The course describes some of the main features of a scientific calculator and encourages you to use your calculator, both for everyday arithmetic and for more complicated calculations that use the function keys as well. Key sequences, which describe which keys to press, are included in all the activities, so you can try out the ideas straightaway.

Due to the wide range of scientific calculators available, for the purposes of this course we will be concentrating on the Casio fx-83ES model. Other calculators may function differently to the methods described within this course.


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This calculator is used on the Open University courses Starting with maths (Y182) and Discovering mathematics (MU123), but would also be useful for many other courses requiring the use of a scientific calculator.

The first 11 sections describe how to use the calculator and how to perform different types of calculations. Section 12 contains a calculator reference guide that you can refer to as needed for some of the main key sequences.

The lower half of the keypad contains the number keys, keys for the basic operations of addition, subtraction, division and multiplication, and the key, which is pressed when you want the calculator to display the result of the calculation you have entered. The keys used to insert brackets into a calculation are in the centre of the row above the number keys.

Some calculator operations are accessed through a system of menus that are displayed on the calculator screen, as shown in Figure 3. The required menu option is selected by pressing the number key associated with the option, as given on the calculator screen.

The figure shows the display on a calculator screen containing four lines of text. The top row of the screen contains a downward pointing arrowhead towards the right end. First line of text is 1 : M t h I O (written as one word) space 2 : Line I O (written as one word). Second line of text is 3 : Deg space 4 : Rad. Third line of text is 5 : Gra space 6 : Fix. Last line of text is 7 : Sci space 8 : Norm.

The calculator has many modes of operation that affect how mathematics is entered and displayed. These will be described later in this guide, but before progressing any further you should reset your calculator to the default course settings.

Basic calculations are entered into the calculator in exactly the same order as they are written on paper, as demonstrated in the following activity. The calculator displays the calculation that you enter. When you press , the answer is displayed at the bottom right of the screen.

Note that the calculator uses the BIDMAS rules. These say that any expression within Brackets should be calculated first, then any Indices (often called powers), followed by Divisions and Multiplications and finally Additions and Subtractions.

There are several keys on the calculator that enable you to perform calculations involving powers. For small powers such as squares or cubes there are dedicated buttons, and , which are located in the function key area of the keypad. These are used in a similar manner to how you would write mathematics; for example, to enter you would press . The display also shows the maths in the same way as you would write it on paper.

In fact, some calculators permit the key to be used for both purposes, but many other calculators require the equivalent of the key to be used for negative numbers. For this reason we shall use to input negative numbers throughout this guide.

You may have been surprised that the correct answer to part (5) is negative. According to the BIDMAS rules, the squaring is performed first, then the negative taken. If we wanted to calculate the square of , we write this mathematically as and would need to use the brackets when evaluating it on a calculator.

You may have noticed that the results of both these exercises were displayed on the calculator as top-heavy fractions. This is the default behaviour of the calculator in Math mode. You can toggle between a top-heavy fraction and its mixed number equivalent using the key sequence .

The expression for the volume of wood requires the value of . You could enter an approximate value for by hand, but this is time-consuming and may be prone to error. The calculator has an approximation for built into it, which is obtained using the key sequence .

into your calculator and press . Can you explain why? Insert a pair of brackets into the expression with the  sign so that it will give the correct answer. Then type this new expression into the calculator and check that you obtain the same answer as in the activity above.

(Note that on some later models of the calculator, the correct answer is obtained without adding the brackets to the denominator; however it is good practice to add the brackets to ensure the correct calculation is carried out).

You could write down the answer to the first part of the calculation on paper, and enter it into the calculator again. However, it is possible that you may make an error either in writing down the number or in typing it into the calculator. A better method is to use the fact that the calculator retains the last calculated answer, which can then be inserted in the subsequent calculation using the key located at the bottom of the keypad.

A variation on the above method is to break the calculation into two parts, and use the memory functions of the calculator to store the result of the first part. The calculator memory is particularly useful when you want to calculate the values of several expressions that have a common part. This common part need be entered only once and its value reused several times subsequently. For example, rewriting the formula for the volume of wood contained in a log as

In Activity 1 you will have already set your calculator to use Norm 2 mode, and we suggest that for the moment you continue to use this. To change the mode, use the key sequence (SETUP) (Norm) followed by (for Norm 1) or (for Norm 2).

Just as there are keys on your calculator for entering powers, roots can also be entered directly. Square roots can be calculated using the key. For example, can be entered using . Cube roots are entered using the second function of this key. For higher roots, such as fourth or fifth roots you need to use the more general template, which is the second function of the key. This template is filled in by using the number and arrow keys (and ) in a way similar to that used when the fraction template is completed.

Sometimes when entering into your calculator an expression involving roots, you may accidentally forget to press the appropriate function key. However, moving the cursor to the correct point and pressing the missing key, as in section 1, will not work as this simply inserts an empty template.

There are various different units in which an angle can be measured, degrees being one of the possibilities. Before using your calculator to find the values of the trigonometric ratios of angles measured in degrees, you need to ensure that it is set to use the correct units.

Your calculator is set to use degrees if the display indicator is shown at the top of the screen. If you see the indicator or , then your calculator is set to use different units for measuring angles.

Note that means first find the sine of , then square the answer. The key sequence to enter into the calculator is thus . The first is necessary to close the bracket automatically opened when pressing , and the second closes the bracket opened at the start of the sequence. Since the calculator evaluates the sine as soon as it encounters the first closing bracket, it is possible to enter this expression using the alternative sequence , but this is not recommended as the former is more clear.

In part (1) of the activity above, you used your calculator to find an angle whose sine is 0.5. This is not the only angle whose sine is 0.5, but you can use this angle to find the other angles. Similar remarks apply to parts (2) and (3).

Natural logarithms, for example , can be evaluated on your calculator using the key. The second function of this key () permits the calculation of powers of . Note that an approximate value for itself can be obtained using the key sequence ().

Most probably think of a co-processor as one of those math chips like the 8087 that were plugged into the IBM PC and clones back in the dark ages. They essentially allowed coprocessor-aware software such as Lotus 1-2-3 to calculate faster because software-only calculations were soooo slow. But, essentially a co-processor can be any processor that is programmed for a somewhat dedicated function: math, I/O, or even scientific calculations. I wrote this sketch for two reasons, one to learn more about using Streams and the many functions available which help to minimize code that I need to write and second because I wanted to experiment with off loading floating point from an Integer Only uC and not bother with dealing with integer arithmetic and then scaling to decimal.

Please accept this sketch as a fun exercise. It is public domain stuff, so bend it, shake it, hack it... but please post enhancements for all. I have not implemented a second uC to use as a command chip, but I am hopeful to complete that effort in a week or so. If this concept works adequately, anyone should be able to host a GPS and off-load the calculations of bearing and distance to the co-processor. With 328P chips being $2 in 25 Qty, the idea of a very cheap calculator that does not impact the main uC should be workable. One idea that is likely to need implementing is a oPin on the Arduino to signify that an answer is ready. This would allow the host uC to use an interrupt routine to snatch the return RS232 answer stream without crudely waiting on an answer.

It's just a sample framework written as a calculator. You can create a verb, say HD1, to turn pin D1 High and another verb, say LD1, to turn it low.... and without further programming, a second uC can control digital pin 1. Or... create one verb called D1? and send a 1 or 0 in the stream to parse with Serial.parseInt ... 2351a5e196

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