Maths Answers

504 Answers

ANSWERS

CHAP

Exer

1 a

b

c

2 a

b

3 a

b

4 a

c

5 a

c

6 a

b

7 a

b

8 a

b

c

9 a

d

10

11

12

Exer

1 a

b

2 a

b

3 a

4 a

b

c

5 a

deposit of $1

b

deposit of $5

LEY_bk953_answers_finalpp Page 504 Thursday, January 13, 2005 3:23 PMTER 1

cise 1A

12, 16, 20, 24, 28, 32, 369, 18, 27, 36, 457, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26,286, 12, 18, 24 c 6, 12, 18, 24 d 6

1, 2, 3, 4, 6, 8, 12, 16, 24, 481, 3, 9, 27 c 3

54 = 2 33 b 84 = 22 3 7

144 = 24 32

80 = 24 5 b 240 = 24 3 5

600 = 23 3 52

35 = 5 7, 60 = 22 3 55 c 420

140 = 22 5 7, 84 = 22 3 728 c 420

84 = 22 3 7, 56 = 23 7, HCF = 28,LCM = 168

100 = 22 52, 75 = 3 52, HCF = 25,LCM = 300

175 = 52 7, 200 = 23 52, HCF = 25,LCM = 1400

4 b 11 c 135 e 6 f 11

a MMMCDXVI b 110 101 011 000

a 2, 3, 4, 6, 9, 12 b 3, 9, 11c 2, 3, 4, 6, 9, 11, 12

4488

cise 1B

2 < 6 c 6 > 2 d 3, 4 e 3 , 4 , 5

5 b 3 c 5

deposit of $15decrease of 30 cm in lengthloss of 8 kg d fall of 15C

c debt of $6

6 a + 1 km b 2 km c 5 km

7 a

b

8 a 2 , , 0, , 1 b 1.8, 1, 0, 1.8, 2.3

9 a 3 > 4 b 5 < 5 c 5 < 0

10 a 13 b 3 c 5

11 a 50 b 30 c 24

12 a 7 b 11 c 6

13 a 11 b 2 c 13d 18 e 21 f 10

Exercise 1C

1

2 3 13 4

5 100 6 7 , ,

8 9 222 kg

10 a $120 b $400 c d $80

11 hundredths

12 8.307 13 4 14 3.375

15 0.17 16 3.85 17 4

18 a 4.64 b 332.4 c 11.9

19 a 30.6 b 5.2

20 a $48.30 b $152 040

21

22 48% 23 24 0.57

25 380% 26 62.5%

27 0.65, 70%,

28 27% 29 30 4.25

31 $54 32 12 m 33 25%

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 87

0 1 2 3 4 5 6 7

12---

12---

12 1110 9 8 7 6 5 4 3 2 1 0

5 4 3 2 1 0 1 2 3 4 5

23---

23---

23---

13---

Shade any 14 squares.

1120------

311------

298

------

3548------

45---

23---

815------

38---

215------

15---

37100----------

45---

320------

505Answers

34 $130 35 $240

36

37

38

39

41

42

44

45

Exerc

1 a

2 a

3 a

c

4 a

5 a

6 ab

7 abc

8 a

Exerc

1 a

2 a

d

3 ad

4 a

5 a

6 a

7 ad

8

9

10

Exercise 1F

LEY_bk953_answers_finalpp Page 505 Thursday, January 13, 2005 3:23 PMA comparison between 2 different quantities, e.g. 30 km/h.

13 : 15

a 3 : 10 b 5 : 18

x = 24 40 $375, $625

15.6, 23.4, 7.8

$9.31 43 315.25 km

a 3300 cm b 4740 cm

12.5 m

ise 1D

(red, blue, green, yellow) b

(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) b

, 70% b , 0.25

0.625, 62.5%

20 b 9 c

b c

tossing a coin and getting a 150% c high probability

getting a number from 1 to 6getting a 7getting an even number

b c d

ise 1E

p + 1 b 3p c 2p + 2 d 3p + 3

6p b gr c 5m

8ab e 3m2 f 5a + 3q

3 p b a b c m m5 x x e 6 p q

3p b 5y c z d 3pq e 0

12 b 60 c 9 d 16 e 64

b c d e

k 3 b 4 m c p q3e 4 e mn t

a 1 b 6 c 4 d 5 e 2

a 24 b 0 c 12 d 5 e 42

a 7 b 1 c 2 d 3 e 3

1 a 22, 27, 32 b 13, 11, 9

2 a 3, 6, 12, 24 b 3, 5, 9, 17

b i

ii The number of matches increases by 5, and points lie in a straight line.

c The number of matches needed is five times the number of pentagons.

d y = 5 x, y = 5x e 10004 a

b Multiply the shape number by 5 and add 1.c 501

5 a 13 b 23 c 1036 5, 7, 9, 11, 13

Exercise 1G

1 a 14x b 6y c 7a2 d 6ac

2 a 60n b 10a c 24m d 35p

3 a 5a b 4m c bc d 4m

4 a wx 3y b 0

5 a b c d 3

6 a a2 an b 2mn2 5mn

c 12p2 + 8p d 8py + 4pw

7 a 31a 23 b 23xy 12x 8y

8 a mn(n + 1) b q(p a)

c 4(p 3d) d 5(5f 3)

9 a 3(k 3) b 4(p + 3d)

10 a A pronumeral is a letter that stands for a number.

b A coefficient is a number in front of a pronumeral.

11 a 24 b

c 59 d 51

14---

110------

710------

14---

920------

14---

12---

113------

15---

45---

25---

35---

t2---

gr---

rg---

4w7

-------

32x------

3 a No. of pentagons 1 2 3 4 5

No. of matches 5 10 15 20 25

No

. of

mat

ches

No. of pentagons

25

20

1510

5

1 2 3 4 5

,

5a7

------

2a15------

q2

5------

288

---------

72

------=

506 Answers

Exercise 1G continued

13

Exer

1 12 a

c

e

g

i

3 a

4 a5 x 6 a

Exer

1

2 a

b (3, 0)

12

LEY_bk953_answers_finalpp Page 506 Thursday, January 13, 2005 3:23 PMa 6d + 23 b

cise 1H

2, 4x = 6 b x = 15x = 9 d x = 7

y = f p = 13

d = 20 h

m = 20 j

b x = 24

No b No+ 23 = 114, x = 91

x 12 b m < 28

cise 1I

b Number of matches equals the number of patterns multiplied by two minus one.

c y = 2x 1d

e (6, 11), (7, 13)4 a (0, 0), (1, 4.5), (2, 9), (4, 18), (5, 22.5),

(10, 45), (20, 90)

b

c $38.25 d 16 kg

a m 1 2 3 4

m 3 1

b N 1 2 3 4 5

L 8 11 14 17 20

13---

23---

43---

3 x 7( )8

--------------------

113

------

c 1410------

75---= =

q 1017------=

p 152

------=

54321

12345

y

x1 1 2 3 4 52345

E (2, 5)

D (3, 2)

B (2, 3) C (3, 4)A (0, 3)

5

6

4

321

1

2

y B

C

A

x1 10 2 3 4 523

3 a No. of patterns 1 2 3 4 5

No. of matches 1 3 5 7 9

5 x 2 1 0 1 2

y 7 5 3 1 1

No

. of

mat

ches

No. of pattern

10

12

14

8

64

2

1 2 3 4 5 6 7

Co

st (

$)

No. of kg

Cost for various quantities of washing powder

253035

201510

5

606570

55504540

95100

90858075

2 4 6 8 10 12 14 16 18 20

507Answers

5

b

Exerc

1 ab

2 a

3 a4 a

5 Fa

6

7 ac

6 a

y 8 a Score Tally Frequency

LEY_bk953_answers_finalpp Page 507 Thursday, January 13, 2005 3:23 PMy = 3x + 6

ise 1J

about 90 beats per minute5 minutes c twice

jogging b c 200

$4 b 50 g23 p.m. b 40 km

vourite snacks

nominal b numericalnumerical

b

c i 60 ii 14 iii The game was a draw.

b 10

x 2 1 0 1 2

y 0 3 6 9 12

32

1

1

3

4

5

6

7

8

2

x1 10 2 323

118------

Hot chips Hamburger Chicken Pie

Kebab

Dis

tan

ce f

rom

ho

me

(km

)

Time

Jacks journey

125

100

7550

25

7 a.m

.

8 a.m

.

9 a.m

.

10 a.

m.

11 a.

m.

1 p.

m.

12 p

.m.

2 p.

m.

0 16

1 9

2 14

3 12

4 6

5 3

Total 60

9 a Score Tally Frequency

1 3

2 5

3 1

4 3

5 3

6 7

7 4

8 3

9 4

10 3

Total 36

|||| |||| |||| |

|||| ||||

|||| |||| ||||

|||| |||| ||

|||| |

|||

Freq

uen

cy

Score

10

12

14

16

18

8

64

2

10 2 3 4 5

Winning margins in a series of soccer matches

|||

||||

|

|||

|||

|||| ||

||||

|||

||||

|||

508 Answers

Exercise 1J continued

10

11

12

Exer

1 O2 S

co

3 You would use a sample of people that like or do

LEY_bk953_answers_finalpp Page 508 Thursday, January 13, 2005 3:23 PMa

b

cise 1K

nly a part of the whole population.ample, as a census is too costly and time nsuming.

skateboarding.4 a 16.5 b 19 c 17 d 105 a 41.48 b 44 c 41 d 366 a Class A: mode = 28 and 46, range = 39,

mean = 43.13, median = 42.Class B: mode = 51, range = 46, mean = 40.67, median = 41.

b Class A

7 a b 208

Exercise 1L

1 Student to answer.2 a 270 mm b 4000 mm3 a 34 cm b 7000 m4 76.4 cm5 a 174.7 cm b 102.94 cm6 126.52 cm7 x = 9.12 cm, y = 12.6 cm, w = 7.2 cm,

z = 12.6 cm, perimeter = 90.2 m

8 29 units2

9 a 180 mm2 b 49 cm2

c 10 m2 d 44 cm2

10 a 104 cm2 b 5400 mm2

c 243 m2

11 a 22 m2 b 2100 cm2

12 a 50 mm b 8 mc 64 cm d 1160 cme 438 mm f 84 m

g 800 mm2 h 72 000 cm2

i 90 cm2

13 a i b ii b2 = a2 + c2

b i PR ii PR2 = QR2 + PQ2

14 a No b Yes15 a 81 b 8.416 a 7.5 cm b 17.1 cm17 a 6.0 cm b 38.7 cm18 a 14.4 cm b 27.2 cm19 50.91 cm20 a diameter b chord

21 22 C = d 23 35.8 cm

24 C = 2 r 25 42.73 cm 26 A = r2

27 a 153.9 cm2 b 11.9 cm2

28 96.8 cm2

Exercise 1M

1 a DCGH b ABCD, EFGHc AEHD, BFGC

Stem Leaf

1213141516

81 2 2 82 2 4 5 5 5 5 6 8 90 0 1 31

Soft

drink

Still

wate

rJui

ce

Tea/

coffe

eOt

her

Freq

uen

cy

Drink

10

12

14

16

18

20

8

64

2

Choice of drink

Soft drink

Still waterJuiceTea/coffeeOther

Drink Frequency

Pric

e ($

)

Day

Price of CML shares

7.207.257.30

7.157.107.057.00

7.557.607.65

7.507.457.407.35

7.807.757.70

M T W T F M T W T F

1350------

310------

509Answers

2 a 2

3 a4 a

5 a

6 a

7 27

8 a

9 a

ce

Exerc

1 482 a3 3 4 a5 7.7 2

Exerc

1 abcd

2 a

b

3 a

LEY_bk953_answers_finalpp Page 509 Thursday, January 13, 2005 3:23 PMb 86.64 cm

338.72 cm2 b 492 cm2

b

b

3163.5 cm3 b 3469.44 cm3

946 cm3

3546.86 cm3 b 793.27 cm3

1000 mm3 b 1 000 000 mL

1 000 000 cm3 d 1000 L1 kL

ise 1N

hours4 min b 5 hours

h 30 min9 h 23 min b 1 h 39 min

17 a.m. 6 3 h 48 minh 20 min 8 317

ise 1O

rectangular prismsrectangular prism and triangular prismcylinder and conecube and square based pyramid

4 5

6 a FE, DE, BE b FE c FD, CA

Exercise 1P

1 a EBD, GEB, alternateb EJO, NOR, corresponding

2 Student to answer.3 a acute b right-angled

c obtuse d right-angled4 a Two or more angles that share a common

vertex and arm and add to give 90.

b

5 a 45 b 120 c 108 d 476 vertically opposite angle7 i 55 straight angle

ii 55 vertically opposite QRU8 a k = 65, co-interior angles, supplementary,

parallel linesb n = 107, straight line is 180

9 a x = 83 vertically oppositeb x = 142 angles at a point

10 a Yesb Yes, corresponding angles equal and

parallel to a third line.

