Cambridge International Mathematics

688 ANSWERS

8 9 male and 4 female costumes 9 x=5, y=2

10 $45call out and$60an hour

11 a a=^59 ,b=¡^1609 b 25 oC

Review set 17A

1a 11 : 4 g/cm^3 b 37 : 9 g c 9230 : 8 cm^3

2at=s+13

3

bt=§ 2 pr 3 x=^2 y¡^3

y¡ 2

4a iV=6£ 8 iiV=8n iii V=ln

bV=25+ln

5ac=¡ 3 bc=6 c c=¡ 10

6ax=¡ 1 ,y=3 bx=2, y=¡ 1 7 x=2, y=7

8ax=¡ 2 ,y=3 bx=5, y=6

9 A sausage costs$0: 80 and a chop$2: 50. 10 9 drivers

Review set 17B

1a204 800units b 7 : 75 cm

2ay=

20 ¡ 6 x

5

or y=4¡^65 x br=

C

2 ¼

3 4 : 46 cm 4ax=

y

2

¡

3

K

bx=

25 c^2

2 M^2

5aC=2+1: 20 bC=2+1: 20 £ 5

c C=p+1: 20 b dC=p+bx

6ax=y=¡ 2 b x=¡ 4 , y=¡ 16

7 x=^2413 ,y=^33138 x=1,y=0 95 and 1710 $1: 50

CHALLENGE

1 3 , 8 and 14 2 x=5, y=1

3 a^01 ¡^1 ¡^11

b 01 ¡ 11 ¡ 1

c 01 1¡ 1 ¡ 1

4 only 3961

5 a=b=c

6ax=3, y=5, z=¡ 2 bx=4, y=2^12 ,z=¡ (^112)
7 ab=¡ 1
EXERCISE 8A.1
1a 8 : 06 cm b 7 : 07 cm c 15 : 3 km
2a 9 : 22 cm b 2 : 06 km c 6 : 72 cm
3ax=
p
11 b x=
p
2 c x=
p
5
4ax=
p 5
4 or
1
2
p
5 bx=
p 10
4 or
1
2
p
10 c x=^12
5ax¼ 5 : 20 b x¼ 7 : 21 c x=2
6ax=
p
17 ,y=2
p
2 bx=
p
29 , y=3
p
5
c x=
p
5 , y=
p
6
7ax¼ 1 : 41 bx=14 8 AC¼ 6 : 24 m
9aAB=
p
17 cm b AB=
p
29 m c AB=
p
41 m
10 Area of trapezium=
³a+b
2

́

(a+b)

Sum of areas of triangles=^12 ab+^12 c^2 +^12 ab

Equate these, etc.

11 3

p

2 cm (¼ 4 : 24 cm)

EXERCISE 8A.2

1a,b,d,fare Pythagorean triples.

2ak=17 bk=10 c k=48 dk=25

ek=24 fk=60

3 (3k)^2 +(4k)^2 =9k^2 +16k^2 =25k^2 =(5k)^2

) there are infinitely many Pythagorean triples asktakes

infinitely many values.

EXERCISE 8B

1b,e,fare right angled. 2aBbAC b AbBC c AbCB

3 Yes, as 68002 + 3500^2 ¼ 76482.

4 AB=

p

117 cm, BC=

p

52 cm

AB^2 +BC^2 = 169 = 13^2 =AC^2

) ¢ABC is right angled at B.

EXERCISE 8C

1 8 : 54 cm 2 3 : 16 cm£ 9 : 49 cm

3a 53 : 7 cm b 160 cm^246 : 63 cm 5 7 : 07 cm

6 25 : 6 cm

7a 15 : 8 km b 22 : 4 km c 22 : 4 km d 25 : 5 km

e 29 : 2 km f 31 : 6 km

8 9 : 43 km 9 5 km

10 a 21 : 5 m b 8 m c 21 : 5 m d 40 : 8 m

11 a x=

p

2 ,y=45 b x=6,h=

p

13

c x=^12 ,y=

p 3

2

1210 : 4 cm 13 a 22 : 2 cm^2 b 8 cm 14 1 : 80 m

1519 : 2 km 16

p

5 ¼ 2 : 24 km 17 13 : 4 km

EXERCISE 8D

1 10 : 9 cm 24 : 66 cm 34

p

3 cm or 6 : 93 cm

(^412)
p
157 ¼ 6 : 26 cm 56 cm 6
6
p
2
¼ 8 : 49 cm
7 3 : 71 cm 84 : 24 cm 912 : 5 cm 10 cm
11 10 : 6 cm 121 : 3 m 13 10 : 05 m 14 ¼ 1 : 42 cm
15 aObBA is a right angle and so BA is a tangent to the circle at
B.
b As PQ^2 =PR^2 +RQ^2 , ¢PRQ is right angled at R and
so PQ is a diameter.
17 AD=16cm
EXERCISE 8E
1 15 cm
2 When placed like this the greatest
length a stirrer could be and lie within
the glass is 11 : 6 cm. So a 12 cm stirrer
would go outside the glass.
3 3 : 16 cm 42
p
3 cm¼ 3 : 46 cm 56 : 80 m 6 61 : 6 cm
7a 10 m b 5
p
5 m¼ 11 : 2 m 812 : 65 m 9 ¼ 66 : 8 m
10 32 : 2 m

Review set 18A

1a

p

29 ¼ 5 : 39 cm b

p

33 ¼ 5 : 74 cm

c 3

p

3 ¼ 5 : 20 cm, 6

p

3 ¼ 10 : 4 cm

2 Right angled at A as AB^2 +AC^2 =25+11

=36

=BC^2

3 52 +11^2 = 146 6 =13^2.

4a 4

p

10 ¼ 12 : 6 units b 4

p

13 ¼ 14 : 4 units

c 4

p

17 ¼ 16 : 5 units

5 3

p

13 ¼ 10 : 8 cm 6 radius is 5

p

2 cm¼ 7 : 07 cm

7 5 : 77 m

8 IfRis the radius of the larger circle andris the radius of the

smaller, then PQ=PR=

p

R^2 ¡r^2.

9ax=2

p

5 ¼ 4 : 47 b x=

p

171 ¼ 13 : 1 10 6 : 55 m

IB MYP_3 ANS

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Y:\HAESE\IGCSE01\IG01_an\688IB_IGC1_an.CDR Thursday, 20 November 2008 4:09:16 PM PETER