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Edexcel_WS_C4_PaperJ

# Edexcel_WS_C4_PaperJ - Worked Solutions Edexcel C4 Paper J...

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Worked Solutions Edexcel C4 Paper J 1. ( a ) We are given that d A d t = 40 cm 2 s 1 after 10 seconds area of circle = 400 cm 2 so πr 2 = 400 r = 400 π cm (2) ( b ) A = πr 2 d A d r = 2 πr d A d t = d A d r × d r d t when r = 400 π we have, 40 = 2 π × 20 π × d r d t d r d t = 1 π = 0 . 56 cm s 1 (2 sig. fig.) (4) 2. ( a ) A = y d x = t = 9 t = 4 y d x d t · d t x = 2 t 1 2 d x d t = t 1 2 = 9 4 (t 2 2 )t 1 2 d t y d x d t = 9 4 (t 3 2 2 t 1 2 ) d t (4) ( b ) A = 2 5 t 5 2 4 t 1 2 9 4 = 2 5 × 243 4 × 3 2 5 × 32 8 = 80 . 4 (3) 3. ( a ) 2 2 x 1 + 3 x + 2 (using ‘cover up’ rule) (3) ( b ) 1 y d y = 2 2 x 1 + 3 x + 2 d x ln y = ln ( 2 x 1 ) + 3 ln (x + 2 ) + c y = 1 , x = 1: ln 1 = ln 1 + 3 ln 3 + c c = − 3 ln 3 ln y = ln ( 2 x 1 )(x + 2 ) 3 27 y = ( 2 x 1 )(x + 2 ) 3 27 4. ( a ) f (x) = 1 + 1 2 x + 1 2 1 2 2 x 2 1 1 2 ( x) + 1 2 3 2 2 ( x) 2 = 1 + 1 2 x 1 8 x 2 1 + 1 2 x + 3 8 x 2 = 1 + 1 2 x + 3 8 x 2 + 1 2 x + 1 4 x 2 1 8 x 2 = 1 + x + 1 2 x 2 (4) ( b ) valid for | x | < 1 (1) ( c ) put x = 1 10 , f 1 10 = 1 + 1 10 1

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Edexcel_WS_C4_PaperJ - Worked Solutions Edexcel C4 Paper J...

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