Exercise 1Q

1 Student to answer.2

3 a x = 56, base angles of isosceles b x = 56, exterior angle of

4 x = 180 120 40 10, x = 10, angle sum of 5 u = 38 (supplementary angles), v = 99 (angle

sum of ), w = 85 (angle sum of ), x = 85 (vertically opposite w), y = 81 (supplementary angles), z = 14 (angle sum of )

6 a b 2 axes of symmetry 4 sides equal diagonals bisect each

other at right angles opposite angles equal opposite sides parallel

3.8 cm

i ii iii

i ii iii

b

510 Answers

Exercise 1Q continued

7 S8 a

Exer

1 a

2

a

3 a

4 y 5 a6 67 S

CHAP

Diag

159

13

Exer

1 a

2 ac

3 a4 a

bcde

5 adgj

Exercise 2B

LEY_bk953_answers_finalpp Page 510 Thursday, January 13, 2005 3:23 PMtudent to answer.b 1 diagonal inside

1 diagonal outside

cise 1R

b

nd

, x = 9 b , x = , y = 20

= 24ST b SU c TU

.75 mtudent to answer.

TER 2

nostic Test

B 2 D 3 D 4 BA 6 D 7 B 8 AC 10 B 11 D 12 CB 14 D 15 A 16 B

cise 2A

45 b 4 to the power 5 c i 4 ii 5

109 b 10 to the power of 9 or to the ninthi 10 ii 9

37 b 210 c 43 d 56 e 24

i 3 ii 5 iii 3 3 3 3 3i 2 ii 4 iii 2 2 2 2i 7 ii 3 iii 7 7 7i 9 ii 6 iii 9 9 9 9 9 9i 5 ii 8 iii 5 5 5 5 5 5 5 51024 b 2401 c 2431 000 000 e 625 f 6561216 h 729 i 32 768390 625

1 a i 7 7 7 ii 7 7 7 7iii 7 7 7 7 7 7 7

b 77 c Yes2 a i 5 5 5 5 ii 5 5

iii 5 5 5 5 5 5

b 56 c Yes3 a i 6 6 6 ii 6 6 6 6 6

iii 6 6 6 6 6 6 6 6

b 68 c Yes

4 a 39 b 212 c 710 d 59 e 416

f 613 g 109 h 220 i 530 j 318

5 a 55 b 38 c 210 d 59 e 712

6 a i 3 3 3 3 3 4 4ii 12 12 12 12 12 12 12

b No, bases are different.7 a i 5 5 5 2 2 2 2 2

ii 10 10 10 10 10 10 10 10b No, bases are different.

8 a i 3 3 3 3 3 3 3ii 9 9 9 9 9 9 9

b No, bases are different.9 a i 2 2 2 2 2 2 2 2

ii 4 4 4 4 4 4 4 4b No, bases are different.

10 a T b F c F d T e Ff F g T h F i F

11 a 213 b 318 c 514 d 410 e 510

Exercise 2C

1 a 36 b 56 c 212 d 315 e 720

f 1010 g 412 h 621 i 324 j 270

2 a 311 b 217 c 514 d 319 e 716

f 218 g 514 h 717 i 328 j 922

Exercise 2D

1 a

b 35 c Yes

2 a

b 72 c Yes3 a

b 25 c Yes4 a 32 b 23 c 56 d 44 e 105

f 64 g 22 h 32 i 41 j 51

k 34 l 55 m 26 n 103 o 78

1 right-angledtriangle

trapesium

38---

15---

95---

3 3 3 3 3 3 33 3

------------------------------------------------------------- 3 3 3 3 3=

7 7 7 7 77 7 7

----------------------------------------- 7 7=

2 2 2 2 2 2 2 22 2 2

---------------------------------------------------------------------- 2 2 2 2 2=

511Answers

5 a T b F c F d Fe

6 arim

Exerc

3 a

c

4 a

c

5 ad

6 ad

Exerc

2

10

10

3 a

c

4 a

c

5 a

e

1

3

2

3

1

3

2

1

1 1 1 1

LEY_bk953_answers_finalpp Page 511 Thursday, January 13, 2005 3:23 PMF f F g F h F35 b 27 c 72 d 58

43 f 38 g 59 h 37

29 j 510 k 23 l 37

26 n 53 o 35 p 710

ise 2E

73 3 = 70 b

70 = 1

95 5 = 90 b

90 = 1

1 b 1 c 11 e 1 f 11 b 1 c 11 e 1 f 1

ise 2F

1 = , 22 = = , 23 = =

1 = , 102 = = ,

3 = =

22 5 = 23 b

23 =

53 7 = 54 b

54 =

b c d

f g h

i j k l

m n o

6 a b c

d e f

g h i

j k l

m n 2 o

7 a 21 b 22 c 28 d 25

e 23 f 51 g 72 h 43

i 34 j 56 k 310 l 61

m 75 n 49 o 101

Exercise 2G

1 a 3 b 3 c

2 a 7 b 7 c

3 a 5 b 5 c

4 a 2 b 2 c

5 a b c

d e f

g h i

j6 a 7 b 2 c 10

d 3 e 5 f 10

7 a b c

d e f

Exercise 2H

1 a Yes b No c No d Yes e No

f Yes g No h No i No j Yes

3 a 3 106 b 7 104 c 8 103

d 6 105 e 5 102

4 a 4.8 103 b 3.92 105

c 6.4 104 d 2.18 106

e 7.6 102

5 a 30 000 b 7000

55 54 53 52 51 50

125 625 125 25 5 1

25 24 23 22 21 20

2 16 8 4 2 1

25 24 23 22 21 20 21 22 23

2 16 8 4 2 1

105 104 103 102 101 100 101 102 103

00 000 10 000 1000 100 10 1

7 7 77 7 7---------------------- 1=

1 1 1

1 1 1

9 9 9 9 99 9 9 9 9----------------------------------------- 1=

1 1 1 1 1

1 1 1 1 1

12---

14---

18---

121------

14---

122------

18---

123------

110------

1100----------

11000-------------

1101---------

1100----------

1102---------

11000-------------

1103---------

2 22 2 2 2 2-----------------------------------------

123------=

1 1

1 1123------

5 5 55 5 5 5 5 5 5-------------------------------------------------------------

154------=

1 1 1

1 1 1154------

131------

143------

125------

182------

154------

1121---------

192------

161------

2 100 101 102 103 104 105 106

1 10 100 1000 10 000 100 000 1 000 000

73------

36------

28------

51------

1105---------

1510--------

1415--------

19---

132------

164------

1625----------

11024-------------

1216----------

181------

181------

13125-------------

1512----------

1343----------

1256----------

1729----------

12---

47---

3

7

53

23

293 29 133

13 273 693

31 47 1953

278

512---

312---

413---

213---

1012---

1213---

512 Answers

Exercise 2H continued

cegi

7 a

d8 a

ce

9 a

b

c

d

e

10

11

12

13

14

15

Exer

1 a

d 6 1015 e 2.0 1012 f 3 1010

6 0

LEY_bk953_answers_finalpp Page 512 Thursday, January 13, 2005 3:23 PM9 000 000 d 400 000800 f 460 0006710 h 3 900 00083 600 j 520 000

3 103 b 7 106 c 5 104

2 105 e 9 102

0.06 b 0.000 0030.002 d 0.00050.000 009

3 104 = 30 000, 34 = 81

5 102 = 0.05, 52 =

2 103 = 2000, 23 = 8

2 105 = 0.000 02, 25 =

4 106 = 4 000 000, 46 = 4096

a 3.72 105 b 5.4 104

c 2.98 106 d 3.4 103

e 6.09 105 f 8.75 104

g 7.698 106 h 3.61 108

i 8.0 103 j 5.6 107

a 5.7 104 b 7.8 105

c 6.1 103 d 2.96 106

e 8.01 104 f 5 107

g 4.39 103 h 2.8 106

i 9 105 j 4.9 109

a 7 320 000 b 52 000c 567 000 d 3800e 92 700 000 f 69 140g 3 275 000 h 700 000i 200 000 000 j 308 000a 0.000 003 98 b 0.000 53c 0.000 070 9 d 0.008 8e 0.000 005 9 f 0.000 000 307g 0.000 6 h 0.000 003i 0.000 027 1 j 0.000 000 000 36

a 1.29 105 b 1.52 108 km

c 2.54 109 cm d 2.6 107 m

e 1.07 105 km/ha 78 300 000 km b 1 400 000 000c 0.000 028 md 0.000 000 002 5 hourse 10 000 000 000 000

cise 2I

1.2 1015 b 2.4 1022 c 4.2 109

g 3 1010 h 2 1012 i 8 1015

j 4.9 1019 k 2.7 1017 l 6.4 1019

2 a 1.536 1020 b 2.43 1019

c 9 108 d 2.7 1018

e 8 106 f 7.5 1019

g 2.5 1021 h 1.4 1012

i 1.6 1033 j 2.704 1011

k 2.16 1038 l 3.125 1037

m 2.5 109 n 3.7 1012

o 3 106 p 5 105

3 a 3.11 108 b Positivec Bigger

4 a 2.5928 108 b Negativec Smaller

5 a 4.37 104 b Positivec Bigger

6 a 4.6 1014 < 7.2 1015

b 4.5 1016 < 3.4 1018

c 9.6 1012 < 6.8 109

d 7.8 108 < 3.8 106

e 2.5 104 < 7.1 105

f 2.9 1016 < 3 1016

g 6.4 1010 < 8.5 1010

h 8.1 1014 < 2.8 1015 < 5.9 1016

i 8.9 108 < 5 106 < 3.9 105

j 7.8 105 < 8.3 103 < 6.3 106

7 1.08 109 km8 Alpha Centauri

9 2.54 103 cm or 0.002 54 cm10 400 days11 a b

12 350 000 m2/person

Non-calculator Activities

1 a 94 b 177

2 a base = 3, index = 11b base = 5, index = 9

3 a 8 8 8 8 8 8 b 7 7 74 a 32 b 81

5 a 612 b 340 c 86

d 319 e 2120

6 a F b F7 a b c

8 a b 6 c 2 d 1

9 a 3.6 105 b 6.5 106

.1 0.01 0.001 0.0001 0.000 01 0.000 001110------

1100----------

11000-------------

110 000------------------

1100 000---------------------

11 000 000--------------------------

125------

132------

0.000 000 3 s 0.3 0 s

174------ 3 103

18---

513Answers

10 a 700 000 b 0.000 12

11

12

13

Lang

1 abcde

2 a

d3 a4 a

5 23

6 Scno

7 Scre

e.i.einre

8 ab

9 3 10

Chec

159

13

Revie

1 a2 a

b3 a4 a5 a

6 a

7 a

8 a

9 a 2.3 107 b 5 105

LEY_bk953_answers_finalpp Page 513 Thursday, January 13, 2005 3:23 PM2 105 = 200 000, 25 = 32

a 1.5 1015 b 3 1023

c 9 1012 d 2 106

a 6.7 1012 < 3.5 1013

b 5.3 1016 < 4.2 1010

uage in Mathematics

three to the power of fiveeight squaredtwo cubedthe square root of seven the cube root of nine

72 b 43 c 65

24 e findex b exponentbase b power, index or exponent

24 = 27 = 128; 47 = 16 384ientific notation is also known as index tation.ientific notation is a way of writing the peated product of numbers,

g. 3 3 3 3 = 34. Write down the base (3), . the number being repeated, and then the dex, i.e. the number of times the base is peated.

The number is not between 1 and 10.The second number is not written as a power of 10.

