Higher November 2017 Unit 1 Q13
13. Given that \(y\) is inversely proportional to \(x^3\) and that \(y\) = 120 when \(x\) = 2,
(a) find an expression for \(y\) in terms of \(x\), [3]
(b) use the expression you found in part (a) to complete the following table. [2]
| \(x\) | 2 | 10 | |
|---|---|---|---|
| \(y\) | 120 | 15 |
| Scheme | Marks | Comments |
|---|---|---|
| \(y\) α \(1/x^3\) OR \(y = k/x^3\) | B1 | Allow \(y\) α \(k/x^3\) |
| \(120 = k/2^3\) OR \(k = 960\) | M1 | F.T. from \(y\) α \(x^3\) or \(y\) α \(1/x^n\) with \(n \gt 0\) and \(n \ne 1\) M1 implies B1 (excluding F.T. case) |
| \(y = 960/x^3\) | A1 | May be seen in part (b). Allow equivalent e.g. \(x^3 = 960/y\) |
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| B2 | Accept equivalent e.g. 960/1000 B1 for one correct value. F.T. provided \(y\) α \(1/x^n\) with \(n \gt 0\) and \(n \ne 1\) used in part (a). SC1 for following through from \(y = k/x\), provided both answers are correct OR SC1 for following through from \(y = kx^3\), provided both answers are correct. |