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2007 PJC Prelim Paper 1_solution

2007 PJC Prelim Paper 1_solution - 2007 J2 Prelim Paper 1...

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h r a 2007 J2 Prelim Paper 1- solution 1. i 1 i w z    ------- (1) 2 (1 i) 6 2i z w ----- (2) From (1), i 1 i z w     ------- (3) Sub (3) into (2), 2i 2 2i i 6 2i w w w 3i 8 2i w w 8 2 1 3 i w i   2 2i w    ; 1 i z 2. Using sine rule, sin sin 6 a b 2 sin a b 3 2 3! b 2 2 1 6 b (shown) Substitute a = 1 cm and b = 3 cm, 3 6 1 0 2.53, 0.167 or 2.36 rad   Since cannot be negative, reject = -2.53. It is assumed that is small, reject = 2.36 Only 1 possible answer for , i.e . =0.167. 3. 2 1 1 2 2 1 n r r n r r 1 2 2 2 1 2 1 1 3 2 2 2 3 1 1 4 2 2 3 4 n n n 1 1 2 2 2 3 2 1 1 1 2 2 2 1 1 1 2 2 1 n n n n n n n n n n n n 1 1 4 2 2 1 2 1 2 1 2 2( 1) 2 ( 1)( 6) 2 n n n n n n n n n n Sum equal to zero ( 1)( 6) 0 2 n n 1 or 6 n n Since 2 6 n n 4. 1 1 2 2 1 1 1 2 1 2 x x x x 1 2 2 1 2 2 1 1 2 2 1 1 . . . ,| | 1 2 2! 1 3 1 2 2 1 2 1 2 . . . ,| | 2! 2 x x x x x x x x 2 2 1 3 1 1 1 2 2 8 2 x x x x x x  2 3 15 1 1 | | 2 8 2 x x x 9 1 3 1 15 1 8 let ; 1 6 8 2 8 8 64 8 3 3 15 1 2 16 512 6 623 2 512 x Therefore, 623 6 256 (one possible answer) 9 1
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