Rates
O Level and IGCSE Mathematics Cheat Sheet – 1.12 Rates
What is a Rate?
- A rate compares one quantity to another with different units.
- Written as “per” (/) or using units notation (e.g., km/h, m/s, $/hour).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Common Measures of Rate
| Rate Type | Formula | Example |
|---|---|---|
| Hourly rate of pay | Pay ÷ Hours | $120 ÷ 8 h = $15/h |
| Exchange rate | Amount × Rate | $200 × 1.3 = £260 |
| Flow rate | Volume ÷ Time | 600 L ÷ 4 h = 150 L/h |
| Fuel consumption | Distance ÷ Fuel used | 500 km ÷ 40 L = 12.5 km/L |
Other Measures of Rate
| Rate Type | Formula | Example |
|---|---|---|
| Pressure | Force ÷ Area | 200 N ÷ 4 m² = 50 N/m² |
| Density | Mass ÷ Volume | 300 g ÷ 100 cm³ = 3 g/cm³ |
| Population density | Population ÷ Area | 50,000 ÷ 25 km² = 2,000 people/km² |
Speed, Distance, Time
- Formula triangle:
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
Example: Cyclist travels 45 km in 3 h 45 min
- Convert time to hours: 3 h 45 min = 3.75 h
- Speed = 45 ÷ 3.75 = 12 km/h
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Units in Rates
- Always match units before calculating.
- Examples:
- 72 km/h = 72 × 1000 m ÷ 3600 s = 20 m/s
- Density in g/cm³ vs kg/m³ — convert as needed.
Exam Special Tips
- Clearly write the formula before substituting values.
- Convert mixed time formats (h & min) to a single unit.
- For currency exchange, check if you are buying or selling — use correct rate.
- In fuel and flow rates, label units in every step.
Common Mistakes & Confusions
- Forgetting to convert minutes to hours before calculating speed.
- Mixing rate units (e.g., using km in numerator but seconds in denominator).
- Swapping rate direction in currency exchange.
- Not squaring or cubing units when working with area/volume-based rates.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course