| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus modulus/argument |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number operations: finding modulus/argument (direct formula application) and complex division (multiply by conjugate). While FP1 content is inherently more advanced than C1-C3, these are routine procedural tasks with no problem-solving required, making it easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \( | z | = \sqrt{58}\) or \(7.62\) |
| \(\arg z = 23.2(°)\) or \(0.405\) or \(0.129\pi\) | B1 | Obtain correct value, 3 s.f. or better; \(\arctan(3/7)\) gets B0 |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Multiply numerator & denominator by conjugate | M1 | \(\frac{28+19i-3}{16+1}\) gets A0 A0 |
| \(\frac{25}{17} + \frac{19}{17}i\) — obtain correct numerator or real part | A1 | |
| Obtain correct denominator or imaginary part | A1 | |
| [3] | ||
| *Or*: Find and attempt to solve a pair of simultaneous equations for real and imaginary parts | M1 | |
| \(\frac{25}{17}\) and \(\frac{19}{17}\) — obtain correct answers | A1 A1 |
# Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $|z| = \sqrt{58}$ or $7.62$ | B1 | Obtain correct value, 3 s.f. or better |
| $\arg z = 23.2(°)$ or $0.405$ or $0.129\pi$ | B1 | Obtain correct value, 3 s.f. or better; $\arctan(3/7)$ gets B0 |
| **[2]** | | |
---
# Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Multiply numerator & denominator by conjugate | M1 | $\frac{28+19i-3}{16+1}$ gets A0 A0 |
| $\frac{25}{17} + \frac{19}{17}i$ — obtain correct numerator or real part | A1 | |
| Obtain correct denominator or imaginary part | A1 | |
| **[3]** | | |
| *Or*: Find and attempt to solve a pair of simultaneous equations for real and imaginary parts | M1 | |
| $\frac{25}{17}$ and $\frac{19}{17}$ — obtain correct answers | A1 A1 | |
---2 The complex number $7 + 3 \mathrm { i }$ is denoted by $z$. Find\\
(i) $| z |$ and $\arg z$,\\
(ii) $\frac { z } { 4 - \mathrm { i } }$, showing clearly how you obtain your answer.
\hfill \mbox{\textit{OCR FP1 2014 Q2 [5]}}