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

1 On the plan of the bathroom in Example 1, what is the width of the window and
Author(s): The Open University

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.

Author(s): The Open University

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. When prompted after exercise 2.2 to watch the video for this unit, return to this page and watch the four clips below. After you've watched the clips, return to the workbook.

Click 'View document' to open the workbook (PDF, 1.0 MB).

Author(s): The Open University

After studying this unit you should be able to:

• understand and use the basic terms for the description of the motion of particles: position, velocity and acceleration;

• understand, use and differentiate vector functions;

• understand the fundamental laws of Newtonian mechanics;

• solve mechanics problems in one dimension by drawing a sketch, choosing a suitable x-axis and origin, drawing a force diagram, applying Newtonâ€™s second law, tak
Author(s): The Open University

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers.

This unit is an adapted extract from the course Author(s): The Open University

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, 0.6 MB).

## Exercise 1

A vector a has magnitude |a|Â =Â 7 and direction Î¸Â =Â âˆ’70Â°. Calculate the component form of a, giving the components correct to two decimal places.

<
Author(s): The Open University

The displacement from a point P to a point Q is the change of position between the two points, as described by the displacement vector

If P and Q represent places on the ground, then it is natural to use a bearing to describe the direct
Author(s): The Open University

In some applications of vectors there is a need to move backwards and forwards between geometric form and component form; we deal here with how to achieve this.

To start with, we recall definitions of cosine and sine. If P is a point on the unit circle, and the line segment OP makes an angle Î¸ measured anticlockwise from the positive x-axis, then cosÂ Î¸ is the x-coordinate of P and sinÂ Î¸ is the y-coordinate of P (
Author(s): The Open University

Ahmed, A. (1987) Better Mathematics, London, HMSO.

DfEE (2001) Key Stage 3 National Strategy: Framework for Teaching Mathematics: Years 7, 8 and 9, London, DfEE.

NCTM (1989) Curriculum and Evaluation Standards for School Mathematics Reston VA, National Council of Teachers of Mathematics.

Author(s): The Open University

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. Section 4.2 of the unit requires you to listen to some audio files. You'll find these on the next page of this unit.

Click on 'View document' to open the workbook (PDF, 4 MB).

Question 1

Although most people immediately think of economic globalisation, Section 1 shows how political, social/cultural and ecological globalisation are also significant in the context of global environmental change.

Question 2

The advocates of â€˜business learnsâ€™ are optimistic about the global free-market civilisation they believe they are building, but they also believe business needs to heed environmental and social concerns for its own sake. â€˜Radic
Author(s): The Open University

People who demand a radical break with the business-dominated path of economic globalisation believe that the claims of the mainstream business community are at best hopelessly inadequate, and at worst deceitful. However, they know they have to come up with some answers of their own. This section outlines ideas that seek to underpin a transition to green economies owned and run at grassroots level. Sounds ambitious? Author(s): The Open University

### Activity 1 What does â€˜globalisationâ€™ mean to you?

Note down on paper or in your learning journalÂ  your first tho
Author(s): The Open University

The material acknowledged below is Proprietary and used under licence, see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following:

## Figures

Figur
Author(s): The Open University

Greenland snowfall differs depending on whether it falls in summer (when snow is comparatively warm and moist) or winter (when snow is cold and dry). These differences mean that as the snow is turned to ice, annual layers are formed that are in many ways similar to tree rings: thick annual layers mean high snowfall and thin annual layers low snowfall. The accumulation of snowfall on the summit of Greenland â€“ and most importantly what is trapped within the crystals as it turns to ice â€“ can
Author(s): The Open University

By the end of this unit you should be able to:

• appreciate how chemical processes in the rest of the world affect the Arctic environment and the species inhabiting it;

• recognise the physical processes that determine atmosphere and oceanic flows in the Arctic;

• appreciate the scientific research process and the use of scientific evidence;

• use quantitative scientific evidence to examine the link between atmospheric carbon dioxide levels a
Author(s): The Open University

Few people agree that individuals should take the main responsibility for tackling environmental issues. For example, in a 2007 poll of over 2000 UK citizens, 70% agreed that the government should take a lead in combating climate change, even if it means using the law to change people's behaviour. However, over 60% disagreed that there was nothing they could do to avert climate change and over half agreed that they would do more if others did more too, although 40% thought that recycling was
Author(s): The Open University

Let's now look at carbon footprint reduction targets in a bit more detail.

The first international agreement to set carbon reduction targets was the 1997 United Nations Kyoto Protocol, which requires developed countries to reduce their human-generated greenhouse gas emissions by an average of just over 5% on 1990 levels by 2008 to 2012. By the time the treaty came into force in 2005, only the USA and Australia had refused to sign. (A new Australian government finally signe
Author(s): The Open University