# Unit 1 Section 4 : Networks

In this section we consider networks.

A network is a system of points with distances between them. A network can represent roads, pipelines, cables etc.
Typical problems with networks involve finding the shortest path between one point in the network and another.
For example, a driver might use a network of distances between places to find the shortest route between two places.

The slideshow below shows an example of finding a "shortest route". Use the left and right arrows to view the slideshow.

Example 1

It can be helpful to cross off paths which are no longer needed as you go along.
You can cross off a path to a particular point if you have already found a shorter
route to that point. The example below shows you how to do this in practice.

Example 2

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

write on the networks while you are working out the answers.

Question 1
The network diagram below shows the distances between some towns and cities.
 (a) Find the shortest route between Manchester and Nottingham.     (i) The shortest route is via Sheffield Buxton Birmingham     (ii) The shortest distance is miles. (b) Find the shortest route between Sheffield and Birmingham.     (i) The shortest route is via Manchester Buxton Nottingham     (ii) The shortest distance is miles.
Question 2
The network diagram below shows the journey times in minutes between five places in a town centre.
The places are marked S, A, B, C and T. You need to find the quickest route from S to T.
 NOTE: In part (a), you can give the route by entering the letters on the route. For example, if you think the quickest route is S to B to C to T, then enter Write your answer in CAPITAL LETTERS and don't put in any SPACES. (a) What is the quickest route? (b) How long will the quickest route take? minutes
Question 3
The network diagram below shows the distances in miles between some towns and cities in the south west of England.
 NOTE: Give the shortest routes by entering the letters on the route as described in Question 2. For example, the route from Minehead to Taunton to Exeter would be entered as MTE. (a) Find the shortest route from Wadebridge to Exeter.  (i) The route is  (ii) The distance is miles (b) Find the shortest route from Plymouth to Minehead  (i) The route is  (ii) The distance is miles
Question 4
The network diagram shows the distances between some places on the Isle of Man.
 Find the shortest distances between these places: (a) Douglas and Sulby miles (b) Ramsey and Port Erin miles (c) Peel and Laxy miles
Question 5
Use the network diagram below to find the shortest distance between Carlisle and Lincoln.
 The shortest distance is miles.

You have now completed Unit 1 Section 4
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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