Cambridge International Mathematics

ANSWERS 687

4az=b

ac

bz=a

d

c z=^2 d

3

dz=§

p

2 a ez=§

p

bn f z=§

p

m(a¡b)

5aa=F

m

br=C

2 ¼

cd=V

lh

dK=b

A

eh=^2 A

b

fT=^100 I

PR

gM= E

C^2

ha=2M¡b

EXERCISE 7B.2

1 y=¡^53 x+6 a ¡^53 b 6

2aa=

d^2

2 bK bi^1 :^29 ii^16 :^2

3ad=st i 180 km ii 120 km iii 126 : 7 km

bt=d

s

i 3 hours ii 4 hours iii 2 hours 12 mins

4an=

I

Pr

bi 2 : 05 years ii 10 years

EXERCISE 7C

1aA= 200£ 17 bA= 200m c A=Dm

2aA= 2000 + 150£ 8 bA= 2000 + 150w

cA= 2000 +dw dA=P+dw

3aC=40+60£ 5 bC=40+60t

cC=40+xt dC=F+xt

4aA= 200¡ 8 £ 5 bA= 200¡ 5 x

cA= 200¡bx dA=P¡bx

5aC= 5000¡ 10 £ 200 bC= 5000¡ 200 r

cC= 5000¡mr dC=L¡mr

6a iP=(2£5+4)m ii P=(2a+4)m

iii P=(2a+b)m

biP=(2£3+4+5)m ii P=(2x+4+5)m

iii P=(2x+y+5)m iv P=(2x+y+z)m

EXERCISE 7D

1ax=

c¡a

3 ¡b bx=

c

a+b c x=

a+2

n¡m

dx= ¡a

b+8

ex=b¡a

c¡ 1

f x=e¡d

r+s

2ar=

q

A

¼

bx=^5

p

aN c r=^3

q

3 V

4 ¼

dx=^3

qn

D

ex=§

q

y+7

4

=§

p

y+7

2

fQ=§

p

P^2 ¡R^2

3aa=d^2 n^2 bl=25T^2 c a=§

p

b^2 +c^2

dd=^25 a

2

k^2

el=gT

2

4 ¼^2

f b=^16 a

A^2

4aa=

P

2

¡b bh=

A¡¼r^2

2 ¼r

c r=

E

I

¡R

dq=p¡

B

A

ex=

3 ¡Ay

2 A

f y=

q

4

M

¡x^2

5ax=

y

1 ¡y

bx=

2 y+3

1 ¡y

c x=

3 y+1

3 ¡y

dx=

y¡ 2

y¡ 5 ex=

2 y+1

y+4 f x=

3 y¡ 7

2 y+3

gx=^3 y¡^1

y¡ 1

hx=¡^4 y+3

y+2

i x=^2 y

y+3

6ar=^3

q

3 V

4 ¼

bi 2 : 12 cm ii 62 : 0 cm

7ad=

q

Gm 1 m 2

F

bi 2 : 22 £ 108 m ii 3 : 02 £ 1010 m

8av=

s

c^2

μ

1 ¡

m 02

m^2

¶

=

c

m

p

m^2 ¡m 02

bv=

p 8

3 c c^2 :^998 £^10

(^8) m/s
EXERCISE 7E.1
1ax=¡ 4 ,y=¡ 6 bx=5,y=7 c x=2,y=6
dx=¡ 4 , y=¡ 7 ex=¡ 2 , y=¡ 8 fno solution
gx=1,y=5 h no solution i x=^25 ,y=0
2ax=^12 ,y=4^12 bx=3,y=4 c x=2,y=¡ 1
dx=0,y=¡ 4 ex=¡ 1 ,y=¡ 1 fx=0,y=6
EXERCISE 7E.2
1ax=2,y=5 bx=3, y=1 c x=0,y=5
dx=5,y=9 ex=0, y=4 f x=2,y=1
2ax=5,y=3 b x=1,y=^25
cx=2,y=1^13 d x=5,y=¡ 2
ex=¡ 3 ,y=¡^12 f x=¡ 412 ,y=¡ (^312)
3areduces to 5=7which is never true
bno solution - the two lines they represent are parallel (same
gradient)
) they never intersect
4areduces to 8 x+6=8x+6 which is always true
binfinite number of solutions - the lines they represent are
coincident
EXERCISE 7E.3
1a 11 x=11 b 4 y=12 c 9 x=9 d 9 x=6
e¡y=11 f ¡ 11 y=¡ 11
2ax=2,y=6 b x=1,y=¡ 2
cx=¡ 1 , y=¡ 3 d x=1,y=¡ 5
ex=2,y=¡ 2 f x=¡ 3 , y=1
3a 10 x+25y=5 b ¡ 3 x+y=¡ 4
c 3 x¡ 21 y=24 d ¡ 10 x¡ 8 y=¡ 18
e¡ 18 x¡ 12 y=12 f ¡ 16 x+8y=¡ 12
4ax=5,y=¡ 2 b x=1,y=2
cx=1,y=¡ 6 d x=5,y=1
ex=1,y=1 f x=¡ 3 , y=4
gx=2,y=¡ 3 h x=1,y=¡ 1
i x=¡ 1 , y=3 j x=5,y=¡ 2
kx=^1629 ,y= 291 l x=¡ 3 , y=¡ 3
mx=¡^3413 ,y=¡^8526 nx=¡ 2 ,y=¡ 3
5ainfinite number of solutions, lines are coincident
bno solution, lines are parallel
EXERCISE 7F
134 and 15 251 and 35 316 and 24
4 nectarines 56 pence, peaches 22 pence
5 adultsE 12 , childrenE 8
615 small trucks and 10 large trucks
724 twenty cent coins and 13 fifty cent coins
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\687IB_IGC1_an.CDR Tuesday, 18 November 2008 2:37:27 PM PETER