4MA0 Higher January 2017 Paper 4R Q13
13 \(P\) is inversely proportional to the square of \(q\).
When \(q = 2\), \(P = 12.8\)
(a) Find a formula for \(P\) in terms of \(q\). (3)
(b) Find the value of \(P\) when \(q = 8\) (1)
| Scheme | Marks |
|---|---|
| \(P = \dfrac{k}{q^2}\) | M1 |
| \(12.8 = \dfrac{k}{2^2}\) oe or \(k = 12.8 \times 2^2\) or \(k = 51.2\) | M1 |
| \(P = \dfrac{51.2}{q^2}\) | A1 |
| (3) |
Notes
M1: Allow \(Pq^2 = k\) or \(q^2 = \dfrac{k}{P}\)
Do not allow \(P = \dfrac{1}{q^2}\)
M1: For correct substitution in a correct equation. Implies first M1
Award M2 if \(k = 51.2\) stated unambiguously
A1: Award 3 marks if answer is \(P = \dfrac{k}{q^2}\) but \(k\) is evaluated in (a) or (b)
SCB2 for \(Pq^2 = 51.2\) or \(q^2 = \dfrac{51.2}{P}\)
| Scheme | Marks |
|---|---|
\(\dfrac{51.2}{8^2}\) Answer: 0.8 | B1ft |
| (1) | |
| (4 marks) |
Notes
B1ft: ft equation in the form \(P = \dfrac{k}{q^2}\) oe