCSE – May/June 2011 0580 21 ( )( )

This question in 0580/21 May/June 2011

8 A car company sells a scale model of the size of one of its cars. Examiner's 10 Use Complete the following table. Scale Model Real Car Area of windscreen (cm2) 135 Volume of storage space (cm3) 408 000 [3]

3 marks

Mark scheme: 8 13500 408 3 M1 135 × 102 or 408000 ÷ 103 oe A1 A1

This question in 0580/22 May/June 2012

9 The scale on a map is 1 : 50 000. The area of a field on the map is 1.2 square centimetres. Calculate the actual area of the field in square kilometres. Answer … km2 [2]

2 marks

Mark scheme: k × 50 000 × 50 000 9 0.3 2 M1 for oe 100 000 × 100 000 If zero scored SC1 for figs 3 15 2 f

This question in 0580/22 Oct/Nov 2015

19 A model of a car has a scale 1 : 20. The volume of the actual car is 12 m3. Find the volume of the model. Give your answer in cubic centimetres. … cm3 [3]

3 marks

Mark scheme: 19 1500 3 3  20  M2 for 12 ÷   oe  100   20  3  100  3 or M1 for   or   oe  100   20  OR M1 for ÷ 203 oe M1 for × 1003 oe

This question in 0580/21 May/June 2019

14 The scale of a map is 1 : 10 000 000. On the map, the area of Slovakia is 4.9 cm2. Calculate the actual area of Slovakia. Give your answer in square kilometres. … km2 [3]

3 marks

Mark scheme: 14 49 000 3 M1 for 4.9 × (10 000 000)2 M1 for ÷ (100 000)2 OR M1 for 1 cm : 100 km M1 for 4.9 × (their 100)2 OR M2 for ( 4.9 × 10 000 000 ÷ 100 000)2 or M1 for 4.9 × 10 000 000 ÷ 100 000

This question in 0580/21 Oct/Nov 2019

2 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: 2 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 0580/21 Oct/Nov 2020

13 On a map, a lake has an area of 32 cm2. The scale of the map is 1 : 24 000. Calculate the actual area of the lake. Give your answer in km2. … km2 [2]

2 marks

Mark scheme: 13 1.8432 2 32 × 24000 × 24000 M1 for oe 100000 × 100000 If 0 scored, SC1 for figs 184[32]... as answer

This question in 0580/21 May/June 2021

6 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: 6(a) 32.8 2 M1 for 8[cm] to 8.4[cm] seen or for their measurement [in cm] multiplied by 4 6(b) 065 1 6(c) X correctly placed 7 cm from P 2 M1 for X on bearing of 140 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 0580/21 Oct/Nov 2021

20 A lake has an area of 3 km2. On a map the area of the lake is 18.75 cm2. Find the scale of the map in the form 1 : n. 1 : … [3]

3 marks

Mark scheme: 20 40 000 3 B2 for 1 cm to 0.4 km or 2.5 cm to 1 km or 1 600 000 000 3 × 10 k or M2 for oe where k > 5 18.75 or M1 for 1 cm2 to 0.16 km2 or 6.25 cm2 to 1 km2 or for 3 × 1010 oe or 1.875 × 10–9 oe or 3 × 106 oe and 1.875 × 10–3 oe

This question in 0580/23 Oct/Nov 2021

14 A map has a scale of 1 : 200 000. Find the area, in square kilometres, of a lake that has an area of 12.4 cm 2 on the map. … km2 [2]

2 marks

Mark scheme: 14 49.6 2 M1 for answer figs 496

This question in 0580/23 Oct/Nov 2022

2 The scale drawing shows the positions of two villages, P and Q. The scale is 1 cm represents 0.5 km. North P North Q (a) Find the actual distance between village P and village Q. … km [2] (b) Measure the bearing of village Q from village P. … [1]

3 marks

Mark scheme: 2(a) 4.4 to 4.6 2 B1 for 8.8 [cm] to 9.2 [cm] or M1 for 0.5 × their written measurement where their measurement is in the range 8 to 10 2(b) 108 to 112 1

This question in 0580/22 May/June 2025