IGCSEMaths: ExtendedCIETopic Questions1. Number1.11 Compound Measures - Speed, Density, Pressure

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First teaching 2021

Last exams 2024

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Compound Measures - Speed, Density, Pressure (CIE IGCSE Maths: Extended)

Topic Questions

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1
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Karel travelled from London to Johannesburg and then from Johannesburg to Windhoek.

The flight from London to Johannesburg took 11 hours 10 minutes.
The average speed was 813 km/h.

Calculate the distance travelled from London to Johannesburg.
Give your answer correct to the nearest 10 km.


 ........................................... km

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2a
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Car A and car B take part in a race around a circular track.
One lap of the track measures 7.6 km.

Car A takes 2 minutes and 40 seconds to complete each lap of the track.
Car B takes 2 minutes and 25 seconds to complete each lap of the track.
Both cars travel at a constant speed.

Calculate the speed of car A.
Give your answer in kilometres per hour.

........................................... km/h

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2b
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Both cars start the race from the same position, S, at the same time.

i)
Find the time taken when both car A and car B are next at position S at the same time.
Give your answer in minutes and seconds.

 

..................... min ..................... s [4]

ii)
Find the distance that car A has travelled at this time.

 

.............................................. km [2]

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3
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Asif cycles a distance of 105 km.
On the first part of his journey he cycles 60 km in 2 hours 24 minutes.
On the second part of his journey he cycles 45 km at 20 km/h.

Find his average speed for the whole journey.

........................................... km/h

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4
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A tank is a cuboid measuring 1.8 space text m end text by 1.5 space text m end text by 1.2 space text m end text.
Water flows from a pipe into this empty tank at a rate of 200 space text cm end text cubed per second.

Find the time it takes to fill the tank.
Give your answer in hours and minutes. 
 

........................ hours ..................... minutes

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5a
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Here is part of a train timetable for a journey from London to Marseille.
All times given are in local time.
The local time in Marseille is 1 hour ahead of the local time in London.

London 07 19
Ashford 07 55
Lyon 13 00
Avignon 14 08
Marseille 14 46

Work out the total journey time from London to Marseille.
Give your answer in hours and minutes.
 

.................. h ...................... min

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5b
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The distance from London to Ashford is 90 km.
The local time in London is the same as the local time in Ashford.
 
Work out the average speed, in km/h, of the train between London and Ashford.
 

...................................... km/h

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5c
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During the journey, the train takes 35 seconds to completely cross a bridge.
The average speed of the train during this crossing is 90 km/h.
The length of the train is 95 metres.
 
Calculate the length, in metres, of this bridge.
 

........................................... m

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6
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cie-igcse-2018-march-p4-q8

The diagram shows two ports, L and P, and a buoy, M.

A ship sails directly from L to P.

The ship leaves L at 20 45 and travels at a speed of 40 km/h.
 
Calculate the time the next day that the ship arrives at P.

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1
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When the local time in Athens is 09 00, the local time in Berlin is 08 00.
A plane leaves Athens at 13 15.
It arrives in Berlin at 15 05 local time.

i)
Find the flight time from Athens to Berlin.
  
........................ h ........................ min [1]
ii)
The distance the plane flies from Athens to Berlin is 1802 km.
 
Calculate the average speed of the plane.
Give your answer in kilometres per hour.
 
........................................ km/h [2]

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2
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The table shows the surface area of some countries and their estimated population in 2017.

Country Surface area (km2) Estimated population in 2017
Brunei 5.77 × 103 433 100
China 9.60 × 106 1 388 000 000
France 6.41 × 105 67 000 000
Maldives 3.00 × 102 374 600

Find the population density of the Maldives.
[Population density = population ÷ surface area]
 

 ...............................people/km2

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3
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cie-igcse-2020-may-june-p4-tz1-q7

The diagram shows the positions of three points A, B and C in a field.

Mitchell takes 35 seconds to run from A to C.

Calculate his average running speed in kilometres per hour.

