Moderate -0.3 This is a standard harmonic form question requiring routine application of the R sin(θ - α) formula (finding R = √10 and α = arctan(3)) followed by solving a straightforward trigonometric equation. While it involves multiple steps, both parts are textbook exercises with no novel insight required, making it slightly easier than average.
Point M: maximum point, \(y\) is maximum when \(\cos\theta = -1\), i.e. \(\theta = \pi\)
M1
Finding \(\theta\) value
M is \((\pi a, 2a)\), \(\theta = \pi\)
A1
Point N: \(y = 0\) when \(\cos\theta = 1\), i.e. \(\theta = 2\pi\)
N is \((2\pi a, 0)\), \(\theta = 2\pi\)
A1
Both coordinates correct
# Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Point M: maximum point, $y$ is maximum when $\cos\theta = -1$, i.e. $\theta = \pi$ | M1 | Finding $\theta$ value |
| M is $(\pi a, 2a)$, $\theta = \pi$ | A1 | |
| Point N: $y = 0$ when $\cos\theta = 1$, i.e. $\theta = 2\pi$ | | |
| N is $(2\pi a, 0)$, $\theta = 2\pi$ | A1 | Both coordinates correct |
---