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

Author(s): The Open University

After studying this unit you should be able to:

• create simple models, given a clear statement of the problem;

• write down the simplifying assumptions that underpin a model;

• identify the key variables and the parameters of a model;

• apply the inputâ€“output principle to obtain a mathematical model, where appropiate;

• obtain mathematical relationships between variables, based on or linking back to the simplifying assumptions
Author(s): The Open University

We have seen that the set [0, 2) has no maximum element. However, [0, 2) has many upper bounds, for example, 2, 3, 3.5 and 157.1. Among all these upper bounds, the number 2 is the least upper bound because any number less than 2 is not an upper bound of [0, 2).

Author(s): The Open University

## Example 4

Trying to understand this example is like trying to un
Author(s): The Open University

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.

Author(s): The Open University

1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

Author(s): The Open University

In general, to square a number, multiply it by itself. This is denoted by writing a small â€˜2â€™ to the top right of the number,

e.g. 4 squared, written 42, is 4 Ã— 4 = 16.

Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

Example 3 Table: Copyri
Author(s): The Open University

1 Look at the diagram below and answer the following questions:

• (a) Write down the coordinates of the points P, Q, R, S and T.

• (b) On this diagram,
Author(s): The Open University

1 Write down the coordinates of A and B.

Author(s): The Open University

Pie charts are representations that make it easy to compare proportions: in particular, they allow quick identification of very large proportions and very small proportions. They are generally based on large sets of data.

The pie chart below summarises the average weekly expenditure by a sample of families on food and drink. The whole circle represents 100% of the expenditure. The circle is then divided into â€˜segmentsâ€™, and the area of each segment represents a fraction or pe
Author(s): The Open University

Experiments or surveys usually generate a lot of information from which it is possible to draw conclusions. Such information is called data. Data are often presented in newspapers or books.

One convenient way to present data is in a table. For instance, the nutrition panel on the back of a food packet:

### Nutrition Information

Author(s): The Open University

This unit is an adapted extract from the course Mathematical methods and models (MST209)

This unit lays the foundations of Newtonian mechanics and in particular the procedure for solving dynamics problems. The prerequisite skills needed for this unit are the ability to solve first- and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a
Author(s): The Open University

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.

Author(s): The Open University

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

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