Higher November 2023 Paper 2 Q14
14 \(y\) is proportional to \(x^2\)
\(y = 3\) when \(x = 0.5\)
\(x\) is inversely proportional to \(w\)
\(x = 2\) when \(w = 0.2\)
Find the value of \(y\) when \(w = 2\) (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 0.48 | P1 | for setting up an equation with a constant term, eg \(y = kx^2\) or \(x = \dfrac{j}{w}\) |
| P1 | for a process to substitute values in one equation, eg \(3 = k \times 0.5^2\) or \(k = 12\) or \(2 = j \div 0.2\) or \(j = 0.4\) | |
| P1 | (dep P2) for combining the two equations ft their values of \(k\) and \(j\) eg \(y = \text{``}12\text{''} \times \left(\dfrac{\text{``}0.4\text{''}}{w}\right)^2\) oe OR for correct process to find the value of \(x\) when \(w = 2\), eg \(x = \text{``}0.4\text{''} \div 2\ (= 0.2)\) | |
| P1 | for substitution into their formula, eg \(y = \dfrac{\text{``}1.92\text{''}}{2^2}\) OR for using found value of \(x\) to find the value of \(y\), eg \(y = \text{``}12\text{''} \times \text{``}0.2\text{''}^2\) | |
| A1 | oe |
Additional guidance
Condone the use of "\(\propto\)" instead of "=" for the first two P marks
Equation can be implied by correct substitution
\(y = \dfrac{1.92}{w^2}\)