Higher November 2018 Paper 2 Q17
17.
(a) Factorise and hence solve the following equation. [3]\[6x^2 - x - 2 = 0\]
(b) Find the \(n\)th term of the following sequence. [2]
4, 7, 12, 19, 28, 39, ......
(c) Calculate the 105th term of a sequence with an \(n\)th term of \(3n^2 - n\). [1]
(d) The expression \(x^2 + 14x + 25\) has a minimum value.
By completing the square, complete the statements below.
You must show all your working. [3]
By completing the square, complete the statements below.
You must show all your working. [3]
‘The minimum value of \(x^2 + 14x + 25\) occurs when \(x =\) ………………….’
‘The minimum value of \(x^2 + 14x + 25\) is ………………….’
| Scheme | Marks | Comments |
|---|---|---|
| \((2x + 1)(3x - 2)\ (=0)\) | B2 | If not B2, award B1 for \((2x \pm 1)(3x \pm 2)\) or \((2x \pm 2)(3x \pm 1)\) |
| \(x = -1/2\) with \(x = 2/3\) | B1 | Do not accept 0.6 for \(2/3\), unless sight of \(2/3\) Allow 0.66(...) or 0.67 for \(2/3\) Strict FT from ‘their pair of brackets’ provided equivalent level of difficulty, with at least one answer a fraction |
| Scheme | Marks | Comments |
|---|---|---|
| \(n^2 + 3\) | B2 | B1 for \(n^2 \pm a\), where \(a \ne 0\) |
| Scheme | Marks | Comments |
|---|---|---|
| 32970 | B1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| \((x + 7)^2 \pm \ldots\) | M1 | |
| (Minimum value at \(x =\)) \(-7\) | A1 | |
| (Minimum value is) \(-24\) | A1 | |
| (9) |