TutorChase logo
Edexcel GCSE Maths (Higher) Study Notes

3.2.2 Advanced Rate Calculations

Understanding rates is crucial in our daily lives, as they help us solve problems related to pressure, density, population density, and movement. This section will guide you through these concepts with practical examples to enhance your problem-solving skills.

Pressure

Pressure is defined as the force exerted per unit area. The formula to calculate pressure is:

Pressure=ForceArea\text{Pressure} = \frac{\text{Force}}{\text{Area}}
  • Units: Newton per square meter (N/m²) or Pascals (Pa)
Pressure illustration

Image courtesy of PSC

Example 1: Calculating Pressure

A book weighing 1.5 kg rests on a table with a surface area of 0.5 m². Calculate the pressure exerted by the book on the table.

Solution:

Force exerted by the book = Mass × Gravity

Force=1.5kg×9.8m/s2=14.7N\text{Force} = 1.5 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 14.7 \, \text{N}Pressure=14.7N0.5m2=29.4Pa\text{Pressure} = \frac{14.7 \, \text{N}}{0.5 \, \text{m}^2} = 29.4 \, \text{Pa}

Density

Density is the mass per unit volume of a substance. The formula to calculate density is:

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}
  • Units: kilograms per cubic meter (kg/m³)
Density illustration

Image courtesy of Adobe Stock

Example 2: Calculating Density

Find the density of an object with a mass of 200g and a volume of 50cm³.

Solution:

  • Convert mass to kg: 200g=0.2kg200 \, \text{g} = 0.2 \, \text{kg}
  • Convert volume to m3m^3: 50cm3=0.00005m350 \, \text{cm}^3 = 0.00005 \, \text{m}^3
  • Density=0.2kg0.00005m3=4000kg/m3\text{Density} = \frac{0.2 \, \text{kg}}{0.00005 \, \text{m}^3} = 4000 \, \text{kg/m}^3

Population Density

Population density measures the number of individuals living per unit area. The formula is:

Population Density=PopulationArea\text{Population Density} = \frac{\text{Population}}{\text{Area}}
  • Units: individuals per square kilometer (people/km²)
Population Density illustration

Image courtesy of Bright Local

Example 3: Calculating Population Density

Calculate the population density of a city with a population of 500,000 and an area of 250 km².

Solution:

Population Density=500,000250=2,000people/km2\text{Population Density} = \frac{500,000}{250} = 2,000 \, \text{people/km}^2

Speed/Distance/Time

The relationship between speed, distance, and time is fundamental in understanding rates of movement. The formula is:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}Speed illustration

Image courtesy of Formasup

Example 4: Using the Speed/Distance/Time Formula

If a car travels 300 km in 4 hours, what is its average speed?

Solution:

Speed=300km4hr=75km/hr\text{Speed} = \frac{300 \, \text{km}}{4 \, \text{hr}} = 75 \, \text{km/hr}

Hire a tutor

Please fill out the form and we'll find a tutor for you.

1/2
About yourself
Alternatively contact us via
WhatsApp, Phone Call, or Email