Proportional Relationships (Cambridge (CIE) AS Maths) : Revision Note

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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 Content Creator (Previous)

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.

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