| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertical stretch y = af(x) |
| Difficulty | Easy -1.3 This is a straightforward C1 question requiring basic sketches of standard functions and identification of a simple vertical stretch transformation. Part (a) tests recall of standard curve shapes, and part (b) is a direct application of the transformation y = af(x) with no problem-solving required—significantly easier than average A-level questions. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| B1 | Excellent curve for \(\frac{1}{x}\) in either quadrant |
| B1 (2) | Excellent curve for \(\frac{1}{x}\) in other quadrant |
| SR B1 | Reasonably correct curves in 1st and 3rd quadrants |
| Answer | Marks |
|---|---|
| B1 (1) | Correct graph, minimum point at origin, symmetrical |
| Answer | Marks |
|---|---|
| Stretch | B1 |
| Scale factor 8 in \(y\) direction or scale factor \(\frac{1}{2}\) in \(x\) direction | B1 (2) |
# Question 2:
**(a)(i)**
| B1 | Excellent curve for $\frac{1}{x}$ in either quadrant
| B1 (2) | Excellent curve for $\frac{1}{x}$ in other quadrant
| SR B1 | Reasonably correct curves in 1st and 3rd quadrants
**(ii)**
| B1 (1) | Correct graph, minimum point at origin, symmetrical
**(b)**
Stretch | B1 |
Scale factor 8 in $y$ direction **or** scale factor $\frac{1}{2}$ in $x$ direction | B1 (2) |
---2
\begin{enumerate}[label=(\alph*)]
\item On separate diagrams, sketch the graphs of
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { y } = \frac { 1 } { \mathrm { x } }$,
\item $y = x ^ { 4 }$.
\end{enumerate}\item Describe a transformation that transforms the curve $y = x ^ { 3 }$ to the curve $y = 8 x ^ { 3 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2007 Q2 [5]}}