| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Symmetric functions of roots |
| Difficulty | Moderate -0.5 This question tests routine matrix operations: computing a 3×3 determinant (part a), recalling that combined transformations multiply matrices (part b(i)), and using the property that det(PQ) = det(P)det(Q) with given constraints (part b(ii)). All parts are standard textbook exercises requiring recall and basic algebraic manipulation, with no problem-solving insight needed. Slightly easier than average due to straightforward application of formulas. |
| Spec | 4.03j Determinant 3x3: calculation4.03k Determinant 3x3: volume scale factor4.03m det(AB) = det(A)*det(B) |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (a) | det = 8 |
| volume scale factor = 8 | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| 1.1 | soi BC |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | (i) |
| [1] | 1.1 | 𝑘 3 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | (ii) |
| Answer | Marks |
|---|---|
| k = − 43 | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | soi |
Question 5:
5 | (a) | det = 8
volume scale factor = 8 | B1
B1ft
[2] | 1.1a
1.1 | soi BC
ft their determinant value
5 | (b) | (i) | QP | B1
[1] | 1.1 | 𝑘 3
Allow ( )𝐏
−1 2
5 | (b) | (ii) | det(Q) = 2k + 3
3(2k + 3) = 1
k = − 43 | B1
M1
A1
[3] | 1.1
1.1
1.1 | soi
3 their (2k + 3) = 1 oe, e.g. 2k + 3 = 1/35
\begin{enumerate}[label=(\alph*)]
\item Find the volume scale factor of the transformation with associated matrix $\left( \begin{array} { r r r } 1 & 2 & 0 \\ 0 & 3 & - 1 \\ - 1 & 0 & 2 \end{array} \right)$.
\item The transformations S and T of the plane have associated $2 \times 2$ matrices $\mathbf { P }$ and $\mathbf { Q }$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Write down an expression for the associated matrix of the combined transformation S followed by T.
The determinant of $\mathbf { P }$ is 3 and $\mathbf { Q } = \left( \begin{array} { r r } k & 3 \\ - 1 & 2 \end{array} \right)$, where $k$ is a constant.
\item Given that this combined transformation preserves both orientation and area, determine the value of $k$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2024 Q5 [6]}}