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8.2.2 The screen

You can see the calculations that you have entered as well as the answers. This means you can easily check whether you have made any mistakes.


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7.2 Square roots

Earlier you met the square function and on most calculators the square root is the second function on the same key. Look to see if this is the case for your calculator and check the calculator handbook on how to use this function. In many cases you will need to press the square root key before the number, instead of afterwards, as for the square key. This is the case on the TI-84. Check that you can find the square root of 25 and of 0.49 (you should get 5 and .7 respectively).

Now find
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3 Aims

The aim of this section is to help you to think about how you study mathematics and consider ways in which you can make your study more effective.


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Pressing onwards

Activity 15

  1. Work through Sections 1.6 and 1.7 of the Calculator Book, using the method suggested above of glancing ahead-pressing on-glancing back, if you find it useful.

  2. A num
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1.1 Mathematics and you

Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood.

Activity 1 Carl Jung's school days

Read
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Why study mathematics?

Figure 1.2
Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches

There are many re
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2 Representing symmetries

In Section 2 we develop an algebraic notation for recording symmetries, and demonstrate how to use the notation to calculate composites of symmetries and the inverse of a symmetry.

Click 'View document' below to open Section 2 (9 pages, 504KB).

Acknowledgements

Unit image

Alist  [Details correct as of 27th June 2008]

 

All other material contained within this unit originated at the Open University.


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2 Functions

In Section 2 we give the general definition of a function, and illustrate how functions can be used to describe a variety of mathematical concepts, such as transformations of the plane. We discuss the idea of composing two functions, and the idea of forming the inverse of a function.

Click 'View document' below to open Section 2 (16 pages, 366KB).

Acknowledgements

All written material contained within this unit originated at the Open University

1. Join the 200,000 students currently studying withThe Open University.


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Introduction

Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply ‘joining up the dots’ can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of t
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4 Open Mark quiz

Now try the quiz  and see if there are any areas you need to work on.


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3.1 Expressing numbers in scientific notation

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

Place value10 0001000100101Author(s): The Open University

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2.5.1 Try some yourself

1 What are the following?

  • (a) 10

  • (b) 01

  • (c) 20

  • (d) 02


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3.2 Negative coordinates

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 (2, 3) or (2, 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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3.1 Positive coordinates

For many towns and cities, an individual book of street maps called an A to Z has been produced. You can look up the name of a street in the index, and it will give you the page number of the map that contains the street, plus the grid reference square for the street. There are different conventions for these grid references. You may have met several of these.


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2.2 Tables and percentages

Tables often give information in percentages. The table below indicates how the size of households in Great Britain changed over a period of nearly 30 years.

Number of people in household1961 (%)1971 (%)1981 (%)1991 (%)
1<
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1 Modelling static problems

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, ‘The arch never sleeps’, 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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Acknowledgements

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

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


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1 Using vectors to model

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.

Click 'View document' to open the workbook (PDF, 1 MB).

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