104 = 30 000 while 34 = 3 3 3 3 = 81.Student to answer.

k Your Skills

A 2 D 3 D 4 BB 6 C 7 B 8 BA 10 C 11 D 12 BC 14 B 15 C 16 D

w Set 2A

24 b 57

base = 7, index = 9base = 3, index = 103 3 3 3 3 b 7 7 7 7 7 76561 b 15 625F b F

532 b 415 c 22 d 76 e 54

b c

b 2 c 3 d 1

10 a 98 000 b 0.000 037

11 7 105 = 700 000, 75 = 16 807

12 a 1.19 1014 b 4 105

c 2.43 1047 d 1.5 106

13 a 4.6 1013 < 3.8 1015

b 7.7 1016 < 3.1 1012

Review Set 2B

1 a 75 b 97


3 a 6 6 6 6 b 7 7 74 a 512 b 729

5 a 313 b 712 c 45 d 611 e 230

6 a F b F

7 a b c

8 a b 3 c 2 d 1

9 a 4.6 104 b 3 104

10 a 40 000 000 b 0.000 001 8

11 4 106 = 4 000 000, 46 = 4096

12 a 1.56 109 b 5 1015

c 2.43 1028 d 1.4 105

13 a 4.1 109 < 5 109

b 3.1 1015 < 4.5 1011

Review Set 2C

1 a 28 b 103


3 a 6 6 b 5 5 5 5 5 5 54 a 625 b 2187

5 a 919 b 215 c 58 d 610 e 246

6 a F b F

7 a b c

8 a b 2 c 4 d 1

9 a 1.7 1010 b 3.5 107

10 a 286 000 b 0.000 306

11 3 104 = 30 000, 34 = 81

12 a 1.59 1013 b 9 106

c 5.329 1031 d 5 103

13 a 2.95 1015 < 2.94 1016

b 6.5 1014 < 1.4 1010

6 53

146------ 3 153

1125----------

175------ 6 93

136------

148------ 3 23

164------

514 Answers

Review Set 2D

1 a2 a

b3 a

b4 a

5 a6 a

7 a

8 a

9 a10

11

12

13

CHAP

Diag

1 B5 C9 D

Exer

2 a

1 a

3 a cf b cf c cf

LEY_bk953_answers_finalpp Page 514 Thursday, January 13, 2005 3:23 PM65 b 58

base = 6, index = 8base = 3, index = 104 4 4 4 42 2 2 2 2 2 21296 b 4096

540 b 370 c 54 d 422 e 345

F b F

b c

b 10 c 5 d 1

2.05 108 b 3.56 104

a 42 100 000 b 0.000 09

2 106 = 2 000 000, 26 = 64

a 2.25 1025 b 6.5 1022

c 1.6 1073 d 7 103

a 4.7 1010 < 7.6 1010

b 3.5 1016 < 2.4 1011

TER 3

nostic Test

2 C 3 C 4 A6 C 7 C 8 B

10 B 11 A 12 B

cise 3A

5 b 19 c 44

4 a 4.2 b 19 c 43.6

e

f x b f x c f x

16 51 80

33 90 164

60 209 336

85 80 387

18 42 440

35 22 315

138

94

96

165------ 34 513

132------

8 3 2

19 8 6

34 19 14

51 23 23

54 25 33

59 26 40

43

45

47

5 a No. of glasses Freq. cf

0 10 10

1 3 13

2 5 18

3 2 20

4 6 26

5 4 30

Total 30

6 a & b Days absent Freq. cf

1 3 3

2 6 9

3 8 17

4 3 20

5 1 21

6 2 23

7 5 28

Total 28

b 2c i 18

ii 20d 12

Freq

uen

cy

No. of glasses

Water drunk by 9 Orange in a day

5

6

7

8

9

10

4

32

1

10 2 3 4 5

c 9d 19

515Answers

Exerc

1 a

b

c7 a

Cumulative frequency

LEY_bk953_answers_finalpp Page 515 Thursday, January 13, 2005 3:23 PMise 3B

d

& b Number of days Freq. cf

1 8 8

2 5 13

3 3 16

4 4 20

5 6 26

6 3 29

7 1 30

Total 30

c 8d 4

Cum

ulat

ive

freq

uen

cy

Class


51015202530354045

5550

147 154 161 168 175 182 189140

26

11

26

37

44

52

Cum

ulat

ive

freq

uen

cy

Class


51015202530354045

79 88 97 106 115 124 13370

6

1319

2327

34

43

2 a Class FrequencyCumulative frequency

2024 8 8

2529 4 12

3034 9 21

3539 12 33

4044 5 38

4549 2 40

b Class FrequencyCumulative frequency

7078 6 6

7987 10 16

8896 11 27

97105 4 31

106114 8 39

115123 6 45

Cum

ulat

ive

freq

uen

cy

Class

10

20

30

40

50

90

80

70

60

50 60 70 80 90 10040

16

29

44

56

7782

Cum

ulat

ive

freq

uen

cy

Class


51015202530354045

5550

25 30 35 40 45 5020

7

2026

43 45

53

516 Answers

Exercise 3B continued

Exer

1 a2 a

3 a

bc

d

c

d

4 a

5 a cf b 3140

LEY_bk953_answers_finalpp Page 516 Thursday, January 13, 2005 3:23 PMcise 3C

26 b 27 c 44 d 6534 b 18 c 56 d 17

27 b 28 c 83 d 24

3039

33

c

d about 33 or 34

c

d 31

Class FrequencyCumulative frequency

4049 4 4

5059 7 11

6069 5 16

7079 8 24

8089 6 30

9099 9 39

Class FrequencyCumulative frequency

2024 9 9

2529 12 21

3034 7 28

3539 4 32

4044 20 52

4549 16 68

Score Frequency cf

09 2 2

1019 5 7

2029 15 22

3039 31 53

4049 7 60

Total 60

Cum

ulat

ive

freq

uen

cy

Class


10

20

30

40

50

60

10 20 30 40 490

27

22

53

60

3

20

47

52

55

6 a cf

165

277

380

509

603

688

761

783

792

Cum

ulat

ive

freq

uen

cyClass


51015202530354045

5550

21 31 41 51 6011

b 3039

Cum

ulat

ive

freq

uen

cy

Age range

Age last birthday

100200

300

400500

600

700

800

10 20 30 40 50 60 70 80 900

517Answers

Exercise 3D

b

b

b

c Scores are not so spread out but the classes

1 a

2 a

3 a

LEY_bk953_answers_finalpp Page 517 Thursday, January 13, 2005 3:23 PMare closer in number.

Exercise 3E

Mean = 10.32 Mean = 122.5

Mean = 87.62 a 11 b 122 and 123 c 893 a 65.3 b 31.8 c 45.3 d 8674 a 64 b 30 c 55 d 8405 a 15 b 25 c 37

d 25.5 e 28 f 37.5g 54.5 h 18 i 20

j 20.5

b 1620 c 18.7

b 32.95

Group Tally Frequency

1019 6

2029 6

3039 11

4049 7

Classes Tally Frequency

410 4

1117 10

1824 12

2531 5

3238 9

Total 40

Classes Tally Frequency

412 7

1321 13

2230 9

3139 11

Total 40

|||| |

|||| |

|||| |||| |

|||| ||

Freq

uen

cy

Class boundaries

Frequency histogram

5

10

15

10 20 30 40 50

6 6

11

7

||||

|||| ||||

|||| |||| ||

||||

|||| ||||

Freq

uen

cy

Classes

Frequency histogram

5

10

15

4 11 18 25 32 38

4

1012

5

9

|||| ||

|||| |||| |||

|||| ||||

|||| |||| |

Freq

uen

cy

Classes

5

10

15

4 13 22 31 39

7

139

11

1 a x f fx b x f fx

8 1 8 121 4 484

9 6 54 122 11 1342

10 5 50 123 11 1353

11 10 110 124 3 372

12 3 36 125 1 125

T 25 258 T 30 3676

c x f fx

85 1 85

86 10 860

87 8 696

88 4 352

89 16 1424

T 39 3417

6 a Class Class centre Frequency

610 8 7

1115 13 8

1620 18 16

2125 23 12

2630 28 4

3135 33 3

7 aNo. of items

Class centre

Frequency fx

1120 15.5 3 46.5

2130 25.5 18 459

3140 35.5 26 923

4150 45.5 6 273

5160 55.5 2 111

55 1813.5

518 Answers

Exercise 3E continued

8 3

c

d i a

9 a

b

Freq

uen

cy

2

4

6

0

LEY_bk953_answers_finalpp Page 518 Thursday, January 13, 2005 3:23 PM1.73 32

The first gives a downward trend while the second one is more even in height.

Class intervals

Tally c.c. Frequency cf

1625 20.5 11 11

2635 30.5 10 21

3645 40.5 8 29

4655 50.5 2 31

5665 60.5 4 35

Class intervals

Tally C.c. Frequency cf

1620 18 5 5

2125 23 6 11

2630 28 4 15

3135 33 6 21

3640 38 5 26

4145 43 3 29

4650 48 1 30

5155 53 1 31

5660 58 2 33

6165 63 2 35

|||| |||| |

|||| ||||

|||| |||

||

||||

Freq

uen

cy

Class intervals

Ages of a ICDL class

5

10

15

20

160 26 36 46 56 65

11 108

24

||||

|||| |

||||

|||| |

||||

|||

|

|

||

||

Class intervals

Ages of a ICDL class

16 21 26 31 36 41 46 51 56 61 65

56

4

65

3

1 12 2

Class intervals

TallyClass centre

Freq. cf

1625 20.5 3 3

2635 30.5 6 9

3645 40.5 11 20

4655 50.5 10 30

5665 60.5 5 35

|||

|||| |

|||| |||| |

|||| ||||

||||

bClass

intervalsTally C.c. f cf

1620 18 2 2

2125 23 1 3

2630 28 3 6

3135 33 3 9

3640 38 7 16

4145 43 4 20

4650 48 4 24

5155 53 6 30

5660 58 2 32

6165 63 3 35

||

|

|||

|||

|||| ||

||||

||||

|||| |

||

|||

Freq

uen

cy

Class interval

2

4

6

8

10

12

16 26 36 46 56 660

3

6

11

5

10

Age of next ICDL classHistogram 1:

ii

519Answers

ef

g10

11

12

13

Non-c

1

4

7

10

13

16

19

22

25

Lang

2 ad

3 abc

d

e

f The grouped data is used to estimate mean Fr

eque

ncy

gii

iii Ty

iv Ttw

LEY_bk953_answers_finalpp Page 519 Thursday, January 13, 2005 3:23 PMi 34.2 ii 34.3 iii 42.8 iv 42.7i 1626 ii 2125, 3135iii3645 iv 3640i 33 ii 33 iii 41 iv 41

a 60 b 104.4c 3144 km d $185 604a 9 b 15 c 15d 11 e 37a 17.25 b 25.3 (1 d.p.)c 8.7 (1 d.p.)a 17.7 (1 d.p.) 14 10.1 15 12 and 6

alculator Activities

3 2 45.88 3 16 290

$693 5 60 6 104

6 8 0.015 9 3417.86

D 11 36 12

9C 14 10 15 0.0007

$60 17 76 18 25

53 20 50 21 5

Yes 23 8 24 24 cm2

4905

uage in Mathematics

cumulative b median c ogivehistogram e frequency f estimateThe mean is the average.The median is the middle score.The centre is used to calculate the mean class.The modal class is the class with the highest frequency.The ogive is another name for cumulative frequency polygon.

for the ogive.4 The mean, mode and median are central to the

study of statistics.

Check Your Skills

1 C 2 C 3 A 4 D5 C 6 A 7 C 8 B9 B 10 D 11 B 12 A

13 B

Review Set 3A

1 a mean = 24.98, mode = 26, median = 26b Student to answer.

b

c 04 d 10.1 e 8

Review Set 3B

1 a mean = 10.88, mode = 9, median = 10b Student to answer.

Class interval

2

4

6

8

16 21 26 31 36 41 46 51 560

21

3 34 4

67

Age of next ICDL class

he first class has a greater number of ounger students.he second histogram shows that there are wo classes that are bigger than the others, hile the first shows them as about the same.

25---

78---

13---

2 a cf

12

21

26

29

30

32

33

34

Cum

ulat

ive

freq

uen

cy

No. of days

No. of time students of 9 Redate take-away

2468

1012141618

2220

5

12

21

26

29 3032

33 34

10 15 20 25 3530 400

242628303234

520 Answers

Review Set 3B continued

bc

d

Revie

1 a

b

b

c

Revie

1 ab

2 a

2 a

LEY_bk953_answers_finalpp Page 520 Thursday, January 13, 2005 3:23 PM28It is within a group and individual scores are not known in this case.39 e 37.7 f 3843

w Set 3C

mean = 6.03, mode = 6, median = 6

Student to answer.

