WORKSHEET ANSWERS FOR NEW CENTURY MATHS

Worksheet Answers1-01 Brainstarters 11 52

2 a 5 b 7 3 5x 234 35 5 horizontal

6 x4 2 7 a 50x5y3 b 3

8 a A = pr2 9 a 360 b 720

10 2h k(k 4) 11 13 cm 12 14 h 50 mins13 a -9 b 3 c 1 1

15d 4

15

e 415

f 1 23

g 2 : 5 h 7 : 4

14 0.0358 15 a 64 b 16 16 50

17 0.1 _6 18 9 km 19 $750

20 a 2.4 b 3600 c 0.2 d 32

21 52 000 22 69 beats/min 23 $96

24 27 25 3 35

26 12 12%

Challenge: 10 100

1-02 Fractions withoutcalculators1 a 7

3b 22

5c 65

7

2 a 138

b 816

c 635

3 a 9 b 8 c 49 d 48

e 1 f 13

4 1624

; 1524

, other answers possible

5 a 95

b 7 c 413

6 a 17, 18 or 19 b 25, 26, 27, 28 or 29c 37, 38, 39, 40, 41, 42, 43 or 44

7 a 25, 1

2, 3

4b 11

15, 5

6, 9

10

8 a 79

b 311

c 114

d 910

e 512

f 1136

g 6 110

h 11130

9 a 1235

b 310

c 123

d 2581

e 127

f 1 111

g 1425

h 1534

10 a $13 b $96 c $115 d $96

1-03 Wheres the point?1 a 26 400 b 27.9 c 4 320.72 d 635 400

e 38.83 f 0.612 g 3.1 h 0.9

i 0.031 j 612 000

2 a 1330 b 3.04 c 2209.2 d 184 100

e 980 f 140 g 0.7 h 2630

i 8.4 j 8.4

3 a 1.2 b 9.36 c 0.51 d 234

e 0.004 f 153 g 2.88 h 5.616

i 3672 j 0.3672

4 a 0.27 b 4500 c 0.26 d 810

e 0.78 f 0.005 g 6.3 h 11.34

i 6300 j 3276

2

Round: to 3 significant figures to 2 significant figures to 1 significant figure

a 12.47 12.5 13 10

b 0.3837 0.384 0.38 0.4

c 8461 8460 8500 9000

d 77.832 77.8 78 80

e 84 925 84 900 85 000 90 000

f 5.904 92 5.90 5.9 6

1-04 Significant figures1 a 4 b 5 c 1 d 3 e 2 f 3 g 6 h 5

i 4 j 3 k 4 l 3 m 2 n 1 o 4 p 3

162 NEWCENTURYMATHS 10: STAGES 5.2/5.3

1-05 Percentages withoutcalculators

1 a 710

b 325

c 25

d 13

e 120

f 34

2 a 0.18 b 0.09 c 0.65 d 0.2

e 0.125 f 0.883

3 a 25% b 20% c 6623% d 90%

e 1212% f 60%

4 a $65 b $11 c $48 d $4.50

e $9 f $149.60 g $2.55 h $140

5 a $336 b $54.60 c $200 d $756

6 A

7 a 20% b 75% c 3313% d 12%

e 12.5% f 80%

8 a 3.2 L b $3.60 c 40 min d $7.50

e 0.6 f 3.75 kg g $3 h $385

9 B

10 a $142.50 b $69.30 c $50 d $385

11 64 12 D 13 $300

14 a 60% b 25% c 1212% d 20%

e 1212% f 80%

15 B 16 $300 17 $74.80 18 6212%

19 60 20 $63 21 $580

3

Round: to 5 significant figures to 4 significant figures to 1 significant figure

a 38.0721 38.072 38.07 40

b 0.062 879 3 0.062 879 0.062 88 0.06

c 543.7003 543.70 543.7 500

d 9803.715 9803.7 9804 10 000

e 682 042 682 040 682 000 700 000

f 2 523 791 2 523 800 2 524 000 3 000 000

4

Expression Unrounded answer No. of significant figuresAnswer correct to2 significant figures

