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Edexcel_WS_C4_PaperD

# Edexcel_WS_C4_PaperD - Worked Solutions Edexcel C4 Paper D...

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Worked Solutions Edexcel C4 Paper D 1. ( a ) y 2 x 2 (2) ( b ) volume = π # 2 0 y 2 d x = π # 2 0 ( 9 x 2 ) d x = π ± 9 x 1 3 x 3 ² 2 0 = π ³ 18 8 3 0 ´ = 46 3 π cubic units. (4) 2. ( a ) cos 3 x = cos x · cos 2 x = cos x( 1 sin 2 x) = cos x cos x sin 2 x (1) ( b ) d d x ( sin 3 = 3 ( sin 2 · cos x (1) ( c ) # µ cos x cos x sin 2 x d x = sin x 1 3 sin 3 x + c (3) 3. Given d S d t = 640 cm 2 s 1 . To fnd d r d t . S = 4 πr 2 d S d r = 8 d S d t = d S d r × d r d t when r = 5 , 640 = 8 π × 5 × d r d t d r d t = 640 40 π = 16 π cm s 1 (4) 4. ( a )2 x + 2 y d y d x 2 + 4 d y d x = 0 d y d x ( 2 y + 4 ) = 2 2 x d y d x = 2 2 x 2 y + 4 = 1 x y + 2 (2) ( b )a t( 4 , 2) gradient oF tangent = 1 4 2 + 2 =− 3 4 equation oF tangent is y 2 3 4 (x 4 ) 4 y + 3 x = 20 (4)

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5. ( a ) x = ln 11 ln 5 ± or log 11 log 5 ² = 1 . 49 (2) ( b ) y = 3 x ln y = ln 3 x ln y = x ln 3 1 y d y d x = ln 3 d y d x = y ln 3 = 3 x ln 3 (3) ( c )e 0 . 4 x = 5 ln e 0 . 4 x = ln 5 0 . 4 x = ln 5 x =− ln 5 0 . 4 4 . 02 (2) 6. ( a ) y = x + 9 x 1 d y d x = 1 9 x 2 at min. point 9 x 2 = 1 ,x = 3 (x > 0 ) when x = 3, y = 3 + 9 3 = 6 so y 6 . (4) ( b ) area = # 9 3 ± x + 9 x ² d x = "
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Edexcel_WS_C4_PaperD - Worked Solutions Edexcel C4 Paper D...

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