Cambridge International Mathematics

ANSWERS 747

c 4 of A and 5 of B d 8 of A and 3 of B

5a No. Cost

Hard x E 20

Soft y E 8

b

ci 8 when 8 hard, 0 soft ii E 600 ( 20 hard, 0 soft)

6a Bats Balls Nets Profit Made/h

Set A 230$3x

Set B 251$5y

bP=3x+5y

cx> 0 , y> 0 , x+y 628 , 3 x+5y 6108 , y 618

d(1) 6 of A and 18 of B or (2) 11 of A and 15 of B or

(3) 16 of A and 12 of B

eFor (1), the making of bats is under-utilised.

For (2), the making of bats and nets is under-utilised.

For (3), the making of nets is under-utilised.

7a A B Profit No.

Deluxe 2 min 2 min $ 25 x

Standard 3 min 1 min $ 20 y

x> 0 , y> 0 , 2 x+3y 648 , 2 x+y 620 , y> 2 x

bP=25x+20y

c

dMax. profit$ 355 when 3 Deluxe and 14 Standard are made.

REVIEW SET 32A

1ax<¡ 4 : 236 orx> 0 : 236 b x< 0 : 675

2ax> 2 ,y 6 ¡ 3

bx> 0 , y> 0 , x+y> 3 , x+3y> 6

3a(2,3),(2,4),(2,5),(3,2),(3,3),(3,4),(4,1),(4,2)

b 3 solutions are removed. Only(3,2),(3,3),(3,4),(4,1)

and(4,2)remain.

4a

b(0,14),(1,13),(2,12),(3,11),(4,10),(5,9),(6,8),

(7,7),(8,6),(9,5),(10,4),(11,3),(12,2)

c 24 when x=0,y=12

5aMeter Gears Dials Time Profit No.

Gas 4 1 8 $20 x

Water 12 1 4 $31 y

bx> 0 , y> 0 , x+3y 615 , x+y 69 , 2 x+y 616

c

dP=20x+31y e $213when 6 gas and 3 water

REVIEW SET 32B

1ax< 0 orx> 0 : 641 b¡ 1 : 186 x 61 : 51

2ax 6 ¡ 2 , y< 2

bx> 0 ,y> 1 , 2 x+y 64 , 3 x+4y 612

3a(0,3),(0,4),(0,5),(1,3),(1,4),(2,2),(2,3)

b(0,3),(1,4) c x=2,y=3with maximum value 22

43 filing cabinets and 5 desks for aE 337 profit

CHAPTER 33

The University of Cambridge Local Examinations Syndicate bears no

responsibility for the example answers to questions taken from its

past question papers which are contained in this publication.

1a i

¡ 2

1

¢

ii

¡ 2

1

¢

b A translation of

¡ 0

¡ 4

¢

.

cx 62 , y>^12 x, y> 0 , y 62 x+4

2a iBbAH=

(8¡2)£ 180 o

8

= 135o

ii So, HbAP=45o

Likewise AbHP=45o

) AbPH=90o fangles of a triangleg

bi 6

p

2 cm ii12(1 +

p

2)cm iii 36 cm^2

iv 288(1 +

p

2)cm^2

ci6(1 +

p

2)cm ii 94 :8%

3a i$250: 00 ii$2600: 00 iii¼ 6 :12%

bi 12 km ii 7 h 12 min iii ¼ 2 : 78 km/h iv 16 : 07

cn= 25 000

4aMaria$350, Carolina$250, Pedro$200

b$275 c $200 d11 : 8 : 4 e$110: 25

cannot have a

negative number

of books

purchased

,

,

as can purchase at

most books

,

as needs to spend

at least.

.

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x

yxy

xy

xy

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0

0+ 20

20

30 +10 240

240

3+ 24

¡¡¡

¡¡

E

5 10 15 20

20

15

10

5

25

R

y

x

xy¡+¡ ¡=¡20

3 ¡+¡ ¡=¡24xy

()2 ¡18,

x

5 10 15 20 25

20

15

10

5

R

y yx¡=¡2

2 ¡+ ¡=¡20xy 2 ¡+¡3 ¡=¡48xy

()5 ¡10,

()3 ¡14,

x

5 10 15 20

15

10

5

y

()8 ¡4,

()16 ¡0,

()0 ¡12,

xy¡+¡2 ¡=¡16

xy¡+¡ ¡=12

R

x

y

R

xy¡+¡ ¡=¡9

2 ¡+¡ ¡=¡16xy

xy¡+¡3 ¡=15

55 1010 1515 2020

1515

1010

55

()0 ¡5,

()6 ¡3,

()7 ¡2,

()8 ¡0,

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