163 d 160

w Set 3D

mean = 22, mode = 22, median = 22Student to answer.

c 24 d 4 e 1.6 f 1 g 1

CHAPTER 4

Diagnostic Test

1 A 2 C 3 B 4 C5 B 6 D 7 C 8 A9 A 10 C 11 A 12 D

13 C 14 A 15 C 16 D17 C 18 C 19 D 20 A21 C 22 A

Exercise 4A

1 a b c d e

2 a b c d e

f g h i 2b j

3 a b c d e

4 a b c d e

f g h i j

5 a b c

d e

6 a b c d

e f 7 g h 2a

i j 10p

7 a b c d e

8 a b c d 4 e

f g 3 h i j

Class Frequency

2025 5

2631 13

3237 12

3843 14

4449 9

5055 5

5662 2

cf

5

14

26

29

29

30

Cum

ulat

ive

freq

uen

cy

Class

Height of Year 9 Red students

5

10

15

20

25

30

150 160 170 180 200140

5

14

2629

190

29 30

2 a & b Score Frequency cf

0 8 8

1 9 17

2 7 24

3 2 26

4 1 27

5 3 30

6y15------

8m6

--------

35k20

----------

30t100----------

30a12

----------

x2---

m3----

t4---

2y3

------

3b4

------

67---

310------

23---

4p3

------

7x10------

15b11

----------

a3---

3m10--------

2k3

------

11x12

---------

19k12

----------

5b8

------

7a10------

2z15------

47t90---------

5w4

-------

17v6

---------

e2---

11x24

---------

mn12--------

km15--------

2pq15

----------

12a35b----------

10bd21ce-------------

6mn7

------------

4km15

-----------

3wz2

-----------

3ab2

----------

2t3u------

12---

34---

40n9

----------

7a5b------

w3z------

pq20------

24mn--------

adbc------

5x12y---------

7a4b------

3p2q------

23---

23---

1235------

13---

28m2-------

10y3

---------

34k------

521Answers

Exercise 4B

1 St2 a3 a4 a

5 a

6 a

7 a

8 a

f9 a

b10 a

fk

Exerc

1 a

f

k

2 a

d

g

3 a

e

i

4 a

d

g

j

5 a

d

g

j

Exerc

123 a

fk

Exercise 4E

LEY_bk953_answers_finalpp Page 521 Thursday, January 13, 2005 3:23 PMudent to answer.i 512 ii 512 b Yesi 15 625 ii 15 625 b Yesi 6561 ii 6561 b Yes

m9 b q15 c t19 d b20 e v13

a2 b x10 c w6 d b e z

b8 b h15 c k16 d z60 e n8

m6 b x3 c b24 d m13 e v70

n g b7 h y 25 i t31 j a6

Bases are different.Bases are different.T b F c F d T e FT g F h T i F j FT l F

ise 4C

x6 b w5 c m2 d k3 e a3

y2 g z h x7 i k9 j m11

a32 l t20 m y5 n a5 o b40

12m12 b 10p10 c 18t12

70a16 e 24w19 f 30b9

24z17 h 80q18 i 18d18

2m5 b 2a5 c 3w2 d

f g h

j

27a12 b 64m18 c 49p10

10 000k8 e 125t33 f x15y10

m12n18 h p28q12 i a8b 20

8x15y 6

8a8b5 b 10m10n8 c 12p11q15

30x10y4 e 12w14z17 f

3x4y7 h i

ise 4D

Student to answer.1 b 1 c 3 d 4 e 91 g 1 h 10 i 8 j 14 l 6 m 13 n 5 o 2

12 Student to answer.

3 a b c d e

f g h

4 a b c d

e f g h56 Student to answer.

7 a b c

d e f

g h

8 a b c

d e f

g h

9 a b c d

e f g h

10 a b c d

e f g h

Exercise 4F


6 a b c d e

7 a a8 b k2 c x11 d n14 e z20

8 a b c

d e f

Exercise 4G

1 a 12z b 4 c 24m

d 3 e k2

2 a a7 b y4 c e2 d n

e b8 f w5 g z2 h k4

i y8 j t 20

3 a 90a2 b 18b7 c 6v 4 d 4y6

e 3p6 f g 125z12 h 32m15

i 9w 12 j 2n2

4 a F b F c T d F e Tf F g F h T i T


4z4

3---------

4k6

3---------

3e4

2---------

m5

3-------

a5

2------

3t7

4--------

3b5

4---------

3a2b4

2----------------

k4m6

5-------------

3a3b5

4----------------

4m5

--------

312---

1212---

x12---

m12---

5k( )12---

5k12---

6y12---

6y( )12---

8 13 p q

3z 2m 5 k 4 t

213---

913---

c13---

w13---

5y( )13---

5y13---

9m( )13---

9m13---

123 353 k3

d3 6m3 6 m3

7v3 7 v3

4712---

p12---

x13---

8p13---

5x12---

6x13---

4x12---

3r13---

53 6 x3 t

5p 6r3 5xy 4pq3

1y 2------

1k---

1m3-------

1x6-----

1t10-------

3k---

13k------

2y 5------

132y 5-------------

3t4----

181t 4------------

3k 2

8------------

522 Answers

Exercise 4H

1 ac

e

gi

2 a

c

e

g

i3 a

dgj

4 a

c

e5 a

dgj

6 adgj

7 adg

j8 a

ceg

i

Exer

1 aceg

i2 a

ce

3 acegi

4 a p(p + 3) b k(k 2)

LEY_bk953_answers_finalpp Page 522 Thursday, January 13, 2005 3:23 PM6w + 15 b 18z 1220a + 15b d 8x 6y

10x2 + 60 f 7ab 14a2

4m2 + 4n2 h 2m3 6mn20b + 10a + 15 j 15x 9y 6z

6ab + 12ac b 12x 2 8xy

60k2 40km d m3 + 2m

y 5 4y 2 f 12xy 30x3

6k4 + 15k2 h 5a5 2a3

2p7 + 6p8 j 10x5 15x3y2y 6 b 5a 10 c 3w 124m + 28 e t 3 f b 66k 15 h 8m + 10 i 7w 34x + 1

6a3 4a2b b 8x3 + 12x2y

9p4 12p3q d 4y5 + 3xy 4

6m6 15m5n4a + 18 b 6b 12 c 12w 110y 17 e 18z 2 f 16 + 8x2 + 6b h 33 + 4y i 8 + 6w14 + 20e2 2a b 14 3y c 3 4b19 2v e 5 6w f 22 15t2 15x h 12 6k i 4 12z7 + 20w13k + 9 b 15m + 11 c 14p + 613a 6 e 25x 11 f 14y + 112v 16 h 22x + 2y i 23a 9b

18a2 2a4k + 9 b 2w + 269t 10 d 13z 82a + 14 f d 1810x + 11y h 4a 12b

2q2 14q + 20 j 12z2 + 7z + 1

cise 4I

2(4a + 5) b 2(3x 2)3(a + 2b) d 5(x + 2y)4(w 3) f 8(2m 1)4(3ab + 2) h 10(m 2n)

6(4k 3n) j 8(2x2 + 3y2)5(x + 3y + 2z) b 3(p 2q + 3r)4(a + 3b 2c) d 6(2m n 3r)10(2xy + 5z + 3)y(y + 7) b m(m 3)m(3n + 4) d p(9 5q)x(x + 5y) f b(2c b)3m(2m 1) h 2a(6a 5b)4p(4q 3p) j 6k(2k + 3)

c w(3w + 2) d z(2z 1)e m(4n 3m) f 2x(x + 4)g 4p(q 3p) h 4p(2q 3r)i 5z(2z 1) j 2m(3k 4m)

5 Student to answer.6 a x(x + 4) b y(y 7)

c a(a + b) d m(m 5n)e 2k(k + 2) f 3y(y 4)g 5b(2b + a) h 3w(3w 2)i 6p(2q 3p) j 8k(2m + 3k)

7 a 2a(b + 2 + 2a) b 3x(2x + 1 + 3y)c 2m(1 3m + 2n) d 5x(y 2 x)e 2k(4k 3 5m)

Language in Mathematics

1 reduce, substitute, apply2 a a factor b zero c index

d algebraic e factorise4 a x squared (to the power of 2)

b square root of xc x cubed (to the power of 3)d cube root of x

5 a parentheses b bracketsc braces

Check Your Skills

1 D 2 C 3 A 4 B5 A 6 D 7 A 8 B9 C 10 C 11 B 12 B

13 D 14 A 15 B 16 B17 A 18 A 19 C 20 B21 A 22 D

Review Set 4A

1 a b

2 a b

3 a b c d

4 a y17 b k6 c p14

d t8 e 125m12 f 6a6b9

5 a 1 b 5 c 1 d 3

6 a b c d e

7 a b c

8 a y 2 b e8 c n20 d 18b5 e 2k2

9 a T b F c F d T e F

10 a 10v 20w b 2a5 + 4a4 c 12x 15

4x18------

15mn20

---------------

4a5

------

3y2

------

11a13

----------

31m24

-----------

8w2

15----------

5x2y------

x 3 x 3x x3 2 x3

1z3-----

2z3-----

18z3---------

523Answers

11 a 10m + 7 b 7a 2b12

Revie

1 a

2 a

3 a

4 a

e5 a

6 a

d

7 a

8 a

9 a

10

1112

Revie

1 a

2 a

3 a

4 a

d5 a

6 a

d

7 a

8 a

d

9 a

101112 a

c

Review Set 4D

LEY_bk953_answers_finalpp Page 523 Thursday, January 13, 2005 3:23 PMa 4(2w + 5) b x(x + 9) c 4q(p 3q)

w Set 4B

b

b 2b

a b c d

m20 b t20 c z24 d b19

16m28 f 20p7q8

1 b 4 c 1 d 3

b c

e

b c

k4 b m3 c n15 d 20n5 e a3

F b T c F d F e F

a 40p 30 b 3m7 m5 c 2a2 + 5a

a 4q + 32 b 4a2 13a 1a 6(2x 3) b y(2y 7)c a(4a 3b + 2)

w Set 4C

b

b

b c d 1

p14 b y8 c t30

1 e 27v 21 f 18x10y14

1 b 7 c 1 d 12

b c

e

b c

d 8 b n c k6

15a3 e

T b F c F d T e F

a 20w + 8x b 2k7 + 4k5 c 4s + 7a t + 4 b 15y

5(3n 4) b 2b(2b + 3)2m(6m + 7n)

1 a b

2 a b

3 a b c d

4 a y13 b k6 c p50 d c8

e 81h10 f 6a13b11

5 a 1 b 8 c 1 d 1

6 a b c

d e

7 a b c

8 a y 7 b n2 c p15 d 15z3 e

9 a F b F c F d T e T

10 a 12xy 6xz b 3a3m3 + 4m5

c 10 + 4a

11 a 23 + 19n b 4a2 a12 a 6(4x + 3) b h(h 8)

c 3(y 2 + 2y 3)

CHAPTER 5

Diagnostic Test

1 C 2 C 3 D 4 D5 A 6 C 7 B 8 C9 B 10 A 11 B 12 B

13 C 14 C 15 B 16 D

Exercise 5A

1 a 60 b 6 c 600

d 6000 e 6 000 000 f

g h i 600 j

2 a 37 000 b 84 000 c 524 000d 8000 e 19 000 f 623 000g 181 000 h 6000 i 3000j 401 000 k 1000 l 0

3 a 5400 b 16 800 c 20 400d 800 e 400 f 240 200g 3100 h 9600 i 500j 100 k 100 l 0

4 a 670 b 2370 c 830d 1060 e 70 f 30g 310 h 20 060 i 410j 1250 k 10 l 0

9x21------

12ab18

-------------

2m3

--------

17y12

---------

2km5

-----------

910------

c 2 c 2c

c3 2c3

1e4-----

3e4-----

181e4------------

12---

12h20

----------

16xy12

------------

w3----

5m7

--------

8d7

------

b8---

4xy3

---------

78---

q 4 q 4q

q3 4 q3

1b5------

3b5------

1243b5----------------

2m7

3-----------

15b24

----------

35pq10

-------------

5h4

------

2p3

------

5k11------

w18------

6ab5

----------

2740------

m 6 m 6m

m3 6m3

1x2-----

2x2-----

14x2---------

2m3

3-----------

61000-------------

610------

6100----------

610 000------------------

524 Answers

Exercise 5A continued5 a

dgj

6 a

b

c

d

e

7 ad

8 ad

9 ad

1011

12

131415

161718

Exer

1 a

2 a 30 b 28 c 28.5

LEY_bk953_answers_finalpp Page 524 Thursday, January 13, 2005 3:23 PM17 b 25 c 82237 e 583 f 26521 h 106 i 30156 k 1 l 0i 47 000 ii 46 800 iii 46 780iv 46 784i 28 000 ii 28 500 iii 28 460iv 28 457i 39 000 ii 39 200 iii 39 170iv 39 166i 8000 ii 8500 iii 8460iv 8462i 183 000 ii 182 700 iii 182 680iv 182 67930 000 b 60 000 c 180 000200 000 e 800 0004000 b 6000 c 24 00080 000 e 20 000700 b 1800 c 32 600100 e 7000

a 38.3 b 38.27 c 38.268a i 8.4 ii 8.44 iii 8.438b i 6.6 ii 6.58 iii 6.584c i 0.9 ii 0.86 iii 0.863d i 0.2 ii 0.19 iii 0.186e i 18.6 ii 18.56 iii 18.556f i 21.6 ii 21.60 iii 21.603g i 4.1 ii 4.06 iii 4.061h i 5.0 ii 5.04 iii 5.044i i 7.0 ii 7.00 iii 7.007j i 3.0 ii 3.00 iii 3.000a 3.60 b 50.0 c 2.690d 13.00 e 1.00 f 4.900g 100.0 h 70.00a 75 b < 85 c 75 no. < 85a 350 b < 450 c 350 no. < 450a i 27 500 ii < 28 500

iii 27 500 no. < 28 500b i 42.5 ii < 43.5

iii 42.5 no. < 43.5c i 5.65 ii < 5.75

iii 5.65 no. < 5.75d i 6.315 ii < 6.325

iii 6.315 no. < 6.325162.5 height < 163.5 cm415 weight < 425 g12.35 time < 12.45 s

cise 5B

2 b 5 c 1 d 7 e 8

d 28.47 e 28.4713 a i 400 ii 430 iii 428

b i 6000 ii 6200 iii 6240c i 8 ii 7.8 iii 7.82d i 0.5 ii 0.53 iii 0.527e i 50 000 ii 54 000 iii 53 700f i 700 000 ii 730 000 iii 726 000g i 0.04 ii 0.039 iii 0.0393h i 0.005 ii 0.0051 iii 0.005 07i i 6000 ii 6100 iii 6100j i 2000 ii 2000 iii 2010

