Date | May 2012 | Marks available | 5 | Reference code | 12M.1.hl.TZ1.5 |
Level | HL only | Paper | 1 | Time zone | TZ1 |
Command term | Simplify | Question number | 5 | Adapted from | N/A |
Question
Let f(x)=sin3xsinx−cos3xcosxf(x)=sin3xsinx−cos3xcosx.
For what values of x does f(x)f(x) not exist?
Simplify the expression sin3xsinx−cos3xcosxsin3xsinx−cos3xcosx.
Markscheme
cosx=0, sinx=0cosx=0, sinx=0 (M1)
x=nπ2,n∈Z A1
EITHER
sin3xcosx−cos3xsinxsinxcosx M1 A1
=sin(3x−x)12sin2x A1 A1
=2 A1
OR
sin2xcosx+cos2xsinxsinx−cos2xcosx−sin2xsinxcosx M1
=2sinxcos2x+2cos2xsinx−sinxsinx−2cos3x−cosx−sin2xcosxcosx A1 A1
=4cos2x−1−2cos2x+1+2sin2x A1
=2cos2x+2sin2x
=2 A1
[5 marks]
Examiners report
Part (a) was well answered, although many candidates lost a mark through not giving sufficient solutions. It was rare for a student to receive no marks for part (b), but few solved the question by the easiest route, and as a consequence, there were frequently errors in the algebraic manipulation of the expression.
Part (a) was well answered, although many candidates lost a mark through not giving sufficient solutions. It was rare for a student to receive no marks for part (b), but few solved the question by the easiest route, and as a consequence, there were frequently errors in the algebraic manipulation of the expression.