Higher June 2018 Paper 1 Q14
14 \(y\) is inversely proportional to \(d^{\,2}\)
When \(d = 10\), \(y = 4\)
\(d\) is directly proportional to \(x^2\)
When \(x = 2\), \(d = 24\)
Find a formula for \(y\) in terms of \(x\).
Give your answer in its simplest form. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(y = \dfrac{100}{9x^4}\) | P1 | for setting up a correct proportional relationship, eg \(d \propto x^2\) or \(d = kx^2\) |
| P1 | for setting up a second proportional relationship, eg \(y \propto \dfrac{1}{d^2}\) or \(y = \dfrac{K}{d^2}\) | |
| P1 | (dep P1) for a process to find one of the constants of proportionality eg \(24 = k \times 2^2\) (\(k = 6\)) or \(4 = K \div 100\) (\(K = 400\)) | |
| P1 | full process to find \(y\) in terms of \(x\) eg \(y = \dfrac{\text{``}400\text{''}}{(\text{``}6\text{''}x^2)^2}\) oe | |
| A1 | \(y = \dfrac{100}{9x^4}\) oe |
Additional guidance
Condone the use of ‘\(\propto\)’ instead of ‘=’ for the four P marks
P1 (full process): Both constants must come from a correct process
A1: Expression must have been simplified, but could be given other equivalent ways eg \(y = 11.111..\,x^{-4}\)