Intermediate November 2018 Unit 1 Q10
10.
(a) Expand \(3x(x^2 - 2)\). [2]
(b) Make \(g\) the subject of the formula \(f = 2 - 3g\). [2]
(c)
(i) Solve \(7x - 3 \lt 29\). [2]
(ii) What is the greatest integer value of \(x\) that satisfies the above inequality? [1]
| Scheme | Marks | Comments |
|---|---|---|
| 3x3 – 6x | B2 | Must be in an expression for B2. B1 for sight of (+)3x3 or −6x. Mark final answer. |
| Scheme | Marks | Comments |
|---|---|---|
| 3g = 2 – f or f – 2 = −3g | B1 | |
| g = \(\dfrac{2 - f}{3}\) or g = \(\dfrac{f - 2}{-3}\) or g = \(\dfrac{2}{3} - \dfrac{f}{3}\) | B1 | FT only from ±3g = ±f ± 2. B1B0 for –g = \(\dfrac{f - 2}{3}\) . B1B0 for g = 2 – f ÷ 3. B1B0 for \(\dfrac{2 - f}{3}\) (‘g=’ missing). Mark final answer. |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 7x < 32 | B1 | Use of ‘=’ is B0B0 unless replaced for final answer. |
| x < 32/7 or x < 44/7 | B1 | FT from 7x < k. Allow x < 4·57(….). Do not allow x < 4·6 or x < 4·5 unless x < 4·57(….) seen. Mark final answer. Penalise consistent use of ‘≤’ by−1 |
| (ii) 4 | B1 | OR F.T. ‘their answer (inequality) in (c)(i)’ if x < a. No FT from x ≤ a. 4x is B0. |