| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Easy -1.2 This is a straightforward C1 question requiring a basic sketch of a reciprocal function and identification of a simple vertical translation. Both parts involve standard, routine knowledge with no problem-solving or multi-step reasoning required. |
| Spec | 1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Reasonably correct curve for \(y = -\frac{1}{x}\) in 1st and 3rd quadrants only | B1 | N.B. Ignore 'feathering' now that answers are scanned. Reasonably correct shape, not touching axes more than twice. |
| Very good curves for \(y = -\frac{1}{x}\) in 1st and 3rd quadrants | B1, 2 | Correct shape, not touching axes, asymptotes clearly the axes. Allow slight movement away from asymptote at one end but not more. Not finite. |
| SC If 0, very good single curve in either 1st or 3rd quadrant and nothing in other three quadrants | B1 | |
| (ii) Translation 4 units parallel to y axis | B1, B1, 2 | Must be translation/translated – not shift, move etc. Or \(\begin{pmatrix}0\\4\end{pmatrix}\) |
**(i)** Reasonably correct curve for $y = -\frac{1}{x}$ in 1st and 3rd quadrants only | B1 | N.B. Ignore 'feathering' now that answers are scanned. Reasonably correct shape, not touching axes more than twice.
Very good curves for $y = -\frac{1}{x}$ in 1st and 3rd quadrants | B1, 2 | Correct shape, not touching axes, asymptotes clearly the axes. Allow slight movement away from asymptote at one end but not more. Not finite.
SC If 0, very good single curve in either 1st or 3rd quadrant and nothing in other three quadrants | B1 |
**(ii)** Translation 4 units parallel to y axis | B1, B1, 2 | Must be translation/translated – not shift, move etc. Or $\begin{pmatrix}0\\4\end{pmatrix}$ | For "parallel to the y axis" allow "vertically", "up", "in the (positive) y direction". Do not accept "in/on/across/up/along the y axis"2 (i) Sketch the curve $y = \frac { 1 } { x }$.\\
(ii) Describe fully the single transformation that transforms the curve $y = \frac { 1 } { x }$ to the curve $y = \frac { 1 } { x } + 4$.
\hfill \mbox{\textit{OCR C1 2011 Q2 [4]}}