| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Modulus-argument form conversion |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number operations: subtraction, modulus, argument, and division. All parts require only direct application of standard formulas with no problem-solving insight. While FP1 content is more advanced than Core modules, these are routine computational exercises that any student who has learned the techniques can execute mechanically. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| \(5 + 12i\) | B1B1 | Correct real and imaginary parts |
| \(13\) | B1ft | Correct modulus |
| \(67.4°\) or \(1.18\) | B1ft 4 | Correct argument |
| Answer | Marks | Guidance |
|---|---|---|
| \(-\frac{11}{85} - \frac{27}{85}i\) | M1 | Multiply by conjugate |
| A1 | Obtain correct numerator | |
| A1 3 | Obtain correct denominator |
## (i)
$5 + 12i$ | B1B1 | Correct real and imaginary parts
$13$ | B1ft | Correct modulus
$67.4°$ or $1.18$ | B1ft 4 | Correct argument
## (ii)
$-\frac{11}{85} - \frac{27}{85}i$ | M1 | Multiply by conjugate
| A1 | Obtain correct numerator
| A1 3 | Obtain correct denominator
---The complex numbers $a$ and $b$ are given by $a = 7 + 6\text{i}$ and $b = 1 - 3\text{i}$. Showing clearly how you obtain your answers, find
\begin{enumerate}[label=(\roman*)]
\item $|a - 2b|$ and $\arg(a - 2b)$, [4]
\item $\frac{b}{a}$, giving your answer in the form $x + \text{i}y$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2010 Q4 [7]}}