Edexcel IGCSE Math A 2.5.A direct and inverse proportion

Practise proportion questions by translating the wording into a formula, finding the constant and simplifying the final relationship.

Exam points

Write direct or inverse proportion formulae with k, powers and square roots.
Find the constant of proportionality from given values before writing the formula.
Simplify formulae involving inverse squares or square roots after substituting k.

[Maximum number: 4]

18 y is inversely proportional to $x^{3}$

y=4 \text { when } x=3

Work out the value of x when y=864

Since y is inversely proportional to $x^3$ ,

y=\frac{k}{x^3}

4=\frac{k}{3^3} \quad\Rightarrow\quad k=4\times3^3=108

864=\frac{108}{x^3} \quad\Rightarrow\quad x^3=\frac{108}{864}=\frac18

Final answer:

x=0.5

M1 for a correct inverse-proportion formula with a constant k.
M1 for substituting x=3 and y=4.
M1 for a method to find $x^3$ .
A1 for 0.5 oe.

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