2007 SAJC Prelim Paper 2 solutions

2007 SAJC Prelim Paper 2 solutions - 2007 H2 Maths Prelim...

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1 2007 H2 Maths Prelim Exam(Paper 2) Solutions Section A 1 4 8 2 4 2 4 i e i 2 4 2 4 3 i z 4 2 3 8 k i e z , k = 0, 1, 2(or -1). 4 2 3 2 k i e z 12 ) 1 8 ( 2 k i e z , k = 0, 1, 2(or -1) 2 i e z , 7 2 i e and 4 5 2 i e (or 4 3 2 i e ) 666 0 1 2 w z z z = 75 6 6 6 12 12 4 (2 ) (2 ) (2 ) i i i e e e  = 2 15 2 7 2 6 2 i i i e e e = 6 222 2 iii e e e     =   ) ( ) ( ) ( 2 6 i i i = i 192 (Shown) Hence Im(w) = -192 2(i) (ii) 0 05 400 dx .x dt  , k = 0.05, c = - 400 1 0 05 400 1 ln 0 05 400 0 05 dx dt . x t C .    ln 0 05 400 = 0.05 t + C 1 0 05 0 05 0 05 0 05 400 0 05 400 8000 .t . x Ae . x A e x B e   When t = 0 , x = 5000 5000 = B + 8000 B = - 3000 Hence 0 05 3000 8000 xe When t = 15, 0 75 3000 8000 6351 0 8000 1649 . x e .  
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2 (iii) When x = 0 , e 0.05 t = 8 0 05 0 9808 3 . t .  t = 19.62 On the 19 th year, the granddaughter will receive her last $400. It will be in year ( 2006+19-1) = 2024 Possible answers for last part: Most rate of returns of fund fluctuates from year to year, so probably not a good model. The returns are normally compounded over discrete time interval (usually years) rather than continuously. So probably not a good model. When x = 0 , the model will no longer valid. So may not be a good model. 3(i) (ii) (iii) (iv) sec sec tan xa dx a d  2 tan sec ya dy a d 2 sec sec tan cos dy dy d dx d dx a a ec dt dx dx dy dt dy ) 2 )( (cos ec At 4 6 cos 2 , 6 dt dy Equation of tangent at point R :   tan cos sec (tan cos sec ) cos y a ec x a y a ec x ec Equation of normal at point R :   1 tan sec cos tan (sin ) cos 2 tan sin y a x a ec a y a x y a x        At point T, 0 y 2 0 (tan cos sec ) cos (tan cos sec ) cos sec (1 sin ) cos a ec x ec a ec x ec a a At point N, 0 y
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3 0 2 tan sin 2 tan sin 2 sec ax a x a   2 cos 2 sec 2 ON OT a a a 4(i) (ii) Given 1 3 0 0 1 5 2 1 7 OA , OB ,OC    , so 21 15 AB , AC          
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This note was uploaded on 08/29/2009 for the course MA 9740 taught by Professor Moe during the Summer '07 term at Singapore Management.

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2007 SAJC Prelim Paper 2 solutions - 2007 H2 Maths Prelim...

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