676 ANSWERS
5a¡(x¡1)(x+ 12) b¡2(x¡1)(x¡3)
c ¡(x+ 7)(x¡2) d¡ 2 x(x¡1)^2
e(a+b+ 3)(a+b¡3) f x(x+4)
6a(2x+ 3)(x+7) b(2x+ 5)(x+3)
c (2x+ 1)(2x+5) d(4x+ 3)(3x+1)
e(x¡5)(6x+1) f (4x+1)^2
g(5x+ 4)(5x¡4) h(12x+ 1)(x¡6)
i 2(6x¡1)(x¡3) j 3(3x+ 4)(x¡1)
k(3x¡5)(4x¡3) l (3x+ 2)(12x¡7)Review set 6B
1a 3 x^2 ¡ 6 x b 15 x¡ 3 x^2 c x^2 ¡ 5 x¡ 24
dx^2 +6x+9 e ¡x^2 +4x¡ 4 f 16 x^2 ¡ 1
g 12 x^2 ¡ 5 x¡ 2 h 2 x^2 +3x¡ 15
2ax^4 +6x^2 +9 b 4 ¡ 9 d^2 cx^3 ¡ 15 x^2 +75x¡ 125
dx^3 +3x^2 ¡ 2 x+8 e 13 x¡ 20 ¡ 2 x^2 f 16 x^2 ¡y^2
3a 3 c b 4 p c 3 rs
4a 3 x(x¡4) b 3 x(5¡ 2 x) c2(x+ 7)(x¡7)
d(x¡3)^2 e(a+b)^2 f(x+ 2)(x¡1)
5a(x¡1)(5 +y) b(3x+ 7)(1 + 2b)
6a(x+ 3)(x+7) b (x¡3)(x+7) c(x¡7)(x+3)
d(x¡2)(x¡3) e4(x¡3)(x+1) f¡(x+4)(x+9)
7a(4x+5)(2x+3) b (6x¡1)(2x¡3) c(4x¡5)(3x+2)
8a(x+p
10)(x¡p
10) b cannot be done
c (x¡4+p
13)(x¡ 4 ¡p
13)Review set 7A
1a 9 x^2 ¡ 6 xy+y^2 b 2 a^2 ¡ 2 ab c ¡ 12 x^2 +x+1
d 4 x^2 +28x+49 e¡25 + 10x¡x^2 f 1 ¡ 49 x^2
g 20 x^2 ¡ 11 x¡ 4 h¡x^2 +7x+18
2a 10 x¡ 11 b 9 x^2 +12x+4 c 64 ¡q^2
d 4 x^2 +21x¡ 18 e 8 x^3 ¡ 12 x^2 +6x¡ 1
f x^3 ¡ 7 x^2 +14x¡ 6
3a 5 b(a+2b) b3(x+ 2)(x¡2) c (x+4)^2
d2(a¡b)^2 e 3 x(x+ 3)(x¡1) f (x¡3)(x¡6)
4 (y¡z)(2x+1)
5a(x+ 5)(x+7) b (x+ 7)(x¡5) c(x¡5)(x¡7)
d2(x¡7)(x+5) e(x¡5)(x¡6) f ¡(x¡2)(x¡10)
6a(x+ 9)(x¡9) b2(x+p
19)(x¡p
19)
c cannot be done
7a(3x+ 2)(4x¡1) b(3x¡2)(4x+3)
c 4(3x¡1)(2x+3)
8a(c+ 3)(d+3) b(4¡x)(x¡1) c (3x¡4)(2x¡3)
9b(5x+ 7)(x¡3) c (5x+ 7)(x¡3)
The same result asb.
EXERCISE 2A
1a i 12 ii 5
iii 2bS^0 =f 1 , 3 , 5 , 6 , 8 , 10 , 12 g
T^0 =f 1 , 2 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 12 g
citrue iifalse iii true difalse iitrue
ex=2 f finite as it contains a finite number of elements
2a?,fag
b?,fag,fbg,fcg,fa,bg,fb,cg,fa,cg,fa,b,cg
c 16 (For a set with 1 element, 2 subsets;
for a set with 2 elements, 4 subsets;
for a set with 3 elements, 8 subsets.)3 ?,f 2 g,f 4 g,f 7 g,f 9 g,f 2 , 4 g,f 2 , 7 g,f 2 , 9 g,f 4 , 7 g,f 4 , 9 g,
f 7 , 9 g,f 2 , 4 , 7 g,f 2 , 4 , 9 g,f 2 , 7 , 9 g,f 4 , 7 , 9 g ( 15 of them)
4aS=f 1 , 2 , 3 , 6 g bS=f 6 , 12 , 18 , 24 , ......g
c S=f 1 , 17 g dS=f 17 , 34 , 51 , 68 , ......g
e S=f 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 g
f S=f 12 , 14 , 15 , 16 , 18 , 20 , 21 , 22 , 24 , 25 , 26 , 27 , 28 g
5a 4 bis infinite c 2 d is infinite e 8 f 13
6aA=f 23 , 29 g, B=f 22 , 24 , 26 , 28 g,
C=f 21 , 22 , 24 , 25 , 26 , 27 , 28 g, D=?
bi 2 ii 0 ciAandD ii BandD
difalse ii true iii false
7a i 7 ii 4 iii 3 iv 2 v 5
b n(S)+n(S^0 )=n(U)
EXERCISE 2B
1atrue btrue c true dtrue
e false ffalse gtrue htrue
2a,b,c,d,f,g,hare rational; eis irrational
3a 0 :7=^79 b 0 :41 =^4199 c 0 :324 =^1237
4a 0 : 527 can be written as 1000527 , and 527 , 1000 are integers
b 0 :9=1
5ae.g.,p
2+(¡p
2) = 0 which is rational
b e.g.,
p
2 £
p
50 =
p
100 = 10 which is rational
6atrue bfalse c true
EXERCISE 2C
1aThe set of all realxsuch thatxis greater than 4.
b The set of all realxsuch thatxis less than or equal to 5.
c The set of all realysuch thatylies between 0 and 8.
d The set of all realxsuch thatxlies between 1 and 4 or is
equal to 1 or 4.
e The set of all realtsuch thattlies between 2 and 7.
f The set of all realnsuch thatnis less than or equal to 3 or
nis greater than 6.
2af 2 , 3 , 4 , 5 , 6 g bf 5 , 6 , 7 , 8 , 9 , ......g
c f......,¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 g d f 0 , 1 , 2 , 3 , 4 , 5 g
e f¡ 4 ,¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 , ......g ff 1 , 2 , 3 , 4 , 5 , 6 g
3afxj¡ 56 x 6 ¡ 1 , x 2 Zg
There are other correct answers.
b fxjx 65 , x 2 Ng There are other correct answers.
c fxjx> 4 , x 2 Zg There are other correct answers.
d fxjx 61 , x 2 Zg There are other correct answers.
e fxj¡ 56 x 61 , x 2 Zg
There are other correct answers.
f fxjx 644 , x 2 Zg There are other correct answers.
4afxjx> 3 g b fxj 2 <x 65 g
c fxjx 6 ¡ 1 orx> 2 g d fxj¡ 16 x 64 , x 2 Zg
e fxj 06 x 66 ,x 2 Ng f fxjx< 0 g
5a bcdef6afinite binfinite c infinite dfinite
e finite finfinite4 5 6 7 8 x -5 4 x-3 5 x -5 x......
06 x -5 0 xIB MYP_3 ANS
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\676IB_IGC1_an.CDR Tuesday, 18 November 2008 2:34:56 PM PETER