| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Single transformation application |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic curve sketching and standard transformations. Part (i) requires sketching a simple reciprocal function, part (ii) tests routine translation knowledge (replace x with x+3), and part (iii) applies a simple y-stretch. All parts are direct application of standard techniques with no problem-solving or insight required, making it 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) |
4 (i) Sketch the curve $y = \frac { 1 } { x ^ { 2 } }$.\\
(ii) The curve $y = \frac { 1 } { x ^ { 2 } }$ is translated by 3 units in the negative $x$-direction. State the equation of the curve after it has been translated.\\
(iii) The curve $y = \frac { 1 } { x ^ { 2 } }$ is stretched parallel to the $y$-axis with scale factor 4 and, as a result, the point $P ( 1,1 )$ is transformed to the point $Q$. State the coordinates of $Q$.
\hfill \mbox{\textit{OCR C1 2009 Q4 [6]}}