Edexcel_WS_C4_PaperA

Edexcel_WS_C4_PaperA - Worked Solutions Edexcel C4 Paper A...

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Worked Solutions Edexcel C4 Paper A 1. ( a ) 3 x (x 1 )(x + 2 ) = 1 x 1 + 2 x + 2 (using ‘cover up’ rule) (3) ( b ) # 3 2 1 x 1 + 2 x + 2 d x = " ln (x 1 ) + 2ln (x + 2 ) # 3 2 = ln 2 + 2ln5 ( ln 1 + 2ln4 ) = ln 2 + 5 4 = ln 2 + ln 25 16 = ln 25 8 (4) 2. ( a ) x = 1 t 3 and x = 2 1 t 3 = 2 t 3 =− 1 t 1 (1) ( b ) d y d t = 2 t , d x d t 3 t 2 d y d x = 2 t 3 t 2 = 2 3 t when t 1, gradient of tangent = 2 3 . equation of tangent is y 2 = 2 3 (x 2 ) 3 y = 2 x + 2 (4) 3. ( a ) d y d x = e x 3 at M e x = 3 x = ln 3 (2) ( b ) area = # ln 3 0 ( e x 3 x) d x = ± e x 3 2 x 2 ² ln3 0 = e ln 3 3 2 ( ln 3 ) 2 ( 1 0 ) = 3 3 2 ( ln 3 ) 2 1 = 2 3 2 ( ln 3 ) 2 (5) 4. ( a )8 x + 6 y d y d x 2 x d y d x + y. 2 = 0 d y d x ( 6 y 2 = 2 y 8 x d y d x = 2 y 8 x 6 y 2 x = y 4 x 3 y x (6) ( b )a t ( 2 , 4 ), d y d x = 4 8 12 2 2 5 equation of tangent at ( 2 , 4 ) is y 4 2 5 (x 2 ) 5 y 20 2 x + 4 5 y + 2 x = 24 (3)
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5. ( a ) ( 1 + kx) n = 1 + nkx + n(n 1 ) 2 · k 2 x 2 + n(n 1 )(n 2 ) 3 . 2 · k 3 x 3 +··· nk =− 6 …[A] n(n 1 ) 2 k 2 = 27 …[B] from [A] k = 6 n .
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Edexcel_WS_C4_PaperA - Worked Solutions Edexcel C4 Paper A...

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