| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Moderate -0.8 This question tests basic function transformations with straightforward applications. Part (i) requires replacing x with (x-4), a standard translation. Part (ii) involves recognizing a vertical stretch by factor 2.5, which is direct pattern recognition. Both parts are routine exercises requiring recall of transformation rules without problem-solving or conceptual depth. |
| Spec | 1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{2}{3+x-4}\) or \(\frac{2}{3+x+4}\) | M1 | Translates curve by \(+/-\ 4\) parallel to the \(x\)-axis |
| \(y = \frac{2}{x-1}\) | A1 [2] | Fully correct, must have \(y =\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stretch | B1 | Must use stretch/stretched/stretching… B0B1 possible e.g. 'enlarge by scale factor…' but not for 'translate by scale factor…' |
| Scale factor \(\frac{5}{2}\) parallel to the \(y\)-axis | B1 [2] | Allow "factor" or "SF" for "scale factor". Allow "vertically", "in the \(y\) direction". Do not accept "in/on/across/up/along the \(y\) axis", "in the positive \(y\) direction", "SF 5/2 units". More than one transformation: B0B0 |
# Question 2:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{2}{3+x-4}$ or $\frac{2}{3+x+4}$ | M1 | Translates curve by $+/-\ 4$ parallel to the $x$-axis |
| $y = \frac{2}{x-1}$ | A1 [2] | Fully correct, must have $y =$ |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stretch | B1 | Must use stretch/stretched/stretching… B0B1 possible e.g. 'enlarge by scale factor…' but not for 'translate by scale factor…' |
| Scale factor $\frac{5}{2}$ parallel to the $y$-axis | B1 [2] | Allow "factor" or "SF" for "scale factor". Allow "vertically", "in the $y$ direction". Do not accept "in/on/across/up/along the $y$ axis", "in the positive $y$ direction", "SF 5/2 units". More than one transformation: B0B0 |
---2 (i) The curve $y = \frac { 2 } { 3 + x }$ is translated by four units in the positive $x$-direction. State the equation of the curve after it has been translated.\\
(ii) Describe fully the single transformation that transforms the curve $y = \frac { 2 } { 3 + x }$ to $y = \frac { 5 } { 3 + x }$.
\hfill \mbox{\textit{OCR PURE Q2 [4]}}