Rates (Copy)

IGCSE CORE Mathematics Cheat Sheet: Measures of Rate, Speed, Density, Pressure & Related Problems

1. Understanding Rate

A rate compares two different quantities with different units. Common rates include:

2. Speed, Distance, Time Formula

You must know this formula:

Speed=DistanceTimetext{Speed} = dfrac{text{Distance}}{text{Time}}

• Distance = Speed × Time
• Time = Distance ÷ Speed

Example:
A cyclist travels 45 km in 3 hours 45 minutes.
Convert time: 3 hrs 45 mins = 3.75 hours
Speed = 45 ÷ 3.75 = 12 km/h

3. Common Rate Calculations

a) Hourly Rates of Pay

If someone earns $72 for 8 hours:
Hourly rate = 72 ÷ 8 = $9/hour

b) Exchange Rates

If £1 = $1.25, convert £200 to dollars:
200 × 1.25 = $250

To convert back:
$500 ÷ 1.25 = £400

c) Flow Rates

If a tank fills 120 litres in 30 minutes:
Flow rate = 120 ÷ 30 = 4 litres/min

d) Fuel Consumption

A car travels 480 km using 40 litres:
Consumption = 480 ÷ 40 = 12 km/litre

4. Other Measures of Rate

a) Pressure Formula

Pressure=ForceAreatext{Pressure} = dfrac{text{Force}}{text{Area}}

Unit: N/m²

b) Density Formula

Density=MassVolumetext{Density} = dfrac{text{Mass}}{text{Volume}}

Units: g/cm³ or kg/m³

c) Population Density

Population Density=PopulationAreatext{Population Density} = dfrac{text{Population}}{text{Area}}

Unit: people/km²

5. Example Questions

• Speed:
  A car travels 150 km in 2.5 hours.
  Speed = 150 ÷ 2.5 = 60 km/h

• Density:
  Mass = 500 g, Volume = 200 cm³
  Density = 500 ÷ 200 = 2.5 g/cm³

• Pressure:
  Force = 300 N, Area = 50 m²
  Pressure = 300 ÷ 50 = 6 N/m²

• Exchange Rate:
  If 1 USD = 0.75 GBP, convert $400 to GBP:
  400 × 0.75 = £300

6. Unit Conversions

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 km = 1000 meters
• 1 litre = 1000 cm³

7. Quick Reference Formulas

8. Tips for Exams

• Always convert time properly (minutes to hours, seconds to minutes, etc.).
• Use correct units in your final answer.
• Read carefully whether it’s direct calculation or conversion.
• For exchange rates, remember:
  • Multiply when converting from base to foreign.
  • Divide when converting back.
• Write the formula clearly before substituting values.