June 2009 Markscheme

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EDEXCEL CORE MATHEMATICS C3 (6665) – JUNE <strong>2009</strong>FINAL MARK SCHEMEQuestionNumber7. (a)2 x − 8f ( x) = 1 − +( x + 4) ( x − 2)( x + 4)Schemex ∈ R, x ≠ −4, x ≠ 2.Marksf ( x)=( x − 2)( x + 4) − 2( x − 2) + x − 8( x − 2)( x + 4)M1 A1=2x x x x+ 2 − 8 − 2 + 4 + − 8( x − 2)( x + 4)=x2+ x − 12[( x + 4)( x − 2) ]A1=( x + 4)( x − 3)[( x + 4)( x − 2) ]M1=( x − 3)( x − 2)A1 cso (5)(b)g( x)=xe − 3xe − 2x ∈ R, x ≠ ln 2.Apply quotient rule:xx⎧ u = e − 3 v = e − 2 ⎫⎪⎪⎨dux dvx⎬⎪ = e = e ⎪⎩ dxdx⎭g ′( x)==x x x xe (e − 2) − e (e − 3)x 2(e − 2)xex(e − 2)2M1 A1A1 cso (3)xe(c) g ′( x) = 1 ⇒ = 1x 2(e − 2)xe (e 2)x 2= − M1x 2x x xe = e − 2e − 2e + 42xxe 5e 4 0− + = A1xx(e − 4)(e − 1) = 0M1xxe = 4 or e = 1x = ln 4 or x = 0A1 (4)(12 marks)6
EDEXCEL CORE MATHEMATICS C3 (6665) – JUNE <strong>2009</strong>FINAL MARK SCHEMEQuestionSchemeMarksNumber8. (a) sin 2x = 2sin x cos xB1 (1)(b) cosec x − 8cos x = 0 , 0 < x < π18cos x 0sin x − = M118cos xsin x =1 = 8sin xcosx( x x)1 = 4 2sin cos1 = 4sin 2xM11sin 2x =4A1{ }{ }Radians 2x= 0.25268..., 2.88891...Degrees 2x= 14.4775..., 165.5225...{ }{ }Radians x = 0.12634..., 1.44445...Degrees x = 7.23875..., 82.76124...A1A1 cao(5)(6 marks)7
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June 2009 Markscheme

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