4 a 370 000 b 240 c 0.005 80d 9.00 e 300 000 f 500g 0.0400 h 0.300 i 0.002 00j 1 000 000

5 a i 555 ii < 565iii 555 no. < 565

b i 8.15 ii < 8.25iii 8.15 no. < 8.25

c i 47.5 ii < 48.5iii 47.5 no. < 48.5

d i 0.715 ii < 0.725iii 0.715 no. < 0.725

e i 36 500 ii < 37 500iii 36 500 no. < 37 500

f i 0.0835 ii < 0.0845iii 0.0835 no. < 0.0845

6 a 482.5 no. < 483.5b 3.855 no. < 3.865c 14 450 no. < 14 550d 0.1275 no. < 0.1285e 56.85 no. < 56.95f 3205 no. < 3215

7 a 295 no. < 305b 2950 no. < 3050c 5995 no. < 6005d 23 950 no. < 24 050e 499 500 no. < 500 500f 0.795 no. < 0.805g 0.3995 no. < 0.4005

8 a 2 b 2 c 4 d 2 e 2f 4 g 2 h 2 i 1, 2 or 3j 1, 2, 3 or 4 k 2, 3, 4 or 5l 1, 2, 3, 4, 5, 6 or 7

9 a 3.64 m is the total nearest cm, 3.640 to the nearest mm

b 5.8 kg is to the nearest 100 g, 5.80 kg to the nearest 10 g

c 12 s is to the nearest second, 12.0 s to the nearest tenth of a second

d 36 cm is to the nearest cm, 36.0 cm is to the nearest mm

525Answers

e 23.8 s is to the nearest tenth of a second,

f

g

h

10

Exerc

1 acd

2 abd

3 ad

4 ace

5 acd

6 ad

7 abc

8 a9 a10

11

12

Exerc

1 a

d

g

j

m

2 a

d

g h i0.61 0.6 1.59 0

LEY_bk953_answers_finalpp Page 525 Thursday, January 13, 2005 3:23 PM23.80 to the nearest hundredth of a second7.29 km is to the nearest 10 m, 7.290 km to the nearest m1.5 t is to the nearest 100 kg, 1.50 t to the nearest 10 kg5.83 L is to the nearest 10 mL, 5.830 L to the nearest mL

Student to answer.

ise 5C

29 153 b 29 200i 12 900 ii 700 iii 15 70029 300 e Differ by 100.5250i 8090 ii 2830 c 5260Differ by 10.18.7 b 2.3 c 18.4Differ by 0.3.143.4 b 142.6Differ by 1.2. d 142.1Differ by 1.3.75.172 b 75i 33 ii 17 iii 2676 e Differ by 1.60 b 4, 20 c 80Differ by 20.2.18i 16.4 ii 7.502.19 d Differ by 0.01.4220 b 4240 c Differ by 20.0.18 b 0.19 c Differ by 0.01.

a 3.3 b 10.89c i 3.32, 11.0224

ii 3.317, 11.002 iii 3.3166, 10.9998 iv 3.31662, 10.99996

a 3 s.f. b 7 s.f. c 4 s.f.d 3 s.f. e 4 s.f.Student to answer.

ise 5D

b c

e f

h i

k l

0.875 b c

e e

j

3 a b c d e

4 a b c d e

5

6 a b c d e

7 a b c d e

8 a b c d e

9 a b c d e

Exercise 5E1 a $3.44/kg b $12.56/h

c 55 words/min d 10.5 km/Le 90 km/h

2 a 0.91 c/cm b 0.125 c/mmc 1.4 L/min d 1.25% per monthe 2.25% per quarter f 16 c/min

g 84 c/min h 1800 g/m2

i 650 g/m2 j 1.9 c/gk 3.6 c/mL l 7.5 g/mL

3 i 1.2 km/min ii 1200 m/miniii 20 m/s


5 i 1 km/min ii 1000 m/min

iii m/s6 i 300 L/h ii 5 L/min

iii mL/s7 a 28.8 km/h b 72 km/h c 126 km/h

d 150 kg/ha e 80 kg/ha f 250 kg/hag $5/kg h $7.20/h i 7.2 L/h j 0.8 kg/L

8 36 km/h9 i 0.125 L/km ii 12.5 L/100 km

iii 125 mL/km10 a 1080 b 25 h c 4 bottles/min

d 180 e 50 min

11 a 320 m2 b 15 L c 0.016 m2/mL

d i 8 m2 ii 3.2 m2

12 a 450 km b 7.5 hc 25 m/s d 135 m

13 a 270 L b 8 h 53 minc 75 mL/s d 1800 mL

14 a 1200 mL b 10 drops/min

0.7 0.35 0.2 8

0.3 25 0.6 784 1.4

6.92 0.4 9 0.2 34

0.03 0.9 0 0.536

0.217

0.5 0.16

0.1 8 1.416 1.6

0.4583

35---

3950------

18---

225------

32125----------

29---

13---

59---

89---

79---

0.9 1=

4699------

9199------

1033------

711------

9899------

586999----------

239999----------

284333----------

47111----------

205333----------

718------

5990------

8390------

16---

110------

4175------

217300----------

343450----------

163180----------

120------

16.6

83.3

526 Answers

Exercise 5E continued15

16

Non-

1 ad

2 a

3 a

d

4 a

5

6 a

Lang

1 D5 a

d

Chec

159

13

Revie

1 a

2 a3 a4 a5 a6 a7 a

d8 a

d9 3

m

10

11

12

13

14

15 120 L/100 km

39---

LEY_bk953_answers_finalpp Page 526 Thursday, January 13, 2005 3:23 PMa 17c/min b 66c c 22c/mind 108.5c e 5 mini 0.072 g/mL ii 72 mg/mLiii 720 mg/10 mL

calculator Activities

35 000 b 7.30 c 152500 e 7.643 b 2 c 1, 2, 3, 4 or 5

b c

e

0.375 b

10 m/s b 1.5 kg/L

uage in Mathematics

fraction b decimal c sumproduct e terminate

k Your Skills

D 2 D 3 D 4 CD 6 C 7 B 8 DD 10 A 11 B 12 AD 14 C 15 B 16 D

w Set 5A

50 b 5 c d 500

2500 b 7930 c 34 d 50 0008.5 b 8.46 c 8.4633.50 b 20.035 b < 45 c 35 no. < 453 b 4 c 250 b 48 c 48.448.35 e 48.3513 b 1 c 32 e 2, 3, 4 or 5

.65 m is to the nearest cm, 3.650 to the nearest m.

a b c

d e

a 0.375 b

a b c

a b

1600 g/m2

Review Set 5B

1 a b 600 c d 60

2 a 13 600 b 4060 c 148 d 100 0003 a 1.6 b 1.56 c 1.5614 a 2.70 b 40.05 163.5 height < 164.5 cm6 a 2 b 1 c 57 a 365 000 b 540 c 0.002 40

d 2.008 a 2 b 2 c 4

d 1 e 1, 2, 3 or 49 1.85 kg is to the nearest 10 g, 1.850 to the

nearest gram.

10 a b c

d e

11 a 0.1875 b

12 a b c

13 a b


15 18 L/h

Review Set 5C

1 a 8 b c d 8000

2 a 13 800 b 770 c 24 d 90 0003 a 13.1 b 13.07 c 13.0654 a 4.20 b 21.05 a 3 b 4 c 26 a 20 b 18 c 17.6

d 17.63 e 17.6317 a 425 b < 435

c 425 no. < 4358 a 3 b 1 c 3

d 2 e 2, 3, 4 or 59 6 cm is to the nearest cm, 6.0 cm to the nearest

mm.

10 a b c

d e

11 a 0.275 b

12 a b c

13 a b

0.4 0.5 2 0.56

0.576 0.2 13

0.4

79---

5100----------

0.2 0.42 0.4 2

0.4 25 0.4 253

1.6

35---

73100----------

69500----------

49---

4199------

610------

61000-------------

0.3 0.36 0.2 8

0.3 14 0.5 678

1.7

310------

81100----------

2671000-------------

89---

4999------

810------

8100----------

0.1 0.37 0.9 2

0.6 37 0.423

1.916

15---

2950------

18---

89---

635999----------

527Answers

14 20 mL/s15

Revie

1 a

2 a3 a4 a5 236 a7 a8 a

e9 12

te

10

11

12

13

14

15

CHAP

Diagn

159

13

Exerc

1 adgjm

2 adg

3 a

c

eg

i

k

4 a 32.0 cm b 2.5 km

LEY_bk953_answers_finalpp Page 527 Thursday, January 13, 2005 3:23 PM$28.80/day

w Set 5D

b 3000 c 3 d 30

78 500 b 510 c 34 d 500 0002.1 b 2.06 c 2.0573.20 b 60.0

5 g weight < 245 g1 b 6 c 524 700 b 67.8 c 0.0507 d 3.003 b 1 c 3 d 21, 2 or 3

s is to the nearest second, 12.0 to the nearest nth of a second.

a b c

d e

a 0.2125 b

a b c

a b

i 1.5 km/min ii 1500 m/miniii 25 m/s7.5 t/ha

TER 6

ostic Test

B 2 A 3 D 4 BD 6 C 7 C 8 BC 10 B 11 B 12 BB 14 A 15 D 16 A

ise 6A

0.21 m b 18 cm c 3.5 km40 mm e 230 cm f 1800 m20 cm h 2.8 m i 520 cm83 mm k 6300 m l 3 cm5000 cm n 3200 mm o 0.83 km400 b 310 000 c 5 300 00032 000 000 e 4 f 750 000 h 73 000 i 4.2

1500 mm2 b 150 000 m2

3.2 m2 d 32.8 m2

2 350 000 cm2 f 365 000 m2

0.000 782 ha h 0.036 542 ha

2300 ha j 420 000 cm2

52 000 cm2 l 2000 mm2

c 150.8 cm d 39.6 cm

5 a 32 cm2 b 180 m2

c 80 cm2 d 144 m2

6 a 14 m2 b 4 cm2 c 640 m2

d 36 cm2

7 a 24 cm2 b 36 cm2 c 120 cm2

8 a 201.06 cm2 b 153.94 m2 c 56.75 cm2

d 30.19 cm2 e 183.85 m2 f 1.25 km2

Exercise 6B

1 a 24 mm2 b 29.925 m2 c 15.48 cm2

2 a 45 cm2 b 27.84 m2 c 19.35 cm2

3 a 32 m2 b 30 cm2 c 98 cm2

d 1190 mm2

4 a 20 cm2 b 58.5 cm2 c 266 m2

5 a 51 m2 b 48 cm2 c 60 mm2

d 82.5 km2 e 108.375 m2 f 23.165 m2

Exercise 6C

1 a 20.6 cm b 25.7 cm c 102.8 md 86.3 m

2 a 21.4 cm b 64.3 mm c 55.7 md 75.7 cm

3 a 14.28 m b 21.42 cm c 57.1 cm

4 a i & ii 4m2 = 12.57 m2

b No difference.5 a 67.99 cm b 45.70 cm c 37.85 cm6 $7447 125 cm8 $237.159 152 m10 8.0 cm11 31.8 m12 a 7200 km b 45 239 km c 1885 km/h13 53 05214 64.80 km15 a 26 cm b 104 cm16 a 6.7 cm b 11.7 cm, 36.8 cm

Exercise 6D

1 a 168 cm2 b 118 cm2 c 65 cm2

d 100.5 cm2 e 126.85 m2 f 117 cm2

2 a 33 m2 b 50 m2 c 38 cm2

d 265.5 cm2 e 52.5 cm2 f 54.54 cm2

3 a 12.6 cm2 b 17 854 m2 c 16.9 cm2

d 301.6 cm2 e 64.7 cm2 f 38.0 cm2

Exercise 6E

1 $2556.17

3100----------

0.9 0.45 0.8 5

0.726 0.4 36

1.416

45---

2425------

109200----------

23---

25---

528 Answers

Exercise 6E continued

2 a

3 a4 $

5 ace

6 3

7 68 1

9 a10

11

12

Exer

1 a

2 ac

3 a

4 a

b

c

d5 a

c

6 a

c

7 A

8 6

Lang

2 aceg

3 abc

d

4 Tp

Chec

15

9 D 10 A 11 D 12 A

LEY_bk953_answers_finalpp Page 528 Thursday, January 13, 2005 3:23 PM400 m2 b $13 120.00

36.6 m2 b $2925.31892.08

263 500 m2 b 26.35 ha18.445 ha d 7.905 ha$1 897 200

8 m2

.3 m2

.914 t

96 cm2 b 6.4 cmDecrease breadth to 6 cm.

