Answers 4754aa=1, b=¡ 2 , c=3
b¢ofx^2 ¡ 2 x+3is¡ 8
) the only real root isx=¡ 3.
5a 1 b ¡ 53 6anot a factor bfactor
7 k=6 8 a=4, b=¡ 1 9 c=3
10 aa=¡ 19 , b=¡ 20 b¡ 5 ,¡ 1 , 4
11 x=¡ 3 ,¡ 1 , 5
REVIEW SET 6B
1a 12 x^4 ¡ 9 x^3 +8x^2 ¡ 26 x+15
b 4 x^4 ¡ 4 x^3 +13x^2 ¡ 6 x+9
2ax^2 ¡ 2 x+4¡^8
x+2
bx¡5+^19 x+30
(x+ 2)(x+3)
3 P(x)=a(4x¡1)(x^2 ¡ 2 x¡4), a 6 =0
4 Fork=3, b=27,x=3or¡ 3.
Fork=¡ 1 ,b=¡ 5 ,x=¡ 1 or 5.
5a¡ 3 b¡ 7 6aa=5 b¡ 12
7b(x¡2)(x^2 +2x¡9) c 2 ,¡ 1 §p
10
8 a=^87 ,b=^1747
9 k=8, the zeros are¡ 1 ,¡ 2 f¡ 2 is a double rootg
10 aa=¡ 20 , b=12 b f(x)=(2x¡1)(x¡6)(x+2)
11 x=¡ 4 , 2 , 3
EXERCISE 7A.1
1agradient=3, y-intercept is 5
bgradient=4, y-intercept is¡ 2
cgradient=^15 , y-intercept is^35
dgradient=¡ 7 , y-intercept is¡ 3
egradient=^16 , y-intercept is^13
fgradient=¡^53 , y-intercept is^83
2ay=x¡ 2 by=¡x+4 c y=2x
dy=¡^12 x+3
3ay=4x¡ 13 by=¡ 3 x¡ 5 c y=¡ 5 x+32
dy=^12 x+^72 ey=¡^13 x+^83 f y=6
4a 2 x¡ 3 y=¡ 11 b 3 x¡ 5 y=¡ 23 c x+3y=5
d 2 x+7y=¡ 2 e 4 x¡y=¡ 11 f 2 x+y=7
g 7 x+2y=18 h 6 x¡y=¡ 40
5ay=^52 x¡ 2 by=¡ 2 x+3 c y=¡ 2
dy=¡^15 x+^25 ey=^16 x¡^116 f y=¡^23 x¡^113
6ax¡ 3 y=¡ 3 b 5 x¡y=1 c x¡y=3
d 4 x¡ 5 y=10 ex¡ 2 y=¡ 1 f 2 x+3y=¡ 5
7ap
45 units b (¡ 1 ,^72 ) c^12 dy=^12 x+4
8ay=^43 x¡ 1 b 2 x¡ 3 y=¡ 13 c y=x+1
d 2 x+y=¡ 2 ey=¡^23 x+2 f 3 x+7y=¡ 9
9aM=^13 p+2 bR=¡^54 n+2 c T=^12 x¡ 1
dF= 101 x+1 eH=¡^12 z+2 f W=¡^16 t¡ 2
10 ax+2y=13 b(13,0)
11 a 3 x+5y=10 b(0,2) 12 54 units^2
EXERCISE 7A.2
1ap
160 units b(¡ 1 ,1) c ¡ 3 dx¡ 3 y=¡ 4
2ay=x¡ 4 by=2x+6 c y=^65 x+^72 dy=1
315 units^2EXERCISE 7B
1a(1,3) b (6,¡3) c(¡ 5 ,3) d (¡ 1 ,¡2)
2a 3 x+5y=9 b(¡ 2 ,3) 3 (4,2)
4ax¡ 3 y=¡ 8 by=¡ 3 x¡ 4 c (¡ 2 ,2)
5a(0,¡1) b 25 units^2
6a(¡ 1 ,0) b 26 units^2730 units^2
8a i(5,0) ii (7,¡4) iii(6,¡2)
bHint: Find the gradients of MN and AC.
ci 15 units^2 ii 20 units^2
EXERCISE 7C
1 (¡ 1 ,¡2)and(^115 ,¡^25 ) 2
p
18 units
3 x¡ 2 y=0 4 (¡^43 ,¡^83 ) and(2,¡1)
5p
125 units 6 x¡ 3 y=¡ 13
7 (3,¡^32 ) and(4,¡1) 8 (^73 ,^52 )
EXERCISE 7D
1ay=^12 x^3 +2 b y=3
p
x¡ 1 , x> 0
cy=3¡x^4 d y=^13 £ 2 x
ey=^2
x
+1 f y=¡^32 £ 3 x+11
2a iy=x^2 +3x iiy=18
biy=¡^12
p
x+
10
p
x
, x> 0 iiy=^17p 3
6
ciy=^5
3 x
£ 2 x iiy=^409
diy=2x^3 ¡ 9 x iiy=27
eiy=^1
x^2
¡^12
x
+36 iiy=32^19
fiy=(x+2)^2 +3 iiy=28
3algy=2x¡ 1 by= 101 £ 102 x
4 y= 1000£ 10
¡^32 x5ay=10 000^1 £ 10 x by= 10 000£( 101 )x
cy=5£ 4 x
6ay=10£ 10(^13) x
by= 1000
7algy=¡^12 lgx+2 by=
100
p
x
8ay=x
(^14)
b y=
1000
x
c y=x^2
p
1000
9aK=7
p
t b K=21 10 a 3 blg 4
EXERCISE 7E
1ax^214916
y 2 11 26 47
c y=3x^2 ¡ 1
b y
O x^2
2 4 6 8 10 12 14 16 18
10
20
30
40
50
(1 2), (4 11),
(9 26),
(16 47),
-1
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 IB HL OPT
Sets Relations Groups
Y:\HAESE\CAM4037\CamAdd_AN\475CamAdd_AN.cdr Tuesday, 8 April 2014 8:33:19 AM BRIAN