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Cambridge IGCSE0607

Using a calculator

International Mathematics 0607 Chapter Notes

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Using a calculator
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In this chapter

  1. 1Do not round inside a calculation
  2. 2Entering powers and roots
  3. 3Time on a calculator
  4. 4Reading the display and money

1. Do not round inside a calculation

Use the calculator efficiently: type a calculation in one go and keep the whole display. Do not round values within a calculation; only round the final answer.

A fraction line acts as a bracket. Work out the top and the bottom, then divide. Carry the full displayed value into the next step, never a rounded copy.

(a × b)/(c - d) = (a × b) ÷ (c - d)

Examiner insight

“This premature rounding of intermediate values should be avoided.” “The most common reason for a loss of a mark was because of premature rounding of intermediate answers.”

Worked example 14 marks

(a) Work out (3.82 × 5.23)/(1.63 - 1.17). Give your answer correct to the nearest 10.

(b) Work out (√(16.84) - 2.39)/5.26. Give your answer correct to 2 decimal places.

  1. 1

    (a) top = 3.82 × 5.23 = 19.9786 and bottom = 1.63 - 1.17 = 0.46 [1]

  2. 2

    19.9786 ÷ 0.46 = 43.43…, so 40 to the nearest 10 [1]

  3. 3

    (b) √(16.84) = 4.1036…, so top = 4.1036… - 2.39 = 1.7136… [1]

  4. 4

    1.7136… ÷ 5.26 = 0.3257…, so 0.33 [1]

2. Entering powers and roots

Enter a value so that the calculator does the order of operations you mean. Put the whole of a power or root in its own brackets when it sits inside a longer line. The root sign must cover exactly what the question puts under it.

Worked example 11 mark

Work out. (3.1)³ - √(18.5)

  1. 1

    (3.1)³ = 29.791 and √(18.5) = 4.3011…, so 29.791 - 4.3011… = 25.4898… = 25.5 [1]

3. Time on a calculator

A calculator works in decimals, but time is in sixties. To enter a time, change the minutes to a fraction of an hour: 2 hours 30 minutes is 2.5 hours. The degrees, minutes, seconds key also takes it, as 2^(°) 30' 0''. There are not 100 minutes in an hour.

To read a time, split the display. The whole number is the hours. Multiply the decimal part by 60 to get minutes. So 3.25 means 3 hours 15 minutes, because 0.25 × 60 = 15.

hhours mminutes = h + m/60hours

minutes = decimal part of the hours × 60

Examiner insight

“Many did not use the correct decimal time for 1 hour 20 min giving, for example 1.2 or 1.3 hours.” “Quite simply there needs to be an emphasis that there are not 100 minutes in an hour.”

Worked example 13 marks

A cyclist rides 50 km at 16 km / h. Work out the time taken. Give your answer in hours and minutes.

  1. 1

    time = distance ÷ speed [1]

  2. 2

    50 ÷ 16 = 3.125 hours [1]

  3. 3

    0.125 × 60 = 7.5, so 3 hours 7.5 minutes [1]

4. Reading the display and money

Read the full display before you round, then round once. Round to the places asked: do not cut the number off. Rounding 70.516 to 2 decimal places gives 70.52, not 70.51.

In money, the display drops a final zero. 4.8 means 4.80 dollars. If a money answer is exact, give it exactly.

4.8 → 4.80dollars

Examiner insight

“Although most knew how to round their answer to 2 decimal places, there were those who just truncated after 2 decimal places.” “Candidates should realise that if a money answer is exact, as this one was, then the exact answer should be given, rather than rounding it.”

Worked example 13 marks

(a) Work out √[3]3375.

(b) Work out 1/3.5². Give your answer correct to 3 decimal places.

  1. 1

    (a) √[3]3375 = 15 [1]

  2. 2

    (b) 3.5² = 12.25 and 1 ÷ 12.25 = 0.08163… [1]

  3. 3

    = 0.082 to 3 decimal places [1]

Recap

  • Do not round within a calculation. Only round the final answer.
  • A fraction line is a bracket: work out the top and the bottom first.
  • Enter 2 hours 30 minutes as 2.5 hours.
  • To read a time, multiply the decimal part by 60 to get minutes.
  • On the display, 3.25 means 3 hours 15 minutes.
  • In money, 4.8 means 4.80 dollars.

End-of-chapter exercise

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

  1. A calculation has four steps. State when you should round your working.1 mark
  2. A calculator shows the cost of a drink as 5.2 dollars. Write this as money.1 mark
  3. Write 3 hours 45 minutes as a number of hours, to enter on a calculator.1 mark
  4. A calculator shows a time of 2.4 hours. Write this in hours and minutes.2 marks
  5. Work out (5.8 × 6.4)/(2.17 - 1.89). Give your answer to the nearest whole number.3 marks
  6. Work out 1/4.5². Give your answer correct to 3 significant figures.2 marks
  7. A car travels 84 km in 1 hour 45 minutes. Work out its average speed in km / h.3 marks
  8. A lorry travels 70 km at 16 km / h. Work out the time taken in hours and minutes.3 marks
  9. An electrician charges 42 dollars for each hour he works, with part of an hour charged in proportion. He works for 2 hours 35 minutes on Monday and 1 hour 50 minutes on Tuesday. Work out his total charge.4 marks
  10. A drone flies 21 km to a farm at 36 km / h. It waits there for 12 minutes, then flies the 21 km back at 28 km / h. (a) Work out the total time for the trip. Give your answer in hours and minutes. (b) Work out the average speed for the whole trip, including the wait. Give your answer correct to 3 significant figures.6 marks

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