Mathematics 0580 · IGCSE
Scale drawings
70 practice questions on Scale drawings, with worked solutions and instant marking.
Complete the sentence. For an angle to count as obtuse, it has to lie between [BLANK] degrees and [BLANK] degrees.
Feb/March 2017
The map’s scale drawing locates two towns, Yatterford (Y) and Rexley (R). It shows that 1 centimetre stands for 15 kilometres.
Feb/March 2018
The scaled sketch plots the locations of an airport (A) and a train station (T) on a map. 1 centimetre on the scale stands for 2 kilometres. The diagram includes a straight segment from T to A, with a north arrow at both T and A. The scale written on the diagram is: Scale: 1 cm to 2 km.
Feb/March 2019
The figure depicts a rectangle together with two semicircles whose diameters are $AC$ and $BD$. It is a scale drawing of a running track. $AC = BD = 60$ m $AB = CD = 120$ m.
Feb/March 2019
The diagram presents an unfinished scale plan of a market place, ABCD, with D situated on CX. The scale is 1 centimetre represents 5 metres. D is placed on CX so that angle DAB = 75^{\circ}.
Feb/March 2019
Work out the actual distance between $R$ and $S$.
Feb/March 2020
On the map, the scale drawing gives the locations of Kendra’s house, $K$, and Latika’s house, $L$. North arrows appear at both $K$ and $L$.
Feb/March 2021
The scale diagram plots the locations of three towns, R, S and T, on a map. RS and ST are straight roads joining the towns. The scale is 1 centimetre represents 8 kilometres.
Feb/March 2023
With $1\text{ cm}$ representing 8 km, plot the position of town $S$.
Feb/March 2024
Two lighthouses, $P$ and $Q$, are shown on this scale drawing. The scale is 1 centimetre represents 0.8 kilometres. A north arrow is drawn upwards at each lighthouse. Scale: 1 cm to 0.8 km.
Feb/March 2025
The scale plan indicates where boat $A$ and boat $B$ are located. On the scale, $1\text{ cm}$ stands for $0.5\text{ km}$. A north arrow is included. The sketch labels the points $A$ and $B$.
Feb/March 2025
The scale plan depicts one edge, $AB$, of a 4-sided field. The drawing scale is 1 centimetre to 20 metres. A north arrow appears at point $A$. The diagram marks point $A$, point $B$, and the north direction.
May/June 2015
The diagram shows a scale drawing of three straight roads, $AB$, $BC$ and $CD$. The scale used is 1 : 5000.
May/June 2015
The map is drawn at a scale of $1 : 1\,000\,000$. On the map, the forest covers an area of $4.6\text{ cm}^2$.
May/June 2016
Measure the bearing of port B from port A.
May/June 2016
The timetable section below is for a bus service. Town Hall: 10 15, 10 35, 10 55, 11 15 City Gate: 10 32, 10 52, 11 12, 11 32 Beacon Hill: 10 58, 11 18, 11 38, 11 58 Kingswood Park: 11 10, 11 30, 11 50, 12 10
May/June 2016
The scale diagram indicates where Bogota ($B$) and Quito ($Q$) are located. Use a scale of 1 centimetre to 150 kilometres.
May/June 2017
The scale drawing of a farmer’s field shows quadrilateral $ABCD$. Side $AD$ is parallel to side $BC$. Angle $DAB$ and angle $ABC$ are right angles.
May/June 2017
Express $568\,000$ cm in metres.
May/June 2018
The scale drawing displays two boundaries, AB and BC, of field ABCD. The scale of the drawing means 1 cm represents 8 m. The diagram includes points A, B and C together with boundary lines AB and BC. Text on the diagram reads: 'Scale: 1 cm to 8 m'.
May/June 2018
Change 3670 centimetres into metres.
May/June 2019
The scale diagram depicts a rock, R. The scale means 1 centimetre represents 30 metres. A lighthouse, L, is 210 m from R, on a bearing of 125^{\circ}. The diagram includes a North arrow and point R. Scale: 1 cm to 30 m.
May/June 2019
For a map drawn at scale $1 : 25\,000$, the lake covers an area of $33.6$ square centimetres.
May/June 2019
The scale diagram places town A, town B and town C on a map. A direct road links town A and town B. The map scale is 1 centimetre represents 8 kilometres.
May/June 2019
The scale diagram depicts a play area, $ABCDE$. The scale means 1 centimetre represents 3 metres. The figure marks points $A, B, C, D, E$, with a dashed perpendicular from $D$ to $EC$ labelled $h$, and a right angle shown at the base.
May/June 2019
A lake’s area on a map is $32\text{ cm}^2$. The map is drawn to the scale $1:24000$.
May/June 2021
Work out the actual distance, in metres, from house A to house B.
May/June 2021
Find the garden’s actual area.
May/June 2021
The scale diagram indicates where town A and town B are located. On this scale, 1 cm stands for 15 km.
May/June 2022
On the map, the separation between town A and town B is 3.5 cm. The map scale is $1 : 250\,000$.
May/June 2023
Calculate the island’s actual length, and give your answer in kilometres.
May/June 2023
On the map, the gap between town A and town B is $3.5\text{ cm}$. The map scale is shown as $1 : 250\,000$.
May/June 2023
Measure angle $ABC$ on the diagram.
May/June 2023
Calculate the actual separation between the two villages. Give your answer in kilometres.
May/June 2024
A map has a scale of $1 : 40\,000$. The map shows the separation between two villages as 37 cm.
May/June 2024
Mark the point for $H$ on the scale drawing.
