Cambridge International Mathematics

0

5

10

15

20

48 50 52 54 56

length (cm)

frequency

706 ANSWERS

6a b 27 babies

c 70%of them

d Upper end point Cumulative frequency

49 1

50 4

51 13

52 23

53 39

54 43

55 48

56 50

e

fi¼ 52 : 1 cm ii 18 babies

EXERCISE 18A

1ax=0: 8 bx¼ 1 : 13 c x¼ 0 : 706

2ax=8 bx=8: 75 c x=4: 8 dx¼ 3 : 18

3a 6 cm bk=1: 5

4atrue bfalse, e.g.,

c true dfalse, e.g.,

5 They arenotsimilar.

Comparing lengths; k=^1612 =^43

Comparing widths; k=^128 =^32

and^436 =^32.

6 FG=2: 4 m

7a

b

and

8 No, any two equiangular triangles are similar.

EXERCISE 18B.1

1 All of these figures have triangles which can be shown to be

equiangular and therefore are similar.

For example, ina,¢CBD is similar to¢CAE as they share an

equal angle at C and CbBD=CbAE=90o.

EXERCISE 18B.2

1ax=2: 4 bx=2: 8 c x¼ 3 : 27 dx=9: 6

e x=11: 2 fx=5 gx¼ 6 : 67 hx=7

i x=7: 2

EXERCISE 18C

1a 7 m b 7 : 5 m 21 : 8 m 3 2 : 67 m 4 1 : 52 m

5 1 : 44 m 69 seconds 7 ¼ 117 m 8 1013 m

9aSU=5: 5 m, BC=8: 2 m

b No, the ball’s centre is¼ 11 cm on the D side of C.

EXERCISE 18D

1ax=18 bx=6 c x=5 dx¼ 4 : 38

2ak=4 b 20 cm and 24 cm c area A:area B=1:16

3ak=2: 5 b 100 cm^2 c 84 cm^24 ED¼ 1 : 45

5aV=80 bV=40: 5 c x¼ 5 : 26 dx=8

6 6750 cm^3 7a 4 cm b 648 cm^386 cm^2

9ak=^23 b14 850cm^3 c 280 cm^2

10 No. Comparing capacities, k¼ 1 : 37

Comparing lengths, k=1: 6

These values should be the same if the containers are similar.

11 a 2 : 5 m b16 : 25 c 64 : 125

REVIEW SET 18A

1

and

2ax¼ 1 : 71 b x¼ 1 : 83 3 x=2: 8

4 Hint: Carefully show that triangles are equiangular, giving

reasons.

5ax¼ 6 : 47 b x=2

p

6 ¼ 4 : 90

6aA=7 b x¼ 8 : 14 7ax=15 by=32

8 ¼ 66 : 7 m wide 9ak=4 b 0 : 99 m c 0 : 5 m^3

REVIEW SET 18B

1

2ak=^75 b49 : 25

3ax=3 bx=4 c x=12

4aBbAC=NMCb =90o fgiveng

]C is common to both ) ¢s ABC and MNC are

equiangular, i.e., similar.

b

x

8 =

6

15 ) x=

48

15 =3:^2 c^6 :^4 cm

5ax=4 bx¼ 42 : 7 6ax=3: 6 b y=6: 4

7aHint: Explain carefully, with reasons, why they are

equiangular.

b CD=7: 2 cm c 22 : 4 cm^2

8 2

p

13 ¼ 7 : 21 cm by 3

p

13 ¼ 10 : 8 cm 9648 cm^3

CHALLENGE

1 ¼ 17 : 1 m 2 3 : 75 m

0

5

10

15

20

25

30

35

40

45

50

55

48 49 50 51 52 53 54 55 56

length (cm)

frequency

Cumulative frequency graph of lengths of newborns

Histogram of lengths of newborn babies

4

4

2 2

3

3

1\Qw_ 1\Qw_

8cm

2cm

8cm

4cm

12 m

3m

12 m

9m

and

8cm

4cm

8cm

4cm

IB MYP_3 ANS

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\706IB_IGC1_an.CDR Thursday, 20 November 2008 4:19:17 PM PETER