Compound-Measures Aqa Higher

Compound measures

What is a compound measure?

• A compound measure is something that is calculated by using more than one measurement

• Compound measures can be used to measure rates

  • This measures how much one quantity changes when the other is increased by 1

  • Examples include:

    • Speed – how much the distance changes for each unit of time

    • Flow rate – how much the volume changes for each unit of time

    • Population density – how many people there are for each unit of area

    • Fuel consumption – volume of fuel used for each unit of distance travelled

How do I find the units for a compound measure?

• You can use the formula for a compound measure to derive its units

  • Use the units for the quantities in the formula to derive the units of the compound measure

  • Write a division as a/b or ab^-1 and pronounce it as “a per b”

• Examples include:

  • 

    • If the distance is measured in km and the time is measured in minutes then the speed is measured in km/min or km min^-1

  • 

    • If the volume is measured in m³ and the time is measured in minutes then the flow rate is measured in m³/min or m³min^-1

How do I find the formula for a compound measure?

• You can use the units for a compound measure to help remember its formula

  • You just need to remember what each unit measures

  • If the unit is a/b then the formula will be the quantity that a measures divided by the quantity that b measures

• Examples include:

  • Density can be measured in kg/cm³

  • kg is a measure of mass and cm³ is a measure of volume

  • Therefore 

What is a formula triangle?

• A formula triangle shows the relationship between the different measures in a compound formula 

  • E.g. for Speed, Distance and Time

• If you are calculating a variable on the top of the triangle, multiply the two variables on the bottom

  • For example,  

• If you are calculating a variable on the bottom of the triangle, divide the top by the other variable on the bottom

  • For example, <img alt=”Speed space equals space Distance space divided by space Time” data-mathml='<math ><semantics><mrow><mi>Speed</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mi>Distance</mi><mo>&#160;</mo><mo>&#247;</mo><mo>&#160;</mo><mi>Time</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%22197%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%