Computers and calculators are the tools of modern mathematicians.

At form 3 level you should be able to do all of the operations in the first eight topics covered so far WITHOUT using computers and calculators.

This section shows you how to do some of those calculations using these tools.

### Calculators

 A typical graphical calculator Try not to use your calculator for simple calculations involving adding, subtracting, dividing and multiplying whole numbers. e.g. 8 × 7 or 56 + 72. Keep the instruction booklet that comes with the calculator. You will need it for the more complicated calculations and functions. Estimate the answer to the calculation before you start. This is a good check in case you press the wrong keys.

There are many makes and types of calculators. The examples below use keys which are common or similar on most calculators.

Basic Operations

Calculators know about the order that calculations are carried out. i.e. BEDMAS

e.g. Calculate 35 + 4 x 27 on a calculator. Press:         143

Rounding

Some calculators do not round numbers. e.g.    gives 0.666666666. This is calledtruncating.

Some calculators round numbers up or down e.g.    gives 0.666666667. This is calledrounding.This number is rounded to 9 decimal places as there are 9 digits after the decimal point.

Rounding Rules

 If the digit to the right of the rounded digit is between 0 and 4. The rounded digit stays the same. If the digit to the right of the rounded digit is 5 or above. The rounded digit has ONE added.

Square roots

To find the square root of a number use this key  e.g. To find the square root of 36, press    6

Square roots are often not whole numbers e.g.     6.08276253

Brackets

The two brackets keys  and  are useful for calculations involving fractions.

e.g. Calculate  Press:            0.351894736

Indices

There is a button for an index of 2 (squared)  e.g. To find 1262, press      15876

To calculate with an index greater than 2 use the button  e.g. To find 234, press      279841

Computer programs such as Microsoft Office and Appleworks include a part called aspreadsheet
Spreadsheets can perform calculations using numbers and formulae arranged in rows and columns of cells
Words or numbers can be typed into the cells and calculations and other mathematical operations can be carried out.

 The spreadsheet on the left shows only 32 cells. Some spreadsheets have thousands of cells.Each cell has its own label. The one highlighted is cell B3. The letters are at the top of the columns.The numbers are at the beginning of rows. To move around a spreadsheet use the cursor or keys such as the TAB, pg up, pg down (the arrow keys)

Many features of a spreadsheet can be changed (formatted) using various menu commands:

• The columns can be made wider
• The rows can be made higher
• Numbers and text in a cell can be made bold, coloured or a different size and font
• Numbers and text in a cell can be put on the left hand side, the right hand side or in the centre.

Calculations

Spreadsheets do calculations differently from normal maths equations and calculators. To do a calculation you have to type in the EQUALS sign first. To do multiplication use the * key and for division use the / key.

Formulae

The values in cells can also be used in calculations.

Sorting

Numbers and words in both rows and columns can be sorted into order.
To do the sort shown below BOTH columns must be selected and the spreadsheet told to sort on the B column.

Graphing

Most spreadsheets will produce graphs, such as pie graphs, line graphs, bar graphs and scattergraphs.
See Unit 45 for instructions and practice with these.