2007 AJC Prelims Paper 2 solutions

2007 AJC Prelims Paper 2 solutions - 2007 H2 Mathematics...

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2007 H2 Mathematics Prelim Paper 2 solutions No. Solutions 1a () 32 2 13 3 1( l n ) 19 ( l n) dy dx x x xx ⎛⎞ == ⎜⎟ + + ⎝⎠ 1b 2 22 33 2 2, 2 1 (2 1) dx dy tt dt t dt dy t t t t dx t t =+ = =− = −− At intersection, 3 2 0 1 2 1 3 x p −=⇒= =+= = 2 23 2 (1 ) rr r r += + +− − ) ) ) ( )( ( [] = = + + + = + n r r n r r r r r r 1 1 1 1 2 2 2 3 2 = + + + = n r r r r r r r 1 1 2 1 2 2 1 = + + + = n r r r r r r r 1 1 1 2 1 2 2 2 1 where = + + = n r r f r f r f 1 ) 1 ( 2 ) ( ) 1 ( r r r f 2 ) ( = (2) (1) 2 (0) (3) (2) 2 (1) (4) (3) 2 (2) .............................. f ff f f ++ ++− + ................................................. ) (3 ) 2 (4 ) ) 2 ) ( 1 ) 2 ( 2 ) ) ( ) 2 ) fn fn fn + +− + + + ) ) ) 2 ( ) ( 1 ) 2 ( 0 f nf n f f + 1 12 22 2 nn + + 22 22 2 n + ( ) 24 2 2 n n 2 1 21 2 n n + Page 1
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Page 2 No. Solutions 1 2 2 ) 3 2 ( = + r n n r r = () = + n n r r r 2 2 3 2 2 1 + + = ∑∑ = = n r n r r r r r 2 1 1 1 2 3 2 2 3 2 2 1 ( ) [] 2 2 1 1 2 2 2 1 4 2 1 1 2 + + + = + n n n n ()() 21 11 41 2 2 24 1 22 1 nn −+ =+ −− + 3a AOB = AOD = 90 ° O B = 2 O A , O D = O A 3a Minimum |z - w| = EC = 3 2 a 3b 1 arg arg z z ⎛⎞ =− ⎜⎟ ⎝⎠ 1 sin a a B E D O A C α y 2 zi aa −= ww i a = + x 6 π αα == = arg arg arg 26 az a ππ + ≤≤+ + 2 arg arg arg 33 a + ≤≤+⇒ arg arg arg z −≤ 4a 45 xy y −−− = 2 2 2 2 2 450 5 0 0 xyy ⎡⎤ + = ⎣⎦ −+− + = = = 0 2 A translation of – 2 units in the y – direction. 4bi)
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Page 3 No. Solutions 4bii) 5i 1 Π : 5 41 3 ⎛⎞ ⎜⎟ •− = ⎝⎠ r y ( ) 2 y fx = 5 Distance of A from 1 Π 65 24 63 15 50 50 •− =− 51 1 50 50 50 =−= 15 4 50 50 > A and O are on the same side of 1 Π 5ii Vector parallel to = 2 Π 56 220 86 1 2 −= −− 6 1 Normal vector of is 2 Π 11 4 2 02 1 2 2 21 0 2 ⎛⎞⎛ ⎜⎟⎜ ×= = ⎝⎠⎝ Angle between and 1 Π 2 Π x () 2, 2 5 2 y = 2 2 y 2, 2 x y 3 2 ( ) ' y =
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Page 4 No.
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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 AJC Prelims Paper 2 solutions - 2007 H2 Mathematics...

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