Cambridge International Mathematics

ANSWERS 731

7a b

p

29 units (¼ 5 : 4 units)

c 158 o

8a i

¡ 1

¡ 4

¢

ii

¡¡ 3

¡ 3

¢

b

¡!

AC=

¡ 5

¡ 3

¢

c

p

34 units

9 k=¡ 10 10 a

¡ 4

¡ 3

¢

b 5 units

11 a

¡!

CA=¡c b

¡!

AB=¡a+b c

¡!

OC=a+c

d

¡!

BC=¡b+a+c

12 a¡DC!=3q b ¡CB!=¡p¡q c¡BT!=^23 (p+q)

REVIEW SET 24B

1

2am=

¡¡ 4

¡ 3

¢

bn=

¡ 0

¡ 4

¢

3 Scale:

1 cm ́ 50 km

4a

b¼ 398 km/h in direction 096 o

5a

¡ 1

¡ 6

¢

b

p

37 units 6 n=6

7a

bd¡e=

¡ 5

¡ 1

¢

ci

¡ 5

7

¢

ii

¡ 18

¡ 2

¢

8 We get the zero vector

¡ 0

0

¢

= 0

9a¡p b^12 q c^12 q¡p d q

10 Scale:

1 cm ́ 2 km/h

11 a i p ii q iii p+q iv 2 p+2q

b

¡!

PQ=^12

¡!

AC which means that PQ and AC are parallel and

PQ is half as long as AC.

c...... triangle isparallelto the third side andhalfits length.

12 A(¡ 2 ,¡4)

13 a i

¡!

UX=^45 v ii

¡!

OX=u+^45 v

bi¡VY!=^54 u

ii

¡¡!

VW=u and

¡!

VY=^54 u )

¡!

VY=^54

¡¡!

VW

Thus VY is parallel to VW and 114 times its length.

i.e., V, Y and W are collinear and VW:WY=4:1.

CHALLENGE

1aThe quadrilateral formed is a parallelogram.

bThe quadrilateral formed by joining the midpoints of the sides

of any quadrilateral is a parallelogram.

2a ra+sb=ma+nb

) (r¡m)a=(n¡s)b

If r¡m 6 =0 and n¡s 6 =0

then akb

But a,b, ) r¡m=0 and n¡s=0

) r=m and n=s

bi¡OP!=k¡OC!

=k(b+^12 a)

ii¡OP!=¡OA!+¡AP!

=a+t¡AB!

=a+t(b¡a)

iii k=^23 ,

¡!

OP=^13 a+^23 b

EXERCISE 25A

1aimpossible b equally likely

cextremely unlikely d very unlikely e certain

fextremely unlikely g very likely

hextremely likely i likely j very unlikely

kextremely unlikely l very likely

2aEventB b EventA

3aunlikely b extremely unlikely c likely

dimpossible e extremely likely

EXERCISE 25B

10 : 55 20 : 84 3 ¼ 0 : 0894 4 ¼ 0 : 256 5 ¼ 0 : 331

6a¼ 0 : 243 b ¼ 0 : 486

7aP(winning)¼ 0 : 548 bP(2child family)¼ 0 : 359

8a 407 people

ci¼ 0 : 229

ii ¼ 0 : 201

iii ¼ 0 : 307

b Brand Freq Rel Freq

Silktouch 125 0: 307

Super 107 0: 263

Just Soap 93 0 : 229

Indulgence 82 0 : 201

Total 407 1

9aOutcome Freq Rel Freq

0 heads 121 0: 247

1 head 259 0: 530

2 heads 109 0: 223

Total 489 1

bi¼ 0 : 247

ii ¼ 0 : 530

iii ¼ 0 : 223

10 a 1083 people

ci 0 : 25

ii 0 : 75

b Colour Freq Rel Freq

Green 361 0 : 25

Red 1083 0 : 75

Total 1444 1

11 a 5235 tickets

c¼ 0 : 207

b Ticket Type Freq Rel Freq

Adult 3762 0: 719

Concession 1084 0: 207

Child 389 0 : 074

Total 5235 1

m -5

2

abc

p q r

d

• e
  d¡-e

N

315°

5 km/h

200 km

E

N

» 5 7.°

400 km/h 40 km/h

IB MYP_3 ANS

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\731IB_IGC1_an.CDR Thursday, 20 November 2008 10:27:11 AM PETER