CAMBRIDGE IGCSE MATHS (0580)
Paper 2 (P2): Maps and Scale Quiz
The scale of a map is 1:500000.
- The actual distance between two towns is 172 km. Calculate the distance, in centimetres, between the towns on the map.
- The area of a lake on the map is 12 cm². Calculate the actual area of the lake in km².
A car company sells a scale model 1/10 of the size of one of its cars.
Complete the following table:
| Scale Model | Real Car | |
|---|---|---|
| Area of windscreen (cm²) | 135 | |
| Volume of storage space (cm³) | 408000 |
A model of a ship is made to a scale of 1:200. The surface area of the model is 7500 cm².
Calculate the surface area of the ship, giving your answer in square metres.
A car, 4.4 metres long, has a fuel tank which holds 65 litres of fuel when full. The fuel tank of a mathematically similar model of the car holds 0.05 litres of fuel when full.
Calculate the length of the model car in centimetres.
The volumes of two similar cones are 36π cm³ and 288 cm³. The base radius of the smaller cone is 3 cm.
Calculate the base radius of the larger cone.
The volume of a child's model plane is 1200 cm³. The volume of the full-size plane is 4050 m³.
Find the scale of the model in the form 1:n.
The two containers are mathematically similar in shape.
The larger container has a volume of 3456 cm³ and a surface area of 1024 cm². The smaller container has a volume of 1458 cm³.
Calculate the surface area of the smaller container.
Hans draws a plan of a field using a scale of 1 centimetre to represent 15 metres. The actual area of the field is 10800 m².
Calculate the area of the field on the plan.
The two cylindrical cans are mathematically similar. The larger can has a capacity of 1 litre and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
The diagram shows two straight lines, AE and BD, intersecting at C.
Angle ABC = angle EDC.
Triangles ABC and EDC are congruent.
Write down two properties of line segments AB and DE.
The scale on a map is 1:50000.
The area of a field on the map is 1.2 square centimetres.
Calculate the actual area of the field in square kilometres.
Two containers are mathematically similar. Their volumes are 54 cm³ and 128 cm³.
The height of the smaller container is 4.5 cm.
Calculate the height of the larger container.
The diagram shows two glasses that are mathematically similar. The height of the larger glass is 16 cm and its volume is 375 cm3. The height of the smaller glass is y cm and its volume is 192 cm3.
Find the value of y.
A map is drawn to a scale of 1:1000000.
A forest on the map has an area of 4.6 cm².
Calculate the actual area of the forest in square kilometres.
The diagram shows a scale drawing of Tariq's garden. The scale is 1 centimetre represents 2 metres.
Tariq puts a statue in the garden. The statue is equidistant from the two trees and 10m from the bird bath.
Find, by construction, the point where Tariq puts the statue. Label the point S.
