| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Roots with special relationships |
| Difficulty | Challenging +1.2 This is a Further Maths AS question requiring systematic use of Vieta's formulas and algebraic manipulation with related roots. While it involves multiple steps and careful algebra, the approach is methodical: use sum of roots to find α, then verify and find p. The relationship between roots provides strong structure, making it more straightforward than it initially appears, though still above average difficulty due to the algebraic complexity and being Further Maths content. |
| Spec | 4.05a Roots and coefficients: symmetric functions |
| Answer | Marks |
|---|---|
| 5 | 2 2 |
| Answer | Marks |
|---|---|
| = 4 | M1 |
| Answer | Marks |
|---|---|
| [7] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | Attempt to use sum of roots |
Question 5:
5 | 2 2
(cid:68)(cid:14) (cid:14)(cid:68)(cid:14) (cid:32)4
(cid:68) (cid:68)
(cid:68)2 (cid:16)2(cid:68)(cid:14)2(cid:32)0
(cid:68)(cid:32)1(cid:114)i
Roots are 1(cid:14)i,1(cid:16)i,2
p(cid:32)(1(cid:14)i)(1(cid:16)i)(cid:14)2(1(cid:14)i)(cid:14)2(1(cid:16)i)
(cid:32)2(cid:14)2(cid:14)2i(cid:14)2(cid:16)2i
= 4 | M1
M1
A1
A1
M1
A1
A1
[7] | 1.1a
3.1a
1.1
3.2a
3.1a
1.1
1.1 | Attempt to use sum of roots
N
Interpret solution of quadratic
Eto get all three roots of cubic
Some correct simplificationThe cubic equation $x^3 - 4x^2 + px + q = 0$ has roots $\alpha$, $\frac{2}{\alpha}$ and $\alpha + \frac{2}{\alpha}$.
Find
\begin{itemize}
\item the values of the roots of the equation,
\item the value of $p$.
\end{itemize}
[7]
\hfill \mbox{\textit{OCR MEI Further Pure Core AS Q5 [7]}}