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Cambridge IGCSE0580

Using a calculator

Mathematics 0580 Chapter Notes

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Using a calculator
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Using a calculator notes

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In this chapter

  1. 1Enter the whole calculation
  2. 2Do not round within a calculation
  3. 3Round the final answer as asked
  4. 4Enter times as decimals of an hour
  5. 5Read the display as money or time

1. Enter the whole calculation

Use the calculator efficiently: enter each calculation as it is written, in one go. Do not work out parts by hand and re-type them.

A fraction line acts as a bracket. The numerator and the denominator are each worked out first. A root sign that covers a whole expression needs brackets round it.

(a + b)/c = (a + b) ÷ c

√(a + b) is entered as √((a + b))

Examiner insight

“The most common wrong answer was –0.8735 (not calculating the denominator and numerator separately for example 6.589 – 2.985 ÷ √0.16).” “A common incorrect answer of –72.997125 was the result of not bracketing or working out the calculation under the cube root.”

Worked example 11 mark

Calculate (6.589 - 2.985)/(√(0.16)).

  1. 1

    numerator = 3.604 and denominator = √(0.16) = 0.4, so 3.604 ÷ 0.4 = 9.01 [1]

2. Do not round within a calculation

Keep every value in the calculator until the end. Round only the final answer.

A rounded value typed back in makes the answer inaccurate. Learn to use the full value the calculator holds.

A value rounded part-way through can cost the accuracy mark, even when the method is right.

Examiner insight

“There was some premature rounding of the ratio to e.g. 0.25 and 0.26 which led to inaccurate answers. Candidates are advised to learn efficient calculator use so that they don’t have to re-type the rounded ratio.” “A premature rounding of intermediate values to 2 significant figures sometimes led to an accuracy error with the final answer.”

Worked example 12 marks

Calculate (0.7 - 3.5³)/4.2², giving your answer correct to 2 significant figures.

  1. 1

    (0.7 - 42.875)/17.64 = (-42.175)/17.64 = -2.39… (unrounded value kept) [1]

  2. 2

    -2.4 to 2 significant figures [1]

3. Round the final answer as asked

Give the answer to the accuracy the question asks for: a number of decimal places or significant figures. Show a more accurate value before you round. Do not add zeros to the rounded answer to make it match another answer.

Examiner insight

“Some candidates incorrectly rounded 8.660 to 8.6 or rounded to 8.66.” “Adding zeros to make the answer have the same number of figures as part (a) spoilt an otherwise correct answer.”

Worked example 12 marks

Calculate 32.7/(8.54 - 2.6). Give your answer correct to 2 decimal places.

  1. 1

    denominator = 5.94, so 32.7 ÷ 5.94 = 5.505… [1]

  2. 2

    5.51 to 2 decimal places [1]

4. Enter times as decimals of an hour

Enter values in a form the calculator can use. A time of 2 hours 30 minutes is entered as 2.5 hours. It can also be entered as 2° 30' 0''.

There are 60 minutes in an hour, so divide the minutes by 60. Do not type the minutes as the decimal part: 2 hours 30 minutes is not 2.30.

time in hours = whole hours + minutes/60

Examiner insight

“This part was generally answered well although the common error was 85 minutes, coming from 8.20 – 7.35 = 0.85, i.e. using time as a decimal value or over reliance on a calculator.” “The most common error saw candidates writing 7 hours and 30 mins as 7.3 or 7.30 instead of the correct decimal form of 7.5 hours.”

Worked example 12 marks

A journey takes 2 hours 30 minutes at an average speed of 84 km / h. Calculate the distance travelled.

  1. 1

    30 minutes = 30 ÷ 60 = 0.5 hours, so time = 2.5 hours [1]

  2. 2

    distance = 84 × 2.5 = 210 km [1]

5. Read the display as money or time

The display is only a number. Its meaning depends on the question. In money, 4.8 means textdollar4.80. In time, 3.25 means 3 hours 15 minutes.

For time, multiply the decimal part by 60: 0.25 × 60 = 15 minutes.

Examiner insight

“This method has a lot of places that errors can be made with the time calculations as many interpreted 3.25 hours as 3 hours and 25 minutes and 30 minutes became 0.3 hours.” “The question indicated that their answer had to be ‘correct to the nearest cent’ so answers of 85.2 did not gain full credit.”

Worked example 12 marks

A calculator shows 3.25 for a time in hours and 4.8 for a cost in dollars. Write the time in hours and minutes and the cost in dollars.

  1. 1

    0.25 × 60 = 15, so 3 hours 15 minutes [1]

  2. 2

    4.8 in money is textdollar4.80 [1]

Recap

  • Enter the whole calculation. A fraction line and a root over an expression need brackets.
  • Never round inside a calculation. Round only the final answer.
  • Round to the accuracy asked. Show a more accurate value first. Do not add zeros.
  • Enter 2 hours 30 minutes as 2.5 hours, or as 2° 30' 0''.
  • In money, 4.8 means textdollar4.80. In time, 3.25 means 3 hours 15 minutes.
  • 0.15 hours is not 15 minutes: 0.15 × 60 = 9 minutes.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Do not use a calculator. A calculator shows 12.6 for the cost in dollars of a book. Write the cost correctly.1 mark
  2. Do not use a calculator. A calculator shows 2.4 for a time in hours. Write this time in hours and minutes.2 marks
  3. Do not use a calculator. Write 2 hours 45 minutes as a number of hours to enter on a calculator.2 marks
  4. Do not use a calculator. A taxi charges a fixed textdollar3.50 plus textdollar2.40 for each kilometre. Calculate the cost of a journey of 7.5 km.2 marks
  5. Calculate (9.6 + 7.2)/(2.4 × 1.4).2 marks
  6. Calculate √(5.6² + 3.3²).2 marks
  7. Calculate 7.3/(2.9² - 4.1). Give your answer correct to 3 significant figures.3 marks
  8. Calculate 800 × 1.035⁴. Give your answer correct to 2 decimal places.3 marks
  9. Do not use a calculator. A ferry sails at an average speed of 28 km / h for the 63 km from a port to an island. It leaves the port at 10 50. The return journey of 63 km takes 2 hours 25 minutes. (a) Find the time the ferry reaches the island. (b) Calculate the average speed for the whole journey, there and back.6 marks
  10. An electrician works from 08 40 to 12 15 and from 13 05 to 16 50. He is paid textdollar27.60 for each hour, with part of an hour paid in proportion. (a) Calculate his pay for the day. (b) Find how long he must work to be paid textdollar250. Give your answer in hours and minutes, correct to the nearest minute.7 marks

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