742 ANSWERS
3ax¼ 21 : 8 oor 158 : 2 o b x¼ 132 : 3 oor 227 : 7 o
c x¼ 12 : 6 o, 77 : 4 o, 192 : 6 o, 257 : 4 o dx¼ 76 : 0 o, 256 o
ex¼ 23 : 5 o, 96 : 5 o, 143 : 5 o, 216 : 5 o, 263 : 5 o, 336 : 5 o
f x¼ 139 : 6 o, 220 : 4 o
4aa=2,b=1 b a=¡ 1 ,b=1 c a=1,b=2
da=1,b=^13 e a=^12 ,b=1 f a=^32 ,b=2
5aa=¡ 1 ,b=1 b a=1: 6 ,b=1 c a=1,b=^12
da=2,b=2 e a=2: 5 ,b=3 f a=¡ 2 ,b=3
REVIEW SET 29A
1a(cos 296o,sin 296o) b¼(0: 438 ,¡ 0 :899)
2ap 3
2 b^1 c ¡
p^1
3 3 ¼^3 :^88 km(^24) x=14
5aa bb c b d¡a 6 ¼ 15 : 8 km
7ax¼ 11 : 1 by¼ 74 : 6 or 105 : 4 c μ¼ 45 : 8
8 AbCB¼ 68 : 3 oor 111 : 7 o
9aBD¼ 278 m b 46 700m^2
10
11 a=2,b=1; y= 2 sinx
REVIEW SET 29B
1aQ(cos 152o,sin 152o) b¼Q(¡ 0 : 8829 , 0 :4695)
2 μ¼ 23 : 4
3aQ(¡a,¡b) b Q(¡cosμ,¡sinμ)
c The angle measured from the positivex-axis is 180 o+μ
) Qis(cos(180o+μ),sin(180o+μ))
) cos(180o+μ)=¡cosμ
4aÁ¼ 115 b x¼ 50 : 8 or 129
c x¼ 89 : 5
5aAB¼ 275 m b 2 : 86 ha 6 x¼ 2 : 83 or 15 : 6
7a¼ 76 : 1 km b 053 : 0 o 8 x¼ 5 : 25
9
10 a=2, b=^1211 x¼ 76 o, 644 o
CHALLENGE
1 The rocket must rise the same height as the earth’s radius.
2atan 75o= tan 60o+2
bi iiBD=2units
BC=
p
3 units
AB=2units
iii tan 75o=2+
p 3
1 =2+
p
3 , tan 60o=
p 3
1 =
p
3
3aCbON= 180o¡ 2 μ d 2 sinμcosμ=
h
r
e sin(2μ) = 2 sinμcosμ
EXERCISE 30A.1
1a
b W/h, as the graph is a straight line passing through the
origin.
cik=12: 5 iiW=12: 5 h
2ayis doubled b yis trebled c xis doubled
d xis halved e yis increased by20%
f xis decreased by30% gcannot be determined
h cannot be determined
3aNo, does not pass through the origin.
b Yes, linear and passes through the origin. c No, not linear.
d No, does not pass through the origin.
4aThe law is of the form C=kr, ka constant.
b k=2¼ ciCis doubled ii ris increased by50%
5ay¼ 229 bx¼ 22 : 6
6aR=0: 006 l b R=0: 3 ohms c l= 500cm
7aA=4: 5 n, 9 litres 8a 78 : 4 m/s b ¼ 10 : 2 sec
EXERCISE 30A.2
1ay
x^2
=4; y=4x^2 ; a= 196
b y
x^2
=3; y=3x^2 ; a=6
2a
y
x^3 =5; y=5x
(^3) ; b= 320
b y
x^3
=^12 ; y=0: 5 x^3 ; b=6
3aA/t^2 ,k=4: 9 b K/x^3 ,k=2
c T/
p
l,k=^15 d V/t^4 ,k= 500
e P/p^3 x,k=4 f V/r^3 ,k=^43 ¼
4aP=48 ba=15
5aM=81 bx=^3
p
40 ¼ 3 : 42
6aD=24 b t= 625 7 $312: 50 889 mm
9 10 : 1 seconds 10 12 : 2 km 11 36%reduction
12 aris multiplied by^3
p
2 (a26%increase)
b volume is decreased by 27 :1%
13 aV/h b V/r^2 c volume increases 22 :4%
EXERCISE 30B
1axy=12 c xy=84
b not inversely proportional
1
0.5
-0.5
-1
x
180°180° 360°360° 540°540° 720°720°
yx¡=¡cos¡
O
yx¡=¡-cos() 2
1
0.5
-0.5
-1
x
180°180° 360°360° 540°540° 720°720°
yx¡=¡cos¡
O
yx¡=¡-cos() 2
yx¡=¡\Qw_\cos( ) 2
25
50
12345
W(£)
h(hours)
O
y
x
84
17126
(^14712)
O
y
x
12
6
A 2 B ~` 3 C O 2468
15° D
15° 30°
1 unit
60°
2
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\742IB_IGC1_an.CDR Friday, 21 November 2008 9:21:14 AM PETER