| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Moderate -0.8 This is a straightforward C1 question on basic function transformations requiring routine application of translation and scaling rules. Part (i) is a standard sketch, part (ii) applies the x→(x+5) translation rule directly, and part (iii) identifies a simple vertical scaling by factor 1/2. All three parts are textbook exercises with no problem-solving or novel insight required, making this easier than average. |
| 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 |
|---|---|---|
| Marks: B1 | B1 | SC B1 [2] |
| Guidance: Excellent curve for \(y = \frac{2}{x^2}\) in either quadrant | Excellent curve for \(y = \frac{2}{x^2}\) in other quadrant and no more. | Reasonably correct curves in 1st and 2nd quadrants and no more |
| Answer | Marks |
|---|---|
| Marks: M1 | A1 [2] |
| Guidance: \(\frac{2}{(x+5)^2}\) or \(\frac{2}{(x-5)^2}\) seen | Fully correct, must include "\(y =\)" or "\(f(x) =\)" |
| Answer | Marks |
|---|---|
| Marks: B1 | B1 [2] |
| Guidance: Or "stretched" etc; do not accept squashed, compressed etc. | oe e.g. scale factor \(\sqrt{2}\) parallel to x-axis |
## (i)
**Answer:** [Graph showing U-shaped curve]
**Marks:** B1 | B1 | SC B1 [2]
**Guidance:** Excellent curve for $y = \frac{2}{x^2}$ in either quadrant | Excellent curve for $y = \frac{2}{x^2}$ in other quadrant and no more. | Reasonably correct curves in 1st and 2nd quadrants and no more
**Additional notes:** N.B. Ignore 'feathering' now that answers are scanned. For Excellent: Correct shape, not touching axes, asymptotes clearly the axes. Allow slight movement away from asymptote at one end but not more. Not finite. For SC B1, graph must not touch axes more than twice.
## (ii)
**Answer:** $y = \frac{2}{(x+5)^2}$
**Marks:** M1 | A1 [2]
**Guidance:** $\frac{2}{(x+5)^2}$ or $\frac{2}{(x-5)^2}$ seen | Fully correct, must include "$y =$" or "$f(x) =$"
## (iii)
**Answer:** Stretch; scale factor $\frac{1}{2}$ parallel to y-axis
**Marks:** B1 | B1 [2]
**Guidance:** Or "stretched" etc; do not accept squashed, compressed etc. | oe e.g. scale factor $\sqrt{2}$ parallel to x-axis
**Additional notes:** 0/2 if more than one type of transformation mentioned; ISW non-contradictory statements for "parallel to the y-axis" allow "vertically", "up", "in the (positive) y direction". Do not accept "in/on/ across/up/along/to/towards the y-axis"
---\begin{enumerate}[label=(\roman*)]
\item Sketch the curve $y = \frac{2}{x^2}$. [2]
\item The curve $y = \frac{2}{x^2}$ is translated by 5 units in the negative $x$-direction. Find the equation of the curve after it has been translated. [2]
\item Describe a transformation that transforms the curve $y = \frac{2}{x^2}$ to the curve $y = \frac{1}{x^2}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q5 [6]}}