4MA0 Higher June 2013 Paper 4R Q17
17 \(y\) is directly proportional to \(x^3\)
When \(x = 10\), \(y = 250\)
(a) Find a formula for \(y\) in terms of \(x\). (3)
(b) Calculate the value of \(x\) when \(y = 54\) (2)
| Scheme | Marks |
|---|---|
| \(y = kx^3\) or \(ky = x^3\) | M1 |
| \(250 = 1000k\) | M1 |
| \(y = \tfrac{1}{4}x^3\) oe | A1 |
| (3) |
Notes
M1: for \(y = kx^3\) but not for \(y = x^3\)
M1: for \(250 = 1000k\)
Also award for \(250 = k \times 10^3\)
A1: for \(y = \tfrac{1}{4}x^3\) oe
Award 3 marks if answer is \(y = kx^3\) and \(k\) is evaluated as \(\tfrac{1}{4}\) oe in part (a) or part (b)
| Scheme | Marks |
|---|---|
| \(54 = \text{“}\tfrac{1}{4}\text{”}x^3\) | M1 |
| 6 | A1 |
| (2) |
Notes
M1: dep on at least first M1 in part (a)
A1: ft from \(x^3 = 54 \div \text{“}\tfrac{1}{4}\text{”}\) oe