| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation application |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic function transformations. Part (i) requires sketching a standard reciprocal curve, part (ii) is a direct application of horizontal translation (replacing x with x-2), and part (iii) involves recognizing a horizontal stretch by factor 3. All parts are routine textbook exercises requiring recall of transformation rules with minimal problem-solving. |
| 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 |
|---|---|---|
| Answer | Marks | Guidance |
| Correct rectangular hyperbola graph | B2 | Excellent curve in both quadrants: correct shape, symmetrical, not touching axes; asymptotes clearly the axes; not finite; allow slight movement away from asymptote at one end but not more |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((y=)-\frac{1}{x-2}\) or \((y=)-\frac{1}{x+2}\) | M1 | \((y=)\frac{1}{x+2}\) or \((y=)\frac{1}{x-2}\) is M0 |
| \(y=-\frac{1}{x-2}\) | A1 | Fully correct, must include "\(y=\)" |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stretch | B1 | Do not accept: squashed, compressed, enlarged etc. 0/2 if more than one type of transformation mentioned |
| Scale factor \(\frac{1}{3}\) parallel to the \(x\)-axis (or \(y\)-axis) | B1 | Correct description. Condone just "factor \(\frac{1}{3}\)" but no reference to units. Must not follow e.g. "reflection". For "parallel to the \(x/y\) axis" allow "vertically", "in the \(x/y\) direction". Do not accept "in/on/across/up/along/to/towards the \(x/y\) axis" |
## Question 2:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct rectangular hyperbola graph | B2 | Excellent curve in both quadrants: correct shape, symmetrical, not touching axes; asymptotes clearly the axes; not finite; allow slight movement away from asymptote at one end but not more |
**B1 only** – correct shape in 2nd and 4th quadrants only. Graph must not touch axes more than once. Finite "plotting" condoned.
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(y=)-\frac{1}{x-2}$ or $(y=)-\frac{1}{x+2}$ | M1 | $(y=)\frac{1}{x+2}$ or $(y=)\frac{1}{x-2}$ is **M0** |
| $y=-\frac{1}{x-2}$ | A1 | Fully correct, must include "$y=$" |
### Part (iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stretch | B1 | Do not accept: squashed, compressed, enlarged etc. **0/2** if more than one type of transformation mentioned |
| Scale factor $\frac{1}{3}$ parallel to the $x$-axis (or $y$-axis) | B1 | Correct description. Condone just "factor $\frac{1}{3}$" but **no reference to units**. Must not follow e.g. "reflection". For "parallel to the $x/y$ axis" allow "vertically", "in the $x/y$ direction". Do not accept "in/on/across/up/along/to/towards the $x/y$ axis" |
---2 (i) Sketch the curve $y = - \frac { 1 } { x }$.\\
(ii) The curve $y = - \frac { 1 } { x }$ is translated by 2 units parallel to the $x$-axis in the positive direction. State the equation of the transformed curve.\\
(iii) Describe a transformation that transforms the curve $y = - \frac { 1 } { x }$ to the curve $y = - \frac { 1 } { 3 x }$.
\hfill \mbox{\textit{OCR C1 2015 Q2 [6]}}