Higher November 2019 Paper 2 Q12
12.
(a) Factorise and hence solve the following equation. [3]\[4x^2 + 16x + 15 = 0\]
(b) Find the \(n\)th term of the following sequence. [2]
7, 10, 15, 22, 31, 42, .......
(c) Ali walks slowly from home through a forest and back home again.
He walks a total distance of \((3x + 1)\) km in a time of \(\left(\dfrac{x}{2} + 6\right)\) hours.
Ali’s average speed is 2 km/h.
He left home at 9 a.m.
At what time did Ali return home? [4]
(d) The expression \(x^2 + 18x + 2\) 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 \(x^2 + 18x + 2\) occurs when \(x =\) ………………….’
‘The minimum value of \(x^2 + 18x + 2\) is …………....’
| Scheme | Marks | Comments |
|---|---|---|
| \((2x + 3)(2x + 5)\ (=0)\) | B2 | If not B2, award B1 for \((2x \pm 3)(2x \pm 5)\) or \((x + 5/2)(x + 3/2)\) |
| \(x = -3/2\) with \(x = -5/2\) ISW | B1 | Strict FT from ‘their pair of brackets’ provided equivalent level of difficulty, with at least one answer a fraction |
| Scheme | Marks | Comments |
|---|---|---|
| \(n^2 + 6\) | B2 | B1 for \(n^2 \pm a\), where \(a \ne 0\) |
| Scheme | Marks | Comments |
|---|---|---|
| \(x = 5.5\) | B2 | B1 for sight of any one of the following:
|
| Total number of hours 8.75 (hours) | B1 | |
| 5(:)45 pm or 17(:)45 | B1 | FT ‘their number of hours’ provided at least B1 previously awarded |
| Scheme | Marks | Comments |
|---|---|---|
| \((x + 9)^2 \pm \ldots\) | M1 | |
| (Minimum value at \(x =\)) \(-9\) | A1 | |
| (Minimum value is) \(-79\) | A1 | |
| (12) |