Answers 4578a if 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 g
ii f 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30 g iii f 1 , 2 , 3 , 6 g
iv f 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 24 , 30 g
b9a b i 72
ii 39
iii 26810 8 11 a 9 b 7 c 17
12 aP=f 1 , 3 , 5 , 7 , 9 g
Q=f 2 , 4 , 6 , 8 , 10 g
bThey are disjoint.cREVIEW SET 1B
1atrue bfalse c true dfalse e false
2a ifx 2 R:5<x< 12 g ii fx 2 Z:¡ 46 x< 7 g
iii fx 2 N:x> 45 g
biinfinite ii finite iii infinite
3 ?,f 1 g,f 3 g,f 5 g,f 1 , 3 g,f 3 , 5 g,f 1 , 5 g,f 1 , 3 , 5 g
4a if 2 , 4 , 6 , 8 g
ii f 2 , 4 , 8 g
iii f 3 , 5 , 7 , 9 gb5a? bs+t
6aneither bclosed cneither
7a iThe set of points which lie on bothAandB(that is, the
point(s) of intersection of lineAand lineB).
ii The set of points which lie on lineAor lineB.
bNo. If the lines are coincident (so,AandBdescribe the
same line), then A\B will be infinite.
cn(A\B)=0or 1
8aC^0 b(A\B)[(A\C) or A\(B[C)
9a b i 27
ii 8
iii 1410 4
11 aA=f 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 g, B=f 1 , 2 , 4 , 5 , 10 , 20 g
bB½Ac12 a 1 b 7 c 15
EXERCISE 2A.1
1a,d,e2a,b,c,e,g,i
3 No, for example(0,4)and(0,¡4)satisfy the relation.
EXERCISE 2A.2
1a,c,f
2anot a function bfunction, one-one
cfunction, not one-one
3a i$ 13 ii yes iiiyes
bino ii no
EXERCISE 2B
1a 2 b 2 c ¡ 16 d¡ 68 e^174
2a¡ 3 b 3 c 3 d¡ 3 e^152
3a i 1 ii¡ 1 b x=¡ 4
4a 7 ¡ 3 a b 7+3a c¡ 3 a¡ 2 d 10 ¡ 3 b
e 1 ¡ 3 x f 7 ¡ 3 x¡ 3 h
5a 2 x^2 +19x+43 b 2 x^2 ¡ 11 x+13
c 2 x^2 ¡ 3 x¡ 1 d 2 x^4 +3x^2 ¡ 1
e 2 x^4 ¡x^2 ¡ 2 f 2 x^2 +(4h+3)x+2h^2 +3h¡ 1
6a i¡^72 ii¡^34 iii ¡^49
bx=4 c^2 x+7
x¡ 2
dx=^95
7 fis the function which convertsxintof(x)whereasf(x)is the
value of the function at any value ofx.
8aV(4) = 6210, the value in dollars after 4 years
bt=4: 5 , the time in years for the photocopier to reach a
value of 5780 dollars.
c 9650 dollars
910 f(x)=¡ 2 x+5
11 a=3,b=¡ 2
12 a=3,b=¡ 1 ,
c=¡ 4EXERCISE 2C
1aDomain=fx:x>¡ 1 g, Range=fy:y 63 g
bDomain=fx:¡ 1 <x 65 g, Range=fy:1<y 63 g
cDomain=fx:x 6 =2g, Range=fy:y 6 =¡ 1 g
dDomain=fx:x 2 Rg, Range=fy:0<y 62 g
eDomain=fx:x 2 Rg, Range=fy:y>¡ 1 g
fDomain=fx:x 2 Rg, Range=fy:y 6254 g
gDomain=fx:x>¡ 4 g, Range=fy:y>¡ 3 gPQU8424121
2
3515103027
26
25
7
11 13 16 171819
6 20
9
1421(^282322)
29
SH
U
(157) (72) (39)
(296)
PQ
U
(^135)
7 9
2 4
6 8
10
MS
U
(8) (5) (10)
(4)
AB
U
6
2
4
8
1
3
(^57)
9
U
A B
1 2 4
51020
40
8
7 9 11
1314 16
17
36
12 15
18 19 21
22 23 24 25 26
27 28 29 30 31
32 33 34 35 36
37 38 39
x
y
(5 3)'
(2 1)'
O
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 IB HL OPT
Sets Relations Groups
Y:\HAESE\CAM4037\CamAdd_AN\457CamAdd_AN.cdr Tuesday, 8 April 2014 8:19:11 AM BRIAN