| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Line intersecting quadratic curve |
| Difficulty | Moderate -0.3 Part (i) is a standard C1 simultaneous equations exercise requiring substitution and solving a quadratic. Parts (ii) and (iii) add mild conceptual steps—recognizing that one solution means tangency, and using this to find the normal—but these are routine applications of standard techniques. Overall slightly easier than average due to straightforward algebra and predictable multi-part structure. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02f Solve quadratic equations: including in a function of unknown1.07m Tangents and normals: gradient and equations |
5 (i) Solve the simultaneous equations
$$y = x ^ { 2 } - 3 x + 2 , \quad y = 3 x - 7 .$$
(ii) What can you deduce from the solution to part (i) about the graphs of $y = x ^ { 2 } - 3 x + 2$ and $y = 3 x - 7$ ?\\
(iii) Hence, or otherwise, find the equation of the normal to the curve $y = x ^ { 2 } - 3 x + 2$ at the point ( 3,2 ), giving your answer in the form $a x + b y + c = 0$ where $a , b$ and $c$ are integers.
\hfill \mbox{\textit{OCR C1 Q5 [6]}}