June 2024 Paper 2 Q3
3. The point \(P(3, -2)\) lies on the curve with equation \(y = \mathrm{f}(x),\ x \in \mathbb{R}\)
Find the coordinates of the point to which \(P\) is mapped when the curve with equation \(y = \mathrm{f}(x)\) is transformed to the curve with equation
| Scheme | Marks | AO |
|---|---|---|
| (i) \((5, -2)\) or e.g. \(x = 5,\ y = -2\) o.e. | B1 | 1.1b |
| (1) | ||
| (ii) \((1.5, -2)\) or e.g. \(x = 1.5,\ y = -2\) o.e. | B1 | 1.1b |
| (1) | ||
| (iii) \((-3, \ldots)\) or \((\ldots, -1)\) or \(x = -3\) or \(y = -1\) o.e. | B1 | 1.1b |
| \((-3, -1)\) or \(x = -3\) and \(y = -1\) o.e. | B1 | 1.1b |
| (2) | ||
| (4 marks) |
Notes
General guidelines for all parts:
Remember to check answers written against the questions.
If there is any contradiction, mark the answers given in the body of the script.
If there is no labelling, mark the responses in the order given.
The coordinates need to be values not just a calculation e.g. not \(-2 \times 3 + 5\) for \(-1\)
Points can be written as a coordinate pair or separately as \(x = \ldots,\ y = \ldots\)
Do not allow coordinates written the wrong way round but isw if necessary e.g. \(x = 5, y = -2 \rightarrow (-2, 5)\) scores B1 and isw
Condone missing brackets (one or both) e.g. 5, \(-2\) or (5, \(-2\) or 5, \(-2\)) for (5, \(-2\))
Condone a missing comma e.g. \((5\ \ -2)\) for \((5, -2)\)
Condone use of a semi-colon e.g. \((5\ ; -2)\) for \((5, -2)\)
Condone vector notation e.g. \(\begin{pmatrix}5\\-2\end{pmatrix}\) for \((5, -2)\) and condone \(\left(\dfrac{5}{-2}\right)\)
(i)
B1: \((5, -2)\) o.e. see above
(ii)
B1: \((1.5, -2)\) o.e. see above
(iii)
B1: One correct coordinate. See above.
B1: Both coordinates correct. See above.
Note that B0B1 is not a possible mark profile.
Note that in part (iii), some candidates show their thinking by transforming the point piecewise e.g. \((3, -2) \rightarrow (-3, -2) \rightarrow (-3, -6) \rightarrow (-3, -1)\)
In such cases, mark their final pair of coordinates.