October 2021 Paper 1 Q3
3 It is given that \(x\) is proportional to the product of the square of \(y\) and the positive square root of \(z\).
When \(y = 2\) and \(z = 9\), \(x = 30\).
(a) Write an equation for \(x\) in terms of \(y\) and \(z\). [2]
(b) Find the value of \(x\) when \(y = 3\) and \(z = 25\). [2]
| Scheme | Marks | AO |
|---|---|---|
| \(x = ky^2\sqrt{z}\) \(30 = k \times 4 \times 3\) \(k = 2.5\) | M1 | 3.1a |
| \(x = 2.5y^2\sqrt{z}\) | A1 | 1.1 |
| [2] |
Notes
M1: Attempt to find value for \(k\)
From \(x = ky^2\sqrt{z}\) or \(x = kz^2\sqrt{y}\) only
Using sum, not product, is M0 but watch for \(+\sqrt{z}\) being used for positive square root
A1: Correct equation
Ignore modulus sign if used around \(\sqrt{z}\)
Allow BOD if initial equation stated explicitly, \(k\) found correctly but then final equation not seen or seen as now incorrect
| Scheme | Marks | AO |
|---|---|---|
| \(x = 2.5 \times 9 \times 5\) | M1 | 1.1 |
| \(x = 112.5\) | A1 | 1.1 |
| [2] |
Notes
M1: Attempt to find \(x\), from equation in terms of \(y\), \(z\) and numerical \(k\)
Could be from using direct proportion and not their equation from (a)
A1: Obtain 112.5
Or any exact equiv