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Edexcel_WS_C4_PaperE

# Edexcel_WS_C4_PaperE - Worked Solutions Edexcel C4 Paper E...

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Worked Solutions Edexcel C4 Paper E 1. ( a ) when y = 1 , 4 x 2 + 3 = 12 x 2 = 9 4 x = ± 3 2 (2) ( b ) differentiating, 8 x + 6 y d y d x = 0 d y d x = − 8 x 6 y = − 4 x 3 y at 3 2 , 1 gradient = − 4 × 3 2 3 = − 2 at 3 2 , 1 gradient = 2 (4) 2. ( 8 + x) 1 3 = 8 1 + x 8 1 3 = 2 1 + x 8 1 3 = 2 1 + 1 3 x 8 + 1 3 2 3 2 x 8 2 + . . . = 2 + x 12 1 288 x 2 + . . . (4) ( b ) for 8 + 3 m + m 2 1 3 , let 3 m + m 2 = x 8 + 3 m + m 2 1 3 = 2 + 3 m + m 2 12 1 288 3 m + m 2 2 = 2 + 1 4 m + 1 12 m 2 1 288 · 9 m 2 + . . . = 2 + 1 4 m + 1 12 m 2 1 32 m 2 = 2 + 1 4 m + 5 96 m 2 . (3) 3. ( a ) d y d x = 1 2 · 2 cos 2 θ sin θ = − cos 2 θ sin θ at θ = π 6 , gradient = − cos π 3 sin π 6 = − 1 2 1 2 = − 1 (2) ( b ) at θ = π 6 , x = cos π 6 = 3 2 and y = 1 2 sin π 3 = 1 4 3 . equation of tangent is y 3 4 = − 1 x 3 2 4 y 3 = − 4 x + 2 3 4 y + 4 y = 3 3 (3) ( c ) y 2 = 1 4 sin 2 2 θ = 1 4 ( 2 sin θ cos θ) 2 = 1 4 · 4 sin 2 θ cos 2 θ = ( 1 cos 2 θ) cos 2 θ. y 2 = ( 1 x 2 )(x 2 ) (3) 4. ( a ) ( 0 , 10 ) (1) ( b ) d y d x = − 10 ( k) e kx at x = 0, gradient = 10 k 10 k = 5 k = 1 2 (3) ( c ) area = 4 0 20 10 e 1 2 x d

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Edexcel_WS_C4_PaperE - Worked Solutions Edexcel C4 Paper E...

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