{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Edexcel_WS_C4_PaperI

# Edexcel_WS_C4_PaperI - Worked Solutions Edexcel C4 Paper I...

This preview shows pages 1–2. Sign up to view the full content.

Worked Solutions Edexcel C4 Paper I 1. ( a ) d y d θ = 1 ( 1 + cos θ) ( sin θ), d x d θ = 2 cos 2 θ d y d x = sin θ ( 1 + cos θ) 2 cos 2 θ where θ = π 6 , gradient = 1 2 1 + 3 2 · 2 · 1 2 = − 1 2 1 + 3 2 = − 1 2 + 3 = − ( 2 3 ) ( 2 + 3 )( 2 3 ) = 3 2 (5) ( b ) gradient = 0 where sin θ = 0 i.e. where θ = 0 at θ = 0, x = 0, y = ln 2 gradient is zero at (0 , ln 2) (3) 2. A d A = e 1 10 t d t A 2 2 = 10 e 1 10 t + c A = 20, t = 0: 400 2 = 10 + c , c = 190 A 2 2 = 10 e 1 10 t + 190 when t = 20 , A 2 2 = 10 e 2 + 190 A = 23 (2 sig. fig.) (7) 3. ( a ) 1 y d y d x + 3 x 2 2 = 0 d y d x = y( 2 3 x 2 ) (3) ( b ) (i) e x d y d x + y e x + 2 y d y d x = 0 d y d x ( e x + 2 y ) = − y e x d y d x = y e x e x + 2 y at (0 , 3) d y d x = 3 1 + 6 = − 3 7 (3) (ii) equation of tangent at (0 , 3) is y 3 = − 3 7 x 3 x + 7 y = 21 (2) 4. ( a ) (i) cos 2 x = 1 2 sin 2 x (1) hence sin 2 x = 1 2 ( 1 cos 2 x) (ii) sin 2 x = 1 2 ( 1 cos 2 x) d x = 1 2 x 1 4 sin 2 x + c (2) ( b ) Integrating by parts, π 8 0 x d d x 1 2 cos 2 x d x = x 2 cos 2 x π 8 0 + π 8 0 1 2 cos 2 x d x = x 2 cos 2 x + 1 4 sin 2 x π 8 0 = − π 16 · 1 2 + 1 4 · 1 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}