Higher November 2022 Paper 2 Q21
21 \(\mathrm{f}(x) = \dfrac{3x + 9}{5} \qquad\) and \(\qquad \mathrm{g}(x) = 6x - 1\)
(a) Show that \(\mathrm{gf}(2)\) is an integer. [2 marks]
(b) Show that \(\mathrm{f}^{-1}(8)\) is not an integer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(6\left(\dfrac{3x + 9}{5}\right) - 1\) | M1 | oe eg \(\dfrac{18x + 49}{5}\) |
| 17 | A1 | SC1 8.4 oe value |
| Alternative method 2 | ||
| \(\dfrac{3 \times 2 + 9}{5}\) or 3 or \(\mathrm{g}(3)\) | M1 | oe eg \(6 \times 3 - 1\) |
| 17 | A1 | SC1 8.4 oe value |
Additional guidance
| Answer 17 | M1A1 |
| Working out \(\mathrm{f}(2)\) and \(\mathrm{g}(2)\) is M0 unless recovered eg1 \(\dfrac{3 \times 2 + 9}{5} = 3 \qquad 6 \times 2 - 1 = 11\) eg2 \(3 \times 11 = 33\) | M0A0 M0A0 |
| 17 followed by further work eg \(17 \times 3 = 51\) | M1A0 |
| SC1 is for \(\mathrm{fg}(2)\) |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{5x - 9}{3}\) or \(\dfrac{5y - 9}{3}\) or \(\dfrac{5 \times 8 - 9}{3}\) | M1 | oe |
| \(\dfrac{31}{3}\) or \(10\dfrac{1}{3}\) or 10.3(…) | A1 | |
| Alternative method 2 | ||
| \(\dfrac{3x + 9}{5} = 8\) | M1 | oe equation |
| \(\dfrac{31}{3}\) or \(10\dfrac{1}{3}\) or 10.3(…) | A1 | |
Additional guidance
| \(\dfrac{31}{3}\) or \(10\dfrac{1}{3}\) or 10.3(…) | M1A1 |
| Ignore conversion attempt after correct answer seen |