Cambridge Additional Mathematics

Answers 465

c

5afy:¡ 106 y 615 g bfy:3 6 y 619 g

cfy:¡ 136 y 637 g dfy:¡ 86 y 6494 g

EXERCISE 3D.4

1acutsx-axis twice, concave up

bcutsx-axis twice, concave up

clies entirely below thex-axis, concave down, negative

definite

dcutsx-axis twice, concave up

etouchesx-axis, concave up

fcutsx-axis twice, concave down

gcutsx-axis twice, concave up

hcutsx-axis twice, concave down

i touchesx-axis, concave up

2aconcave up

b¢=17which is> 0

cx-intercepts

¼ 0 : 22 and 2 : 28

dy-intercept=1

e

3a¢=¡ 12 which is< 0

bnegative definite

cvertex is (2,¡3),

y-intercept=¡ 7

d

4aa=1which is> 0 and¢=¡ 15 which is< 0

so is entirely above thex-axis.

ba=¡ 1 which is< 0 and¢=¡ 8 which is< 0

so is entirely below thex-axis.

ca=2which is> 0 and¢=¡ 40 which is< 0

so is entirely above thex-axis.

da=¡ 2 which is< 0 and¢=¡ 23 which is< 0

so is entirely below thex-axis.

5 a=3which is> 0 and¢=k^2 +12which is always> 0

fask^2 > 0 for allkg ) always cutsx-axis twice.

6 ¡ 4 <k< 4

EXERCISE 3E

1ay=2(x¡1)(x¡2) by=2(x¡2)^2

cy=(x¡1)(x¡3) dy=¡(x¡3)(x+1)

ey=¡3(x¡1)^2 fy=¡2(x+ 2)(x¡3)

2ay=^32 (x¡2)(x¡4) by=¡^12 (x+ 4)(x¡2)

cy=¡^43 (x+3)^2

3ay=3x^2 ¡ 18 x+15 by=¡ 4 x^2 +6x+4

cy=¡x^2 +6x¡ 9 dy=4x^2 +16x+16

4ay=^32 x^2 ¡ 6 x+^92 by=¡^13 x^2 +^23 x+5

5ay=¡(x¡2)^2 +4 by=2(x¡2)^2 ¡ 1

cy=¡2(x¡3)^2 +8 dy=^23 (x¡4)^2 ¡ 6

ey=¡2(x¡2)^2 +3 fy=2(x¡^12 )^2 ¡^32

EXERCISE 3F

1a(1,7)and(2,8) b(4,5)and(¡ 3 ,¡9)

c(3,0)(touching) dgraphs do not meet

2 c=¡ 9 3 m=0or¡ 8 4 ¡ 1 or 11

5ac<¡ 9

bexample: c=¡ 10

6ac>¡ 2 b c=¡ 2 cc<¡ 2

7am<¡ 1 orm> 7 bm=¡ 1 orm=7

c¡ 1 <m< 7

8 Hint: A straight line through (0,3)will have an equation of

the form y=mx+3.

EXERCISE 3G

17 and¡ 5 or¡ 7 and 5 25 or^15314

418 and 20 or¡ 18 and¡ 20 515 sides

63 : 48 cm 7b 6 cm by 6 cm by 7 cm

811 : 2 cm square 9 no

11 ay=¡^89 x^2 +8

bNo, as the tunnel is only 4 : 44 m high when it is the same

width as the truck.

12 bThe graph is a parabola. c 21 : 25 m

df(x)=¡ 0 : 05 x^2 +2x+1: 25 e yes

EXERCISE 3H

1amin.¡ 1 , whenx=1 bmax. 8 , whenx=¡ 1

cmax. 813 , whenx=^13 dmin.¡ 118 , whenx=¡^14

emin. 41516 , whenx=^18 f max. 618 , whenx=^74

2a 40 refrigerators b$ 4000

4500 mby 250 m 5c 100 mby 112 : 5 m

6a 4123 mby 4123 m b 50 mby 3114 m

7b 318 units 8ay=6¡^34 x b 3 cm by 4 cm

REVIEW SET 3A

1a¡ 2 , 1

bx=¡^12

c 4

d(¡^12 ,^92 )

ffy:y 692 g

e

y

x

-7

f(x) = -x + 4x - 7 2

O V,(2 -3)

y

x

1

0.22 2.28

y=2x -5x+1 2

O

y

x

-2

&'*-QwOw

1

4

x=-Qw

y = -2(x + 2)(x - 1)

O

y

x

-10

10

y=x-10¡¡¡¡

y=2x -3x-7 2

O

y

O x

y = x - 12x + 5 42

5 V,(4)Ew

Qw Tw

y = x - 12x + 5|| 42

V,(Ew-4)

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
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