714 ANSWERS
EXERCISE 21A
1ax=§ 10 b x=§ 5 c x=§ 2
dx=§ 3 e no solution f x=0
gx=§ 3 h no solution i x=§p
2
2ax=4or¡ 2 b x=0or¡ 8 c no solution
dx=4§
p
5 e no solution f x=¡ 2
gx=2^12 h x=0or¡^43 i x=
§
p
6 ¡ 3
2
EXERCISE 21B.1
1ax=0 ba=0 c y=0 d a=0orb=0
ex=0ory=0 fa=0orb=0orc=0 ga=0
hp=0orq=0orr=0ors=0 i a=0orb=0
2ax=0or 5 b x=0or¡ 3 c x=¡ 1 or 3
dx=0or 7 e x=0or¡ 1 f x=¡ 6 or^32
gx=§^12 h x=¡ 2 or 7 i x=5or¡^23
j x=0 k x=5 l x=^13
EXERCISE 21B.2
1ax=0or 7 b x=0or 5 c x=0or 8
dx=0or 4 e x=0or¡ 2 f x=0or¡^52
gx=0or^34 h x=0or^54 i x=0or 3
2ax=1or¡ 1 b x=3or¡ 3 c x=5
dx=¡ 2 e x=¡ 1 or¡ 2 f x=1or 2
gx=¡ 2 or¡ 3 h x=2or 3 i x=¡ 1 or¡ 6
j x=¡ 2 or¡ 7 k x=¡ 5 or¡ 6 l x=¡ 5 or 3
m x=¡ 6 or 2 n x=3or 8 ox=7
3ax=¡ 4 or¡ 5 b x=¡ 4 or¡ 7 c x=¡ 4 or 2
dx=¡ 4 or 3 e x=3or 2 f x=2
gx=3or¡ 2 h x=12or¡ 5 i x=10or¡ 7
j x=¡ 5 or 2 k x=3or 4 l x=12or¡ 3
4ax=^12 or 2 b x=¡ 3 or^13 c x=¡ 4 or¡^53
dx=^12 or¡ 3 e x=^12 or 5 f x=¡ 1 or¡^52
gx=¡^13 or¡ 4 h x=¡^25 or 3 i x=^12 or¡ 9
j x=1or¡^52 k x=^43 or¡ 2 l x=^32 or¡ 6
5ax=^13 or¡^52 b x=^23 or¡^12 c x=¡^12 or¡^13
dx=¡ 211 or 3 e x=^25 or¡^12 f x=¡ 103 or 1
6ax=¡ 4 or¡ 3 b x=¡ 3 or 1 c x=§ 3
dx=¡ 1 or^23 e x=¡^12 f x=^52 or 4
7ax=§p
6 b x=§p
8 c x=§p
10
dx=4or¡ 3 e x=¡ 1 or¡ 5 f x=2or¡ 1
gx=^12 or¡ 1 h x=1or¡^13 i x=¡ 1 or 4
8ax=¡^12 or 2 b x=1or¡ 3 c x=¡^13 or¡ 1dx=1or (^117)
9ax=§ 1 or§ 2 bx=§
p
3 or§ 2 c x=§
p
5
EXERCISE 21C.1
1ax=¡ 2 §
p
7 b x=¡ 3 § 2
p
2 c x=¡ 2 §
p
11
dx=¡ 1 §
p
3 e x=3§
p
7 f x=2§
p
5
gx=
3 §
p
5
2
h x=¡ 4 §
p
11 i x=
1 §
p
3
2
j x=^1 §
p
2
3
k x=^2 §
p
3
5
l x=¡^3 §
p
7
2
2ax¼ 5 : 24 or 0 : 76 b x¼ 0 : 22 or¡ 2 : 22
c x¼ 0 : 72 or¡ 1 : 12 d x¼¡ 1 : 22 or 0 : 55
e x¼ 2 : 62 or 0 : 38 f x¼ 2 : 30 or¡ 1 : 30
3ax=¡^1 §
p
29
2
b x=¡^1 §
p
5
2
c x=1§
p
3
d x=1§ 2
p
2 e x=
7 §
p
217
6
f x=
3 §
p
13
2
EXERCISE 21C.2
1ax=^3 §
p
¡ 39
2
) no real solutions exist
b x=¡ 1 §
p
¡ 3 ) no real solutions exist
c x=
1 §
p
¡ 7
4
) no real solutions exist
2ax=§ 5 bno real solutions exist c x=§
p
7
d no real solutions exist ex=§^32
f no real solutions exist gno real solutions exist
h x=5or¡ 1 i no real solutions exist
j no real solutions exist kx=
3 §
p
19
2
l x=
¡ 1 §
p
17
4
EXERCISE 21D
1a,c,dandeare quadratic functions.
2ay=0 by=5 c y=¡ 15 dy=12
3aNo bYe s c Ye s d No eNo fNo
4ax=¡ 3 b x=¡ 3 or¡ 2 c x=1or 4
d no solution
5ax=0or 1 b x=3or¡ 1 c x=^12 or¡ 7
d x=2or 3
EXERCISE 21E.1
1a
b
c
x
y
(-3' 23)
(-2' 16)
(-1' 11)
(0' 8) (1' 7) (2' 8)
(3' 11)
y=xX- 2 x+ 8
O
x
y
(-3' -14)
(-2' -7)
(-1' -2)
(0' 1) (1' 2)(2' 1)
(3' -2)
y=-xX+ 2 x+ 1
O
x
y
(-3' 9)
(-2' 2)
(-1' -1) (0' 0)
(1' 5)
(2' 14)
y= 2 xX+ 3 x (3' 27)
O
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\714IB_IGC1_an.CDR Wednesday, 19 November 2008 2:05:51 PM PETER