4MA0 Higher January 2017 Paper 3 Q14
14 \(T\) is directly proportional to \(\sqrt{x}\)
\(T = 400\) when \(x = 625\)
(a) Find a formula for \(T\) in terms of \(x\). (3)
(b) Calculate the value of \(T\) when \(x = 56.25\) (1)
| Scheme | Marks |
|---|---|
| \(T = k\sqrt{x}\) | M1 |
\(400 = k\sqrt{625}\) or \(k = 16\) or \(400 = \sqrt{m625}\) or \(m = 256\) | M1 |
| \(T = 16\sqrt{x}\) | A1 |
| (3) |
Notes
M1: or for \(T = \sqrt{mx}\)
\(k\) may be numeric (but not 1)
M1: implies the first M1
A1: accept \(T = \sqrt{256x}\)
Award 3 marks if \(T = k\sqrt{x}\) but \(k\) is evaluated correctly in part (a) or (b).
SC: B2 for correct formula for \(x\) in terms of \(T\)
| Scheme | Marks |
|---|---|
| 120 | B1 |
| (1) | |
| (4 marks) |
Notes
B1: ft for a correct answer from a substitution into an equation (or expression) in the form (\(T =\)) \(k\sqrt{x}\) except for \(k = 1\)