| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation application |
| Difficulty | Standard +0.3 This is a straightforward multi-part question on function transformations requiring standard techniques: applying a horizontal stretch (substituting 2x for x), finding a derivative for the normal gradient, and verifying tangency by solving a quadratic. All steps are routine AS-level procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x)1.07m Tangents and normals: gradient and equations |
I notice that the extracted mark scheme content you've provided appears to be incomplete or empty. The section shows only question labels and headers (9 (i) and 9 (ii)) without any actual marking criteria, annotations (M1, A1, B1, etc.), or guidance notes.
To clean this up properly, I would need the actual mark scheme content that includes:
- Marking points and their criteria
- Marking annotations (M1, A1, B1, DM1, etc.)
- Any guidance notes or working
Could you please provide the complete mark scheme content for Question 9?9 The curve $y = ( x - 1 ) ^ { 2 }$ maps onto the curve $\mathrm { C } _ { 1 }$ following a stretch scale factor $\frac { 1 } { 2 }$ in the $x$-direction.\\
(i) Show that the equation of $\mathrm { C } _ { 1 }$ can be written as $y = 4 x ^ { 2 } - 4 x + 1$.
The curve $\mathrm { C } _ { 2 }$ is a translation of $y = 4.25 x - x ^ { 2 }$ by $\binom { 0 } { - 3 }$.\\
(ii) Show that the normal to the curve $\mathrm { C } _ { 1 }$ at the point $( 0,1 )$ is a tangent to the curve $\mathrm { C } _ { 2 }$.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2018 Q9 [9]}}