 Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

• Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right.

• Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

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All circles are the same shape – they can only have different sizes.

In a circle, all the points are the same distance from a point called the centre. The centre is often labelled with the letter O. Author(s): The Open University A quadrilateral is a shape with four straight sides.
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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
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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 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
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## SAQ 26

Find the distance between the numbers 2 − i and 1 + 3i.

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In this section we have seen that the complex number system is the set R × R together with the operations + and × defined by From this, one can justify the performance of ordinary algebraic operations on expressions of the form
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Section 6 contains solutions to the exercises that appear throughout sections 1-5.

Click the link below to open the solutions (13 pages, 232KB).

Section 6

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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 ## Study another free course

There are more than 800 courses on OpenLearn for you t
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Discount can be calculated in the same way as an increase by a percentage. For example, £8 with 15% discount means you actually pay

£8 less (15% of £8)

15% of 8 = × 8 =
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## Activity 20

Convert each of the following to percentages. Round off the percentages to whole numbers.

• (a)

• (i) 0.8

• (ii) 0.
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## Activity 17

Express each of the following percentages as fractions:

• (a) 40%

• (b) 8%

• (c) 70%

• (d)
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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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## Activity 5

Convert each of the following fraction ratios to decimal ratios.

• (a) [Image_Link]https://www.open.edu/op
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Although ratios are often given as fractions, they can also be expressed as decimals. You need to deal with a mixture of fractions and decimals, and to compare ratios given in either form, so you need to be able to convert between the two forms.

## Example 4

The ratio of the circ
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Time conversions are also ratios. The ratio of time measured in minutes to time measured in seconds is one to sixty (1:60), as there are sixty seconds in a minute.

## Example 2

Adam's grandfather ran a mile in
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To make short crust pastry, one recipe book says ‘use one part of fat to two parts of flour’; another recipe says ‘use fat and flour in the ratio of one to two’; and yet another says ‘use half as much fat as flour’. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

[Image_Link]https://www.open.edu/openlearn/ocw/pluginfile.php/
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Course image: rod
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