| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number operations: plotting points, multiplication, and division. All parts are routine calculations with no conceptual challenges—part (i) is simple plotting, part (ii) is direct multiplication, and part (iii) requires standard rationalization of a complex fraction. While it's FP1 content, the mechanical nature and low mark allocation make it easier than average A-level questions. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
Question 4:
4
Ê1 -2 kˆ Ê-5 -2+2k -4-kˆ
10 You are given that A =Á2 1 2˜ and B=Á 8 -1-3k -2+2k˜ and that AB is of the
Á ˜ Á ˜
Ë3 2 -1¯ Ë 1 -8 5 ¯
Êk-n 0 0 ˆ
form AB=Á 0 k-n 0 ˜.
Á ˜
Ë 0 0 k-n¯
(i) Find the value of n. [2]
(ii) Write down the inverse matrix A–1 and state the condition on k for this inverse to exist. [4]
(iii) Using the result from part (ii), or otherwise, solve the following simultaneous equations.
x - 2y + z = 1
2x + y + 2z = 12
3x +2y - z = 3
[5]
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© OCR 2007 4755/01 June 07Two complex numbers, $\alpha$ and $\beta$, are given by $\alpha = 1 - 2\mathrm{j}$ and $\beta = -2 - \mathrm{j}$.
\begin{enumerate}[label=(\roman*)]
\item Represent $\beta$ and its complex conjugate $\beta^*$ on an Argand diagram. [2]
\item Express $\alpha\beta$ in the form $a + b\mathrm{j}$. [2]
\item Express $\frac{\alpha + \beta}{\beta}$ in the form $a + b\mathrm{j}$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2007 Q4 [7]}}