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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), 32dydx=0     M1A1

dydx=32     A1

[6 marks]

METHOD 2

3x2y2+2x3ydydx=πsin(πy)dydx     A1A1A1

dydx=3x2y2πsin(πy)2x3y     A1

At (1, 1), dydx=3(1)2(1)2πsin(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.

Syllabus sections

Topic 6 - Core: Calculus » 6.2 » Implicit differentiation.

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