Other compound measures (Edexcel GCSE Maths): Revision Notes
Other compound measures
What are compound measures?
Compound measures are measurements that combine two or more basic measurements together. They help us describe more complex quantities by using simpler measurements we already understand.
Speed is a perfect example of a compound measure because it combines distance and time to tell us how fast something is moving.
Think of compound measures as mathematical recipes - they take simple ingredients (basic measurements like length, time, mass) and combine them to create something more complex and useful!
Pressure
Definition
Pressure measures how much force is applied over a specific area. Think of it as how "squashed" or "pushed" something gets when a force acts on it.
Understanding Pressure
Imagine pressing your thumb on a piece of paper versus pressing a sharp pencil point with the same force. The pencil creates much higher pressure because the same force is concentrated over a much smaller area.
Units of pressure
- Newtons per square centimetre (N/cm²)
- Newtons per square metre (N/m²)
Pressure formulas
You can remember these using the pressure triangle:
Worked Example: Water Pressure on Diving Mask
At a depth of 15m, water creates a pressure of 14.7 N/cm². If a diving mask has a surface area of 360 cm², what force does the water apply to it?
Solution:
Answer: The water applies a force of 5292 N to the diving mask.
Rates
What makes something a rate?
Key Rule for Identifying Rates
If the bottom unit in a compound measure is time, then it is a rate. This means rates tell us how quickly something changes over time.
Common types of rates
- Speed = Distance ÷ Time (how fast you travel)
- Rate of climb = Height ÷ Time (how quickly you go up)
- Rate of flow = Volume ÷ Time (how quickly liquid moves)
- Rate of pay = Salary ÷ Time (how much you earn per hour/day)
Notice how each of these rates has time as the denominator - this is what makes them rates rather than just compound measures!
Complex problem solving approach
Multi-Step Problem Strategy
When solving multi-step compound measure problems:
- Work out what you need to find first - identify all the steps needed
- Calculate each step carefully - don't rush the calculations
- Check your units - make sure they make sense for your final answer
- Plan your strategy before starting the calculations
Worked Example: Fishtank Filling Problem
A cuboid fishtank measures 120cm × 90cm × 40cm. Aaron fills it with water at a rate of 12 litres per minute. How long will it take to fill half the tank?
Step-by-step solution:
Step 1: Find the total volume
Step 2: Find half capacity
Step 3: Calculate time using rate formula
Answer: It will take 18 minutes to half fill the tank.
Exam tips
Key Exam Strategies:
- Look at the units to work out what calculation you need to do
- Use the formula triangles to help you rearrange formulas
- Plan your strategy for complex problems before you start calculating
- Check your answer makes sense - does it give a sensible number with sensible units?
Key Points to Remember:
- Compound measures combine two or more basic measurements
- Pressure = Force ÷ Area and is measured in N/cm² or N/m²
- Rates have time in the denominator and show how quickly something changes
- Break complex problems into steps - find what you need first, then calculate step by step
- Always check your units to make sure your answer makes sense