Proportional Relationships (CIE A Level Maths: Pure 1)

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Proportional Relationships

Proportional relationships

  • Proportional relationships describe a proportional connection between two variables
  • This can happen in two ways
    • Direct proportion y space equals space k x
      • one variable increases or decreases the other does the same
    • Inverse proportion y space equals space k over x
      • one variable increases the other decreases and vice versa
  • Proportional relationships use the symbol proportional to which means is proportional to

Proportional Relationships Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

  • Both direct and inverse proportion can be represented graphically 
    • Direct proportion creates a linear graph where k is the gradient
    • Inverse proportion creates a reciprocal graph

Direct proportion

  • y space proportional to space x means y is proportional to x
  • y increases as x does, k determines the rate (gradient)
  • by changing this to the equation y space equals space k x we can substitute in given values and solve to find k 
    • Note that this means the ratio of x and y is constant k = y / x

    Proportional Relationships Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

Inverse proportion

  • y space proportional to space 1 over x means y is proportional to 1 over x or y is inversely proportional to x
  • y decreases as x increases and vice versa, k determines the rate
  • by changing this to the equation y space equals space k over x we can substitute in given values and solve to find k 
    • Note that this means the product of x and y is constant k = xy Proportional Relationships Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes 
  • Set up your proportional relationship using proportional to then change to = k
  • Be clear about what y is proportional to …
    • “… the square of x” (x2)
    • “… x plus four” (x + 4)
  • Calculate or deduce the value of k from the information given or a graph
  • Once you've found k sub it back in to your original proportion equation 
  • You can now find any values using this proportional relationship

  • y = mx + c rearranges to y – c = mx so (y - c) is directly proportional to x
  • Proportional relationships are often used in modelling

Worked example

Proportional Relationships - Exampl, A Level & AS Level Pure Maths Revision Notes Proportional Relationships - Example Diagram 2, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.