2007 IJC Prelims Paper 1 Solution

2007 IJC Prelims Paper 1 Solution - Prelim 2 H2 P1 Mark...

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Prelim 2 H2 P1 Mark scheme 1 Obtaining 7 abc ++= 9 3 11 a bc - += 25 5 99 + += Augmented matrix 1 1 17 9 3 1 11 25 5 1 99   -  Alt: 1 7 11 99 a bA c - = where 111 9 31 2 5 51 A =- 2 3 y xx = +- 2 0.4 (10 ) dy yy dx 1 0.4 ( 1 0) dy dx = - ∫∫ or equivalent Mthd 1: 1 10 0.4 10 (10 ) dy dx -+ = - or using partial fraction. Obtain 1 11 0.4 10 ) dy dx += - Mthd 2: 2 1 0.4 25 ( 5) dy dx y = -- Obtaining 1 ln 10 10 y y - = 0.4 x + C or equivalent 4 10 xC y e y + = - , 44 10 x Cx y e or Ae y + - When x = - 1, y = 5 4 Ae = , or C = 4, 10 x y e y + = - ( 1 x y ey + 10 1 x x e y e + + = + 3(i) 1 3 3 ( 9e) x y 3 2 23 3 3 3 9e d 3 3e d d e9 d x x x y y y x y x = - or 3 2 / 33 1 ( 9 ) ( 3) 3 dy ee dx - = d 90 d y x
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3(ii) 2 2 22 2 d dd 2 ( ) 30 d y yy yyy xx x + -= When x = 0, y = 2. d1 d4 y x =- 2 2 d 13 d 16 y x 2 1 13 2 ( ) ( ) ... 4 16 2! x yx = +- +- + 2 1 13 2 4 32 y = -- +… 3(iii) Equation of tangent is 1 2 4 4 i2 z - += 4i w + = PQ = PC + CQ = 2 2 2 2( 2 1) + + =+ Recognising 45 ° rt- ed and attempt to find opp side or adj side. Obtaining x or y =-+ 2 2 i( 2 2) w = + + -+ 5(i) 1 47 1 , 3 ,2 1 21 OA OB OC -   = = -  uuur Find any 2 of the 3 vectors: 31 18 2 , 5 ,3 132 AB BC AC = = - Since AB u u ur not parallel to BC (or equivalent), A , B & C not collinear. 5(ii) 1 38 2 5 23 1 3 12 or       ××    or equivalent, Vector to plane ABC = 1 2 7 - (or 1 2 7 - - ) 5(iii) 2 4 7 OP = and 4 4 6 OQ = 2 0 1 PQ = - 2 - 2 - 4 Q P C
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Mthd 1: length of proj n = 2 12 0 2 13 1 74 1 4 49 54 P Qn n       × -- ×    == ++ u u ur % % 4 169 16 7 14 22 54 or
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2007 IJC Prelims Paper 1 Solution - Prelim 2 H2 P1 Mark...

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