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Using a Calculator

Surds & Exact Values

Using a Calculator

Why the fuss about using a calculator?

  • GCSE Mathematics goes beyond using the basic features of a calculator and explores many of the special functions of a scientific calculator
  • It is important to get to know your calculator, the earlier you get one and learn about the scientific functions the better you will be at using them
  • It’s not just maths that uses these, some of the scientific functions can be used in science exams too

What do I need to know?

  • The notes below apply to most if not all scientific calculators but the images are based on the Casio fx-83GTX
  • The Casio fx-85GTX is the same model but also has solar power. Both are labelled “Classwiz” too but be careful here at there is a more advanced “Classwiz” calculator that is used at A level (fx-991EX)

Calculator, IGCSE & GCSE Maths revision notes

The Casio fx-83GTX Classwiz

 
  • Be aware if you have an old or very basic scientific calculator that they may work backwards
  • For example, if you wanted to find sin (57) you would type 57 then press the sin button
  • Modern calculators tend to work in the order in which we write things

1. Mode/setup

  • Make sure you know how to change the mode of your calculator, especially if someone else has used it
  • The “Angle Unit” needs to be degrees – normally indicated by a “D” symbol across the top of the display
  • Make sure you can switch between “exact” answers (fractions, surds, in terms of π, etc) and “approximate” answers (decimals)
  • Most calculators default to “Math” mode with the word Math written across the top of the display or using a symbol
  • When in “Math” mode you can switch whatever is on the answer line between exact and decimals by pressing the “S-D” button

2. Templates

  • These are largely the shortcut buttons – the fraction button, the square, cube and power buttons, square roots
  • You can also use SHIFT and these buttons to access functions including mixed numbers, cube roots, and n th roots

buttons, IGCSE & GCSE Maths revision notes

Calculator shortcut buttons

3. Trigonometry (sin/cos/tan)

  • Remember to use SHIFT (sometimes called 2nd or INV button) when finding angles
  • When using these buttons you will find that before you type the angle the calculator automatically gives you an open bracket “(“. You should get into the habit of making sure you use a closed bracket “)” after typing the angle in
  • This is very important if there is something else to type in that comes after sin/cos/tan

4. Standard Form and π

  • Find the ×10 x button and know how to use it
  • Modern calculators display standard form in the way it is written
  • Older models may use a small capital letter ” E” in place of ×10 x on the display line
  • π is often near or under SHIFT with the standard form button

5. Memory

  • The ANS (answer) button is very useful – especially when working with decimals in the middle of solutions that you should avoid rounding until your final answer
  • ANS recalls the last answer the calculator calculated

6.Table

  • If your calculator has a table function or mode, use it
  • This can be extremely useful in those “complete the table of values and draw the graph” type questions

7. Brackets and negative numbers

  • Use as you would in written mathematics
  • Remember to use the (-) button for a negative number, not the subtract button

8. Judgement and special features

  • The rule of thumb is to use your calculator to do one calculation at a time
  • However, you can also make a judgement call on this as to how many marks are available in the question and whether a question asks you to “write down all the digits on your calculator display”
  • You are better off writing too much down than not enough!

9. Practise!

  • This is a long list but we will finish by going back to the start – there is nothing better you can do than getting a calculator early and learning how to use it by practising the varying types of questions you are likely to come across

Exam Tip

  • Always put negative numbers in brackets. For a quick example, try using your calculator to work out -32 and then (-3)2.In working out always write down more digits than the final answer requires and don’t round them (write something like 9.3564… using the three dots shows you haven’t rounded).  Use the ANS button when you next need that number on your calculator. 

Worked example

Use your calculator to work out

fraction numerator square root of 4.69 end root over denominator 0.34 cubed space plus space sin open parentheses 45 degree close parentheses end fraction

Give your answer as a decimal.

Write down all the figures on your calculator display. 

It is best to type the whole thing into your calculator in one go using the fraction, square root, cube and sin buttons.

Make sure to press the fraction button first as use the arrow keys to navigate around.
Remember to close the bracket after sin(45 and check that your calculator is in degree mode.

Check that what is shown on your calculator screen looks exactly the same as the question. 

Write down all of the digits shown on your calculator display.

2.901406085

  

Worked example

a to the power of 5 space equals space fraction numerator p space plus space q over denominator p squared q end fraction

Find the value of a when  p = 1.2 × 10 -4  and  = 7.83 × 10 5.

Give your answer to 3 decimal places. 

Before doing any work on your calculator, rearrange the equation to make  a the subject.  

table row cell a space end cell equals cell space fifth root of fraction numerator p space plus space q over denominator p squared q end fraction end root end cell end table

Show your working by writing down what you plan to type into your calculator.
It is a good idea to use brackets around each bit of standard form. 

table attributes columnalign right center left columnspacing 0px end attributes row cell a space end cell equals cell space fifth root of fraction numerator open parentheses 1.2 cross times 10 to the power of negative 4 end exponent close parentheses space plus space open parentheses 7.83 cross times 10 to the power of 5 close parentheses over denominator open parentheses 1.2 cross times 10 to the power of negative 4 end exponent close parentheses squared cross times open parentheses 7.83 cross times 10 to the power of 5 close parentheses end fraction end root end cell end table

Type everything into the calculator in one go, starting with the root index blank of blank button and inserting the fraction inside. Remember to close all the brackets and double check that what is showing on your calculator screen looks the same as what you’ve written down.

Write down more than 3 decimal places before rounding. 

table row cell a space end cell equals cell space fifth root of fraction numerator open parentheses 1.2 cross times 10 to the power of negative 4 end exponent close parentheses space plus space open parentheses 7.83 cross times 10 to the power of 5 close parentheses over denominator open parentheses 1.2 cross times 10 to the power of negative 4 end exponent close parentheses squared cross times open parentheses 7.83 cross times 10 to the power of 5 close parentheses end fraction end root equals 37.0107172... end cell end table

Round to 3 decimal places.

bold italic a bold space bold equals bold 37 bold. bold 011 bold space stretchy left parenthesis 3 space d. p. stretchy right parenthesis

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