Square; by 9 cm2

a 105 cm2 b 5.78 cmc Rectangle

cise 6F

b c

4.2 cm, 12.2 cm b 10.5 cm, 20.5 cm4.2 cm, 28.2 cm

8.4 cm2 b 26.2 cm2 c 25.1 cm2

P = 58.8 m, A = 215 m2

P = 37.9 m, A = 69.8 m2

P = 123.9 m, A = 283.5 m2

P = 631.4 m, A = 23 082 m2

17.96 m b 32.4 m185.8 m d 11.1 m

19.9 m2 b 64.2 m2

2166 cm2 d 6.8 m2

= 169.64 cm2, P = 75.4 cm

5.6 m2

uage in Mathematics

circle b quadrilateralcomposite d rhombuskite f sectortrapezium h triangleA semicircle is half a circle.A quadrant is quarter of a circle.Composite shapes are calculated by dividing up the area.Composite areas may be found in more than one way.

he area of a rhombus or a kite is half the roduct of the diagonals.

k Your Skills

C 2 A 3 C 4 DA 6 A 7 D 8 B

13 C 14 B 15 C 16 C

Review Set 6A

1 a 85 cm = 0.85 m b 15 000 m2 = 1.5 hac 3.5 km = 3500 m

2 a 20 m b 46.3 m c 12 cmd 25 cm

3 a 370 m b 60 cm4 a 51.7 cm b 73.5 cm5 44 611 km

6 a 40 m2 b 147 cm2

7 a 23.4 m2 b 52 cm2 c 126.4 cm2

Review Set 6B

1 a 4.28 ha = 42 800 m2

b 3 cm2 = 300 mm2

c 4300 cm = 43 m2 a 30 cm b 44 cm c 30.86 m

d 97.1 m3 a 76 m b 40 cm4 a 34.3 cm b 34.7 cm5 19.1 cm

6 a 13.65 cm2 b 326.2 m2 c 19.6 m2

7 a 46 m2 b 102.7 cm2

Review Set 6C

1 a 20 cm b 66 cm

2 a A = lb b A = xy

c A = h(a + b)

3 a 129 cm2 b 132 cm2

4 $18 441.86

5 a 1664 cm2 b 2.5936 m2

6 a P = 29.7 m, A = 61.7 m2

b P = 23.9 m, A = 26.8 m2

Review Set 6D

1 a 32 cm b 69 cm

2 a A = h(a + b) b A = xy

c A = B H

3 a 280 cm2 b 759 cm2

4 5.004 km5 $419.306 a 25.7 cm b 36.4 m

60360----------

16---=

120360----------

13---=

20360----------

118------=

12---

12---

12---

12---

529Answers

Cumulative Review: chapters 26

1 ab

c

d

e

f

g

h

2 ab

c

d

e

3 a

b

i

ii 38c i Class Frequency

LEY_bk953_answers_finalpp Page 529 Thursday, January 13, 2005 3:23 PMi 66 ii 511

i base = 7, index = 8ii base = 4, index = 11i 4 4 4 4 4 4ii 3 3 3 3 3 3 3i 625 ii 2048

i 520 ii 384 iii 53

iv 424 v 348

i False ii False

i ii iii

i ii 8 iii 5 iv 1

i 3.25 108 ii 7.4 105

i 62 100 000 ii 0.000 03

4 106 = 4 000 000but 46 = 4 4 4 4 4 4 = 4096

i 1.95 1025 ii 4.86 1022

iii 4.10 1075 iv 7 105

7.5 1016, 2.4 1011, 6.7 1010,7.6 1010

i mean = 6.05, mode = 6, median = 6ii Student to answer.

iii 160169 iv 163

4 a i ii

b i ii 9m

c i ii

iii iv

d i p12 ii y12 iii t35 iv c10

v 27v15 vi 21x10y15

e i 1 ii 7 iii 1 iv 12

f i ii iii

g i ii iii

h i d7 ii n3 iii k10

iv 15a6 v

i i True ii False iii Falseiv True v False

5 a i 35w + 14x ii 2k7 + 3k5

iii 4s + 8b i 11t + 2 ii 2x 16yc i 5(5n 4) ii 2b(4b + 3)

iii 4m(3m + 4n)

6 a i 300 ii 30 iii iv 3000

b i 13 500 ii 41iii 780 iv 80 000

c i 24.1 ii 24.07 iii 24.071d i 4.2 ii 20.97e i 4 ii 2 iii 8f i 80 ii 81 iii 81.5

iv 81.46 v 81.461

g i 735 iiiii 735 number < 745

h i 4 ii 2 iii 4iv 3 v 2, 3, 4 or 5

i 15 s is to the nearest second but 15.0 s is to the nearest tenth of a second. 15.0 s is more accurate.

i cf

5

12

28

30

30

31

175------ 24 413

181------

Class

Cum

ulat

ive

freq

uen

cy

Height of Year 9 students

5

10

15

20

25

30

35

150 160 170 180 200140 190

i

iii grouped dataiv 3237v 37.5vi 3237

2025 5

2631 15

3237 27

3843 20

4449 8

5055 8

5661 2

15 h25

-----------

20xy15

------------

w4----

5d7

------

4b8

------

b2---=

xy3-----

1516------

t 9 t 9t

1c5-----

4c5-----

14c( )5

--------------

2m5

3-----------

3100----------

744.9

530 Answers

Cumulative Review: chapters 26 continued

7 a

b

c

d

e

f

CHAP

Diag

159

13

Exer

1 a2 a3 a

d

g

4 a

d

g

5 a

d

Exer

1 a

c

e

2 a

c

e

Exer

1 a

2 a b = c 2 d3--- 3--- 1--- 5---

LEY_bk953_answers_finalpp Page 530 Thursday, January 13, 2005 3:23 PMi ii iii

iv v

i 0.2375 ii

i ii

iii

i ii

i 2 km/min ii 2000 m/min

iii m/s8.5 t/ha

TER 7

nostic Test

C 2 D 3 C 4 AA 6 B 7 C 8 AC 10 B 11 A 12 AB 14 D 15 A 16 B

cise 7A

(5, 4) b (7, 3) c (5, 6)(2, 6) b (5, 5) c (3, 6)(1, 3) b (2, 3) c (3, 1)(4, 1) e (1, 2) f (4, 1)

(0, 4 ) h (1 , 0) i (2, 14)

(3, 3) b (1, 4) c (2, 3)

(0, 0) e ( , 1) f (1, 3)

(3 , 2) h (2 , 1 ) i (0, 0)

(4, 5 ) b (2, 2 ) c (3, 3)

(16, 15) e (7 , ) f (3 , 5 )

cise 7B

5 b

d

f

b 13

d

f 5

cise 7C

b c

3 a b c d 11

Exercise 7D

1 a +2 b c 4 d +2

e f g

2 a 0 b c d

e f g undefined

3 a 0 b c

d 1 e 2 f 94 a OP, PQ, RS, TU b QR, ST, UV

c TU d ST e VW f PQ

5 a b c

d e f

6 a b c d

7 a 1 b c

d e 2 f

8 a 2 b 13 c 6

d e f

Exercise 7E

1 a b

c d

e f

g h

2 a y = 3, y = 4, y = 8, y = 3

0.8 0.43 0.8 5

0.723 0.4 36

1.583

610------

35---=

92100----------

2325------=

5441000-------------

68125----------=

23---

2445------

33.3

12---

12---

12---

12---

12---

12---

12---

12---

12---

12---

12---

12---

18 4.24=

41 6.40= 85 9.22=

34 5.83= 74 8.60=

122 11.05=

97 9.85= 160 12.65=

73 8.54=

320------

15---

34---

4 6 2 3

79---

38---

13---

43---

25---

53---

34---

15---

35---

76---

73---

92---

13---

23---

411------

49---

45---

35---

110------

47---

43---

43---

45---

43---

43---

23---

12---

14---

1125----------

512------

1140------

y

x

3

y

x1

y

x2

y

x

4

y

x5

y

x

8

y

x

3

y

x7

531Answers

b (0, 3), (0, 4), (0, 8), (0, 3)3 a

b4 a

5 a

Exerc

2 a

b y = x + 3

1 a

b

c

d

e

f

g

h

LEY_bk953_answers_finalpp Page 531 Thursday, January 13, 2005 3:23 PMx = 1, x = 2, x = 5, x = 7(1, 0), (2, 0), (5, 0), (7, 0)

b y = 0c between y = 1 and

y = 1

b x = 0c between x = 1 and

x = 1

ise 7F

y = x + 1

c y = x 1

d y = 4 x

e y = 2x 2

f y = 3 2x

3 a y = x, y = x 2, y = 2x + 1, y = x + 1,y = x + 3, y = x 1, y = 2x 2

b y = x, y = 5 x, y = x, y = 8 2x,

y = 1 3x, y = 4 x, y = 3 2x

x 1 2 3 4 5

y 1 2 3 4 5

x 1 0 1 2 3

y 3 2 1 0 1

x 2 1 0 1 2

y 2 1 0 1 2

x 2 1 0 1 2

y 7 6 5 4 3

x 2 1 0 1 2

y 3 1 1 3 5

x 2 1 0 1 2

y 1 0 1

x 2 1 0 1 2

y 12 10 8 6 4

x 2 1 0 1 2

y 7 4 1 2 5

x 2 1 0 1 2

y 1 0 1 2 3

y

x

21

12

y

2112

12---

12---

y

x1

y = x + 1

x 2 1 0 1 2

y 1 1 3 5 7

x 2 1 0 1 2

y 3 1 1 3 5

x 2 1 0 1 2

y 6 5 4 3 2

x 2 1 0 1 2

y 6 4 2 0 2

x 2 1 0 1 2

y 7 5 3 1 1

y

x

3y = x + 3

y

x1

y = x 1

y

x

4 y = 4 x

y

x1

y = 2x 2

2

y

x

3

y = 3 2x

12---

532 Answers

Exercise 7F continuedc

d

4 a

c

e

g

i

k

m

o p y y

LEY_bk953_answers_finalpp Page 532 Thursday, January 13, 2005 3:23 PMThe coefficient of x is positive for a positive gradient and the coefficient of x is negative for a negative gradient.i positive ii negative iii negativeiv positive v positive vi negative

b

d

f

h

j

l

n

5 a Yes b No c Nod Yes e No f Nog Yes h Yes i Yes

6 a C b A c D d E e B7 a Yes b Yes c No

d No e No f Yesg Yes h No i Yes


Exercise 7G

b

2 a

b

c

y

x4

4

y = x 4

y

x4

4y = x + 4

y

x

y = 2x

y

x

1

1y = 1 x

y

x

y = x2

y

x

y = 2x + 3

34

32

4

y

x3

3

x + y = 3

y

x1

1

x + y = 1

y

x8

8

x y = 8

y

x6

6

x y = 6

y

x4

4

y = 4 + x

y

x8

8

x + y = 8

y

x4 6

3y 2x = 12

y

x2

y = 23x2

43

1 a x 4 3 2 1 0 1 2 3 4

y 16 9 4 1 0 1 4 9 16

x2 3

2x 3y = 6 x6

10 5x + 3y = 30

12---

12---

14---

14---

y

x4 4

y = x2

y

x

12

y = x2y = 2x2

y = x2

y

x

14

y = x2

y = 4x2y = 3x2

y = x2

y

x

2

1

1

y = x2 + 2y = x2 + 1

y = x2 1

y = x2

533Answers

3 Student to answer.4 a

b

Lang

1 ab

cd

e

2 ad

3 abcde

f

4 Inpo

Chec

159

13

Revie

1 a

2 a

3

4 a

5 y

6 a b

35---

y y

LEY_bk953_answers_finalpp Page 533 Thursday, January 13, 2005 3:23 PMAll pass through (0, 1).

uage in Mathematics

64 yearsLoci and set work, received a law degree and became Kings Councillor.OneAs many of his achievements were published after he died.Concerning the Comparison of Curved and Straight Lines.vertical b horizontal c gradientdistance e oblique f slopeThe y axis has the equation x = 0.The x axis has the equation y = 0.An uphill gradient is a positive slope.The midpoint of a line is in the middle.If a line goes downhill the gradient is negative.The length of an interval is found using Pythagoras theorem.

coordinate geometry an interval joins two ints and has length, a midpoint and slope.

k your Skills

B 2 A 3 D 4 BD 6 A 7 C 8 CD 10 B 11 A 12 BC 14 B 15 B 16 C

w Set 7A

(7, 3) b (2, 7) c (6, 3 ) d (3, 1)

b

b

= 2x 2

c d

e f

7 When x = 4, y = 3 Yes8

Review Set 7B

1 a (3 , 3) b (3, 5 )

2 a b

3 a b

4

5 a b

c d

6 No since 1 (3) = 2 not 4.

7 a , , 1, 2, 4, 8

y

x

1

y = 4x

y = 3x

y = 2x

12---

52 20

511------

12---

x

3 x

4

y

x3

3

y = x + 3

y

x

y = 4 3x4

43

y

x5

5

x + y = 5

y

x2

2

x y = 2

y

x

y = x2

12---

12---

63 65

74---

56---

13---

y

x4

4

y = x + 4

y

x

y = 2 3x2

23

y

x8

8

x + y = 8y

xx y = 0

14---

12---

534 Answers

Review Set 7B continued

b

Revie

1 a

c

2 a

3

4 a

5

6 a

c

e

g

7 N8 a

Review Set 7D

52---

LEY_bk953_answers_finalpp Page 534 Thursday, January 13, 2005 3:23 PMw Set 7C

(8, 3) b (2, 5)

