1.4.2 The functional group approach

It is the classification of functional groups that simplifies the study of organic chemistry (the chemistry of compounds that contain carbon). With many millions of known organic compounds, and more being added by the day, it would be hopeless if their properties could not be systematised in some way. It turns out that a given functional group usually has the same chemical properties whatever carbon chain it is bonded to, so once the general properties of each functional group are known, all
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1.4.1 Salicylic acid

The structural formula of salicylic acid, 2.1, looks quite complicated. However, it becomes less daunting if you unpack it a bit. One of the first things to do when confronted with an unfamiliar structure is to check that all the valencies are correct (four for carbon, two for oxygen and one for hydrogen). If any atoms have the wrong valency, it follows that there is a mistake somewhere and the molecule does not exist as drawn. It looks OK for the structure of salicylic acid. You proba
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1.3 The aspirin story

As long ago as 400 BC the physician Hippocrates, from the island of Kos (now a popular Greek holiday destination) prescribed a concoction made from willow leaves to help relieve the pain of childbirth. Ever since then (and probably even before) herbal remedies based on the leaves or bark of willow trees have been used for the alleviation of pain and fever. In the 1840s the chemists of the day were able to extract the substance salicin from the bark of willow trees by treating it with boiling
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4.10 Parliamentary control

Initially, Parliament has control in that the enabling or parent Act passed by Parliament sets out the framework or parameters within which delegated legislation is made. In addition, there are scrutiny committees in both Houses of Parliament whose role is to consider the delegated powers proposed by a Bill. However, these committees have limited power. European legislation is considered by a specific committee and local authority byelaws are usually subject to the approval of the Department
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3.5.1 Review of skills

Activities 5, 8 and 9 allowed you to demonstrate numeracy skills by performin
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2.1 Treaties, conventions and constitutions

International human rights are part of a much wider area, public international law, which in broad terms encompasses law relating to the legal rights, duties and powers of one nation state in relation to its dealings with other nation states. These rights, duties and powers are set out in international treaties or conventions. Such treaties and conventions may be global in their application or restricted to certain regions of the world. Reference to a work on international human rights treati
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5.3.2 Directives

A directive is a Community act which ‘shall be binding, as to the result to be achieved, upon each Member State to which it is addressed, but shall leave to the national authorities the choice of form and methods’. A directive therefore has to be implemented by each EU member state through its own domestic legislative process. After the enactment of a directive, the EU member states will generally be given a period of time within which to bring their domestic law in line with the objectiv
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3.4.1 Try some yourself

1 For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result.

  • (a) 22.12 ÷ 4.12

  • (b) 0.897 ×
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1.1 Writing mathematics

How do you write mathematics that can be read and easily understood by anyone else, such as a tutor or another student?

It takes practice, but the following guidelines may be helpful.

  • Ensure that what you write consists of sentences. Too many people believe that mathematics is a language which is entirely made up of unfamiliar symbols. It is not. Many symbols act in part merely as abbreviations which, when read, can be translated back into spoke
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8 Get some practice

Now that you’ve learned how to do subtraction on paper, you might want to practice your new skills.

To practice subtracting whole numbers, including borrowing where necessary, go to the Practice Subtracting  section of the Numbers website and click on Get sum. Then follow the instructions.

To practise subtracting decimals, go to the
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6 Dividing on paper

If the numbers you want to divide are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper. In the example below, click on each step in turn to see how to divide 126 by 6.

Active content not displayed. This content requires JavaScript to be enabled, and a
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Learning outcomes

By the end of this unit you should be able to:

  • explain the terms surface, surface in space, disc-like neighbourhood and half-disc-like neighbourhood;

  • explain the terms n-fold torus, torus with n holes, Möbius band and Klein bottle;

  • explain what is meant by the boundary of a surface, and determine the boundary number of a given surface with boundary;

  • construct certa
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Neighbourhood nature
There is a fascinating world of nature all around us which we can see if we know how to look for it. Wherever you live, be it in a city or the countryside, you will find areas that support a range of wildlife. This unit will provide you with basic scientific and observational skills so that you can go into your local neighbourhood to discover the animals and plants in open spaces. You will learn how to observe, identify and record the wildlife around you, building up a picture of a small part of
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Three Anti-Social Skills to Improve Your Writing
You need social skills to have a conversation in real life -- but they're quite different from the skills you need to write good dialogue. Educator Nadia Kalman suggests a few "anti-social skills," like eavesdropping and muttering to yourself, that can help you write an effective dialogue for your next story.  (03:46)

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