maths sample1 - STUDENT SAMPLE (SOLUTIONS) Mathematics C...

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STUDENT SAMPLE (SOLUTIONS) Mathematics C Final Examination Paper Time Allowed: 3 hours Reading Time: 5 minutes
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UNSW Foundation Studies UNSW Global Pty Limited UNSW Sydney NSW 2052 Copyright © 2009 All rights reserved. Except under the conditions described in the Copyright Act 1968 of Australia and subsequent amendments, this publication may not be reproduced, in part or whole, without the permission of the copyright owner.
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MATHEMATICS C SOLUTIONS TO STUDENT SAMPLE FOR THE FINAL EXAMINATION 1. (i) 2 1 3 6 8 4 2 3 6 6 = + = + = x x x x (ii) 3 : 5 favour in odds 8 5 ) ( = E P (iii) 2 3 3 2 3 7 3 2 = = + = m m x y (iv) 9 2 Red) ( = P (v) Geometric progression: 3 2 and 12 = = r a Next term: 27 64 3 2 9 32 = × (vi) 5 15 5 3 5 12 45 5 12 = + = + 15 = a
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(vii) 4 5 1 2 32 2 5 1 = = + = = + x x x (viii) 56 ! 6 ! 6 7 8 ! 6 ! 8 = × × = (ix) 7 = y (x) () x x x x x e e e e e 7 5 2 5 2 = × = × (xi) 7 7 8 7 7 7 7 1 7 = + = + (xii) C x dx x dx x + = = ln 2 1 2 2 2. (i) x x f x x f 12 ) ( 6 1 ) ( 2 = = (ii) ) 2 ( log ) 2 ( log log 3 3 3 + = + + x x x x
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(iii) (iv) A (v) () 5 3 5 3 3 + + = x x e e dx d (vi) 29 8 9 12 = + + = B A n (vii) 3 + = x y y x 2 4 -2 -4 2 4 6 8 10 (viii) 2 1 0 1 2 > > x x (ix) 2 1 7 4 2 1 2 1 2 2 2 2 2 3 0 2 1 0 1 1 = + + + = + + + = = r r
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3. (i) (a) () 2 2 2 3 2 1 ) 1 ( ) 2 ( 1 = + = x x x x dx dy (b) ) 1 ( 2 1 ) 1 ln( 2 1 ) 1 ln( 2 1 + = + = + = x dx dy x x y (ii) better. is monthly compounded % 1 . 8 08407 . 0 1 12 081 . 0 1 monthly, 8.1% For 08402 . 0 1 4 0815 . 0 1 quarterly, 8.15% For 12 4 = + = = + = e e r r (iii) 3 2 : Solution < < x (iv) 6 7 5 11 4 6 3 = = + + + + x x The fifth score is 6 (v) (a) 0 since 1 1 2 2 2 2 > + = + = OP x OP x OP
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(b) 6 1 speed distance time time distance speed 2 + = = = x 4. (i) (a) 5 64 0 4 5 2 2 5 2 5 2 5 4 0 2 5 4 0 2 3 = = = x dx x (b) [] () 3 ln 2 1 1 ln 3 ln 2 1 1 2 ln 2 1 1 2 2 1 2 1 = = = x x dx (ii) (a) ( ) 4 , 0 and 0 , 2 2 , 0 and 4 , 0 0 4
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maths sample1 - STUDENT SAMPLE (SOLUTIONS) Mathematics C...

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