Edexcel_WS_C4_PaperB

Edexcel_WS_C4_PaperB - Worked Solutions Edexcel C4 Paper B...

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Worked Solutions Edexcel C4 Paper B 1. ( a ) xy 2 y + 5 x 10 = 12 x d y d x + y. 1 2 d y d x + 5 = 0 d y d x (x 2 ) =− (y + 5 ) d y d x = y + 5 2 x ( 2) ( b )a t ( 4 , 1 ) , d y d x = 1 + 5 2 4 3 gradient of normal = 1 3 equation of normal is y 1 = 1 3 (x 4 ) 3 y = x 1 (3) 2. ( a ) A = πr 2 d A d r = 2 (1) ( b )g i v e n d r d t = 1 4 . d A d t = d A d r × d r d t r = 3, d A d t = ( 2 π × 3 ) × ± 1 4 ² = 3 π 2 cm 2 s 1 (4) 3. ( a )1 + 1 2 ( 8 x) + 1 2 ± 1 2 ² 2 ( 8 2 + 1 2 ± 1 2 ²± 3 2 ² 3 . 2 ( 8 3 + ... = 1 + 4 x 8 x 2 + 32 x 3 ( 3) ( b ) 1 8 <x< 1 8 (1) ( c ) ( 1 + ax)( 1 + 4 x 8 x 2 + 32 x 3 ) = 1 + 4 x 8 x 2 + 32 x 3 + ax + 4 ax 2 8 ax 3 4 + a 8 + 4 a 12 = 3 a, a = 4 coef. of x 3 = 32 8 a = 32 32 = 0 (6) 4. ( a ) t = 10, m = 500 e 0 . 2 = 409 . 4 grams (1) ( b ) m = 300, 300 = 500 e 0 . 02 t e 0 . 02 t = 3 5 ln e 0 . 02 t = ln ± 3 5 ² 0 . 02 t = ln 3 5 t = 25 . 5 years (2) ( c ) d m d t = 500 × ( 0 . 02 ) e 0 . 02 t when t = 1, d m d t = 500 × ( 0 . 02 ) × e 0 . 02 9 . 8 g/year mass is decreasing at 9.8 g/year (3)
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5. ( a ) (i) # ( 1 + e x + e x + 1 ) d x = 2 x + e x e x + c (2) (ii) # ( 6 x 1 ) 1 2 d x = 2 × 1 6 ( 6 x 1 ) 1 2 + c = 1 3 6 x 1 + c (2) ( b ) # π 6 0 x cos
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Edexcel_WS_C4_PaperB - Worked Solutions Edexcel C4 Paper B...

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