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Does it make sense?

Example 3

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Puzzling out the Soma cube

The mathematical writing in Example 3 also uses diagrams but for a very different purpose. It arises from a particular three-dimensional puzzle, sometimes called a Soma cube, pictured below.

Figure 1.10

Packaging the pictures

Here's Example 2 again.

Activity 7

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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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6 Solutions to the exercises

Section 6 contains solutions to the exercises that appear throughout sections 1-5.

Click 'View document' below to open the solutions (15 pages, 468KB).

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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2.6 Negative powers

Now look at what happens when the power is negative. What does 10−3 mean? What is the result of the following calculation?

100 ÷ 100 000

What you are actually being asked to find is:

But look at the calculation again. Using the rule for the division
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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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Introduction

This unit reminds you about powers of numbers, such as squares and square roots. In particular, powers of 10 are used to express large and small numbers in a convenient form, known as scientific notation, which is used by scientific calculators.

This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offer in Author(s): The Open University

3.4.1 Try some yourself

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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1.1.1 Try some yourself

1 On the plan of the bathroom in Example 1, what is the width of the window and
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1.1 Understanding scale diagrams

Plans of houses and instructions for assembling shelves, etc., often come in the form of scale diagrams. Each length on the diagram represents a length relating to the real house, the real shelves, etc. Often a scale is given on the diagram so that you can see which length on the diagram represents a standard length, such as a metre, on the real object. This length always represents the same standard length, wherever it is on the diagram and in whatever direction.


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1.2: Converting to geometric form

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector a = a 1 i + a 2 j, what are its magnitude |a| and direction θ?

The first part of this question is dealt with using Pythagoras’ Theorem: the magnitude of a v
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Learning outcomes

On completion of this unit you should be able to:

  • convert a vector from geometric form (in terms of magnitude and direction) to component form;

  • convert a vector from component form to geometric form;

  • understand the use of bearings to describe direction;

  • understand the difference between velocity and speed;

  • find resultant displacements and velocities in geometric form, via the use of components.


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3 Work on your own mathematics

Two activities are given below. You are asked to work on them in turn and to record not only your working, but observations on what you notice about your emotions as you work through step by step.

Activity 3 Constrained numbers

W
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1 Forces for development

Working in mathematics education involves a sense of both past and future, and how the two combine to influence the present. It may seem that, because the past has already happened, it cannot be altered; however, you can alter how you perceive the past, and what lessons you take from it. Each of us has a personal past in mathematics education—the particular events of our personal lives, who taught us, where, what and how they taught us, and what we took from the experiences. Each of us also
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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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