May/June 2024
The scale diagram marks the locations of villages P and Q, with $1\text{ cm}$ standing for $0.5\text{ km}$.
May/June 2025
The scale diagram indicates where ship $A$ is located. The scale used is 1 centimetre represents 50 kilometres. A north arrow appears above point $A$. Diagram text: "North" written above an upward-pointing arrow, with point "$A$" labelled at the lower end. Scale text: "Scale: 1 cm to 50 km". Ship $B$ lies 300 km from ship $A$ on a bearing of $105^{\circ}$.
May/June 2025
The scale diagram indicates the position of a hospital, H. The scale is 1 centimetre represents 6 kilometres. A north arrow is drawn pointing upwards.
May/June 2025
The scale sketch illustrates a route from S to P. On the drawing, 1 cm stands for 2.5 km. North arrows are indicated at both S and P.
May/June 2025
The warehouse covers a floor area of $800\text{ m}^2$. Its plan is produced at a scale of $1 : 50$.
May/June 2025
The scale drawing shows where the Police station, $P$, and the Fire station, $F$, are located in a town. The scale means $1$ centimetre represents $40$ metres.
Oct/Nov 2015
Calculate the field's actual area in square kilometres.
Oct/Nov 2015
The scale sketch shows villages A and B, linked by a straight road. The scale is 2 centimetres represents 1 kilometre. The sketch includes village A with a North arrow pointing upward, village B with a North arrow pointing upward, and a straight line joining A to B.
Oct/Nov 2015
The scale diagram shows where three towns A, B and C are located on a map. The map scale is 1 centimetre represents 10 kilometres.
Oct/Nov 2015
A scale diagram shows where towns X and Y are situated. The scale used is 1 centimetre represents 5 kilometres.
Oct/Nov 2016
Find the true distance from village A to village B.
Oct/Nov 2016
A house model is constructed to a scale of $1 : 30$. Its volume is $2400\text{ cm}^3$.
Oct/Nov 2017
The scale diagram shows where towns A, B and C are situated. The scale is 1 centimetre represents 12 kilometres. A North arrow is indicated for each town.
Oct/Nov 2017
This diagram gives the locations of two towns, A and B. Its scale is 1 centimetre corresponds to 10 kilometres. It also includes a North arrow pointing upward, point A, point B, and the label 'Scale: 1 cm represents 10 km'.
Oct/Nov 2017
The scale diagram gives the locations of town $A$ and town $B$. The scale is 1 centimetre represents 12 kilometres.
Oct/Nov 2018
Work out the actual distance, in kilometres, between S and L.
Oct/Nov 2018
This scale drawing locates towns A, B and C on a map. The scale states that 1 centimetre represents 10 kilometres. North arrows are shown at towns A and B.
Oct/Nov 2018
The map is drawn to a scale of 1 : 10 000 000, and Slovakia covers 4.9 $\text{cm}^2$ on the map.
Oct/Nov 2019
The scale diagram indicates where two buoys, $A$ and $B$, are positioned in the sea. The scale used is 1 centimetre stands for 20 kilometres. The sketch includes land and sea, a North arrow beside each buoy, and the caption "Scale: 1 cm to 20 km".
Oct/Nov 2019
Henry is decorating a room.
Oct/Nov 2019
This scale drawing gives the locations of town A and town B. The scale means 1 centimetre stands for 12 kilometres. North arrows appear at A and at B. The diagram is labelled "Scale: 1 cm to 12 km".
Oct/Nov 2019
The triangular field $ABC$ has $AC = 500\text{ m}$ and $BC = 650\text{ m}$. Work to a scale where $1\text{ cm}$ stands for $100\text{ m}$. Side $AB$ has already been drawn.
Oct/Nov 2020
Work out the latest time Sami can leave his house.
Oct/Nov 2020
The scale diagram gives the locations of two towns, P and Q. The scale is 1 cm represents 4 km. A north arrow marked North is shown at each town.
Oct/Nov 2021
The scale drawing indicates the locations of two towns, $P$ and $Q$. On the drawing, $1$ cm stands for $4$ km. North arrows are drawn at towns $P$ and $Q$. This diagram is not drawn to scale.
Oct/Nov 2021
Determine the scale of the map in the form $1 : n$.
Oct/Nov 2021
Calculate $EF$.
Oct/Nov 2021
The map uses a scale of $1 : 200\,000$.
Oct/Nov 2022
Bayside, Millwater and Westbridge are towns located alongside a lake. The scale diagram indicates where Bayside (B) and Millwater (M) are placed. The scale is 1 centimetre represents 2 kilometres.
Oct/Nov 2023
The scale diagram gives the positions of the two ships, $A$ and $B$. The scale is $1\text{ cm}$ represents $6\text{ km}$. A North arrow points straight up from $A$. The segment from $A$ to $B$ slopes down to the right.
Oct/Nov 2024
The scale diagram indicates where town K and town L are placed. The scale is 1 cm represents 10 km. North arrows are shown at each town.
Oct/Nov 2024
The scale drawing marks the locations of towns K and L. The scale reads 1 cm represents 10 km. In the diagram, towns K and L are connected by a line. At K, an arrow labelled "North" points north. At L, an arrow labelled "North" points north. The text below the diagram says "Scale : 1 cm to 10 km".
Oct/Nov 2024
This scale drawing gives the locations of town A and town B. Its scale is 1 centimetre represents 10 kilometres.
Oct/Nov 2025
The scale drawing indicates the location of ship A. The scale means that 1 centimetre represents 40 kilometres.
Oct/Nov 2025