(5 , 2 ) d 2 , )

b

b

b

d

f

o, since 3(2) 1 = 7 not 5.b

1 a (1, 2) b (5 , 5)

2 a b

3 a b

4 15 a b

c d

6 Yes, since 1 + 5 = 4

b

Chapter 8

Diagnostic Test

1 C 2 D 3 B 4 D5 C 6 A 7 B

Exercise 8A

1 b

c 540

y

x

y = 2x

12---

12---

12---

12---

50 41

47---

513------

311------

y

x

5 y = 5

y

x

x = 2

2

y

x2

2y = x 2

y

x

y = 5 4x5

54

y

x12

1

y = 2x + 1

y

x1

1

x + y = 1

y

x6

6

x y = 6

y

x

y = x2 + 22

y

x

y = 3x

7 a x 2 1 0 1 2 3

y 1 3 9 27

12---

85 20

67---

13---

y

x3

3

y = 3 x

y

x3

3 y = 2x 3

y

x1

1

x + y = 1y

x6

6

x y = 6

19---

13---

y

x

y = 3x

1

A

A A

535Answers

3 (n

4 a

d5 a6 a7 a8 a

bcdefghi

9 1310

Inves

1 a2 b3 c4 c5 366 a

b

Exerc

1 ac

2 a3 244 a

d5 216 a7 228 16

Investigation 22

q

LEY_bk953_answers_finalpp Page 535 Thursday, January 13, 2005 3:23 PM 2)

108 b 120 c 128

135 e 140 f 1443960 b 16580 b 70 c 77720 b i 50 ii 70 iii 65x = 50 (angle sum of quadrilateral is 360)x = 165 (angle sum of pentagon is 540)x = 120 (angle sum of hexagon is 720)x = 20 (angle sum of quadrilateral is 360)x = 120 (angle sum of hexagon is 720)x = 60 (angle sum of pentagon is 540)x = 40 (angle sum of hexagon is 720)x = 125 (angle sum of septagon is 900)x = 135 (angle sum of octagon is 1080)

5135

tigation 1

All 72 b 360360360360

0i 180 ii 180180 c 180 d 360

ise 8B

45 b 135, straight line is 180108018 b 162 c 3240

sides36 sides b 20 sides c 15 sides4 sides

sides31 sides b 21 sides c 22 sides

sides sides

1 a 120 b 3 hexagons, 360c A regular polygon will tessellate if the size of

the interior angles divides exactly into 360.2 108 does not divide exactly into 360.

b Triangle, square, hexagon.

Language in Mathematics

1 a A pentagon has five sides.b A regular polygon has all sides equal.c A polygon with eight sides is an octagon.d The exterior angle sum of a polygon is 360.

2 To find the interior angle sum of a polygon subtract two from the number of sides and multiply by one hundred and eighty degrees.

Check Your Skills

1 D 2 C 3 B 4 A5 C 6 A 7 B

Review Set 8A

1 a b c 720

2 a x = 100 (angle sum of a hexagon is 720)b x = 105 (angle sum of a pentagon is 540)

3 a 135 b 3604 a 36 b 6120

Review Set 8B

1 a 1800 b 1502 a x = 67 (angle sum of a pentagon is 540)

b x = 120 (angle sum of a hexagon is 720)3 1654 a 14.4 b 165.6 c 4140

Review Set 8C

1 a 6120 b 1702 a x = 32 (angle sum of a hexagon is 720)

b x = 60 (angle sum of a pentagon is 540)

PolygonNumber of sides

Number of triangles

Angle sum of polygon

uadrilateral 4 2 360

pentagon 5 3 540

hexagon 6 4 720

heptagon 7 5 900

octagon 8 6 1080

nonagon 9 7 1260

decagon 10 8 1440

n-gon n (n 2) (n 2) 180

47---

3 aRegular polygon

Number of sides

Angle sum

Interior angle size

triangle 3 180 60

square 4 360 90

pentagon 5 540 108

hexagon 6 720 120

heptagon 7 900 128

octagon 8 1080 135

nonagon 9 1260 140

decagon 10 1440 144

47---

536 Answers

Review Set 8C continued

3 14 1

Revie

1 a

2 ab

3 14 4

CHAP

Diag

1 B5 B9 D

Exer

b

b

b

1 a

2 a

3 a

86 43

LEY_bk953_answers_finalpp Page 536 Thursday, January 13, 2005 3:23 PM202

w Set 8D

b c 540

x = 40 (angle sum of a pentagon is 540)x = 87.5 (angle sum of a hexagon is 720)

505

TER 9

nostic Test

2 C 3 C 4 B6 B 7 A 8 D

cise 9A

36.5% c 12%

12 c Student to answer.

4

5

Exercise 9B

1 a b c 0 d 1 e

2 a b c d e

f 1 g 0 h

3 a 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

b c d e f 0

4 a = b = c

d 0 e = f =

g = h i 1

5 a b c d e

f g h 0 i

6 a H, T b M, Fc HH, HT, TH, TT d 1, 2, 3, 4, 5, 6e ABC, ACB, BAC, BCA, CBA, CAB

7 a b 1 c d e 0

8 a b = c

9 a b c 0 d 1

10 a b c

11 a b c 1 d 0

12 a b =

13 a b = c

14 In days 3 + =

15 a b No

Exercise 9D

1 a False, few names start with z not .

Outcome FrequencyRelative

frequencyPercentage

Rough 86 86/200 43%

Smooth 114 114/200 57%

Country FrequencyRelative

frequencyPercentage

Australia 146 146/400 36.5%

Japan 128 128/400 32%

Korea 56 56/400 14%

Germany 48 48/400 12%

Other 22 22/400 5 %

Colour NumberRelative

frequencyPercentage

White 53 53/200 26.5

Red 48 48/200 24

Blue 27 27/200 13.5

Green 25 25/200 12.5

Yellow 21 21/200 10.5

Black 12 12/200 6

Silver 8 8/200 4

Other 6 6/200 3

43100----------

12---

4754-------------

2377-------------=

12855000-------------

2571000-------------=

14---

14---

34---

16---

16---

16---

12---

12---

56---

110------

12---

12---

910------

312------

14---

412------

13---

512------

912------

34---

812------

23---

812------

23---

512------

14---

152------

14---

126------

113------

313------

213------

1013------

13---

13---

56---

16---

26---

13---

12---

18---

38---

25---

45---

35---

310------

710------

1100 000----------------------

950000100 000----------------------

1920------

910------

8100----------

225------

22100----------

30365----------

30366----------

14634453-------------

16---

126------

537Answers

b False, some teams are better than others.cd

e

f

g

h2 a

bc

Exerc

1 5 50

2 a

b3 a

b4 a

b5 St

Non-c

147

10

13

16192225

Lang

2 ad

3 a

b

4 Probability estimates become more stable as the

LEY_bk953_answers_finalpp Page 537 Thursday, January 13, 2005 3:23 PMFalse, some players are better than others.False, some colours stay on longer than others.True, 4 aces from 52 is .

True, P(6) = .

True, if you know nothing about the horses and just pick one. However, the probability of a particular horse winning is not .True.It assumes that people who dont work are unemployed. They may be retired etc.The sample space is too small.The students in 9 Red are not representative of the sample.

ise 9E

kicks : 4 goals and 1 miss kicks : 34 goals and 16 missesi Digits 0, 1, 2, 3, 4, 5, 6, 7, 8 signify a goal

and the digit 9 is a miss.ii 45 goals, 5 misses45 goals c Student to answer.i 0, 1, 2, 3, 4, 5, 6 represents a goal

7, 8, 9 represents a missii 35 goalssame c Student to answer.i 0, 1, 2, 3, 4, 5, 6, 7 represent survival

8, 9 represent non-survivalii Student to answer.Student to answer.

udent to answer.

alculator Activities

0.8 2 35% 3 141$36 5 35 6 210 minutes7 8 0.16 9 35 654.3C 11 B 12

14 5 15 203.024

$100 17 2 250 000 18 2236 20 30 21 2030 23 24 1012 345 000

uage in Mathematics

chance b event c probabilityrandom e prediction f theoreticalRelative frequencies are used to estimate probability.Random number generators are used to simulate events.

number of trials increases.

Check Your Skills

1 C 2 B 3 C 4 B5 A 6 C 7 C 8 C9 C

Review Set 9A

b 83%

2 a b c d

3 False, not all teams are equal in ability.4 a i 0, 1, 2, 3, 4, 5, 6, 7 represent a goal,

8, 9 a missii 43

b overestimate c Student to answer.

Review Set 9B

1 Wrong, expect 1

2 a b c p d

3 a b c

4 Some colours are showing for longer times than others.

Review Set 9C

b c

2 a b c

3 True4 a i 0, 1, 2, 3, 4, 5, 6, 7, 8 represent survival

9 represents no survivalii Student to answer.

b Student to answer.

113------

16---

124------

23---

27---

916------

56---

1 a Relative frequency Percentage

166/200 83%

34/200 17%

1 a Country FrequencyRelative

frequencyPercentage

Australia 195 195/400 48.75%

Japan 103 103/400 25.75%

Korea 62 62/400 15.5%

Germany 34 34/400 8.5%

Other 6 6/400 1.5%

16---

16---

12---

13---

317------

917------

517------

817------

1100----------

9100----------

11100----------

195400----------

103400----------

16---

13---

13---

538 Answers

Review Set 9D

1

2 a

3 N

n

4 F

CHAP

Diag

15913172125

Exer

1 ad

g

j

m

psv

2 a

e3 a

e

i

l

o

r

u

w4 a

eim

5 a

e

hlo

r x2 4x + 2

5---

LEY_bk953_answers_finalpp Page 538 Thursday, January 13, 2005 3:23 PMb c d

either and both as a small number of trials is

ot accurate. Theoretically .

alse, not all of equal ability.

TER 10

nostic Test

D 2 C 3 A 4 CC 6 B 7 B 8 BA 10 D 11 C 12 DA 14 B 15 B 16 AD 18 B 19 D 20 CA 22 D 23 A 24 BD 26 A

cise 10A

9a b 5x c 3x2b e 3x f 4x

x h 2x i 2a2

7x + 3 k 11x2 l 17x 7

16x n x2+ x o 8b

6b q 2b2 r 5ab0 t 4ab u 3xyp w 7b x 2abc

10x b 2y c 5a2 d 16ab

9x2y f 2q g 0 h 8ab i p2q9x 2 b m + 11 c 2x + 6 d 3y + 34p 5 f 7 + 3x g 3t + 4 h 21n 16

5p2 + p j 8k 8 k 3a2 7a

7cd 2 m m2 + 5n n 8x + 2y

2a + 2b p 2ab + 3b2 q 10x 10

9a ab s 2n + 2n2 t 4 + 2a

3x x2 v mn 8m

5a2b + 2ab2x 2x2 + 6x3

3x b 11x c 3x d 5d7d f 5d g 7n h 7n15n j 3a + 2 k 3 d l 3x2g n 4a o ac3a + 10 b 6a + 8 c 4a + 6 d 5a + 4b

4a2 + 3a f 3ab + 3b2 g 8y + 2

2n2 i 7c + 1 j 7x k 32p 5 m 10 12x n 14p 89x 2 p 6 7x q 6x 13

6 a 5l 10 b 3x c 4x y d ab 2b e 3x 8 f 5t + 6

g a + 1 h a2b + 7b i 6d 3c + 2

j 3p5 p4 k 4m2 2n2 l 2s2t 4s2

7 a 4x + 10 b 4x 6 c 4y + 6d 3x 1 e 3y f 4x + 5

8 Let x m be the length of the longer side, let y m be the length of the shorter side. a 4x + 4; 4y 8 b 4x + 6; 4y 6c 4x + 10; 4y 10

9 x m is the length of the shorter side 3x + 10y m is the length of the middle side 3y + 1z m is the length of the longest side 3z 11

