Inverse Proportion (Cambridge (CIE) IGCSE International Maths)

Inverse Proportion

What is inverse proportion?

• Inverse proportion means as one variable goes up the other goes down by the same factor

  • If two quantities are inversely proportional, then we can say that one is directly proportional to the reciprocal of the other 

• The symbol, , is used to show that one quantity is "directly proportional to the reciprocal of" (inversely proportional to) another quantity

  • "y is inversely proportional to x" is written

• If x and y are inversely proportional then

  • will always be the same

  • there will be some value of k such that 

• The graph of  is shown below

How do I use inverse proportion with powers and roots?

• Problems may involve a variable being inversely proportional to a power or root of another variable

• For example

  • y is inversely proportional to the square of x

    • 

    • means that

  • y is inversely proportional to the square root of x

    • 

    • means that

  • y is inversely proportional to the cube of x

    • 

    • means that

  • y is inversely proportional to the cube root of x

    • 

    • means that

  • Each of these would have a different type of graph, depending on the power or root

How do I find the equation between two inversely proportional variables?

• Inverse proportion questions always have the same process:

  • STEP 1
    Identify the two variables and write down the formula in terms of k

    • E.g. y is inversely proportional to x

    • write down the formula

  • STEP 2
    Find k by substituting any given values from the question into your formula, then solving to get k

    • E.g. if you are told y = 5 when x = 6

    • then giving

  • STEP 3
    Rewrite the formula with the known value of k from above (substitute it in)

    • 

    • This is the equation relating the two variables

  • STEP 4
    Use the equation to answer other parts of the question

    • E.g. find y when x = 2

    • gives