Aims The main aim of this section is to introduce some ideas about making valid comparisons and to focus on ways of extracting information from tables and graphs.

Author(s): The Open University

Are we getting better off? Politicians and journalists often make sweeping claims about whether or not â€˜weâ€™ are getting better off.

• Who is this â€˜weâ€™ of whom they speak?

• On what do they base these claims?

• What does being better off mean to you?

• How would you go about assessing how well-off you are?

In attempting to resolve some of these questions, a number of important mathemat
Author(s): The Open University

Pretend that you are the marker of another solution to the same problem. How would you mark Solution B?

## Example 16 Billions

You may think that you know what the word billion means but do you really have a feel for its size?

Author(s): The Open University

First write out a full solution to the following problem.

## Example 16: Billions

You may think that you know what the word billion means but do you really have a feel for its size?

Author(s): The Open University

The following table summarises some of the types of instructions you will encounter.

Write down â€¦ Determine â€¦ Show â€¦
What isâ€¦ Find â€¦ Prove â€¦
Calculate â€¦
A simple answer will do but generally g
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

## Example 14

Suppose you have decided to tile the wall using square tiles of side 10 cm. You are proposing to use the tiles across the full 5 metre width of the wall up to a height of 1.8 m.

Find the number of boxes of tiles that you will require to cover the wall if the tiles are sold in boxes o
Author(s): The Open University

Before you can attempt a question, you must read and understand it. This may sound obvious but you will need to know, before you start, what is expected by way of an answer. In particular, you will need to know the meaning of the instructions contained in the question. This section contains a discussion of the precise meanings attached to words like â€˜findâ€™, â€˜showâ€™, â€˜write downâ€™ and â€˜determineâ€™ in mathematics questions. The different types of instruction are illustrated by posi
Author(s): The Open University

By the end of this unit you should be able to:

• lay out and, where appropriate, label simple mathematical arguments;

• understand the precise mathematical meaning of certain common English words;

• understand and use common mathematical symbols;

• write clear, unambiguous mathematical solutions using appropriate notation;

• identify and modify some sources of ambiguity or inappropriate use of notation in a mathematical solution;
Author(s): The Open University

Do you want to improve your ability to subtract one number from another, especially if decimals are involved, without having to rely on a calculator? This unit will help you get to grips with subtraction and give you some practice in doing it.

You can start with some practice in subtracting small numbers in your head if you want to. Then we will show you how to subtract bigger numbers on paper. Finally we look at how to subtract decimal numbers.

You donâ€™t need to complete the
Author(s): The Open University

The example of 25546 divided by 53 is suitable for long division. First write the calculation down on paper in the same way you did before.

<
Author(s): The Open University

When you divide by a number up to 10, the steps are as follows:

1. Take each digit of the number under the line in turn, starting from the left.
2. Work out how many times the dividing number goes into it.
3. Write the answer to the division above the line
4. If there is a remainder, carry it by putting it in front of the next digit on the right.
5. Work out how many times the dividing number goes into the next digit, including any car
Author(s): The Open University

1. Data in the form of counts of individual entities (for example, people, animals, power stations) in a small set of discrete categories can be presented in bar charts or pie charts. For most purposes, bar charts are preferable. Pie charts draw particular attention to the proportions in which the entities are split between the different categories. However, they do so by representing the proportions by angles, and even when the main interest lies in the propo
Author(s): The Open University

For the six ordered data items 1, 3, 3, 6, 7, 7, the lower quartile is given by

In other words, the lower quartile qL is given by the number three-quarters of the way between x (1)=1 and x (2)=3. The difference betwe
Author(s): The Open University

Figure 19 shows a histogram of chest measurements (in inches) of a sample of 5732 Scottish soldiers.

Author(s): The Open University

The time taken to cook a fresh chicken depends on its mass, as given by the following formula:

Roughly how long will a chicken with a mass of 2.2Â kg take to cook?

To use the formula, you need to substitute the mass of the chicken into the right-hand side of the equ
Author(s): The Open University

Patterns occur everywhere in art, nature, science and especially mathematics. Being able to recognise, describe and use these patterns is an important skill that helps you to tackle a wide variety of different problems. This unit explores some of these patterns ranging from ancient number patterns to the latest mathematical research. It also looks at some useful practical applications. You will see how to describe some patterns mathematically as formulas and how these can be used to solve pro
Author(s): The Open University

We saw above that the vector 2v can be regarded as the vector v â€˜followed byâ€™ the vector v; we can also quite naturally describe this vector as being the â€˜sumâ€™, v + v, of the vector with itself.

Analogously, if p is the vector 2 cm E and q is the vector 3 cm NE, we can think of the â€˜sumâ€™ p + q of the vectors as follows. Starting from a given point, O say, draw the vector p; starting from its finishi
Author(s): The Open University

In lots of everyday situations percentages are used to make predictions and comparisons.

## Example 14

The number of casualties handled by the outpatients department of a hospital increases by approximately 8% per year. The number of casualties this year was 1920. Make a prediction for the number
Author(s): The Open University

The Impact of Geography on International Politics [Audio]
Speaker(s): Tim Marshall | Editor's note: Some questions have been removed from this podcast due to inaudiblity. Foreign Affairs Broadcaster and Journalist, Tim Marshall, author of new book Prisoners of Geography explains how decisions made by world leaders are constrained by geography. It is true that to understand world events (such as President Putin's invasion of Crimea and events in the Middle East), you need to understand people, ideas and movementsâ€¦ but if you donâ€™t know geography, yo
Author(s): No creator set