## Example 3

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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.

Here's Example 2 again.

## Activity 7

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

There are many re
Author(s): The Open University

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

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

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).

## Unit image

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

Author(s): The Open University

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).

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

100 Ã· 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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1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

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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

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 On the plan of the bathroom in Example 1, what is the width of the window and
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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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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 aÂ =Â a 1 iÂ +Â a 2 j, what are its magnitude |a| and direction Î¸?

The first part of this question is dealt with using Pythagorasâ€™ Theorem: the magnitude of a v
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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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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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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 educationâ€”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
Author(s): The Open University

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
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