Unit 8 — Sinusoidal functions and complex numbers
Grade conversion
Total points converted to the IB grade (1–7).
| Points | IB grade |
|---|---|
| 58 – 70 | 7 |
| 46 – 57 | 6 |
| 35 – 45 | 5 |
| 25 – 34 | 4 |
| 16 – 24 | 3 |
| 8 – 15 | 2 |
| 1 – 7 | 1 |
Questions
Each card opens its question.
Circular sector: the sprinkler
Angle of rotation in radians, exact in terms of $\pi$; Length of the arc traced by the end of the jet; Area of the watered region…
Sinusoidal model: tides in a harbour
Values of $a$ and $d$ and their meaning in context; Period of the model and values of $b$ and $c$; Depth of the water at 13:00…
Complex numbers in polar and Euler form
$z_1$ and $z_2$ in modulus–argument and Euler form, exact; $z_1z_2$ and $z_1/z_2$ in modulus–argument form; $z_1z_2$ in Cartesian form; $z_2^6$ in Cartesian form, justifying the method…
A spiral on the Argand diagram
$z_1$ in Euler form and in Cartesian form; Expression for $z_n$ in terms of $n$; First time the point is less than 1 unit from the origin…
Adding two alternating voltages
Justify $V = \operatorname{Im}\left(e^{100\pi t\,i}\left(120e^{\frac{\pi}{6}i} + 90e^{\frac{2\pi}{3}i}\right)\right)$; $V$ in the form $R\sin(100\pi t + \alpha)$; Period and frequency of the resulting voltage…