Cambridge International Mathematics

750 ANSWERS

bi5(16¡11), 10(26¡16)

iin([2n+6]¡[n+ 6]) =n^2

11 a n^210 ¡^1 ¡^2

A 49 16 1 4 25

B 125 27 1 ¡ 1 ¡ 27

C 256 16 0 16 256

D 256 16 1 161 2561

biCesar’s ii Dan’s c a=16, b=4,c=16

dn^2 +13 is one of them

12 a¼ 553 cm^3 bi 32 cm by 24 cm ii¼ 21 :5%

ci$0: 48 ii$5: 76 di$0: 71 ii ¼ 12 :7%

13 a 52 +12^2 = 25 + 144 = 169 = 13^2 b 7

ciy^2 +(x¡2)^2 =x^2 gives y=

p

4 x¡ 4

fymust be> 0 g

ii 48 and 14 iii 99 and 20

iv 3 , 4 , 5 or 6 , 8 , 10 or 8 , 15 , 17 or 10 , 24 , 26

or 12 , 35 , 37 fany 2 of theseg

14 a iLHS=RHS=^256 iiLHS=RHS=^4912

iii LHS=RHS=^12130

b1+^32 ,1+^23 ; 1+^34 , 1+^43

c e.g., 135 £ 223 =1^35 +2^23

d

³

1+x

y

́³

1+y

x

́

=

³

1+x

y

́

+

³

1+y

x

́

LHS=RHS=(x+y)

2

xy

15 a i 7 th; A -$70,B-$64,C-$49

iinth; A -$10n,B-$2n¡^1 ,C-$n^2

biA-$550,B-$1023,C-$385

iischeme A ($1710) iii 15 th birthday

16 a iboth= 2418 iiboth equal 1512

b 43 £68 = 34£ 86

c In the digit form ‘ab’ thearepresents the 10 s and thebthe

ones. So ‘ab’=10a+b

d 12 £63 = 21£ 36 , 12 £84 = 21£ 48 , 23 £64 = 32£ 46 ,

23 £96 = 32£ 69 , 31 £26 = 13£ 62 , 34 £86 = 43£ 68 ,

48 £42 = 84£ 24 , 46 £96 = 64£ 69 , 93 £13 = 39£ 31 ,

14 £82 = 41£ 28 , 36 £84 = 63£ 48 , 21 £24 = 12£ 42

17 a n 12 3 4

n^214916

n^411681256

bp=5,q=30,r=17,s=35,t=98,u= 354

c Row X£Row Y=5£Row Z

diX= 2870 iiY= 1259 e722 666

18 a i(x+3)cm ii(x+3)cm iii 2 xcm

bi 60 o ii equilateral iiix=3

ci 18 o ii sin 9o= x

x+3

iiix¼ 0 : 56 cm

dAbOB=^360

o

n

, x=

3 sin

¡ 180

n

¢o

1 ¡sin

¡ 180

n

¢o

19 a135 = 3^3 £ 5 , 210 = 2£ 3 £ 5 £ 7 , 1120 = 2^5 £ 5 £ 7

bi 5

iie

iii 210 and 1120

c^196

354

278

20 a 13

bid=2c^2 iie=2(c+h)^2

iii PR=h,QR=e¡d=2(c+h)^2 ¡ 2 c^2

) QR=4ch+2h^2

iv m=

4 ch+2h^2

h

=4c+2h

v c=3, h=0: 5 and 4 c+2h=13 X

vi c=3, h=0: 1 , m=12: 2

vii ahapproaches 0 b gradient approaches 12

B MODELLING QUESTIONS

1a 12 b 324

ci 357 ¡xybulbs ii xy= 357

As 357 = 3£ 7 £ 17 then x=17, y=21

2aa=5, b=4 and c=30

b d= 5 + 4 sin(420o)¼ 8 : 46 c ¼ 1 : 54 m

d 9 m eat 0300 and 1500

f 1 m when sin(30t)o=¡ 1

i.e., at 0900 and every 12 hours thereafter.

3a ia=2 iiq=10,r=2: 5

iii M=^160

2 t

iv

Rate of change is ¡^95

3 : 4

ftangent slopeg¼¡ 28

) decreasing at about 28 g/min.

biOn graph3 a iii. ii t=1min

iii A reflection inM=80.

4a

bia=25, b=^12 ii r=18: 75 , s¼ 4 : 69

iii Max. effect¼ 26 : 5 units att¼ 2 : 89 hours

iv between 48 min and 7 h 9 min

O t

y

t

y t

23

=^15

t

y t

22

=^10

t

1 2 3 4 5

200

150

100

50

m¡=¡160¡-¡M

M

160

()1 ¡80,

()2 ¡40,

()3 ¡20, ()4 ¡10,

M= 160 ́ 2 - t

t

1 2 3 4 5

200

150

100

50

M

160

95 tangent att¡=¡2

»3.4

M= 160 ́ 2 - t

IB MYP_3 ANS

cyan magenta yellow black

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100 100
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100 100
Y:\HAESE\IGCSE01\IG01_an\750IB_IGC1_an.CDR Friday, 21 November 2008 9:56:13 AM PETER