| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch rational function from transformation |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic curve sketching and transformations of a simple rational function. Part (i) requires sketching a standard reciprocal square curve, part (ii) applies a horizontal translation (routine transformation), and part (iii) identifies a vertical stretch by factor 2. All three parts involve standard textbook techniques 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 |
|---|---|---|
| (i) | B1, B1, 2 | Correct curve in one quadrant; Completely correct |
| (ii) | M1, A1√, 2 | Translate (i) horizontally; Translates all of their (i) \(\begin{pmatrix} 3 \\ 0 \end{pmatrix}\) |
| (iii) (One-way) stretch, sf 2, parallel to the y-axis | B1, B1, B1, 3 | \(3\) must be labelled or stated; Stretch (Scale) factor 2; Parallel to y-axis o.e. SR: Stretch B1; Sf \(\sqrt{2}\) parallel to x-axis B2 |
**(i)** | B1, B1, 2 | Correct curve in one quadrant; Completely correct
**(ii)** | M1, A1√, 2 | Translate (i) horizontally; Translates all of their (i) $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$
**(iii)** (One-way) stretch, sf 2, parallel to the y-axis | B1, B1, B1, 3 | $3$ must be labelled or stated; Stretch (Scale) factor 2; Parallel to y-axis o.e. **SR:** Stretch B1; Sf $\sqrt{2}$ parallel to x-axis B24 (i) Sketch the curve $y = \frac { 1 } { x ^ { 2 } }$.\\
(ii) Hence sketch the curve $y = \frac { 1 } { ( x - 3 ) ^ { 2 } }$.\\
(iii) Describe fully a transformation that transforms the curve $y = \frac { 1 } { x ^ { 2 } }$ to the curve $y = \frac { 2 } { x ^ { 2 } }$.
\hfill \mbox{\textit{OCR C1 2006 Q4 [7]}}