Cambridge International Mathematics

ANSWERS 745

REVIEW SET 31A

1a bA reflection in the

line y=x

cDomain is

fxjx> 0 , x 2 Rg

Range is

fyjy 2 Rg

2alogaax=x bx= logby

3a 4 b ¡ 1 c^52 d^32

4alog 5 y=x blog 7 y=¡x

5a 3 y=x bn=4^3 T

6ax=5y bx=

10 w

3

cx=^12 log 7 (3q)

7af¡^1 (x) = log 5

³x

4

́

bf¡^1 (x)=3

x

2

8ax¼ 3 : 3219 bx¼¡ 4 : 9829 c x¼ 105 : 03

9a¼ 492 wasps b¼ 52 : 8 days

10 a log 6 blog 36 c log 21125

11 a logy= 3 loga¡2 logb

blogM= log 3 +^12 loga¡^12 logb

12 aT=

1000

10 x

bN=

c^2

d

13 aa+b bb¡a c 1+b

14 ay=u^4 by=^1

v^2

c y=

p

uv

15 ¼ 2 : 4650 16 a x¼ 0 :076 63 b x¼ 1 : 533

REVIEW SET 31B

1a bFor y=3x:

Domain isfxjx 2 Rg

Range is fyjy> 0 ,y 2 Rg

For y= log 3 x:

Domain isfxjx> 0 ,x 2 Rg

Range is fyjy 2 Rg

2a^12 b ¡^32 c 6 d^32

3ax= log 4 y bn=¡logay

4ad=2y bk=a^2 M

5ax=3y bx=b

T

3

cx=¡1 + log 2

¡ 3 t

5

¢

6af¡^1 (x) = log 6 x bf¡^1 (x)=5^2 x

7ax¼ 7 : 288 bx¼ 5 : 671 c x¼ 1 : 732

8a$400 b¼$15 200 c Year 2024

9alog 215 blog 34 clog(2:5) dlog 2 (^252 )

10 a logD=2¡2 logn b2 logG= 3 logc+ logd

11 a M=10^2 x+1 orM=10£ 100 x bG=

p

d

10

12 ab¡a ba+b ca¡ 1

13 ay=c^2 by=

p (^3) c
d^2
14 ¼ 2 : 723
15 ax¼¡ 3 : 288 or 0 : 8342 bx¼ 0 : 9149 or 4 : 284
CHALLENGE
1 The last step fdividing by log(^12 )which is negative reverses
the inequality signg.
2ax¼ 1 : 58 or 2 : 32 b x=4asxmust be> 0
3ax¼ 1 :584 962 501 b ) 2 p=3q
LHS is even and RHS is odd
...... is irrational
EXERCISE 32A
1ax>¡ 2 b x>¡ 1 cx> 112 d x>^13
ex> 2 f x>^14
2ax 6 ¡ 2 orx> 3 b¡ 46 x 63
c¡ 56 x 62 d¡ 1 : 45 <x< 3 : 45
ex>¡ 2 f x<¡ 1 : 25 or 0 : 445 <x< 1 : 80
3ax 6 ¡ 1 : 30 orx> 2 : 30 bx> 0 : 631
cx 6 ¡ 1 : 93 orx> 1 : 26
dx<¡ 0 : 767 or 2 <x< 4
e¡ 2 : 13 <x< 0 fx< 0 orx> 0 : 682
413 : 7 o<x< 76 : 3 oor 193 : 7 o<x< 256 : 3 o
5 ¡^23 <x< (^113)
EXERCISE 32B
1ax 60 andy> 0 by 64 cy>¡ 1
dx 62 e x>¡ 1 f 06 y 63
gy<¡ 1 ory> 1 h¡ 26 x 62 and¡ 2 <y< 3
i y 6 x, 06 x 64 , 06 y 63
2a b
cd
ef
gh
i
x
1
1
y yx¡=¡
yx¡=¡logx
y¡=¡2x
O
x
1
1
yyx¡=¡
yx¡=¡logc
y¡=¡3x
O
y
x
R
O 4
y
x
R
-1 O
y
x
R
O
y¡=¡2
y
x
R
O
y¡=¡-1
y
x
R
O
x¡=¡0 x¡=¡3
y
R O x
y¡=¡2
y¡=¡-1
y
x
R
O
x¡=¡-2 x¡=¡3
y
x
R
O
y¡=¡4
y¡=¡-1
y
x
R
O
x¡=¡0 x¡=¡3
y¡=¡1
y¡=¡4
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\745IB_IGC1_an.CDR Thursday, 20 November 2008 2:15:46 PM PETER