In the next activity you will be able to build upon the previous one and observe the way in which the debate on the new EU constitution has progressed and moved to another level on its way to ratification.

## Activity 7 A snapshot from the EU constitutional debate (2)

Author(s): The Open University

A fraction is written as one number over another (such as ) and means the top number divided by the bottom number. The top number, 3, is called the numerator and the bottom number, 10, is call
Author(s): The Open University

For many towns and cities, an individual book of street maps called an A to Z has been produced. You can look up the name of a street in the index, and it will give you the page number of the map that contains the street, plus the grid reference square for the street. There are different conventions for these grid references. You may have met several of these.

Once you have done a calculation, with or without the aid of a calculator, it is important that you pause for a moment to check your calculation.

You need to ask yourself some questions.

1. Have I done the right calculation in the right order?

2. Have I given due consideration to units of measurement?

4. Did I make a rough estimate to act as a check?

Author(s): The Open University

## Activity 14

Measurement of a ceiling gives a length of 6.28 m and a width of 3.91 m.

• (a) Make a rough estimate of the area of the ceiling (the length times the width).

Author(s): The Open University

Numbers are often approximated to make them easier to handle, but sometimes it doesnâ€™t help very much to round to the nearest 10 or the nearest 100 if the number is very large. For example, suppose the monthly balance of payments deficit was actually Â£24Â 695Â 481. Rounded to the nearest 10, it's Â£24Â 695Â 480; and to the nearest 100, it's Â£24Â 695Â 500. But Â£24Â 695Â 500 is still a complicated number to deal with in your head. That's why it was rounded to Â£25 000 000 in the newspaper
Author(s): The Open University

The blouse in the figure above was Â£19 and you may well have thought of it as roughly Â£20. In this case you would be rounding to the nearest ten (pounds).

The rule for rounding to the nearest hundred can be adapted easily to rounding to the nearest ten. Instead of looking at the tens digit look at the units digit.

So Â£23 is rounded down (to Â£20) and Â£36 is rounded up (to Â£40).

Author(s): The Open University

You will probably think to yourself that the coat shown costs about Â£300. Â£290 is considerably closer to Â£300 than it is to Â£200, so Â£300 is a reasonable approximation. In this case, 290 has been rounded up to 300. Similarly, 208 would be rounded down to 200 because it is closer to 200 than it is to 300. Both numbers have been rounded to the nearest hundred pounds.

When rounding to the nearest hundred, anything below fifty rounds down. So 248 rounds to 200. Anything o
Author(s): The Open University

## Question 1

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

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.

Author(s): The Open University

In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification.

## Example 15

Suppose you now decide to place your new bath (length 1.7 m, height 0.8 m) against this wall as shown in the diagram below.

Author(s): The Open University

In this section we shall develop the correspondence between C and RÂ Ã—Â R by obtaining a geometric representation of elements of C and operations on C. We shall define the polar form of a complex number and the modulus and argument of a complex number. We shall see that not only does Author(s): The Open University

In Section 4 we introduce the hyperbolic functions sinh, cosh and tanh, which are constructed from exponential functions. These hyperbolic functions share some of the properties of the trigonometric functions but, as you will see, their graphs are very different.

Click the link below to open Section 4 (5 pages, 104KB).

Section 4
Author(s): The Open University

## 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
Author(s): The Open University

To make short crust pastry, one recipe book says â€˜use one part of fat to two parts of flourâ€™; another recipe says â€˜use fat and flour in the ratio of one to twoâ€™; and yet another says â€˜use half as much fat as flourâ€™. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

Author(s): The Open University

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): Creator not set

Transport and sustainability
This free course, Transport and sustainability, explores the issues around sustainable transport and how the role of technology and society can interact to lower the overall impact of transport. First published on Fri, 26 May 2017 as Transport and sus
Author(s): Creator not set

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

Living without oil
Crude oil is currently our most important global source of energy. It is vital in the manufacture of many modern materials. But the worlds supply of oil is finite, its price is unstable and our reliance on oil has damaging environmental consequences. This free course, Living without oil, explains why developing alternatives to oil is an essential and urgent task for humanity.
Author(s): Creator not set

Water for life
Atoms, elements and molecules are the building blocks of everything that makes up our world, including ourselves. In this free course, Water for life, you will learn the basic chemistry of how these components work together, starting with a chemical compound we are all very familiar with water. First published on Wed, 17 Jan 2018 as Author(s): Creator not set