• recognise that many scientific findings follow from the use of theoretical models in addition to consideration of empirical data;

• be aware that numerical values provided by scientists may be derived directly from data, or from the application of theoretical models to a data set.

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To review and consolidate the learning which you have gained from studying this course, you might like to consider the following questions:

• Why do you think that different ways of running a business have developed under English law (e.g. sole trader, partnership, company)?

• What do you think are the advantages and disadvantages of running
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## Activity 23

Candles are sold in boxes of 40. How many candles are there in 30 boxes?

One box has 40 candles.

10 boxes have 40 Ã—
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## Activity 10

This table categorises Tom's activities for the day.

Activity<
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Tables often give information in percentages. The table below indicates how the size of households in Great Britain changed over a period of nearly 30 years.

Number of people in household1961 (%)1971 (%)1981 (%)1991 (%)
1Author(s): The Open University

## Activity 6

The table below indicates the cooling rate of tea in a teapot.

Time/mins
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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

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If the digit at the top of any column in your subtraction is smaller than the digit at the bottom of the same column, you need to borrow (or carry) from the next column on the left.

There is an example of this below. Click on each step in turn to see how to carry out the calculation.

Active content not displayed. This content req
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The sum of the angles of any triangle is 180Â°. 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.

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## 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
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A quadrilateral is a shape with four straight sides.
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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.

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When two straight lines cross, they form four angles. In the diagram below, these angles are labelled Î±, Î², Î¸ and Ï† and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called vertically opposite angles. Here Î± and Î² are a pair of vertically opposite angles, as are Î¸ and Ï†. Although such angles are called â€˜vertically oppositeâ€™, they do not need to be vertically above and bel
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## 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.

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You can use the fact that the sum of angles at a point is 360Â° 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
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The modulus function provides us with a measure of distance that turns the set of complex numbers into a metric space in much the same way as does the modulus function defined on R. From the point of view of analysis the importance of this is that we can talk of the closeness of two complex numbers. We can then define the limit of a sequence of complex numbers in a way which is almost identical to the definition of the limit of a real sequence. Another analogue of real analysis arises
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Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence

Course image:
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## 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
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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