In Section 5 we show how functions may be used to sketch curves in the plane, even when these curves are not necessarily the graphs of functions.

Click the link below to open Section 5 (8 pages, 151KB).

Section 5

Author(s): The Open University

A fundamental concept in mathematics is that of a function.

Consider, for example, the function f defined by

This is an example of a real function, because it associates with a given real number
Author(s): The Open University

Our everyday experience of percentages includes percentage increases (like VAT at %, or a service charge of 15%) and percentage decreases (such as a discount of 15%).

For example, Â£8 plus
Author(s): The Open University

Proportion is another way of expressing notions of part and whole. You might say that the proportion of village inhabitants who are children is a quarter, or that the proportion of fruit juice in the punch is two thirds, or that the proportion of sand in the concrete is three quarters.

All these examples involve the fractions Author(s): The Open University

The doâ€“talkâ€“record triad (DTR) is a description of what is likely to take place in collaborative mathematics classrooms. It is concerned with observable events, and with the learner rather than the teacher, though many teaching insights flow from it. Although the order of the triad suggests that it should be followed in a particular sequence, this is not necessarily the case. Sometimes talking comes before doing or recording before talking. It also takes time for a learner to move
Author(s): The Open University

The so-called â€˜content/processâ€™ debate in mathematics involves discussion of the relative importance of content and process in mathematics. It originated as part of a discussion about the nature of mathematics, particularly of school mathematics, and of the purposes for which mathematics is learned. Identifying content and process in mathematics draws attention to the idea that mathematics is a human activity.

As a teacher of mathematics in the UK, you are faced with a national curr
Author(s): The Open University

World in transition: Migration and Trade
What does it mean to be poor, or an immigrant? What form should Aid take? This album begins to explore the complex issues of international development in a globalised world, starting with a look at schemes which attempt to alleviate poverty. Small business owners are empowered by micro-financing in Glasgow, while in Argentina a disastrous economic collapse has led to people taking matters into their own hands by creating an alternative social exchange currency. Migrant communities, such as Greek
Author(s): The OpenLearn team

World in transition: Managing Resources
Do you take your access to water for granted? The Peruvian and Tanzanian communities featured in this album certainly donâ€™t. This album examines how development agencies can empower communities to help themselves by introducing simple technologies, and facilitate the sharing of ideas through education. In the Andean mountains, scarce supplies of water and agricultural challenges give rise to conflict; but the changes engineered by development agencies can start to show a way out of poverty. Me
Author(s): The OpenLearn team

Reducing your ecological footprint
Concerned about your impact on the environment? Interested in learning how to shape a more sustainable future? This album shows you simple ways to adapt your lifestyle and how to think globally. Five video tracks demonstrate how to assess the â€˜ecological footprintâ€™ of your household, examine the effects of personal transport on the environment, and explore how your decisions as food consumers are part of a supply chain stretching across Europe and the rest of the world. They feature an energ
Author(s): The OpenLearn team

This course will facilitate your exploration of a viable way of life by identifying actions that individuals can take to reduce environmental impacts while sustaining community well-being. You will be required to develop a worked example of how to go about doing this based on your own experience. In particular, you will explore how identifying a balance between reducing environmental impacts and sustaining community well-being should be an ongoing Author(s): The Open University

Nature Matters considers environmental responsibility and what may matter from a caring perspective and an accountability perspective. A reading by Andrew Light reflects on four key debates in environmental ethics regarding the way in which nature is valued, and prompts the question on how such debates might inform environmental responsibility.

Section 2 examines the formal processes involved in developing accountability in the context of sustainable development. The persuasiveness of t
Author(s): The Open University

Introducing the environment: Ecology and ecosystems
What is ecology and why is it important to our understanding of the world around us? This free course, Introducing the environment: Ecology and ecosystems, looks at how we can study ecosystems to explore the effect that humans are having on the environment. First published on Fri, 18 Mar 2016 as Author(s): Creator not set

This course provides an introduction to global warming. We will be considering the history of global warming by looking at the pattern of ice ages and analysis of recorded temperatures. We will aim to gather meaningful information from this data. We will briefly assess the impact and influence of humans on global warming and, finally, we will examine climate models and how to predict future changes.

This OpenLearn course provides a sample of postgraduate study in Author(s): The Open University

Environmental management and organisations
It is believed that environmental management requires action at all levels and by organisations of all types and sizes. However it is not always clear what we mean by environmental management and the role that organisations do and could play. This free course, explores the different interpretations and viewpoints involved by using system thinking to provide a framework with which to better understand environmental management and organisations. Author(s): Creator not set

Earth's physical resources: petroleum
The discovery of the world's first major underground oil field in Pennsylvania, USA in 1859 sparked the continuing era of the world's reliance on cheap energy from oil and gas. This free course, Earth's physical resources: petroleum, begins by examining the geological characteristics of petroleum and the key ingredients necessary to form oil and gas accumulations. Then there is a brief description of industrial operations during the life cycle of an oil field, starting with subsurface analysis a
Author(s): Creator not set

Effects of pollutants on the aquatic environment
Effects of pollutants on the aquatic environment is a free course. It begins with an introduction to water and goes on to briefly outline the major sources of water pollution (these being sewage works, manufacturing and industrial plants, the farming and animal husbandry sectors, landfill sites and urban surface water run-off). It considers the major water pollutants and describes the effects they have on water. Author(s): Creator not set

1. Reconstructions based on direct temperature measurements (back to 1860) and proxy data (Box 7) reveal that the Earth's GMST varies naturally on many different time-scales: from year-to-year, over periods of several decades and, in the longer term, according to the roughly 100 000-year rhythm of glacial/interglacial cycles. The past 10 000 years has been marked by the relatively stable global climate of the present interglacial (the Holocene).

2. Author(s): The Open University

State-of-the-art models are designed to simulate the workings of the climate system (in so far as this is currently understood), and include the 'internal' interactions that generate short-term natural variability in the real world. They provide modellers with a means of carrying out 'virtual' experiments on the climate system. In the present context, an important aim of these experiments is to identify the 'signal' of a human influence on climate, so studies typically involve 'feeding' into
Author(s): The Open University

To put the temperature records reported by the IPCC in context, we start with a longer-term geological perspective on the Earth's GMST.

Author(s): The Open University

Here are some quotes from the 'Summary for Policymakers' (SPM) included in the report from the scientific working group in the IPCC TAR (IPCC, 2001a):

• The Earth's climate system has demonstrably changed on both global and regional scales since the pre-industrial era, with some of these changes attributable to human activities.

• Globally, it is very likely that the 1990s was the warmest decade and 1998 the warmest year in the instrumental
Author(s): The Open University