Time, Currency & ConversionsCambridge IGCSE Maths: Revision notes
Section 1
How do I calculate with units of time?
Key conversions:
- 60 seconds = 1 minute
- 60 minutes = 1 hour
- 24 hours = 1 day
- 7 days = 1 week
- 365 days = 1 year (for this syllabus)
When adding or subtracting time, be careful — time does NOT work in base 10. For example, 1 hour 45 minutes + 30 minutes = 2 hours 15 minutes, not 1 hour 75 minutes.
A common error is treating decimal time as base-10, e.g. writing 2.5 hours as 2 hours 5 minutes instead of 2 hours 30 minutes (0.5 x 60 = 30 minutes).
Section 2
How do I work with the 12-hour and 24-hour clock?
24-hour clock: written as 4 digits, e.g. 1430 or 14:30 (2:30pm) 12-hour clock: uses am/pm, e.g. 2:30pm
Converting 24-hour to 12-hour: if the hour is 13 or more, subtract 12 and add "pm"; if it's 12, keep as 12pm; if 00, write as 12am.
Example: 1930 = 7:30pm. 0715 = 7:15am.
Section 3
How do I solve problems with timetables and time zones?
Timetables: read departure/arrival times directly from the table; journey time = arrival time − departure time (careful crossing the hour boundary).
Time zones: places east of Greenwich are AHEAD in time (add hours); places west are BEHIND (subtract hours).
Example: It is 14:00 in London. Dubai is 4 hours ahead. The time in Dubai is 18:00.
Local time and journey duration: when flying between time zones, calculate elapsed flight time using the departure and arrival times in the SAME time zone (usually convert both to one reference zone first) before adding the flight duration.
Section 4
How do I convert currency?
Use the given exchange rate as a multiplier or divisor.
Example: If £1 = 100 To convert back from dollars to pounds, divide by the same rate: 100 ÷ 1.25 = £80
Always check which direction the conversion goes — multiply to convert INTO the second currency using the given rate, divide to convert back.
Section 5
How do I convert between metric units?
Metric units scale in powers of 10 (or 1000 for volume/mass, 100 for length in cm/m):
| Quantity | Conversion |
|---|---|
| Length | 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km |
| Area | 100 mm² = 1 cm²; 10,000 cm² = 1 m² |
| Volume | 1000 mm³ = 1 cm³; 1,000,000 cm³ = 1 m³ |
| Capacity | 1000 ml = 1 l |
| Mass | 1000 g = 1 kg |
Key idea: for area, the conversion factor is squared; for volume, it is cubed.
Example: Convert 3 m² to cm²: 3 x 10,000 = 30,000 cm²
Students often use the linear conversion factor (e.g. 100) for area or volume instead of squaring or cubing it — always square for area, cube for volume.
Must Know
- Time is not base-10: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day
- 24-hour clock has no am/pm; subtract 12 from hours ≥13 to convert to 12-hour pm times
- East of Greenwich = ahead in time; west = behind
- Currency conversion: multiply by the exchange rate to convert, divide to convert back
- Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km
- Area conversions square the length factor; volume conversions cube it
That's the notes covered.
Carry on to the next subtopic.