1. Overview
Time is a fundamental concept in IGCSE Mathematics, essential for calculations involving durations, schedules, and rates. This revision note covers time units, conversions between them, and calculations using both 12-hour and 24-hour clock formats. Mastering these skills is crucial for success in the IGCSE exam and for real-world applications.
Key Definitions
- 12-hour Clock: A time system that divides the 24 hours of a day into two periods: a.m. (ante meridiem - before noon) and p.m. (post meridiem - after noon).
- 24-hour Clock: A time system where the day runs from midnight (00:00) to 23:59.
- Time Interval/Duration: The amount of time that passes between a start time and an end time.
- Leap Year: A year occurring every four years that has 366 days (February has 29 days instead of 28).
Core Content
A. Units of Time and Conversions
Time does not use a base-10 system. You must memorize these conversions:
- 1 minute (min) = 60 seconds (s)
- 1 hour (h) = 60 minutes = 3600 seconds ($60 \times 60$)
- 1 day = 24 hours
- 1 week = 7 days
- 1 year = 52 weeks = 12 months = 365 days (366 in a leap year)
Worked example 1 — Converting hours and minutes to seconds
Question: Convert 3 hours and 22 minutes into seconds.
| Step | Working | Explanation |
|---|---|---|
| 1 | $3 \times 3600 = 10800 \text{ s}$ | Convert the hours to seconds ($1\text{ h} = 3600\text{ s}$) |
| 2 | $22 \times 60 = 1320 \text{ s}$ | Convert the minutes to seconds ($1\text{ min} = 60\text{ s}$) |
| 3 | $10800 + 1320 = 12120 \text{ s}$ | Add the results together |
| 4 | Answer: 12120 seconds |
B. The 12-hour and 24-hour Clock
- To convert p.m. to 24-hour time: Add 12 to the hours (e.g., 3:00 p.m. $\rightarrow 3 + 12 = 15:00$).
- To convert 24-hour time (from 13:00 onwards) to p.m.: Subtract 12 from the hours.
- Note: 12:00 a.m. is 00:00; 12:00 p.m. is 12:00.
C. Calculating Time Intervals
When calculating how long a journey takes, it is often safer to "bridge" to the next hour rather than using column subtraction.
Worked example 2 — Calculating duration across days
Question: A bus departs at 22:35 and arrives at 03:20 the following day. Calculate the duration of the journey.
| Step | Working | Explanation |
|---|---|---|
| 1 | $22:35 \rightarrow 23:00 = 25 \text{ mins}$ | Calculate minutes to the next full hour |
| 2 | $23:00 \rightarrow 00:00 = 1 \text{ hour}$ | Calculate hours to midnight |
| 3 | $00:00 \rightarrow 03:20 = 3 \text{ hours } 20 \text{ mins}$ | Calculate time from midnight to arrival |
| 4 | $25\text{m} + 1\text{h} + 3\text{h } 20\text{m} = 4\text{h } 45\text{m}$ | Sum the intervals |
| 5 | Answer: 4 hours 45 minutes |
D. Reading Timetables
Timetables are read vertically (for one journey) and horizontally (to compare different transport times).
Extended Content (Extended Only)
In the Extended curriculum, you are often required to convert between fractional/decimal time and hours/minutes to use in Speed, Distance, and Time formulas ($Speed = \frac{Distance}{Time}$). You also need to be comfortable with more complex time interval calculations, including those involving multiple days or time zones.
Worked example 3 — Decimal Time to Hours and Minutes
Question: A program runs for 2.75 hours. Express this duration in hours and minutes.
| Step | Working | Explanation |
|---|---|---|
| 1 | $2 \text{ hours}$ | The whole number represents the hours |
| 2 | $0.75 \times 60 = 45 \text{ minutes}$ | Multiply the decimal part by 60 to find minutes |
| 3 | Answer: 2 hours 45 minutes |
Worked example 4 — Minutes to Decimal Time
Question: Convert 5 hours 12 minutes into hours (decimal).
| Step | Working | Explanation |
|---|---|---|
| 1 | $12 \div 60 = 0.2$ | Divide the minutes by 60 |
| 2 | $5 + 0.2 = 5.2 \text{ hours}$ | Add to the whole hours |
| 3 | Answer: 5.2 hours |
Worked example 5 — Calculating duration across multiple days
Question: A ship departs port at 14:40 on Monday and arrives at its destination at 09:15 on Wednesday. What is the total duration of the voyage?
| Step | Working | Explanation |
|---|---|---|
| 1 | $14:40 \text{ Monday} \rightarrow 14:40 \text{ Tuesday} = 24 \text{ hours}$ | Calculate the time to the same time the next day |
| 2 | $14:40 \text{ Tuesday} \rightarrow 14:40 \text{ Wednesday} = 24 \text{ hours}$ | Calculate the time to the same time the next day |
| 3 | $14:40 \text{ Wednesday} \rightarrow 09:15 \text{ Wednesday} = -5 \text{ hours } 25 \text{ mins}$ | Calculate the difference between 14:40 and 09:15. Note that since we are going backwards in time, this is negative. |
| 4 | $24 \text{ hours} + 24 \text{ hours} - 5 \text{ hours } 25 \text{ mins} = 42 \text{ hours } 35 \text{ mins}$ | Sum the intervals |
| 5 | Answer: 42 hours 35 minutes |
Key Equations
- Time Conversion (Seconds): $\bf{T_{(s)} = T_{(h)} \times 3600}$
- Time Conversion (Minutes): $\bf{T_{(min)} = T_{(h)} \times 60}$
- Time Duration: $\bf{\text{Duration} = \text{End Time} - \text{Start Time}}$
- Decimal Time: $\bf{\text{Hours} + \frac{\text{Minutes}}{60}}$
Common Mistakes to Avoid
- ❌ Wrong: Calculating 1 hour 45 minutes as 1.45 hours.
- ✓ Right: 1 hour 45 minutes is $1 + \frac{45}{60} = 1.75$ hours.
- ❌ Wrong: Converting 150 seconds to hours by dividing by 60.
- ✓ Right: Divide by 3600: $150 \div 3600 = 0.0417$ hours (approximately).
- ❌ Wrong: Subtracting times like $16:15 - 15:50 = 1: -35$.
- ✓ Right: Borrow an hour (60 minutes) to make the subtraction work: $16:15 - 15:50 = 0:25$ (25 minutes). Or use the bridging method.
- ❌ Wrong: Assuming a journey that arrives at 01:00 after departing at 23:00 lasted only 2 hours.
- ✓ Right: Recognize the journey crosses midnight and add the segments: 1 hour (23:00 to 00:00) + 1 hour (00:00 to 01:00) = 2 hours.
Exam Tips
- Command Words: "Calculate" or "Find the duration" are common. Always show the "bridging" steps to secure method marks even if your final addition is wrong.
- Calculator Tip: Most scientific calculators have a "DMS" button (marked as $^\circ \ ' \ ''$). You can use this to input hours and minutes directly. For example, pressing
2 [,] 30 [,]represents 2 hours 30 minutes. - Real-world Context: Be prepared for questions involving "Time Zones." If a plane leaves London (GMT) and flies to a country at GMT+4, add the 4 hours to the travel duration calculation.
- Values to Memorize:
- 30 days: September, April, June, November.
- 31 days: January, March, May, July, August, October, December.
- 28/29 days: February.
- Final Check: Does your answer make sense? If a flight from London to New York says "25 hours," re-read the question for time zone differences or errors in your subtraction. Also, double-check that you've provided the answer in the units requested by the question (e.g., hours, minutes, or seconds).