| Date | May 2018 | Marks available | 2 | Reference code | 18M.1.hl.TZ1.2 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Let \(y = {\text{si}}{{\text{n}}^2}\theta ,\,\,0 \leqslant \theta \leqslant \pi \).
Find \(\frac{{{\text{d}}y}}{{{\text{d}}\theta }}\)
[2]
a.
Hence find the values of θ for which \(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2y\).
[5]
b.
Markscheme
attempt at chain rule or product rule (M1)
\(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta \) A1
[2 marks]
a.
\(2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta = 2{\text{si}}{{\text{n}}^2}\theta \)
sin θ = 0 (A1)
θ = 0, \(\pi \) A1
obtaining cos θ = sin θ (M1)
tan θ = 1 (M1)
\(\theta = \frac{\pi }{4}\) A1
[5 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