........................................ km/h

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4
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cie-igcse-2020-may-jun-p4-tz2-q5

The diagram shows a field ABCD.
AB = 400m, BC = 350m, CD = 450m and AD = 624m.

Jono runs around the field from A to B, B to C, C to D and D to A.
He runs at a speed of 3 m/s.
 
Calculate the total time Jono takes to run around the field.
Give your answer in minutes and seconds, correct to the nearest second.
 

.................. min .................. s

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5a
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Amol drives his truck at an average speed of 50 km/h.
He leaves at 07 00 and arrives at 11 15.
 
Calculate the distance he drives.
 

............................................. km

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5b
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Priya drives her van a distance of 54 km.
She leaves at 10 55 and arrives at 12 38.
 
Calculate her average speed.
 

.......................................... km/h

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6
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The diagram shows the positions of three cities, Geneva (G), Budapest (B) and Hamburg (H).

cie-igcse-2018-oct-nov-p4-tz2-q8

A plane flies from Geneva to Hamburg.
The flight takes 2 hours 20 minutes.

Calculate the average speed in kilometres per hour.
 

....................................... km/h

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7
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A car takes 18 seconds to travel 400m along a road.

Calculate the average speed of this car in km/h.
 

........................................ km/h

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8a
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Karel travelled from London to Windhoek.

The total time for Karel’s journey was 15 hours 42 minutes.
The total distance travelled from London to Windhoek was 10 260 km.

Calculate the average speed for this journey.
 

 ........................................ km/h

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8b
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The cost of Karel’s journey from London to Windhoek was $470.

i)
Calculate the distance travelled per dollar.
 
 ........................... km per dollar [1]
ii)
Calculate the cost per 100 km of this journey.
Give your answer correct to the nearest cent.
 
$ .............................. per 100 km [2]

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1
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A model train is 61 cm long and travels at a speed of 18 cm/s.
It takes 4 seconds for the whole of the train to cross a bridge.

Calculate the length of the bridge.


........................................... cm

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2
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cie-igcse-2019-oct-nov-p4-tz1-q5a

The diagram shows a triangular field, ABC, on horizontal ground.

Olav runs from A to B at a constant speed of 4 m/s and then from B to C at a constant speed of 3 m/s.
He then runs at a constant speed from C to A.
His average speed for the whole journey is 3.6 m/s.

Calculate his speed when he runs from C to A.

............................................. m/s

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3
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Carol walks 12 km at x km/h and then a further 6 km at left parenthesis x minus 1 right parenthesis km/h.
The total time taken is 5 hours.

Write an equation, in terms of x, and show that it simplifies to  5 x squared minus 23 x plus 12 equals 0.

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4
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Brad travelled from his home in New York to Chamonix.

  • He left his home at 16 30 and travelled by taxi to the airport in New York. 
    This journey took 55 minutes and had an average speed of 18 km/h.
     
  • He then travelled by plane to Geneva, departing from New York at 22 15. 
    The flight path can be taken as an arc of a circle of radius 6400 km with a sector angle of 55.5 °.
    The local time in Geneva is 6 hours ahead of the local time in New York.
    Brad arrived in Geneva at 11 25 the next day.
     
  • To complete his journey, Brad travelled by bus from Geneva to Chamonix.
    This journey started at 13 00 and took 1 hour 36 minutes.
    The average speed was 65 km/h. 
    The local time in Chamonix is the same as the local time in Geneva.

Find the overall average speed of Brad’s journey from his home in New York to Chamonix.
Show all your working and give your answer in km/h. 
 

 .......................................... km/h

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5
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A truck is used to transport some wood panels.
Each wood panel is a cuboid measuring 2.4 m by 1.2 m by 1.8 cm.
The density of each wood panel is 750 kg/m3
.
The truck can carry 15 tonnes of these wood panels.

Calculate the maximum number of wood panels that the truck can carry.
Show how you decide.

The formula for density is mass over volume.

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