Higher June 2019 Paper 1 Q20
20 \(h\) is inversely proportional to \(p\)
\(p\) is directly proportional to \(\sqrt{t}\)
Given that \(h = 10\) and \(t = 144\) when \(p = 6\)
find a formula for \(h\) in terms of \(t\) (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(h = \dfrac{120}{\sqrt{t}}\) | P1 | for setting up a proportional relationship between \(h\) and \(p\), eg \(h \propto \dfrac{1}{p}\) or \(h = \dfrac{k}{p}\) OR a proportional relationship between \(p\) and \(t\), eg \(p \propto \sqrt{t}\) or \(p = K\sqrt{t}\) |
| P1 | for process to substitute at least 2 values, eg \(10 = \dfrac{k}{6}\ (k = 60)\) or \(6 = K\sqrt{144}\ (K = 0.5)\) | |
| P1 | for full process leading to \(h = \dfrac{\text{``}60\text{''}}{p}\) oe and \(p = \text{``}0.5\text{''}\sqrt{t}\) oe | |
| A1 | \(h = \dfrac{120}{\sqrt{t}}\) oe eg \(h = \dfrac{120\sqrt{t}}{t}\) or \(h = \dfrac{60}{0.5\sqrt{t}}\) |
Additional guidance
Condone the use of ‘\(\propto\)’ instead of ‘=’ for the first two P marks
Relationship may be implied by substitution
Both constants must come from a correct process
Formula for h in terms of t
Does not need to be in simplest form