| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Type | Division then Solve Polynomial Equation |
| Difficulty | Standard +0.3 This is a slightly easier than average A-level question. Part (i) requires straightforward algebraic manipulation (equating the curves and multiplying through by x). Part (ii) uses the given root to factor the cubic via polynomial division, then solving the resulting quadratic—all standard C2 techniques with no novel insight required. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
4.\\
\includegraphics[max width=\textwidth, alt={}, center]{30d4e6e5-8235-44b0-ad8e-c4c0b313677f-1_572_803_1336_461}
The diagram shows the curves with equations $y = 7 - 2 x - 3 x ^ { 2 }$ and $y = \frac { 2 } { x }$.\\
The two curves intersect at the points $P , Q$ and $R$.\\
(i) Show that the $x$-coordinates of $P , Q$ and $R$ satisfy the equation
$$3 x ^ { 3 } + 2 x ^ { 2 } - 7 x + 2 = 0$$
Given that $P$ has coordinates $( - 2 , - 1 )$,\\
(ii) find the coordinates of $Q$ and $R$.\\
\hfill \mbox{\textit{OCR C2 Q4 [8]}}