4MA0 Higher June 2014 Paper 4 Q17
17 \(F\) is inversely proportional to the square of \(x\).
\(F = 0.8\) when \(x = 5\)
(a) Find a formula for \(F\) in terms of \(x\). (3)
(b) Work out the positive value of \(x\) when \(F = 320\) (2)
| Scheme | Marks |
|---|---|
| \(F = \dfrac{\text{“}k\text{”}}{x^2}\) | M1 |
| \(0.8 = \dfrac{k}{5^2}\) or \(k = 20\) | M1 |
| \(F = \dfrac{20}{x^2}\) | A1 |
| (3) |
Notes
M1: \(k\) must be a letter not a number
M1: for substitution (implies first M1)
A1: Award 3 marks for \(F = \dfrac{\text{“}k\text{”}}{x^2}\) and \(k = 20\) stated anywhere (even in (b)) unless contradicted by later work
| Scheme | Marks |
|---|---|
| \(x^2 = \dfrac{\text{“}20\text{”}}{320}\) or \(x = \sqrt{\dfrac{\text{“}20\text{”}}{320}}\) | M1 |
| 0.25 oe | A1 |
| (2) | |
| (5 marks) |
Notes
M1: ft if \(k \neq 1\) for correct rearrangement
NB. The only ft is for the value of \(k\) in \(F = \dfrac{k}{x^2}\)
A1: cao (ignore ±)