Higher June 2024 Paper 3 Q20
20 \(P\), \(Q\), and \(R\) have positive values.
- \(P\) is directly proportional to \(Q\)
- When \(P = 8\), \(Q = 2\)
- \(R\) is inversely proportional to \(Q^2\)
- When \(R = 10\), \(Q = 3\)
Work out the value of \(R\) when \(\quad P = 0.5\) [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(P \propto Q\) or \(P = kQ\) or \(8 = k \times 2\) or \(R \propto \dfrac{1}{Q^2}\) or \(R = \dfrac{c}{Q^2}\) or \(10 = \dfrac{c}{3^2}\) | M1 | oe |
| \(k = \dfrac{8}{2}\) or \(k = 4\) or \(c = 10 \times 3^2\) or \(c = 90\) | M1dep | oe implied by \(P = 4Q\) implied by \(R = \dfrac{90}{Q^2}\) |
| \(P = 4Q\) and \(R = \dfrac{90}{Q^2}\) or \(k = 4\) and \(c = 90\) | A1 | oe |
| \(Q = \dfrac{0.5}{\text{their } 4}\) and \(R = \dfrac{\text{their } 90}{\left(\text{their } \frac{0.5}{4}\right)^2}\) or \(R = \dfrac{\text{their } 90}{0.125^2}\) | M1 | oe eg \(R = \dfrac{1440}{0.25}\) ft their equations of the form \(P = kQ\) and \(R = \dfrac{c}{Q^2}\) their 90 must not be 4 |
| 5760 | A1ft | ft their equations of the form \(P = kQ\) and \(R = \dfrac{c}{Q^2}\) with 3rd M1 scored |
Additional guidance
| Allow \(k\) and \(c\) to be any letters, including using both as \(k\) | |
| Correctly using constants on the left side of their equations – follow the spirit of the mark scheme | |
| 5760 with no errors in working | 5 marks |
| \(P \propto kQ\) or \(R \propto \dfrac{c}{Q^2}\) is M0 unless recovered |