| Date | May 2018 | Marks available | 4 | Reference code | 18M.2.sl.TZ1.7 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Hence and Find | Question number | 7 | Adapted from | N/A |
Question
Let \(f\left( x \right) = {{\text{e}}^{2\,{\text{sin}}\left( {\frac{{\pi x}}{2}} \right)}}\), for x > 0.
The k th maximum point on the graph of f has x-coordinate xk where \(k \in {\mathbb{Z}^ + }\).
Given that xk + 1 = xk + a, find a.
Hence find the value of n such that \(\sum\limits_{k = 1}^n {{x_k} = 861} \).
Markscheme
valid approach to find maxima (M1)
eg one correct value of xk, sketch of f
any two correct consecutive values of xk (A1)(A1)
eg x1 = 1, x2 = 5
a = 4 A1 N3
[4 marks]
recognizing the sequence x1, x2, x3, …, xn is arithmetic (M1)
eg d = 4
correct expression for sum (A1)
eg \(\frac{n}{2}\left( {2\left( 1 \right) + 4\left( {n - 1} \right)} \right)\)
valid attempt to solve for n (M1)
eg graph, 2n2 − n − 861 = 0
n = 21 A1 N2
[4 marks]
