Date | May 2008 | Marks available | 6 | Reference code | 08M.2.hl.TZ1.6 |
Level | HL only | Paper | 2 | Time zone | TZ1 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
Find the gradient of the tangent to the curve x3y2=cos(πy) at the point (−1, 1) .
Markscheme
METHOD 1
3x2y2+2x3ydydx=−πsin(πy)dydx A1A1A1
At (−1, 1), 3−2dydx=0 M1A1
dydx=32 A1
[6 marks]
METHOD 2
3x2y2+2x3ydydx=−πsin(πy)dydx A1A1A1
dydx=3x2y2−πsin(πy)−2x3y A1
At (−1, 1), dydx=3(−1)2(1)2−πsin(π)−2(−1)3(1)=32 M1A1
[6 marks]
Examiners report
A large number of candidates obtained full marks on this question. Some candidates missed π and/or dydx when differentiating the trigonometric function. Some candidates attempted to rearrange before differentiating, and some made algebraic errors in rearranging.