{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Maths Revision Book

# Maths Revision Book - Mathematics C Semester 2 Revision...

This preview shows pages 1–8. Sign up to view the full content.

Mathematics C Semester 2 Revision Book SOLUTIONS 2008

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
UNSW Foundation Year UNSW Global Pty Limited UNSW Sydney NSW 2052 Copyright © 2008 UNSW Global Pty Limited, trading as UNSW Foundation Year 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.
1 MATHEMATICS C SOLUTIONS TO REVISION EXERCISES #1 9 and 16 3 9 16 3 3 9 16 6 3 4 3 5 10 ) 3 2 )( 3 2 5 ( . 1 = = = = + = y x y x ********************************************************************************* 3 1 3 10 3 or 3 10 15 26 12 36 ) 2 )( 13 ( ) 6 )( 6 ( 6 13 2 + 6 G.P. a form 13 , 6 , + 2 Then . be number Let the . 2 2 2 = = + + = + + + + = + + + + = + + + x x x x x x x x x x x x x x x x x x ********************************************************************************* 3. f(x) x 2 12 (a) f(x) x (b) (c) y 33 x ********************************************************************************* units. 5 16 9 ) 2 6 ( ) 1 2 ( ) ( ) ( ) a ( . 4 2 2 2 1 2 2 1 2 = + = + + = + = y y x x d AB 0 10 3 4 4 4 6 3 3 4 ) 1 ( 3 4 2 1 2 2 6 ) ( : AB line of Equation ) b ( 1 1 1 2 1 2 = + + = = + = + = = = y x x y x y x x m y y x x y y m AB 3 4 = AB to parallel line of Gradient ) c ( = AB m 0 13 3 4 16 4 3 3 ) 4 ( 1 ) ( is C(4,1) through line of Equation 3 4 1 1 = = = = y x x y x y x x m y y *********************************************************************************

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 5. ) 3 ( ) 3 )( 3 ( lim 3 9 lim ) a ( 3 2 3 + = x x x x x x x 6 3 3 ) 3 ( lim 3 = + = + = x x 12 4 ) 2 ( 2 ) 2 ( ) 4 2 ( lim ) 2 ( ) 4 2 )( 2 ( lim 2 8 lim ) b ( 2 2 2 2 2 2 2 = + = + = + + + = + + x x x x x x x x x x x ********************************************************************************* 6. nU () = 99 nA = =− = 33 99 33 66 ********************************************************************************* 2 1 3 4 5 2 3 4 4 2 4 4 4 2 3 3 1 3 3 1 3 3 1 3 ) c ( 2 3 4 1 2 7 1 ) b ( ) a ( . 7 2 5 2 7 = + = + = + + = = = = = = = x dx dy x x x x y x x x dx dy x x x x x x x x x dx dy x x x y x x x y *********************************************************************************
3 ). 2 , 3 ( is point The 2 1 ) 3 ( 2 ) 3 ( find to curve the of equation the into 3 substitute parabola, on the lies point the Since 3 6 2 4 2 2 4 4 is tangent the of gradient the line, the to parallel is tangent the As 4 gradient 2 2 0 7 4 : Line 1 2 : Curve (c) 4 gradients, equal have lines Parallel 4 1 4 gradient 0 7 4 : Line (b) 2 2 (a) . 8 2 2 = + = = = = = + = = + = = + + = = = = = + + = y y y x x x x dx dy m x dx dy y x x x y m m y x x dx dy l ********************************************************************************* 2 2 3 1 2 3 1 3 3 ) 3 ( ) 3 ( 9 27 . 9 + + + = = = x x x x x x Since the bases are equal, equate indices: 2 2 2 3 = + = x x x ********************************************************************************* . 4 3 reject 3 or 4 0 ) 3 )( 4 ( 0 12 1 3 4 1 3 log 4 log ) 1 ( log 3 log 4 log log . 10 2 = = = = = + = = = = x x x x x x x x x x x x x x b b b b b b *********************************************************************************

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 SOLUTIONS TO REVISION EXERCISES #2. 2 5 3 3 or 2 45 3 2 36 9 3 0 9 3 27 9 3 0 9 4 18 9 ) 3 2 )( 3 2 ( ) 3 )( 6 ( . 1 2 2 2 2 ± ± = + ± = = = = + + + = + + x x x x x x x x x x x x ********************************************************************************* below graph see 1 3 0 ) 1 )( 3 ( 0 3 2 3 2 ) c ( 6 4 4 6 6 2 4 (b) 4 20 5 3 24 4 2 3 24 ) 2 ( 2 6] [ 2 4 3 2 ) a ( . 2 2 2 + + + < < < < < < + + × + x x x x x x x x x x x x x x x x x x x f(x) x -3 1 ********************************************************************************* n n n n a n S d n a T n d a n n 32 4 128 160. 4 4 4 68 ) 192 68 ( 2 32 4 ) 1 ( 68 192 ) ( 2 ) 1 ( : find To . 192 , 4 , 68 with A.P. an is This 192. + . . . + 72 + 68 find To . 3 = = = + = + = + = + = + = = = = = A A A *********************************************************************************
5 () . 4 and 0 then , 2 4 2 If . 2 4 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 . 4 2 2 = = = + = + + + = + + + = + b a b a ********************************************************************************* 58 1 0 8 0 81 0 8 45 4 9 22 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 42

Maths Revision Book - Mathematics C Semester 2 Revision...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online