| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| 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 testing basic function transformations. Part (i) requires sketching a simple square root function, part (ii) identifies a vertical translation (a standard transformation), and part (iii) applies a horizontal stretch using a standard rule. All parts involve direct application of well-rehearsed transformation rules with no problem-solving or conceptual challenges, making it easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
| Answer | Marks | Guidance |
|---|---|---|
| Graph in bottom right quadrant only | B1 | One to one graph only in bottom right hand quadrant |
| Correct graph passing through origin | B1 [2] | Correct graph, passing through origin |
| Answer | Marks |
|---|---|
| Translation | B1 |
| Parallel to \(y\)-axis, 5 units | B1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| \(y = -\sqrt{\dfrac{x}{2}}\) | M1 | \(\sqrt{2x}\) or \(\sqrt{\dfrac{x}{2}}\) seen |
| A1 [2] | cao |
## Question 6:
### Part (i):
Graph in bottom right quadrant only | B1 | One to one graph only in bottom right hand quadrant
Correct graph passing through origin | B1 [2] | Correct graph, passing through origin
### Part (ii):
Translation | B1 |
Parallel to $y$-axis, 5 units | B1 [2] |
### Part (iii):
$y = -\sqrt{\dfrac{x}{2}}$ | M1 | $\sqrt{2x}$ or $\sqrt{\dfrac{x}{2}}$ seen
| A1 [2] | cao
---6 (i) Sketch the curve $y = - \sqrt { x }$.\\
(ii) Describe fully a transformation that transforms the curve $y = - \sqrt { x }$ to the curve $y = 5 - \sqrt { x }$.\\
(iii) The curve $y = - \sqrt { x }$ is stretched by a scale factor of 2 parallel to the $x$-axis. State the equation of the curve after it has been stretched.
\hfill \mbox{\textit{OCR C1 2009 Q6 [6]}}