In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification.
Example 15
Suppose you now decide to place your new bath (length 1.7 m, height 0.8 m) against this wall as shown in the diagram below.
Author(s):
Example 14
Suppose you have decided to tile the wall using square tiles of side 10 cm. You are proposing to use the tiles across the full 5 metre width of the wall up to a height of 1.8 m.
Find the number of boxes of tiles that you will require to cover the wall if the tiles are sold in boxes o
4.1 Understanding the question
Before you can attempt a question, you must read and understand it. This may sound obvious but you will need to know, before you start, what is expected by way of an answer. In particular, you will need to know the meaning of the instructions contained in the question. This section contains a discussion of the precise meanings attached to words like â€˜findâ€™, â€˜showâ€™, â€˜write downâ€™ and â€˜determineâ€™ in mathematics questions. The different types of instruction are illustrated by posi
By the end of this unit you should be able to:
lay out and, where appropriate, label simple mathematical arguments;
understand the precise mathematical meaning of certain common English words;
understand and use common mathematical symbols;
write clear, unambiguous mathematical solutions using appropriate notation;
identify and modify some sources of ambiguity or inappropriate use of notation in a mathematical solution;
Do you want to improve your ability to subtract one number from another, especially if decimals are involved, without having to rely on a calculator? This unit will help you get to grips with subtraction and give you some practice in doing it.
You can start with some practice in subtracting small numbers in your head if you want to. Then we will show you how to subtract bigger numbers on paper. Finally we look at how to subtract decimal numbers.
You donâ€™t need to complete the
The example of 25546 divided by 53 is suitable for long division. First write the calculation down on paper in the same way you did before.
9 Summary of what you’ve learned so far
When you divide by a number up to 10, the steps are as follows:
 Take each digit of the number under the line in turn, starting from the left.
 Work out how many times the dividing number goes into it.
 Write the answer to the division above the line
 If there is a remainder, carry it by putting it in front of the next digit on the right.
 Work out how many times the dividing number goes into the next digit, including any car

Data in the form of counts of individual entities (for example, people, animals, power stations) in a small set of discrete categories can be presented in bar charts or pie charts. For most purposes, bar charts are preferable. Pie charts draw particular attention to the proportions in which the entities are split between the different categories. However, they do so by representing the proportions by angles, and even when the main interest lies in the propo
1.4.7.2 Quartiles when the sample size is awkward
For the six ordered data items 1, 3, 3, 6, 7, 7, the lower quartile is given by
In other words, the lower quartile q_{L}
is given by the number threequarters of the way between x
_{(1)}=1 and x
_{(2)}=3. The difference betwe
1.4.5.1 Chest measurements of Scottish soldiers
Figure 19 shows a histogram of chest measurements (in inches) of a sample of 5732 Scottish soldiers.
The time taken to cook a fresh chicken depends on its mass, as given by the following formula:
Roughly how long will a chicken with a mass of 2.2Â kg take to cook?
To use the formula, you need to substitute the mass of the chicken into the righthand side of the equ
Patterns occur everywhere in art, nature, science and especially mathematics. Being able to recognise, describe and use these patterns is an important skill that helps you to tackle a wide variety of different problems. This unit explores some of these patterns ranging from ancient number patterns to the latest mathematical research. It also looks at some useful practical applications. You will see how to describe some patterns mathematically as formulas and how these can be used to solve pro
We saw above that the vector 2v can be regarded as the vector v â€˜followed byâ€™ the vector v; we can also quite naturally describe this vector as being the â€˜sumâ€™, v + v, of the vector with itself.
Analogously, if p is the vector 2 cm E and q is the vector 3 cm NE, we can think of the â€˜sumâ€™ p + q of the vectors as follows. Starting from a given point, O say, draw the vector p; starting from its finishi
3.5 More examples of percentages
In lots of everyday situations percentages are used to make predictions and comparisons.
Example 14
The number of casualties handled by the outpatients department of a hospital increases by approximately 8% per year. The number of casualties this year was 1920. Make a prediction for the number
The Impact of Geography on International Politics [Audio]
Speaker(s): Tim Marshall  Editor's note: Some questions have been removed from this podcast due to inaudiblity. Foreign Affairs Broadcaster and Journalist, Tim Marshall, author of new book Prisoners of Geography explains how decisions made by world leaders are constrained by geography. It is true that to understand world events (such as President Putin's invasion of Crimea and events in the Middle East), you need to understand people, ideas and movementsâ€¦ but if you donâ€™t know geography, yo
Climbing Droplet
By: Vivienne Self propulsion of a droplet on an incline
China  Economic Miracle or Economic Timebomb?
The growth of China in recent years has been described as an economic miracle with Western companies and governments rushing to build partnerships with the new power in the East.
The opening up of the Chinese market and the expansion of industry, technology and production within the country has, however, had a profound effect on the people of China, its political leaders and the rest of the world. This impact can be seen in the growing inequalities within China, the loss of jobs in the west a
4.6 Consequences of neural ageing
While we are beginning to understand the underlying molecular and cellular changes that take place in the ageing brain, the consequences of these changes are all too familiar. As people age, their mental competence may change and their ability to cope with the demands of everyday life may alter. A decline in the spee
1.2.2 Offshore fragments of industry
The rise of global factories in the 1970s owed much to the rapid improvement in transport and communications technologies which took place at that time and which made it possible to keep in touch with, and control, production processes in different parts of the world. Just as significant was the fragmentation of industrial production whereby parts of the manufacturing process could be relocated over vast distances. Sewing in garment and footwear production, for instance, was among the