June 2023 Paper 2 Q7
7 The coefficient of \(x^8\) in the expansion of \((2x+k)^{12}\), where \(k\) is a positive integer, is 79 200 000.
Determine the value of \(k\). [4]
| Scheme | Marks | AO |
|---|---|---|
| \((2x)^8\) soi | M1 | 3.1a |
| \({}^{12}\mathrm{C}_8\) or \({}^{12}\mathrm{C}_4\) or 495 seen | B1 | 1.1 |
| \(495 \times 256 \times k^4\ [x^8] = 79\,200\,000\ [x^8]\) oe | M1 | 1.1 |
| \(k = 5\) cao isw | A1 | 3.2a |
| [4] |
Notes
M1: allow recovery from bracket error; may be implied by award of second M1
M1: allow M1 for \(495 \times 2 \times k^4 = 79\,200\,000\) oe;
“\(= 79\,200\,000\)” may be implied by \(k = 5\)
A1: not from wrong working; but allow recovery from \(x^8\) on one side of equation only
allow SC2 for \(k = 5\) unsupported