Before going any further, click on 'View document' below and read pages 68â€“71 from Douglas Palmer's Atlas of the Prehistoric World.

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Author(s): The Open University

Figure 8 showed that if the data have a normal distribution the mean value corresponds to the peak of the distribution. Normal distributions of data are very common in science, but by no means universal. Author(s): The Open University

Scientists collect many different types of information, but sets of data may be very loosely classified into two different types. In the first type, so-called â€˜repeated measurementâ€™, an individual quantity is measured a number of times. An astronomer wanting to determine the light output of a star would take many measurements on a number of different nights to even out the effects of the various possible fluctuations in the atmosphere that are a cause of stars â€˜twinklingâ€™. In the seco
Author(s): The Open University

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

All materials included in this unit are derived from content originated at the Open University.

Author(s): The Open University

There is no single right way of calculating percentage increases or decreases. The next examples show two different approaches to the same problems.

## Example 1

A railway season ticket from my local station to London costs (at current prices) Â£825. Calculate the cost of a new ticket, if pric
Author(s): The Open University

Now return to the old till receipt and look at the section which deals with VAT.

 VAT-CODE NET-VAL VAT-VAL S=17.5% Â£8.04 Â£1.41

These three pieces of information might be read as follows:

• <
Author(s): The Open University

There is some information about Value Added Tax (VAT) on the receipt. VAT is charged on many goods purchased in the UK. At the time of the purchase on this receipt, the VAT rate was 17.5%. This means that on every Â£100 net cost, Â£17.50 would be charged in VAT, bringing the total to Â£117.50. In other words:

Net cost + VAT = Gross cost

Â£100.00 + Â£17.50 = Â£117.50

So the shop would charge Â£100, the tax office Â£17.50 and the customer would pay Â£117.50.

Because you
Author(s): The Open University

Multiplying a number by itself is called squaring it and there is a key on scientific and graphics calculators which does this. On the TI-84 the key is marked .

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If you would like some more calculator practice, try your hand at the following puzzles. No answers are given because most of these activities have no single numerical answer. You may like to try them out with your friends â€“ or make up some of your own.

## Brain stretcher: Doing it with your eyes closed!

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A way of forcing a calculator to perform a calculation in a different order to that given in Section 2.3 is to use the bracket keys. For example the following sequence, on a scientific or graphics calculator:

7 2 Author(s): The Open University

Your calculator will interpret the order in which you press the keys, in a particular way. For example if you press the key sequence:

2 3 Author(s): The Open University

Here are a few points from the Exercise 1:

• The negative or minus sign for the answer âˆ’2 maybe slightly smaller and higher than the one used for subtraction in 5 âˆ’ 7. There maybe two minus keys on your calculator keypad, as there are on the TI-84. The one which means do the operation subtract is Author(s): The Open University

Some calculators, like the TI-84, provide you with several different screens for menus, drawing graphs, writing programs and so on. The most important screen, where calculations are carried out, is called the Home Screen. If you should find yourself trapped on another screen, the â€˜panicâ€™ buttons to return â€˜homeâ€™ are usually one or other of the following:

Author(s): The Open University

First have a look at your calculator keyboard. Some of the main features are described below.

The screen (also called the display) is at the top. This is where calculations and so on are displayed. The remainder of the calculator, where the various keys are located, is called the keyboard.

The number keys are usually in the bottom part of the keyboard and there are also the four operation keys: Author(s): The Open University

As you have been working through this unit, have you thought about how you are studying, and what this process involves? Do you feel confident or concerned about whether you will be able to learn mathematics and use it in the future? Put your study methods under the spotlight now, before moving on with your studies.

Learning rarely happens passively. A number of aspects of this unit have been designed to encourage your more active participation and involvement. However, even that
Author(s): The Open University

This unit lays the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit â€“ Modelling static problems â€“ considers why objects stay put.

Please note that this unit assumes you have a good working knowledge of vectors.

This is an adapted extract from the Open University course Author(s): The Open University

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

All materials included in this unit are derived from content originated at the Open University.

Author(s): The Open University

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 1 MB).

After studying this unit you should:

• know some basic definitions and terminology associated with scalars and vectors and how to represent vectors in two dimensions;

• understand how vectors can be represented in three (or more) dimensions and know both plane polar and Cartesian representations;

• know ways to operate on and combine vectors.

Author(s): The Open University

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

This is an adapted extract from the Open University course Mathematical methods and models (MST209)
Author(s): The Open University