| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Unknown constant, verify then factorise |
| Difficulty | Moderate -0.3 This is a straightforward C2 Factor Theorem question requiring substitution to find k, then factorisation of a cubic. While it involves multiple steps (verify constant, factorise, solve quadratic), each step uses standard techniques with no novel insight required. Slightly easier than average due to being a guided, routine application of the Factor Theorem. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
5.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{de1a3480-0d83-43c2-a5a2-2f117b8a50fd-2_515_771_246_438}
\end{center}
The diagram shows the curve $y = \mathrm { f } ( x )$ where
$$f ( x ) = 4 + 5 x + k x ^ { 2 } - 2 x ^ { 3 }$$
and $k$ is a constant.
The curve crosses the $x$-axis at the points $A , B$ and $C$.\\
Given that $A$ has coordinates $( - 4,0 )$,\\
(i) show that $k = - 7$,\\
(ii) find the coordinates of $B$ and $C$.\\
\hfill \mbox{\textit{OCR C2 Q5 [7]}}