This unit is an adapted extract from the course Pure mathematics (M208)

The idea of vectors and conics may be new to you. In this unit we look at some of the ways that we represent points, lines and planes in mathematics.

In Section 1 we revise coordinate geometry in two-dimensional Euclidean space,
Author(s): The Open University

We have used the video sequence below to highlight the emic/etic problem and we would like you to carry out a short exercise using it to consolidate your understanding of these terms.

The video introduces St Mungo Museum of Religious Life and Art in Glasgow, which has been described as the first public museum of religion in the world. Do note, however, that the Museum of Religions at the University of Marburg, Germany was founded in 1927 by Rudolf Otto. It contains a considerable number
Author(s): The Open University

So what do these devices that are manufactured in such vast quantities look like? Processors are manufactured as integrated circuits. Essentially they are circuits, around the size of a fingernail, which contain many millions of electronic components manufactured as one very complex circuit. Figure 4(a) shows how a processor manufactured as an integrated circuit is packaged so it can be used as a component in an electronic circuit. The pins of the package are connected to the integrated circu
Author(s): The Open University

The legal system plays a significant and growing role in society as our lives become governed by an increasing number of laws. As our society has become more sophisticated, a greater number of laws have been required. This in turn has resulted in our legal system becoming increasingly more complex. Changes in technology, the way in which we live and the types of relationships we have are all reflected by the law. Society expects the law to reflect its ideas, values and culture, so the law has
Author(s): The Open University

## Example 47

• (a) Find the angle between each of the pairs of vectors:

(3, 1) and (1, âˆ’2); i + 2j and âˆ’3i + j âˆ’ 2k.

• Author(s): The Open University

Often plans run into difficulties because of unforeseen problems or changing circumstances. For example you may be running over your deadlines, the resources or support available to you may have changed, or your personal circumstances may have changed. Plans are only a means to an end, however. If you run into difficulties, take some time to think about what effect these difficulties are having on your plans, and what changes you may need to make to your overall strategy to achieve the outcom
Author(s): The Open University

The basic function of the ATM adaptation layer is to convert the user data supplied by higher layers into 48-byte blocks of data. The ATM adaptation layer is divided into two sub-layers â€“ the convergence sub-layer, and the segmentation and re-assembly sub-layer. The convergence sub-layer provides services to higher layers through a set of protocols, but I do not need to describe these here. The segmentation and re-assembly sub-layer separates the messages from the conve
Author(s): The Open University

## Activity 1

A friend is painting the inside walls of a garage. So far she has used a 2 litre tin of emulsion paint and covered an area of 9 m2. She needs some more paint. How much more would you advise her to
Author(s): The Open University

For a variety of reasons, not least the very wide dynamic range of human hearing, the decibel (symbol dB) is often used as a unit for the amplitude of sound waves. The decibel is also used in other contexts, such as specifying the amplification of amplifiers or the degree to which a signal is affected by noise. In the context of sound, the use of the decibel as a unit captures something of the subjective impression of the way loudness changes with amplitude.

The decibel unit has
Author(s): The Open University

Pakistan mob kills woman and girls, over "blasphemous" Facebook post
A seven year old girl, her baby sister and her grandmother are killed by an angry mob in Pakistan over a "blasphemous" Facebook posting, Deborah Lutterbeck reports. Subscribe: http://smarturl.it/reuterssubscribe More updates and breaking news: http://smarturl.it/BreakingNews Reuters tells the world's stories like no one else. As the largest international multimedia news provider, Reuters provides coverage around the globe and across topics including business, financial, national, and internati
Author(s): No creator set

Rocks are classified into three types according to how they were formed. Igneous rocks are formed by crystallisation from the molten state; sedimentary rocks are deposited at the Earth's surface from water, air or ice; and metamorphic rocks are rocks of any origin that have been subsequently transformed (metamorphosed) by heat and/or pressure, often several kilometres below the Earth's surface.

Rocks are generally either crystalline, i.e. formed of interlocking mineral crystals, or frag
Author(s): The Open University

One way of illustrating the possible ways of moving material around the rock cycle is to draw a diagram that places the processes into their geological contexts. Since the rock cycle involves processes occurring on the Earth's surface and also within its interior, we use a cross-section through the Earth's crust and uppermost mantle to do this, as shown in Figure 19. In this diagram we have concentrated on the most common processes within the rock cycle.

Author(s): The Open University

The rocks that erupt from volcanoes are called extrusive igneous rocks, simply because they are formed by the extrusion of magma on to the Earth's surface. Igneous rocks can also form deep underground, and these are called intrusive igneous rocks, because the magmas were intruded into pre-existing rocks and then slowly cooled. The reason that intrusive igneous rocks are now visible at the surface is that over many millions of years erosion has stripped away the overlying rocks.
Author(s): The Open University

A mineral is a solid material, formed by natural processes and with a chemical composition that falls within certain narrow limits. Its constituent atoms are arranged in a regular three-dimensional array or pattern and because of this, minerals form crystals with characteristic shapes.

Although several thousand different kinds of mineral have been discovered, only a few are very common; for example, the mineral quartz, which forms many of the sand grains on a beach or in a desert. Becau
Author(s): The Open University

Pupils should be taught that science uses the experimental method to test ideas, and, in particular, about certain basic techniques such as the use of controls. It should be made clear that the outcome of a single experiment is rarely sufficient to establish a knowledge claim.

Author(s): The Open University

Pupils should be taught that observation and measurement are core activities of scientists; most measurements are subject to some uncertainty but there may be ways of increasing our confidence in a measurement.

Author(s): The Open University

Pupils should appreciate why much scientific knowledge, particularly that taught in school science, is well established and beyond reasonable doubt, and why other scientific knowledge is more open to legitimate doubt. It should also be explained that current scientific knowledge is the best that we have but may be subject to change in the future, given new evidence or new interpretation of old evidence.

Author(s): The Open University

In reality, most mainstream science curricula relegate explicit teaching about the nature of science to the margins â€“ a situation almost universally condemned by science educators. Donnelly (2001) describes recent history in one particular example of curriculum design, where Nature of Science (NoS) issues still remain a peripheral element within the National Curriculum for England and Wales. Donnelly describes the policy confusions that reflect tensions about some fundamental issues about s
Author(s): The Open University

In all subjects â€“ and science no less so than others â€“ definitions are problematic. At one level, science is a body of knowledge about the natural world. But this begs the question: what is peculiar about scientific knowledge as opposed to, taking just one example, an explanation of the origin of the Universe rooted in folklore and superstition? Others might argue that the scientific approach is unique â€“ that the processes involved in doing science are distinct. That might
Author(s): The Open University

In this course we'll be concerned with what type of science forms the basis of science education, and for what purpose. You'll explore these issues by reading the text that follows and by tackling the activities that are included; there are also a number of readings. In the latter part of this course (Sections 10â€“14) we'll consider some of the practical problems involved in delivering an effective curriculum in science and look at key questions relevant to all three educational tiers
Author(s): The Open University