Intermediate November 2016 Unit 2 Q18
18.
(a) Factorise \(x^2 - 2x - 24\), and hence solve \(x^2 - 2x - 24 = 0\). [3]
(b) Solve the equation \(\dfrac{4x - 3}{2} + \dfrac{7x + 1}{6} = \dfrac{29}{2}\). [4]
| Scheme | Marks | Comments |
|---|---|---|
| (x – 6)(x + 4) | B2 | B1 for (x ... 6)(x ... 4). |
| (x =) 6 AND (x =) – 4 | B1 | Strict F.T. from their brackets. Allow the following. B2 for x – 6 (=0) AND x + 4 (=0) (B1) (x =) 6 AND ( x =) − 4 (B1) B1 for x + 6 (=0) AND x − 4 (=0) (B0) ( x =) −6 AND (x =) 4 (B1) FT B1 if only (x =) 6 AND ( x =) – 4 seen (B1) |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{12x - 9 + 7x + 1}{(6)} = \dfrac{87}{(6)}\) | B2 | F.T. until 2nd error. B1 for 1 error. Subsequent work may show use of common denominator in order to award the B2. |
| 19x = 95 | B1 | |
| x = 5 | B1 | B0 for 95/19. If a F.T. answer is not a whole number then allow answer in form ‘a / b’. Mark final answer. Allow a correct embedded answer. |