In Section 3 we consider how to sketch the graphs of more complicated functions, sometimes involving trigonometric functions. We look at graphs which are sums, quotients and composites of different functions, and at those which are defined by a different rule for different values of x.

Click 'View document' below to open Section 3 (7 pages, 133KB).

Scientific notation can be very useful when estimating the answers to calculations involving very large and/or small decimal numbers.

## Example 9

A lottery winner won Â£7851 000. He put the money straight into a deposit account which earns 7.5% interest per annum (i.e. each year). If he wanted to
Author(s): The Open University

Earlier you looked at place values for numbers, and why they were called powers of ten.

Place value10 0001000100101Author(s): The Open University

1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

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1 Write the following as a number to a single power:

• (a) 26 Ã· 22

• (b) 1010 Ã· 107

• (c) 78 Ã· 74

• Author(s): The Open University

1 The new home owners from Example 4 above want to price grass seed, as well as the turf (transport only). The best buy seems to be loose seed, which says â€˜1 kilo covers 80 m2â€™. They wonder what length the side of an 80 m2
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Given any number, you now know how to find its square. But, given the squared number, how do you find the original number?

## Example 3

1 Evaluate the following:

• (a) 62

• (b) 0.52

• (c) 1.52

## Answer<Author(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

1 Write down the coordinates of the point P on each of the graphs below and interpret these coordinates in terms of the labels on the axes.

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Up to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (âˆ’2, 3) or (âˆ’2, âˆ’3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinates.

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1 The frequency diagram below shows the numbers of people in different age groups in a sample of the UK population.

• (a) What is the width of each age group?

• (b) Which age group conta
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1 On the plan of the bathroom in Example 1, what is the width of the window and
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The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, â€˜The arch never sleepsâ€™, which discusses a practical application of some of the ideas in workbook.

Click 'View document' to open the workbook (PDF, 0.8
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This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.

This unit is an adapted extract from the course Mathematical methods and models (MST209
Author(s): The Open University

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
Author(s): The Open University

After studying this unit you should:

• be able to perform basic algebraic manipulation with complex numbers;

• understand the geometric interpretation of complex numbers;

• know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.

Author(s): The Open University

Mailing or discussion lists are email-based discussion groups. When you send an email to a mailing list address, it is sent automatically to all the other members of the list.

The majority of academic-related mailing lists in the UK are maintained by Jiscmail. You will find details of joining these mailing lists on the Jiscmail website. Mailing lists are useful for getting in touch with like-minded colleagues. They are also handy for keeping up to date with current thinking and research
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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 peopleâ€™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 elseâ€™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
Author(s): The Open University

An original piece of work, whether it is text, music, pictures, sound recordings, web pages, etc., is protected by copyright law and may often have an accompanying symbol (Â©) and/or legal statement. In the UK it is the Copyright, Designs and Patents Act 1988 which regulates this.

In most circumstances, works protected by copyright can be used in whole or in part only with the permission of the owner. In some cases this permission results in a fee.

However, the UK legislation incl
Author(s): The Open University

If you find you have a long unmanageable list of favourites/bookmarks you might like to try social bookmarks as an alternative.