| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Graphical equation solving with auxiliary line |
| Difficulty | Moderate -0.3 This is a standard C1 curve sketching question with routine algebraic techniques: verifying a root by substitution, factorising a cubic by inspection/division, sketching using roots and end behavior, then solving a linear-cubic intersection algebraically. All steps are textbook procedures requiring no novel insight, though the multi-part nature and algebraic manipulation place it slightly below average difficulty for A-level. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02q Use intersection points: of graphs to solve equations |
11 You are given that $\mathrm { f } ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 23 x + 12$.\\
(i) Show that $x = - 3$ is a root of $\mathrm { f } ( x ) = 0$ and hence factorise $\mathrm { f } ( x )$ fully.\\
(ii) Sketch the curve $y = \mathrm { f } ( x )$.\\
(iii) Find the $x$-coordinates of the points where the line $y = 4 x + 12$ intersects $y = \mathrm { f } ( x )$.
\hfill \mbox{\textit{OCR MEI C1 2012 Q11 [13]}}