Using a Calculator (Cambridge (CIE) IGCSE Maths)

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Using a Calculator

Why are calculator skills important?

  • There are many special functions on a scientific calculator

    • To answer questions successfully you need to be able to use your calculator effectively

  • You may need to use some of the functions on the calculator in other subjects such as Science

  • There are many different models of calculator

    • Any scientific calculator will have the functions you need but may be accessed in different ways

    • You need to know how to use the features on your specific model

  • If you have an old or very basic scientific calculator the functions may be used backwards

    • To find the sine of an angle on a newer calculator, type sin (57)

    • On an older calculator you may need to type 57 then press the sin button

  • The notes below apply to most if not all scientific calculators but the images are based on the Casio fx-83GT

Calculator

The Casio fx-83GTX Classwiz

How do I make sure that I have the correct settings on the calculator?

  • Check you know how change the mode of your calculator

    • There is usually a button marked 'MODE'

    • Most calculators default to 'MATH' mode with the word MATH written across the top of the display or using a symbol

  • The 'Angle Unit' needs to be degrees

    • There is usually a button marked 'SETUP' where you can find the angle unit options

    • A 'D' symbol at the top of the display is used to indicate that the calculator is in the degrees setting

  • Make sure you can switch between 'exact' answers (e.g. fractions) and 'approximate' answers (e.g. decimals)

    • When in 'MATH' mode press the 'Sleft right double arrowD' button  to switch between answer types

What are the shortcut buttons on the calculator?

  • There are several very useful shortcut buttons on the calculator that you should know

    • The fraction, square, cube, power and square root buttons are all frequently used

    • Use the 'SHIFT' (2nd or INV) button to access functions including mixed numbers, cube roots, and nth roots

Calculator shortcut buttons

Why is using brackets important?

  • Applying brackets correctly on your calculator helps you to avoid errors in your calculations

    • Use brackets as you would in written mathematics

    • Put brackets around negative numbers in calculations

      • Remember, negative 3 squared gives you a different result to open parentheses negative 3 close parentheses squared

      • Use the '(-)' button for negative values, not the minus button

Which buttons are useful for trigonometry?

  • Use the sin, cos and tan buttons when finding missing sides of a triangle 

    • Remember to make sure that your calculator is in degrees mode

  • Use sin-1, cos-1 and tan-1 when finding missing angles of a triangle

    • Access these by using the 'SHIFT' button

  • When using a trig function, the calculator gives you an open bracket '('

    • Remember to use a closed bracket ')' after typing the angle in

Which buttons are useful for standard form and calculations involving π?

  • To write a number in standard form on the calculator, use the ×10x 

    • Modern calculators display standard form in the way it is written, e.g., 2 x 105

    • Older models may use a small capital letter 'E' in place of ×10x, e.g., 2E5 

  • bold italic pi  is often near the standard form button

    • You may need to use the 'SHIFT' button to access it

What is the Ans function?

  • The Ans (answer) button recalls the last answer the calculator calculated

    • Use this when working with decimals in the middle of solutions to avoid rounding until your final answer

What is the table function?

  • If your calculator has a table function or mode it can be used in 'complete the table of values and draw the graph' type questions

    • This can help you to reduce the number of calculations you have to do

    • It can also help to reduce errors

How do I use my calculator for time calculations?

  • Remember that time can be given in different formats

    • Time can be given in hours/minutes/seconds, e.g. 3 hours 46 minutes

    • Time can be given as a decimal, e.g. 2.7 hours

  • You can use the degrees, minutes and seconds function box enclose degree apostrophe double apostrophe end enclose to enter time on your calculator

    • E.g. 3 minutes 45 seconds would be entered as 0 degree 3 apostrophe 45 double apostrophe

    • You can convert between an answer on the calculator, given in either format of time, by pressing this button

Examiner Tips and Tricks

  • Get a calculator early and learn how to use all the essential functions

  • When using your calculator in an exam do one calculation at a time

    • Make sure you write down on paper each calculation that you do

    • Always write down more digits than the final answer requires in your working

    • Only round your final answer 

Worked Example

(a) Use your calculator to work out

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

Give your answer as a decimal.
Write down all the figures on your calculator display.

Type the calculations in the numerator and the denominator into your calculator separately
Write down the decimal answers
Use '...' to show that you have not rounded them
You need to show this working to get full marks

square root of 4.69 end root equals 2.165 space 64 space...

0.34 cubed plus sin open parentheses 45 close parentheses equals 0.746 space 410 space...

Type the whole calculation into your calculator in one go
Use the fraction button, square root button, cube button and remember to close the bracket after the sine function

bold 2 bold. bold 901406085

(b) Given that

a equals fraction numerator p plus q over denominator p squared q end fraction    

Find the value of a when p equals 1.2 cross times 10 to the power of negative 3 end exponent and q equals 7.83 cross times 10 to the power of 5.
Give your answer to 3 significant figures.

Type the numerator of the right-hand side of the equation into your calculator, substituting in the values for p and q
Write this down to show your working

p plus q equals 1.2 cross times 10 to the power of negative 3 end exponent plus 7.83 cross times 10 to the power of 5 equals 783 space 000.0012

Type the denominator of the right-hand side of the equation into your calculator, substituting in the values for p and q
Use brackets when expressions get long or awkward
Write this down to show your working

p squared q equals open parentheses 1.2 cross times 10 to the power of negative 3 end exponent close parentheses squared cross times open parentheses 7.83 cross times 10 to the power of 5 close parentheses equals 1.12752

Write down all the digits on your calculator display for the working stages

a equals fraction numerator 783 space 000.0012 over denominator 1.12752 end fraction equals 694 space 444.4455

Round to 3 significant figures

bold italic a bold equals bold 694 bold space bold 000 (3 s.f.) 

(c) Complete the table of values for y equals x cubed minus 6 x plus 1.

x

-3

-2

-1

0

1

2

3

y

 

5

 

 

 

 

10

Use brackets around negative values and the '(-)' button

open parentheses negative 3 close parentheses cubed minus 6 cross times open parentheses negative 3 close parentheses plus 1 equals negative 8

Use arrow keys to go back to the input line and change each '-3' to '-1'

open parentheses negative 1 close parentheses cubed minus 6 cross times open parentheses negative 1 close parentheses plus 1 equals 6

Repeat for each of the remaining values in the table, 0, 1 and 2

0 cubed minus 6 cross times 0 plus 1 equals 1
1 cubed minus 6 cross times 1 plus 1 equals negative 4
2 cubed minus 6 cross times 2 plus 1 equals negative 3

Alternatively, use the 'Table' mode/feature if your calculator has one

Complete the table with the values

x

-3

-2

-1

0

1

2

3

y

-8

5

6

1

-4

-3

10

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Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.