| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Polynomial with line intersection |
| Difficulty | Moderate -0.3 This is a straightforward C1 curve sketching question requiring basic polynomial expansion to find intercepts, sketching a cubic and linear function, and reading off an intersection. The tasks are routine: find roots/intercepts (standard), sketch both graphs (textbook exercise), identify intersection graphically (visual observation), and locate α between consecutive integers (direct reading). While multi-part with 7 marks total, each step uses only fundamental techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02q Use intersection points: of graphs to solve equations1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
\begin{enumerate}[label=(\roman*)]
\item Sketch on the same diagram the graphs of $y = (x - 1)^2(x - 5)$ and $y = 8 - 2x$.
Label on your diagram the coordinates of any points where each graph meets the coordinate axes. [5]
\item Explain how your diagram shows that there is only one solution, $\alpha$, to the equation
$$(x - 1)^2(x - 5) = 8 - 2x.$$ [1]
\item State the integer, $n$, such that
$$n < \alpha < n + 1.$$ [1]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q4 [7]}}