Date | May 2008 | Marks available | 6 | Reference code | 08M.2.hl.TZ1.7 |
Level | HL only | Paper | 2 | Time zone | TZ1 |
Command term | Solve, Express, and Hence | Question number | 7 | Adapted from | N/A |
Question
A system of equations is given by
cosx+cosy=1.2
sinx+siny=1.4 .
(a) For each equation express y in terms of x.
(b) Hence solve the system for 0<x<π, 0<y<π .
Markscheme
(a) y=arccos(1.2−cosx) A1
y=arcsin(1.4−sinx) A1
(b) The solutions are
x = 1.26, y = 0.464 A1A1
x = 0.464, y = 1.26 A1A1
[6 marks]
Examiners report
The majority of candidates obtained the first two marks. Candidates who used their GDC to solve this question did so successfully, although few candidates provided a sketch as the rubric requires. Attempts to use “solver” only gave one solution.
Some candidates did not give the solutions as coordinate pairs, but simply stated the x and y values.