Negative numbers occur in financial matters, in temperature or height measurements and many other practical situations.

Example 26

• (a) If the value of a painting increases by Â£20 a year and it is worth Â£200 today, how much will it be wort
Author(s): The Open University

Activity 55

Author(s): The Open University

Before considering division of fractions, it is helpful to think about division of whole numbers.

6 Ã· 2 asks for the number of twos in 6: 6 Ã· 2 = 3, since three twos are six (3 Ã— 2 = 6).

In a similar way, 6 Ã· Author(s): The Open University

Activity 30

Carry out the following calculations, without your calculator.

• (a) 3 Ã— (60 + 70).

• (b) (3 Ã— 60) + 70.

• (c) (70 âˆ’ 60) Ã· 5.

• Author(s): The Open University

There are two very famous formulas for circles:

circumference of a circleÂ =Â Author(s): The Open University

You may like to add the area formulas in this section to your notes for future reference.

The simplest areas to find are those of rectangles. The area of a rectangle is its length multiplied by its breadth. Sometimes the dimensions of a rectangle are referred to as the base and the height, instead of the length and the breadth. The area is then expressed as the base multiplied by the height.

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A fundamental concept in mathematics is that of a function.

Consider, for example, the function f defined by

This is an example of a real function, because it associates with a given real number
Author(s): The Open University

School mathematics curricula often focus on lists of content objectives in areas like number, arithmetic, statistics, measurement, geometry, trigonometry, and algebra. A typical list of content objectives might contain over one hundred objectives to be introduced or revisited and learned each year. These can be seen as hierarchical in nature but many textbooks do not attempt to organise the objectives in ways that enable the bigger underpinning ideas to become apparent to the pupils. In addit
Author(s): The Open University

Climate change is a natural process of warming and cooling that has occurred all through the Earth's history. Throughout geological time there have been â€˜hot-houseâ€™ periods and ice ages. In order to understand the current situation, it is necessary to have some sense of context and perspective, from historical and geological time-scales. The document below shows a chart showing a generalised temperature history of the Earth.

Click on the link below to see the chart

Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Grateful acknowledgement is made to the following sources for permission to use material:

Course image: Sorin Mutu in Flickr made available under
Author(s): The Open University

We are also guilty of importing exotic species, some of which, like the rhododendron (imported from Asia to Europe), have run riot in the absence of natural predators or primary consumers, and so have tended to out-compete native plants. Sometimes introductions have been accidental; rats and many disease-causing organisms have spread around the world via relatively modern transportation such as sailing ships. However, deliberate introductions, such as the rhododendron, have been made with wor
Author(s): The Open University

The international level can be viewed as an arena of politics in its own right and not just as a context for states and other actors. If we think of the international world in this way, how should relations between states, and other actors on the international stage, be constructed? To what extent should those relations be regulated? We can ask whether relations between states, and states' policy making, should be dictated by allegedly universally shared human rights principles, or by other o
Author(s): The Open University

The Ministerial Declaration adopted by WTO members at Doha on 14 November 2001 fails to address the most pressing needs either of the poorest countries or of the world's most vulnerable communities. This means that the people who most need a share in global prosperity are still those least likely to obtain it.

(A joint statement by Actionaid, CAFOD, Christian Aid, Oxfam, Save the Children and five other charities a
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Energy policy and climate change
The 2009 United Nations Climate Change Conference in Copenhagen presents a new focus for international debate and decisions about energy and its use. What are the countries of Western Europe and Scandinavia doing to promote sustainable energy production? Just how different will the future energy map of Europe look? And is energy policy principally a scientific issue or a political one? This album contains a series of films exploring energy policy in various countries around Europe in 2006, frame
Author(s): The OpenLearn team

Structural Integrity: Materials Testing
How is safety built into the design of new structures? What sort of tests are used to ascertain the safety of proposed designs? Structural integrity, the study of the safe design and assessment of materials and structures under load, has become crucial in engineering design. Concepts within stress analysis have wide applicability, as there are very few manufactured components and products that do not experience any loading during their life. The tracks on this album demonstrate a selection of
Author(s): The OpenLearn team

Water Treatment
Do you think about where your water comes from? In the UK each of us uses an average of about 150 litres of water per day! The seven video tracks in this album consider issues of demand and quality in water supply as well as treatment processes. They give information on methods of minimising waste, emergency water treatment and effluent control. This material forms part of T308 Environmental monitoring, modelling and control.Author(s): The OpenLearn team

Waste Management
How much do you think about what you throw away? A waste management cycle is essential for a sustainable future. This album considers the policy and legislation that is driving waste management processes across the EU. By modelling the overall environmental impacts of solid waste disposal methods, the UK government has now created a hierarchy of waste and local management strategies. The 12 video tracks in this album offer an in depth look at each of these processes, concentrating on waste coll
Author(s): The OpenLearn team

Noise Pollution
How do your ears work and what kind of sound levels can damage your hearing? The five video tracks in this album explain basic concepts such as units of noise, sound insulation and noise control. Car manufacturers like Lexus have developed the quiet car, but this kind of technology benefits the driver, not the people living beside busy roads. Locals from a Derbyshire village explain how the construction of the A50 has affected their lives. The Transport Research Laboratory analyses tyre noise on
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The Four Generations of Computers
Computers play a huge part in almost all of our lives, but how did these machines become so powerful and important? And what were some of the earliest models like? This collection of videos takes us through the Four Generations of computers, starting with Colossus, the world's first electronic computer (launched in 1944), and finishing with the BBC Micro (launched in 1981) and Fourth Generation Computers, looking at how technology changed throughout these years. Visiting locations such as The Na
Author(s): The OpenLearn team