June 2018 Paper 1 Q5
5 In the expansion and simplification of \(\quad (x - 3)(x^2 + 5x + k) \quad\) the coefficient of \(x^2\) is equal to the coefficient of \(x\).
\(k\) is a constant.
Work out the value of \(k\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((x^3) + 5x^2 + kx - 3x^2 - 15x\ (-\ 3k)\) | M1 | allow one sign error in the \(x^2\) or \(x\) terms |
| their \((5 - 3)\) = their \((k - 15)\) | M1dep | \(5x^2 - 3x^2 = kx - 15x\) on its own, is not enough for M1dep |
| 17 | A1 |
Additional guidance
| For the first M1, we do not need to see the \(x^3\) term or the \(-\ 3k\) term, but we do need to see the other 4 terms (3 terms, if they combine the \(x^2\) terms). The terms of the expansion might appear in a grid, which can score the first M1 Mark positively … terms in a grid might differ from terms written as a string of terms … mark the better version. |