| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Fully specified polynomial: verify factor and solve |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring students to verify f(-1)=0, then perform polynomial division to find the quadratic factor, and finally solve using the quadratic formula or factorisation. All steps are routine AS-level techniques with no problem-solving insight required, making it easier than average but not trivial due to the algebraic manipulation involved. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
I don't see any actual mark scheme content in your message—just section headers for Question 6 parts (i) and (ii) without any marking points, criteria, or guidance notes.
Could you please provide the full extracted mark scheme content that needs to be cleaned up? Once you share the actual marking points and annotations, I'll be happy to convert the unicode symbols to LaTeX and format it clearly.6 In this question you must show detailed reasoning.\\
You are given that $\mathrm { f } ( x ) = 4 x ^ { 3 } - 3 x + 1$.\\
(i) Use the factor theorem to show that $( x + 1 )$ is a factor of $\mathrm { f } ( x )$.\\
(ii) Solve the equation $\mathrm { f } ( x ) = 0$.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2018 Q6 [5]}}