The value of the mathematical constant , pronounced pi, is stored on scientific and graphics calculators. The TI-84 has as the second function on
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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
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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
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As you have probably observed, there are many mathematical functions on your calculator, but most users only need to use a few of them regularly. This is an opportunity to be introduced to some of the more useful ones informally. Many functions are directly visible on the keys of the keyboard, but your calculator may have additional functions, e.g. on a MATH menu.

This section is designed to give you a whistle-stop introduction to some of the important functions on your calculato
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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.)

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## Example 4

Trying to understand this example is like trying to un
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Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches

There are many re
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This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics.

In order to complete this unit you will need
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6 Solutions to the exercises

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

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

2 Representing symmetries

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).

Acknowledgements

## 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.

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2 Functions

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).

Acknowledgements

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

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

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Acknowledgements

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

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

1. Join the 200,000 students currently studyi
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3.2.1 Try some yourself

1 Use the method outlined in Example 9 to estimate each of the following, and then use yo
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2.6 Negative powers

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
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2.5.1 Try some yourself

1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

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1 Find the following powers by hand, as estimates for calculator work.

• (a) 107

• (b) 108

• (c) 34

• (d) (âˆ’2)2
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Given any number, you now know how to find its square. But, given the squared number, how do you find the original number?