| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Basic factored form sketching |
| Difficulty | Easy -1.2 This is a straightforward C1 curve sketching question requiring only basic recall of standard function shapes and simple factorization. Part (i) is a standard reciprocal graph, part (ii) requires factoring to find x-intercepts (0, ±1) with no calculus needed, and part (iii) is a reflected square root function. All three are textbook examples with no problem-solving or novel insight required. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^2 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | Marks | Guidance |
| Correct curve in \(+ve\) quadrant | B1 | |
| in \(-ve\) quadrant | B1 2 | |
| (ii) | Marks | Guidance |
| Positive cubic with clearly seen max and min points | M1 | |
| \((-1.0), (0.0), (1.0)\) | A1 | Any one point stated or marked on sketch |
| A1 3 | Curve passes through all 3 points and no extras stated or marked on sketch | |
| (iii) | Marks | Guidance |
| Graph only in bottom right hand quadrant | B1 | |
| Correct graph, passing through origin | B1 2 | |
| 7 |
**(i)** | **Marks** | **Guidance**
---|---|---
Correct curve in $+ve$ quadrant | B1 |
in $-ve$ quadrant | B1 2 |
**(ii)** | **Marks** | **Guidance**
---|---|---
Positive cubic with clearly seen max and min points | M1 |
$(-1.0), (0.0), (1.0)$ | A1 | Any one point stated or marked on sketch
| A1 3 | Curve passes through all 3 points and no extras stated or marked on sketch
**(iii)** | **Marks** | **Guidance**
---|---|---
Graph only in bottom right hand quadrant | B1 |
Correct graph, passing through origin | B1 2 |
| **7** |5 On separate diagrams,\\
(i) sketch the curve $y = \frac { 1 } { x }$,\\
(ii) sketch the curve $y = x \left( x ^ { 2 } - 1 \right)$, stating the coordinates of the points where it crosses the $x$-axis,\\
(iii) sketch the curve $y = - \sqrt { } x$.
\hfill \mbox{\textit{OCR C1 2005 Q5 [7]}}