Date | May 2010 | Marks available | 6 | Reference code | 10M.1.sl.TZ1.4 |
Level | SL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The straight line with equation y=34x makes an acute angle θ with the x-axis.
Write down the value of tanθ .
Find the value of
(i) sin2θ ;
(ii) cos2θ .
Markscheme
tanθ=34 (do not accept 34x ) A1 N1
[1 mark]
(i) sinθ=35 , cosθ=45 (A1)(A1)
correct substitution A1
e.g. sin2θ=2(35)(45)
sin2θ=2425 A1 N3
(ii) correct substitution A1
e.g. cos2θ=1−2(35)2 , (45)2−(35)2
cos2θ=725 A1 N1
[6 marks]
Examiners report
Many candidates drew a diagram to correctly find tanθ , although few recognized that a line through the origin can be expressed as y=xtanθ , with gradient tanθ , which is explicit in the syllabus.
A surprising number were unable to find the ratios for sinθ and cosθ from tanθ . It was not uncommon for candidates to use unreasonable values, such as sinθ=3 and cosθ=4 , or to write nonsense such as 2sin35cos45 .