10 x(x + 1), y(y 1).11 a 1 3x b 4x + 2 c 11 5x

d 10x 3 e 3 x f 10x + 2g x + 1 h 11 3x i 19 18xj 16 14x k 2x 5 l 6x 6

12 a 5x + 3 b 5y + 9 c p + 8

d 5 5x e 2d2 f 7d

g 3n2 + 3n h n2 + n i 15x + 23

j 4x2 + x k ac bc l 2x2 + 5x + 6

m 2x2 + x 25 n x 1

o 4x2 + 6x + 12 p 2x2 + x 12

q 5x2 7x 6 r 9x 1313 a i 3(x + 5) ii 3x + 15

b i 4x(2x + 7) ii 8x2 + 28xc i 3(3x + 1) ii 9x + 3

d i y(x + y) ii xy + y2

Exercise 10B

1 a b c d

e f g h

i j k l

m n o p

2 a b c d

e f g h

i j k l

m n m o 0 p

74188----------

372594-------------=

113------

12---

14---

313------

50100----------

5a6

------

b10------

7c4

------

5x14------

7b12------

2t9-----

5m21--------

d2---

p3---

22r35---------

4x21------

m9----

x8---

3r16------

26m55

-----------

3d20------

x 2+2

------------

y 33

------------

a 4+2

------------

b 122

---------------

x 82

------------

10 x5

---------------

3a2

------

4b3

------

4a3

------

a2

------

8x7

------

5x2

------

8x3

---------

7x60------

539Answers

3 a

c

e

g

i

Exerc

1 x2

4

6

7 a

c

8 a

d

g

j9 a

ei

10

11

Exerc

1 a

c

e

g

i

k

2 a

c y2 18y + 81 d 9x2 6x + 111x 5a 25m 14p

12---

12---

LEY_bk953_answers_finalpp Page 539 Thursday, January 13, 2005 3:23 PMb

d

f

h

ise 10C

+ 6x 2 x2 + 5x 3 x2 3x

(x2 + 3x) 5 (x + 3)(x + 1)

(x + 7)(x + 2)

x2 + 6x + 5 b x2 + 9x + 14

x2 + 11x + 24

x2 + 6x + 8 b x2 x 6 c x2 + 4x 12

x2 + x 12 e x2 2x 15 f x2 + 4x 45

x2 7x 30 h x2 11x + 28 i x2 + 6x 7

x2 5x + 6 k x2 15x + 54 l x2 15x 3621 b 71 c 23 d 5561 f 35 g 6 h 1245 j 187 k 234 l 52

a 2x2 + x 3 b 2x2 21x + 40

c 3x2 20x + 25 d 9x2 9x 10

e 6x2 + 23x 18 f 16x2 25

g 12x2 x 1 h 6x2 19x + 10

i 8x2 + 2x 15 j 49x2 4

k 10x2 31x + 15 l 12x2 17x 5

a x2 10 b 6x2 + 11x 4

c x2 7x 14 d x2 + 2x + 10

e 3x2 8x + 14 f 10x 4

g x2 + x + 10 h 2x2 + 16x + 5

i 2x2 + 13x 6

ise 10D

x2 + 4x + 4 b x2 + 12x + 36

y2 + 20y + 100 d 9x2 + 6x + 1

4x2 + 12x + 9 f 16a2 + 40a + 25

25x2 + 40x + 16 h 9y2 + 6y + 1

16 + 24x + 9x2 j 1 + 4x + 4x2

25 + 20x + 4x2 l 16 + 40x + 25x2

x2 4x + 4 b x2 12x + 36

e 4x2 12x + 9 f 25a2 40a + 16

g 9x2 24x + 16 h 16y2 8y + 1

i 25 20x + 4x2 j 1 6x + 9x2

k 25 30x + 9x2 l 16 16x + 4x2

3 a x2 + 10x + 25 b x2 10x + 25

c 4x2 28x + 49 d 4x2 + 28x + 49

e 9x2 30x + 25 f 16x2 + 24x + 9

g 25 + 20x + 4x2 h 9 42x + 49x2

4 a x2 9 b x2 16 c x2 36

d x2 100 e x2 1 f 4x2 25

g 9x2 4 h 25x2 1 i 49x2 64

5 a x2 20x + 100 b x2 + 14x + 49 c x2 64

d x2 121 e x2 + 8x + 16 f x2 49

g x2 14x + 49 h x2 144 i x2 + 24x + 144

6 a x2 + 6x + 9 b x2 14x + 49 c x2 4x + 4

d (x 3)2 = x2 6x + 9

e (x 5)2 = x2 10x + 25

f (x + 6)2 = x2 + 12x + 36

g (x + 7)2 = x2 + 14x + 49

h (x + 9)2 = x2 + 18x + 817 a 9 b 25 c 16 d 4 e 36

f 81 g h i j

k l

Exercise 10E

1 a 3(a b) b 5(m + 2n) c q(p r)d x(x 5) e x(4x + 1) f 3x(5 + x)g q(p 3q) h 2(R r) i 6xy(x 3y)j 7ap(4p 3) k 9xy(x + 3) l 3pq(r 5p)

2 a 3(a + b) b 2x(2x + 1) c 4(2a b)d 4(1 + 2b) e (3 + x) f 9x(2x 1)

3 a B(6 + a + c) b R(4 x + y)c x(6 + 14y 3z) d 8x(x 3y + 2yz)e (x 2)(4 + y) f (x 1)(3 + y)g (x + 1)(a + 3) h (x 4)(x 1)i (p 3)(3 + x + y) j (a + 1)(x 1 y)

4 a (2x + 1)(2 + x) b (x 1)(3 + z)c (x + 5)(y + 3) d (x 2)(y + 4)e (x 7)(x + y) f (4 x)(x + y)g (y + 3)(x 2) h (y 4)(2x + 5)i (3x 7)(y + 4) j (3 x)(x + t)k (a b)(3 + c) l (3x 2)(x + y)m (4 3x)(1 + y) n (6 5y)(a + b)o (4 3p)(p q)

4----------------------

10--------------------------------

64a 125p20

-----------------------------

65p 27r15

-------------------------

52m 35n10

----------------------------

45a 88b20

--------------------------

3t 17m12

----------------------------

62r 119m28

------------------------------

80x 21y15

-------------------------

494

------

2254

----------

94---

814

------

14---

14---

540 Answers

Exercise 10F

1 acegikmo

2 ad

3 a

bc

Exer

1 a

d

g

j

2 a

d

g

j

3 a

d

Exer

1 acegik

2 acegik

3 acegik

4 ace

g (x 8)(x 8) h (x + 16)(x 4)

LEY_bk953_answers_finalpp Page 540 Thursday, January 13, 2005 3:23 PM(x 2)(x + 2) b (y + 3)(y 3)(z 4)(z + 4) d (a 3)(a + 3)(c + 5)(c 5) f (x + y)(x y)(a c)(a + c) h (m n)(m + n)(2x 1)(2x + 1) j (3x 2)(3x + 2)(3x + 1)(3x 1) l (4y 3)(4y + 3)(5y 4x)(5y + 4x) n (10x 9y)(10x + 9y)(8a 5b)(8a + 5b) p (11r 3t)(11r + 3t)1200 b 800 c 20006 e 1.87 f 1711

(x y)(x + y)(x2 + y2)

(2a 3b)(2a + 3b)(4a2 + 9b2)4pq

cise 10G

(x + 5)2 b (x 10)2 c (x + 9)2

(x 8)2 e (x 7)2 f (x + 11)2

(y 3)2 h (y + 1)2 i (x 12)2

(p 4)2 k (m + 3)2 l (a 5)2

(2x + 5)2 b (5x + 6)2 c (4x 9)2

(3x + 8)2 e (11x 6)2 f (9x + 5)2

(7x + 10)2 h (5x 2)2 i (2x + 11)2

(7x 3)2 k (3x + 5)2 l (10x 9)2

(p + q)2 b (m n)2 c (r + t)2

(d p)2 e (n t)2 f (r + y)2

cise 10H

(x + 7)(x + 1) b (x + 6)(x + 2)(x + 12)(x + 1) d (x + 9)(x + 1)(x + 6)(x + 4) f (x + 10)(x + 3)(x + 6)(x + 5) h (x + 10)(x + 2)(x + 5)(x + 4) j (x + 6)(x + 3)(x + 18)(x + 1) l (x + 7)(x + 6)(x 5)(x 1) b (x 7)(x 1)(x 11)(x 1) d (x 4)(x 2)(x 8)(x 1) f (x 5)(x 2)(x 10)(x 1) h (x 5)(x 3)(x 15)(x 1) j (x 7)(x 2)(x 14)(x 1) l (x 8)(x 3)(x + 8)(x 1) b (x + 5)(x 2)(x + 2)(x 1) d (x 7)(x + 6)(x + 6)(x 2) f (x 12)(x + 1)(x 8)(x + 3) h (x + 8)(x 3)(x + 7)(x 3) j (x 21)(x + 1)(x + 20)(x 3) l (x + 9)(x 6)(x + 18)(x + 1) b (x 9)(x + 2)(x + 18)(x 1) d (x + 9)(x + 6)(x + 54)(x 1) f (x 27)(x + 2)

i (x 32)(x + 2) j (x 5)(x + 7) k (x 3)(x + 10) l (x 5)(x 10)

Exercise 10I

1 a (2x + 3)(x + 1) b (2x + 1)(x 5)c (3x 1)(x + 2) d (3x + 1)(x 2)e (2x + 5)(x + 1) f (2x 1)(x + 2)g (7x + 2)(x + 1) h (2x + 5)(x + 1)i (5x + 1)(x 3) j (5x 3)(x + 1)k (5x 3)(x 1) l (11x + 2)(x 1)

2 a (2x 3)(x + 4) b (3x + 2)(x 3)c (3x + 4)(x + 1) d (2x + 3)(x 3)e (3x + 1)(x + 4) f (3x 2)(x 5)g (3x + 2)(x + 2) h (5x + 2)(x 3)i (3x 2)(x + 4) j (2x 1)(x + 9)k (2x 3)(x + 6) l (2x 3)(x + 7)

3 a (2x 5)(x + 7) b (3x 4)(x + 3)c (5x 3)(x 1) d (3x + 2)(x 1)e (5x 4)(x 5) f (7x + 1)(x + 2)g (11x 3)(x + 5) h (7x 5)(x 8)i (5x 7)(x 9)

4 a (4x + 1)(2x + 3) b (5x + 2)(3x 1)c (7x + 1)(3x + 2) d (3x + 1)(2x + 1)e (6x + 1)(x + 3) f (5x + 1)(2x + 3)g (7x + 1)(2x + 5) h (21x + 1)(x 3)

i (2x + 1)2 j (5x 2)(2x + 1)

k (3x 2)2 l (3x + 2)(x + 4)5 a (2x 3)(3x + 1) b (4x 3)(x 5)

c (3x 4)(3x + 2) d (4x 1)(3x 5)e (3x + 2)(4x 5) f (12x + 5)(x 7)g (5x 3)(2x + 5) h (4x 7)(5x + 1)i (9x 4)(2x + 3)

Exercise 10J

1 a x(3x + 2) b (x + 9)(x 9)

c 2(p2 + 4) d 3(b + 5)(b 5)

e 2(x 4)(x + 4) f n2(n + 2)(n 2)g (x 9)(x + 1) h (d + 7)(d 1)i 3(x 6)(x + 6) j 2(g 11)(g + 5)k (2a 3d)(2a + 3d) l 4t(1 + 2t)m 1(x + 12)(x 1) n 5(a 2)(a + 1)

o 2(c 3)(c 1) p x2(x + 1)(x 1)

q d2(d + 3)(d 1) r (b + 7)(b 4)

s ab2(a + 1)(a 1) t (x 3)(x + 2)

u x(x + 2)2 v x2(3x 2)(3x + 2)

w (x + 9)(x 1) x 2(a + 3)2

2 a (x + 7)(x 2) b (x + 7)2

c 4a(a + b)(a b) d 2x(3 x)(3 + x)e a(b + c 2) f ab(ab 2)

541Answers

g 2x(x 1)2 h xy(x + 2)(x 2)i

k

mo

q3 a

ce

g

i

kmoqsu

w

4 ac

e

gikm

oqs

uw

Exerc

1 a

d

g

2 a

e

3 a

c

e

4x 14+ 2x 12+

LEY_bk953_answers_finalpp Page 541 Thursday, January 13, 2005 3:23 PM(a + b 3)(a + b + 3) j x(x 4)

4(x2 + 4)(x + 2)(x 2) l (x 2)(y z)

(x + 1)(a + b) n (x2 + a2)(x + a)(x a)(x y)(a + 1) p (x + 2)(x + 3)

(x + 1)(x2 + 1) r (x2 + 1)(x + 2)3x(x + 3) b (2x + 1)(2x 1)5x(x 3) d x(3 5x)(x + 8)(x 5) f (x + 4)(x 4)

x2(x + 2) h (x + 3)(x 3)

3x(x2 + 2) j 3(x + 2)(x 2)

3x2(x + 2) l (x + 5)2

(x 3)(x + 2) n 4x(x + 2)(3x 5)(3x + 5) p (x 13)(x 3)7x(x 3) r 2(x + 5)(x 5)9x(1 2x) t 4x(2x 3)(2x 1)(2x + 3) v 13x(x 4)

(x + 3)(x 1) x x2(x 9)

x(x2 + x + 1) b (x 12)(x + 5)3(x + 3) (x 3) d (x 4)(x + 2)

(x + 2)2 f (3x 2)(2x + 3)

(x 3)(x 2) h 36x2 + 254(x 5)(x + 3) j

Maths Answers

Documents

Transcript of Maths Answers