Although much can be learned from samples of rocks in the laboratory or at home, the ‘natural habitat’ of rocks is outdoors. Here the distribution and layout of different rocks is visible wherever rocks are exposed in places such as stream beds, cliffs, rocky shorelines, quarries, or road cuttings. The exposed rocks can be studied in just the same detail as individual laboratory samples, and geological fieldwork allows the size and extent of each rock unit to be seen and the relationships

Now that we have covered the features found in igneous, sedimentary and metamorphic rocks, and seen how these features can be explained by the processes that formed the rocks, here is a useful point at which to have a break before continuing with the next section. Before returning, you might like to see for yourself what types of rock you can find in your area. Can you identify their texture, or spot any fossils? Surfaces that haven't been obscured by grime or lichens are by far the best, as

1.4.5 Fossils and ancient environments

An essential component of any environment is the plant and animal life that is adapted to the prevailing conditions. Fossil plants and animals are therefore wonderful sources of information about ancient environments. Plants can leave behind remains ranging from roots, leaves and twigs to seeds and pollen. Leaves and twigs are relatively fragile, and require a comparatively low energy environment (e.g. the mudflats of an estuary) for their preservation. Seeds, pollen and spores are surprising

The **magnitude** of an earthquake is a measure of the amount of *seismic energy* released by it, so it is a *quantitative* scale. The scale of earthquake magnitude is called the **Richter scale**. Its development is described in Box 4, *Charles Richter and the Richter earthquake magnitude scale*. The Richter magnitude is calculated by first measuring the size of the largest ground motion recorded by a seismometer, a sensitive instrument that detects the ground movements

This course is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the *boxplot*. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. The other topic, is that of dealing with data presented in tabular form. You are, no doubt, familiar with such tables: they are common in the media and in reports an

## Activity 15

Suggest appropriate units for each of the following:

(a) the age of the kitten when it is weaned;

(b) the distance between one train station and the

2.10 The complex exponential function

Consider the real exponential function *f* (*x*) = *e*^{x} (that is, *f* (*x*) = exp *x*). We now extend the definition of this function to define a function *f*(*z*) = *e*^{z} whose domain and codomain are Author(s):

After studying this course, you should be able to:

understand the arithmetical properties of the rational and real numbers

understand the definition of a

**complex number**perform arithmetical operations with complex numbers

explain the terms modular addition and modular multiplication

explain the meanings of a relation defined on a set, an equivalent relation and a partition of a set.

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Course image: Stuart Rankin in Flickr made available under Creative Commons Attribution-NonCommercial 2.0 Licence.

All materials included in this course are

After studying this course, you should be able to:

create simple models, given a clear statement of the problem

identify the simplifying assumptions that underpin a model

identify the key variables and the parameters of a model

apply the input–output principle to obtain a mathematical model, where appropriate.

The sum of the angles of any triangle is 180°. This property can be demonstrated in several ways. One way is to draw a triangle on a piece of paper, mark each angle with a different symbol, and then cut out the angles and arrange them side by side, touching one another as illustrated.

## Question 1

Draw a line of symmetry on each of the shapes below.

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but

Two straight lines that do not intersect, no matter how far they are extended, are said to be **parallel**. Arrows are used to indicate parallel lines.

1.3.4 Vertically opposite angles

When two straight lines cross, they form four angles. In the diagram below, these angles are labelled *α*, *β*, *θ* and *φ* and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called **vertically opposite** angles. Here *α* and *β* are a pair of vertically opposite angles, as are *θ* and *φ*. Although such angles are called ‘vertically opposite’, they do not need to be vertically above and bel

## Question 1

A company carried out a survey, recording how staff in a particular office spent their working time. The table shows the average number of minutes spent in each hour on various activities.

You can use the fact that the sum of angles at a point is 360° to draw a pie chart.

## Example 4

Over a five-year period a mathematics tutor found that 16 of her students gained distinctions, 32 gained pass grades and 12 failed to complete the course. Draw a pie chart to re

## Activity 14

A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three program

Climate change: transitions to sustainability

Human societies have to take urgent action to end their dependences on fossil fuels. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This free course, Climate change, takes on the task of trying to chart some of the ways in which it might be possible.Author(s):

The frozen planet

This free course is a general introduction to the frozen planet, including the temperature in the polar regions; the energy from the Sun and the seasons; reading and understanding graphs and maps; and how the Arctic and Antarctic regions are defined. First published on Thu, 23 May 2019 as Author(s):