Higher June 2022 Paper 1 Q17
17 \(y\) is directly proportional to the square root of \(t\).
\(y = 15\) when \(t = 9\)
\(t\) is inversely proportional to the cube of \(x\).
\(t = 8\) when \(x = 2\)
Find a formula for \(y\) in terms of \(x\).
Give your answer in its simplest form. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(y = \dfrac{40}{\sqrt{x^3}}\) | P1 | for setting up an equation with a constant term, eg \(y = k\sqrt{t}\) or \(t = \dfrac{K}{x^3}\) |
| P1 | for a process to substitute values in one equation, eg \(15 = k\sqrt{9}\) or \(k = 5\) or \(8 = \dfrac{K}{2^3}\) or \(K = 64\) | |
| P1 | (dep P2) for combining the two equations ft their values of \(k\) and \(K\), eg \(y = 5\sqrt{\dfrac{64}{x^3}}\) OR for \(y = 5\sqrt{t}\) and \(t = \dfrac{64}{x^3}\) | |
| A1 | oe |
Additional guidance
Condone the use of ‘\(\propto\)’ instead of ‘=’ for the first two P marks
Equation can be implied by correct substitution
Formula must include 40
Accept other forms for the power of \(x\) but must be a single term in \(x\)