| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Given factor, find all roots |
| Difficulty | Moderate -0.8 This is a structured multi-part question that guides students through standard techniques: graphical solution, algebraic manipulation to show equivalence, verification of a given root, and factorization. While it requires multiple steps, each part uses routine C1 methods (graphing, algebraic rearrangement, factor theorem application, solving quadratics) with significant scaffolding. The question is easier than average because students are told what to verify and the path is clearly signposted. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02q Use intersection points: of graphs to solve equations |
\includegraphics{figure_12}
Fig. 12 shows the graph of $y = \frac{4}{x^2}$.
\begin{enumerate}[label=(\roman*)]
\item On the copy of Fig. 12, draw accurately the line $y = 2x + 5$ and hence find graphically the three roots of the equation $\frac{4}{x^2} = 2x + 5$. [3]
\item Show that the equation you have solved in part (i) may be written as $2x^3 + 5x^2 - 4 = 0$. Verify that $x = -2$ is a root of this equation and hence find, in exact form, the other two roots. [6]
\item By drawing a suitable line on the copy of Fig. 12, find the number of real roots of the equation $x^3 + 2x^2 - 4 = 0$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2011 Q12 [12]}}