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Edexcel_WS_C4_PaperF

# Edexcel_WS_C4_PaperF - Worked Solutions Edexcel C4 Paper F...

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Worked Solutions Edexcel C4 Paper F 1. d y d t = cos t, d x d t = 2 + sin t d y d r = cos t 2 + sin t stationary points where d y d x = 0. i.e. cos t = 0 t = π 2 , 3 π 2 . when t = π 2 ,x = 2 · π 2 cos π 2 = π ; y = 2 t = 3 π 2 = 2 · 3 π 2 cos 3 π 2 = 3 π ; y = 1 + sin 3 π 2 = 0 The stationary points are ( π, 2) and (3 0) (5) 2. ( a )f (x) = ( 2 + x)( 3 x) ( 2 3 + ( 3 + 3 = 2 x 9 x 2 (2) ( b (x) = 2 x 9 1 x 2 9 ! = 2 9 x 1 x 2 9 ! 1 = 2 9 x 1 + ( 1 ) x 2 9 ! + ( 1 )( 2 ) 2 x 2 9 ! 2 + ... = 2 9 x ± 1 + 1 9 x 2 + 1 81 x 4 + ² = 2 9 x + 2 81 x 3 + 2 729 x 5 + (4) 3. ( a ) d m d t = Ak e kt when t = 0 ,m = 4 : 4 = A e 0 A = 4 t = 0 , d m d t = 8 : 8 = 4 k · e 0 k = 2 . (5) ( b ) m = 4e 2 t 20 = 2 t ln 5 = 2 t t = 1 2 ln 5 ( = 0 . 8047 ...) (3) 4. 2 x + x d y d x + y + 2 y d y d x = 0 d y d x (x + 2 y) =− ( 2 x + d y d x ( 2 x + x + 2 y at (1 , 2) gradient 4 5 equation of tangent is y 2 4 5 (x 1 ) 5 y + 4 x = 14 (6) 5. ( a ) area = # 4 0 ( 2 x + 1 ) 1 2 = ± 2 3 × 1 2 ( 2 x + 1 ) 3 2 ² 4 0 = 1 3 · 9 3 2 1 3 = 8 2 3 units 2 (4) ( b ) volume = π # 4 0 ( 2 x + 1 ) d x = π h x 2 + x ³ 4 0 = 20 π units 3 (4)

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6. ( a ) At point of intersection 2 + λ =− 3 + 2 µ 3 + 4 λ = 4 + µ 1 + 2 λ 2 + µ
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Edexcel_WS_C4_PaperF - Worked Solutions Edexcel C4 Paper F...

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