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1.1: Converting to component form

In some applications of vectors there is a need to move backwards and forwards between geometric form and component form; we deal here with how to achieve this.

To start with, we recall definitions of cosine and sine. If P is a point on the unit circle, and the line segment OP makes an angle θ measured anticlockwise from the positive x-axis, then cos θ is the x-coordinate of P and sin θ is the y-coordinate of P (
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Acknowledgements

All materials included in this unit are derived from content originated at the Open University.


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1.3 Designing alternative programmes and curricula

Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
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Introduction

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

This unit is from our archive and is an adapted extract from Teaching mathematical thinking at Key Stage 3 (ME624) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other cour
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1.6.5 RSS

RSS (‘Really Simple Syndication’ or ‘Rich Site Summary’) newsfeeds supply headlines, links, and article summaries from various websites. By using RSS ‘feedreader’ software you can gather together a range of feeds and read them in one place: they come to you, rather than you having to go out and look for breaking news. The range of RSS feeds on offer is growing daily. There is probably a feed to cover all aspects of your life where you might need the latest information, and you may
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1.5.9 Plagiarism

Referencing is not only useful as a way of sharing information, but also as a means of ensuring that due credit is given to other people’s work. In the electronic information age, it is easy to copy and paste from journal articles and web pages into your own work. But if you do use someone else’s work, you should acknowledge the source by giving a correct reference.

Taking someone's work and not indicating where you took it from is termed plagiarism and is regarded as an infringemen
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1.5.8 Bibliographic software

If you are considering taking your studies further you might like to consider using bibliographic software. Bibliographic software can be used to sort references, annotate them, manage quotations or create reading lists.

There are several software packages on the market. Some are listed below.

  • BibTex

  • EndNote

  • Procite

  • Reference Manager

  • RefWorks

If you are not sure
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1.5.1 Why is it important to be organised?

  • 87% of items that are filed into a filing cabinet are never looked at again. STANFORD UNIVERSITY

  • The world is producing nearly two exabytes of new and unique information every year – an exabyte is a new term that had to be coined for a billion gigabytes. All the words ever spoken by human beings comes to five exabytes. UNIVERSITY OF CALIFORNIA (BERKELEY)

  • More new information has been produc
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1.4.1 PROMPT

There is so much information available on the internet on every topic imaginable. But how do you know if it is any good? And if you find a lot more information than you really need, how do you decide what to keep and who to discard?

In this section we are going to introduce a simple checklist to help you to judge the quality of the information you find. Before we do this, spend a few minutes thinking about what is meant by information quality.

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3.1 Who will make the decisions?

Where will the decisions be made that will result in meaningful action on climate change, and who will make them stick? Following climate change politics in the media can give the impression that most of the action on climate change is going on between national decision makers in international forums. It is important to keep in mind that these forums have resulted from persistent pressure from a combination of grassroots environmental activists and a global network of science and policy exper
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Summary

In this part I have presented evidence showing that even apparently remote regions of our planet are intimately connected through physical processes. For example, once an organic POP is transported to the poles, then biological processes can take over and through bioaccumulation perhaps cause harm. But this physical connection has allowed the ice to preserve unique proxy records of the past climate of our planet. Directly measuring the gases trapped in the ice has enabled histories of past at
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5 The contemporary Arctic climate

There is a remarkable seasonality in the Arctic climate. For example, the flow in some of the great rivers of Russia and North America that empty into the Arctic Ocean almost stops in winter (Figure 21). During May, ice in the rivers starts to break and in June there is a rapid flood of fresh water followed by a
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3.1 Greenland's snowfall

Greenland snowfall differs depending on whether it falls in summer (when snow is comparatively warm and moist) or winter (when snow is cold and dry). These differences mean that as the snow is turned to ice, annual layers are formed that are in many ways similar to tree rings: thick annual layers mean high snowfall and thin annual layers low snowfall. The accumulation of snowfall on the summit of Greenland – and most importantly what is trapped within the crystals as it turns to ice – can
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Introduction

The scientific theory of plate tectonics suggests that at least some of these Arctic lands were once tropical. Since then the continents have moved and ice has changed the landscape. This unit will concentrate on evidence from the last 800,000 years using information collected from ice cores from Greenland and Antarctica, and will use this evidence to discuss current and possible future climate. The cores show that there have been nine periods in the recent past when large areas of the Earth
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6.4 The role of governments and business

Despite all the possibilities for individual and group action to lighten carbon footprints, there will still be people, groups and organisations who will not be doing much. Many individuals limit themselves to ‘every little bit helps’, with relatively minor effects on their carbon footprint, like reusing plastic bags or recycling paper. This avoids having to consider more significant changes in car and air travel, home energy use, diet or shopping. Others will simply carry on producing an
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4.2 Carbon reduction targets

Let's now look at carbon footprint reduction targets in a bit more detail.

The first international agreement to set carbon reduction targets was the 1997 United Nations Kyoto Protocol, which requires developed countries to reduce their human-generated greenhouse gas emissions by an average of just over 5% on 1990 levels by 2008 to 2012. By the time the treaty came into force in 2005, only the USA and Australia had refused to sign. (A new Australian government finally signe
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4.1 Your carbon footprint

Most of this section requires you to continue using the Quick Carbon Calculator (linked in the box below).

If you've completed the carbon calculator , you'll have a good idea of your carbon footprint and the relative contribution to the total load made by different components of consumption. You'll also know how your footprint compares to that of an average person in the UK.

If you live outside the UK, you may have used a calculator that provides somewhat different information abo
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2.2.4 Identifying the carbon heavyweights

I've focused on two studies of the carbon footprint of UK individuals and households, but there are many others (e.g. WWF, 2006; Goodall, 2007 and Marshall, 2007a).


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2.2 The carbon footprint of UK individuals and households

The simplest way of calculating the average (mean) carbon footprint of an individual living in the UK can be obtained by dividing total UK annual CO2 emissions by the number of people in the country. Using the official government information in Figure 3(a), this produces a mean footprint
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1.2 Individual and household carbon footprints

I'll be referring mainly to the carbon footprint arising directly and indirectly from the activities of individuals and households.

The carbon footprint of individuals and households is important because they are ultimately the main consumers of the energy, food and other goods and services that produce those emissions.

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