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IGCSE Mathematics — Speed, Distance & Time
Complete notes with worked examples, graphs, and self‑test quizzes.
1) Core Formula
Speed = Distance ÷ Time • Distance = Speed × Time • Time = Distance ÷ Speed
Keep units consistent before calculating.
Example 1
A car travels 150 km in 3 hours. Find average speed.
Solution Speed = 150 ÷ 3 = 50 km/h.
Self‑Test 1
- A cyclist travels 60 km in 4 hours. Average speed?
- A runner runs at 12 km/h for 45 minutes. How far?
2) Unit Conversions
- 1 km = 1000 m, 1 hour = 3600 s
- km/h → m/s: multiply by 5/18
- m/s → km/h: multiply by 18/5
Example 2
Convert 72 km/h to m/s → 72 × 5/18 = 20 m/s.
Self‑Test 2
- Convert 54 km/h to m/s.
- Convert 15 m/s to km/h.
3) Average Speed
Average speed = Total distance ÷ Total time
Do not average speeds directly.
Example 3
Annette cycles 30 km in 2 h, rests 0.5 h, then 40 km in 2.5 h.
Solution Distance = 70 km, Time = 5 h → Average speed = 14 km/h.
Self‑Test 3
A car travels 120 km at 60 km/h, then 180 km at 90 km/h. Find overall average speed.
4) Distance–Time Graphs
Gradient = speed. Horizontal line = stationary. Steeper = faster.
Example 4: 40 km in 1 h, rest 0.5 h, 30 km in 1.5 h. Total distance 70 km, total time 3 h, average ≈ 23.3 km/h.
Self‑Test 4
Plot: 20 km in 30 min → rest 15 min → 10 km in 30 min. Find average speed.
5) Speed–Time Graphs
Gradient = acceleration. Area under graph = distance.
Example 5: Accelerate to 20 m/s in 10 s, travel 15 s, stop in 5 s. Acceleration = 2 m/s², Distance = 450 m.
Self‑Test 5
- Decelerate from 30 m/s to 0 in 15 s. Find deceleration.
- Find distance travelled during this time.
6) Bearings & Trigonometry
Bearings measured clockwise from North (3 digits).
Example 6
Ship sails 60 km east then 80 km north → Distance = √(60²+80²) = 100 km.
Self‑Test 6
Plane flies 100 km north then 240 km east. Find distance from start and the bearing from start.
Answer Key (Self‑Tests)
Show/Hide Answers
- Self‑Test 1: (1) 15 km/h. (2) 9 km.
- Self‑Test 2: (1) 15 m/s. (2) 54 km/h.
- Self‑Test 3: Time = 2 h + 2 h = 4 h, Distance = 300 km → 75 km/h.
- Self‑Test 4: Distance = 30 km, Time = 1.25 h → 24 km/h.
- Self‑Test 5: (1) 2 m/s² deceleration. (2) ½ × 15 × 30 = 225 m.
- Self‑Test 6: Distance = √(100² + 240²) = 260 km. Bearing = arctan(240/100) ≈ 067°.
🕒 Time and Duration — Learner Success Notes
🕐 1. Reading and Writing Time
A. 12-Hour Clock → 24-Hour Clock
| 12-Hour Time | Meaning | 24-Hour Time |
|---|---|---|
| 12:00 am (midnight) | Start of new day | 0000 |
| 1:00 am | Morning | 0100 |
| 7:40 am | Morning | 0740 |
| 12:00 pm (noon) | Midday | 1200 |
| 3:25 pm | Afternoon | 1525 |
| 6:00 pm | Evening | 1800 |
| 11:59 pm | Late night | 2359 |
B. 24-Hour Clock → 12-Hour Clock
| 24-Hour Time | 12-Hour Time | Meaning |
|---|---|---|
| 0000 | 12:00 am | Midnight |
| 0740 | 7:40 am | Morning |
| 1200 | 12:00 pm | Noon |
| 1525 | 3:25 pm | Afternoon |
| 1800 | 6:00 pm | Evening |
| 2359 | 11:59 pm | Late night |
✅ Quick Tips
- Write 24-hour times as four digits with no colon (e.g. 0705).
- For PM, add 12 to the hour (except 12 PM).
- For AM, keep the same hour (except 12 AM → 0000).
⏰ 2. Calculating Time Differences (Same Day)
- Subtract start time from end time.
- If end minutes are smaller, borrow 1 hour (add 60 minutes).
Example: Start = 1015, End = 1340 → 3 h 25 min
🌙 3. Time Across Midnight
- Count time up to midnight (2400).
- Add time from midnight to end time.
Example: Start = 2040, End = 0610 → To midnight = 3 h 20 min + 6 h 10 min = 9 h 30 min
➕ 4. Adding and Subtracting Time
| Conversion | Formula |
|---|---|
| 1 hour | 60 minutes |
| 1 minute | 60 seconds |
| 1 day | 24 hours |
Example: 1326 − 7 h 36 min = 0550
⏳ 5. Converting Between Units
| From | To | Operation |
|---|---|---|
| Minutes | Hours | ÷ 60 |
| Seconds | Hours | ÷ 3600 |
| Days | Hours | × 24 |
| Weeks | Days | × 7 |
Example: 10 260 s ÷ 3600 = 2.85 h
🚀 6. Average Speed Problems
Speed = Distance ÷ Time Time = Distance ÷ Speed Distance = Speed × Time
Example:
Distance = 7882 km + 2156 km = 10 038 km
Flying time = 11 h 48 min = 11.8 h
Speed = 10 038 ÷ 11.8 = 850 km/h (approx.)
🌏 7. Time Zone and Flight Problems
- Adjust for time difference between locations.
- Include stopover or waiting time if any.
- Work in one time zone before subtracting.
- Convert your final answer to hours and minutes.
Tip: Sketch a timeline of the journey to stay organised.
🚌 8. Timetables and Schedules
- Journey time: Arrival − Departure
- Latest departure: Arrival − Journey time
Always check for AM / PM and whether the trip goes into the next day.
🕰️ 9. Clock Face and Angles
| Movement | Rate |
|---|---|
| Minute hand | 6° per minute |
| Hour hand | 0.5° per minute |
Angle formula: |30 × hour − 5.5 × minutes|
Example: 2:30 → |30×2 − 5.5×30| = |60 − 165| = 105°
📅 10. Common Time Facts
| Quantity | Equivalent |
|---|---|
| 1 hour | 60 min = 3600 s |
| 1 day | 24 h = 1440 min = 86 400 s |
| 1 week | 7 days = 168 h |
| 1 month (31 days) | 2 678 400 seconds |
🧠 11. Exam Strategy Checklist
- Write times vertically for clear subtraction.
- Watch for midnight or next-day crossings.
- Convert all times into 24-hour format.
- Label every step — method marks count.
- Use a timeline for multi-step flights.