GCSE Maths (AQA)

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Advanced Proportionality Equations

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Ratio, Proportion and Rates of Change Ratio, Proportion and Rates of Change

Advanced Proportionality Equations

8:42 Advanced Proportionality
Spec R13
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  • Proportionality describes the relationship between a variable and the power of another variable.
  • If two variables are proportional, multiplying one by a number results in multiplying the other by the same number.
  • Algebraic representation of proportionality includes constants, e.g., y = Kx�� for direct proportionality to the square of x.
  • Inverse proportionality means multiplying one variable by a number results in dividing the other variable by that number, e.g., y = K/x��.
  • Proportionality can also relate to the roots of variables, e.g., y = K���x or y = K/���x for direct and inverse proportionality to the square root, respectively.
  • Common errors in exams include deriving incorrect proportionality equations.
  • Example problem: U inversely proportional to the cube of V. Given U = 2 when V = 2, find V when U = 20. Steps include determining the equation form, substituting known values, solving for the constant of proportionality, and using it to find the new value of V.
  • Another example: Time (T) taken for a ball to fall is proportional to the square root of the height (H) from which it is dropped. Given T = 0.4s for H = 4m, find T for H = 5m. Steps involve setting up the equation, finding the constant of proportionality, and calculating T for the new height.
  • Both examples emphasize the importance of correct rounding in final answers, based on specified decimal places.

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