The value of the mathematical constant , pronounced pi, is stored on scientific and graphics calculators. The TI-84 has as the second function on
Author(s): The Open University

There is a key on most scientific and graphics calculators which will give the reciprocal of a number. This is one over the number. So the reciprocal of 2 is or 0.5. The reciprocal of 4 is Author(s): The Open University

Another problem surfaces if you start with a negative number and try to find its square root. For example try to find the square root of âˆ’4 on your calculator. Depending upon how your calculator is set up, you may either get an error message or an unfamiliar number like 2i or 2j. This is because there is no real number which squared will give you the negative number âˆ’4. Every real number, whether positive or negative, has a positive square. There are some numbers, ca
Author(s): The Open University

Earlier you met the square function and on most calculators the square root is the second function on the same key. Look to see if this is the case for your calculator and check the calculator handbook on how to use this function. In many cases you will need to press the square root key before the number, instead of afterwards, as for the square key. This is the case on the TI-84. Check that you can find the square root of 25 and of 0.49 (you should get 5 and .7 respectively).

Now find
Author(s): The Open University

The term learning file is used to mean a record of your work in some sort of filing system. This may consist of a file, a box, note books, a filing cabinet, files on your computer or something else that suits you. Whatever the content, you will certainly need some way of organizing your written notes so that they stay together and in order.

Author(s): The Open University

## Activity 13

Take a very quick look through Section 1.5 of the Calculator Book, entitled â€˜Everyday calculationsâ€™. Do not read it all yet!

Use the headings, subheadings, diagrams, and so on to give yourself an overview of
Author(s): The Open University

Ever since recorded mathematics began, people have been making use of mathematical aids. Four thousand years ago, Babylonian scribes were consulting mathematical tables which included multiplication tables, tables of squares and square roots, and tables of reciprocals of numbers. These values were recorded as marks on clay tablets that were then baked hard in the sunâ€”and some have survived to the present day. (There are several originals to be seen in the British Museum.)

Author(s): The Open University

The aims of this section are for you to:

• gain greater fluency, confidence and skill in using your calculator;

• begin to appreciate how the calculator can be used as a tool for learning mathematics;

• develop an effective means of working from the Calculator Book.

In order to complete this section you will need to have obtained a Texas Instruments TI-83 calculator and the book Tapping into M
Author(s): The Open University

1.3 What is a mathematician?

In Section 1.2 you looked in detail at four pieces of very different mathematical writing:

• an investigation of patterns within our system of numbers;

• mathematical diagrams being used to convey statistical information about the real world;

• a solution of a geometrical problem which arose from someone's curiosity;

• use of algebraic symbols.

Author(s): The Open University

Introducing algebra

## Example 4

Trying to understand this example is like trying to un
Author(s): The Open University

Does it make sense?

## Example 3

Author(s): The Open University

Puzzling out the Soma cube

The mathematical writing in Example 3 also uses diagrams but for a very different purpose. It arises from a particular three-dimensional puzzle, sometimes called a Soma cube, pictured below.

Here's Example 2 again.

## Activity 7

Author(s): The Open University

Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches

There are many re
Author(s): The Open University

Section 6 contains solutions to the exercises that appear throughout sections 1-5.

Click 'View document' below to open the solutions (15 pages, 468KB).

In Section 2 we develop an algebraic notation for recording symmetries, and demonstrate how to use the notation to calculate composites of symmetries and the inverse of a symmetry.

Click 'View document' below to open Section 2 (9 pages, 504KB).

## Unit image

AlistÂ  [Details correct as of 27th June 2008]

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All other material contained within this unit originated at the Open University.

Author(s): The Open University

In Section 2 we give the general definition of a function, and illustrate how functions can be used to describe a variety of mathematical concepts, such as transformations of the plane. We discuss the idea of composing two functions, and the idea of forming the inverse of a function.

Click 'View document' below to open Section 2 (16 pages, 366KB).

All written material contained within this unit originated at the Open University

1. Join the 200,000 students currently studying withThe Open University.

Author(s): The Open University

Now look at what happens when the power is negative. What does 10âˆ’3 mean? What is the result of the following calculation?

100 Ã· 100 000

What you are actually being asked to find is:

But look at the calculation again. Using the rule for the division
Author(s): The Open University