a 9.7 0.43 4.171 4 4.2

b31:773

26:01p 6.23 3 6.2

c 35 946 33 110 4 33 000d 109.48 0.805 136 3 140

e365:028

12:3 4:748.03 4 48

5

ExpressionNo. of significant figures in

each value in exp. Unrounded answerAnswer correct to nsignificant figures

a 8.25 4.17 3 34.4025 34.4

b22:61

0:48444 46.676 300 58 46.68

c 58 810p 2 1 650.708 939 1700d (7.43)2 3 55.2049 55.2

e 0.063 12 49.85 4 3.146 532 3.147f 2 600 000 45 2 57 777.777 78 58 000

163ANSWERS

22 a $20 b 4%

23 900 24 30% 25 15%

1-06 No calculators1 a 7:10pm b 9:45am

2 a 1540 h b 0025 h

3 a 56 b 436 c 132 d 86

4 a 96 b 462

5 a $150 b $165 c $16 d $6.60

6 8.4

7 a 93 b 140 c 460 d 72

e $24.70 f $43.80

8 a 910

b 3 : 5 c 38

d 11 : 7

9 4.89, 4.809, 4.098, 4.089

10 a 74 b 62 c 208 d 120

11 a $90 b $90 c $10.50 d $18

12 6:55pm

13 a 2200 b 90 c 260

14 a 8.91 b 5940 c 2.7 d 27

15 200

16 a 450 b 16 c 675 d 176

e 612 f 1188

17 38

18 7 hours 35 minutes

19 a 110 b 240 c 800 d 14e 16 f 14

20 $3500

21 a 20 b 33 c 5 d 2

22 a 2.6 b 26 c 6240 d 6.24

1-07 Scientific notation1 a 4:213 107 b 1:81 10-2 c 3:4 103

d 2 104 e 3:5 10-3 f 2 10-4

g 3:3 10-1 h 4 10-3 i 2:3 102

j 7:23 10-5 k 6:1 108 l 8 10-8

2 a 740 000 b 0.312 c 1850

d 0.000 66 e 0.002 54 f 475 100 000

g 0.078 h 300 i 0.054 87

j 32 160 k 0.082 l 6 020 000

3 a 4:7 10-4 b 6:211 1012 c 3:94 109

d 2 10-5 e 7:035 10-10 f 8:6 1016

4 a 24 000 000 b 0.000 000 03 c 7510

d 0.000 064 2 e 0.000 000 000 915

f 81 620

5 1:2 1010 years 6 4 500 000 000 years7 0.000 000 03 mm

8 152 600 000 km

9 1:27 104 km10 0.000 001 m 11 9 461 000 000 m

12 7:8 10-7 m 13 0.000 000 14214 a 6 109, 1:9 107 b 0.317%

1-08 Ratio problems1 a 2 : 5 b 7 : 3 c 3 : 2 d 2 : 3

e 1 : 5 f 1 : 12 g 10 : 3 h 6 : 25

2 450 mL 3 2 : 3 4 $42

5 24 750 cm or 247.5 m 6 7 : 9 7 3 : 35

8 cordial 100 mL; water 350 mL

9 24 cm

10 a 704 b 88

11 1 : 9000 12 Bulldogs 23 140; Raiders 21 360

13 252 14 420 mL

15 Cindy $140; Carmen $112 16 135

17 cricket 7 227 290; tennis 4 129 880 18 7 : 2

19 $5100 : $8500 20 19 cm

21 living 93 m2; sleeping 62 m2

22 45

23 petrol 3.75 L; oil 1.25 L

24 wins 24; losses 15

25 cement 8 kg; sand 20 kg

1-09 Rates problems1 66 words/min 2 plumber 3 $33.60

4 a 140 L b 6

5 2.4 cm/week 6 2512

min 7 5.2 L/min

8 18 cents/min 9 2.71 persons/km2

10 9.1 L/100 km 11 $20.44 12 712

hours

13 98 c/L

14 a $6.50 b $5.72

15 a 1680 kWh b 18.3 kWh

16 34 cents/min 17 105 L/min

18 16 min 19 3.68c

20 $1.60

21 a 250 008 b 135 421

22 1212

min 23 3.75 runs/over 24 $2.64

25 a 77.35 kL b $70.39

26 20 m/s 27 480 km


1-10 Numbers crosswordAcross:

2 gradient 5 grouping

7 fraction 9 estimate

12 negative 14 exponent

16 denominator 20 places

23 significant 24 Fibonacci

26 recurring 28 equivalent

29 ratio 30 ascending

Down:

1 power 3 integer

4 rate 6 decrease

8 average 10 hundred

11 consumption 13 enlargement

15 numerator 17 terminating

18 descending 19 reciprocal

21 stationary 22 scientific

25 density 27 hour

2-01 Brainstarters 2

1 2 1625

3 a 13.25 b 12

4 6ab 5 115 6 x 5767 + 58510 8 x4 7

9 a 8.94 units b -2

10 5ba 1156

12 7% 13 10

14 a b

15 a 37.70 cm b 113.10 cm2

16 a 384 cm2 b 512 cm3

17 a 10 000 b 1000

18 a triangular prism b 5

c rectangle, triangle d 45 cm3

19 a 84.82 b 113.10

20 A 12a bh

21 a rhombus b 38.5 cm2

22 220 cm 23 7 cm

24 Prism has uniform cross-section, side faces of pyramidmeet at a point

25 8 m

26 a 15 cm2 b 12 cm2 c 13.96 cm2

27 6 cm

Challenge: 23

2 1625

6 x = 576 7 58510

2-02 Area ID2 A 36 cm2 3 A 10 cm2

4 parallelogram, A bh 48 cm2

5 triangle, A 12bh 25 cm2

6 square, A s2 36 cm2

7 circle, A r2 28:27 cm2

8 trapezium, A 12a bh 68 cm2

9 rhombus, A 12xy 6 cm2


11 rectangle, A lb 28 cm2

12 triangle, A 12bh 27 cm2

13 kite, A 12xy 16 cm2


15 square, A s2 64 cm2

16 trapezium, A 12a bh 27:5 cm2

17 triangle, A 12bh 10:5 cm2

18 rhombus, A 12xy 22:5 cm2



21 trapezium, A 12a bh 34 cm2

22 semi-circle, A 12r2 76:97 cm2

23 kite, A 12xy 22 cm2

24 sector of a circle, A 360

r2 16:76 cm2

2-03 A page of prisms and cylinders1 56 cm3, 100 cm2 2 502.65 cm3, 351.86 cm2

3 91.13 cm3, 121.5 cm2 4 72 cm3, 114 cm2

5 1560 cm3, 1020 cm2 6 791.68 cm3, 490.09 cm2

7 1920 cm3, 1088 cm2 8 336 cm3, 320 cm2

9 1092 cm3, 740 cm2 10 1296 cm3, 720 cm2

11 6361.73 cm3, 1922.65 cm2 12 570 cm3, 554 cm2

13 540 cm3, 600 cm2 14 342 cm3, 256 cm2

15 1049.68 cm3, 827.14 cm2 16 2646 cm3, 1218 cm2

17 240 cm3, 272 cm2 18 593.76 cm3, 527.79 cm2

19 364 cm3, 300 cm2 20 343.23 cm3, 287.10 cm2

165ANSWERS

2-05 A page of solid shapes1 54 cm2, 27 cm3

2 46 cm2, 15 cm3

3 100.53 cm2, 75.40 cm3

4 64 cm2, 28 cm3

5 576 cm2, 512 cm3

6 222 cm2, 132 cm3

7 294 cm2, 343 cm3

8 716 cm2, 1280 cm3

9 150.80 cm2, 100.53 cm3

10 472 cm2, 360 cm3

11 240 cm2, 180 cm3

12 1320 cm2, 2880 cm3

13 360 cm2, 400 cm3

14 240 cm2, 264 cm3

15 113.10 cm2, 113.10 cm3

16 678.58 cm2, 1017.88 cm3

17 37.70 cm2, 16.76 cm3

18 314.16 cm2, 523.60 cm3

19 628.32 cm2, 1005.31 cm3

20 276.46 cm2, 385.37 cm3

2-06 Back-to-front problems 11 l 7 cm 2 h 2 cm3 h 4 cm 4 s 7 cm5 h 12 m 6 r 4 cm7 h 13 cm 8 r 8 cm9 h 13 mm 10 h 3 m11 h 14 cm 12 s 3:8 cm13 r 4:5 cm 14 h 15 mm15 s 30 mm 16 h 25 cm

2-08 Investigating paper sizes4 a A10 b A6 c A7 d A5

6 a 6 cm2 b no c 4 d area 99 a A0 b A1 c A2

11 a 16 b 256 c 1024

12 a 2 b 8 c 64

13 a 64 b 4 c 8

14 a 4 b 32 c 8

2-10 Surface area and volumecrosswordAcross:

2 length 3 square

6 perpendicular 8 height

10 radius 12 hemisphere

14 closed 16 diameter

17 cone 20 apex

22 rectangular 23 capacity

24 open 25 surface

26 pi 27 net

28 triangular 29 volume

Down:

1 slant 3 sphere

4 prism 5 oblique

6 parallelepiped 7 cross section

9 trapezoidal 11 squared

13 Pythagoras 15 formula

16 dimension 18 semicircle

19 composite 21 pyramid

23 cubed

3-01 Brainstarters 31 2000 2 $2242.31

3 n 1 4 area of a rhombus/kite5 $625 6 (2m 3)(m 5)7 108

8 a 3a 7 b p2

59 6.28 cm2 10 t r 3p11 x 2 1

212 SSS, SAS, AAS, RHS

13 x = 19 14 502.65 cm2

15 a 2 b 64 c 4 d 3 e 30 f 49

162:25

p, 0.16

, 3.51

17 8 and 9

18 a 3pr 3p2 b 36k2 25c 9x2 6xy y2 d 2x2 7x 4

19 a 4 and 16 b 25 and 49

20 a 18a4 b7x4

6c 3 d

4

m2e 32d10 f a

21 a 25 and 3 b 16 and 5 or 4 and 20

22 a false b true

2358

punits

Challenge:2

p: 1

3-02 Surds1 a

7

p,

3

pb

1003

p,

10

p

c p, 0.219 37. . . d28

p

2 a 4, 5 b 9, 10 c 6, 7 d 7, 8 e 3, 4 f 5, 6


3 a 25 b 7 c 10 d 8

e 12 f 4 g 11 h 2

4 a 10 b 10 c 30 d 30 e 12

f 12 g 28 h 28 i 9 j 9

5 16, 25, 36, 49, 64, 81, 100

6 a 35

pb 3

2

pc 4

3

pd 10

3

p

e 53

pf 2

3

pg 2

2

ph 7

2

p

i 26

pj 4

5

pk 6

3

pl 2

7

p

7 a 117

pb 6

3

pc 4

5

pd

11

pe 9

6

p 10pf 6

2

p 2 3p g 5 2p h 4 3p i 2 5p j 8 3p

3-04 Newtons method1 3 and 4 2 3.166 667

3 3.162 281 4 3.162 278, 3.162 278

5 Answers equal 6 7 and 8

3-05 Simplifying surds3.141 592 653 589

793 238 462 643

3-06 Surds code puzzle1 N 2 C 3 A 4 N

5 I 6 H 7 B 8 K

9 A 10 G 11 P 12 O

13 Q 14 W 15 R 16 T

17 L 18 M 19 D 20 F

21 U 22 Y 23 E 24 S 25 O

Because they are irrational and go on and on without any

clear pattern.

3-07 Multiplying and dividingsurds1 a

6

pb

77

pc 4 d 2

5

p

e 32

pf 8 g 10 h 3

1

p4

i 75 j 163

pk 36 l 40

3

p

m 65

pn 14

1

p4 o 45

2

p

2 a 23

p 6 b 8 4 5pc 6

2

p 30 d 6 7p 6 3pe 4

5

p 5 f 6 2 2pg 5

6

p 2 3p h 7 3p 6pi 4

5

p 6 2p j 40 6p 30 2pk 9 18 3p l 10 10p 25 2p

3 a 13 6 5p b 10 2pc 5

3

p 1 d 16 10p 53e 1 f 18

g 4 h 5 3 2pi 31 10 6p j 5 2 6pk 18 8 2p l 29 12 5p

4 a3

p3

b 25

p5

c6

pd 5

7

p

e 75

p10

f 1253

p g 52

p3

h1

p5

3

i3

p5

5j

6

p 4 2p4

k 210

p 7 2p2

l 23

p 3 2p3

5 a 0.707,2

p2

, 0.707 b 1.155, 23

p3

, 1.155

c 2.887, 53

p3

, 2.887 d 0.866,3

p2

, 0.866

e 2.858, 76

p6

, 2.858 f 3.828, 22

p 1, 3.828

3-08 Rationalising thedenominator

1 52

p2

26

p2

31

p5

34

2

p2

56

p6 5

3

p0

127 2

5

p 15p5

830

p 3 6p6

9 23

p 2 10 75

p 515

11 210

p 6p 12 70p 313 4

2

p 3p2

14 710

p 15 2p30

15 30 62

p23

165

p 1

17 32

p 2 3p2

18 56

p 30p5

19 26

p 3 2p 20 13 5 2p7

3-09 Indices squaresawIn rows along the tops:

56 a4b4 1 1a2 ; 55 ab4 916 1542 9

16 a3p 48; a2 a12 ap 1612

3-10 Surds and indices crosswordAcross:

2 negative 5 rational

6 law 8 root

14 zero 15 irrational

18 expand 20 positive

21 factor 22 simplify

24 difference 25 denominator

29 indices 30 notation

31 square 32 exponent

Down:

1 real 3 evaluate

4 binomial 7 approximate

9 fractional 10 integer

11 surd 12 power

13 express 16 quotient

17 expression 19 rationalise

23 product 26 index

27 base 28 cube

167ANSWERS

4-01 Brainstarters 41 1

92 20 5

6m=s

3 a 523.60 cm3 b 314.16 cm2

4 A 5

6 56

7 2 km

8 a41

pb 4

5

9 1 050 000 10 4x2 12x 911 4 : 25 12 12.20

13 6 10-3

14 a a = 4 b p 1 14

c y = 6 d x = 9

15 8

16

1 2 3 4 5 6 d

17 a 25

pb 7

2

p

18 Yes 19 14r 420 37, 39, 41

21 a k < -16 b z4 -3

22 a 2 2 6p b 3 1 3p

23

1

0 1 2 3

y = 3x 2

x

y

-1-1

-2

-3

-2

2

24 110

25 a (x 7)(x 4) b y(y 7)c (p 3)(5p1) d 3(w 2)(w 2)

26 x = 3

27 a $240 b 3 hours

28 5, 25

Challenge: 2

4-02 Equations code puzzle1 N -6 2 F -9 3 Q 84 D 3 5 R 2 6 K 4

7 B 7 8 X 1 9 I 910 T -4 11 E 10 12 A -113 O 18 14 L -8 15 S -316 H 11 17 U -5 18 W 519 P 6 20 R 16 21 E -722 A 12 23 M -2 24 V 1525 T -10From their number plates. One reads 4MULA1 while the

other reads EVALU8.

4-04 Testing simultaneousequations1 x 1, y 3 2 x -1, y 53 x 6, y -3 4 x 5, y 95 x 3, y 10 6 x 7, y 25

4-05 Intersection of lines1 (3, 5) 2 (1, 0) 3 (4, -2) 4 (-2, 6)

4-06 Simultaneous equationsorder activityElimination method: 8, 14, 6, 5, 17, 12, 1, 9, 19, 18

Substitution method: 10, 3, 15, 20, 13, 21, 2, 16, 14, 6, 5, 11,

7, 4, 19, 18.

4-08 Quadratic equations puzzle1 W 2 G 3 Q 4 X

5 O 6 C 7 E 8 V

9 H 10 D 11 M 12 P

13 A 14 F 15 U 16 T

17 J 18 I 19 S 20 B

21 O 22 E 23 A 24 T

25 I 26 Y 27 K 28 R

29 L 30 N

Playing this game is like graphing lines and curves on a

number plane. Youve got to look for the intercepts.

4-09 Problems involvingquadratic equations1 a k 5 b k2 5k

c 8 and 3 or -8 and -3

2 6 or -7 3 9, 12, 15

4 17, 19 5 8 and 9 or - 8 and - 9

6 a 36 m b 4 m/s


7 5 and 12

8 a 40 m b 25 m

c 5 s

d 1 or 3 s, ball goes up then down

e 2 s, 45 m

9 12 cm

10 a L = 12 W c 2 m and 10 md length 6 cm, width 6 cm, a square

4-11 Equations and inequalitiesreview1 c = -24 2 d = 12

3 x = 2 4 k > -1314

5 d = 25

p6 b = 2 4

13

7 y = -6 or 3 8 a = -93

9 u = 12

or -3 10 e5 - 23

11 x = 3 2p 12 n5 35

13 w = -4 22

p3

14 r > 14 12

15 x = 3, y = 2

16 x = 2, y = -7 17 h 3Vr2

18 x = 3, y = 1 or x = 7, 17

19 a = -43; b 10 7

9or a = 5; b = -23

20 p = -1 or 4


1

25a22 B

3 6 4 3 2y5 trapezoidal prism

6 a 169.65 cm3 b 169.65 cm2

7 58

8 k = 10

9 36 10 d 26 23

11

0 1 2 3 x12 11.5%

13 length 125 cm, width 100 cm

14 560 km 15 rectangle

16

17 360

18 SSS, SAS, AA, RHS

19 equilateral

20 a 275 km b 6.5 cmc 1 : 5 000 000

21

22 a a = 72 b y = 110

c p = 240 d e = 60

e u = 45 f x = 135

23 8

24 a false b true c false

25 25, 25

26 a AAS b TQ

27 a J b d 32 12

Challenge:

x

x

x

x

x

Other solutions possible

5-02 Naming quadrilaterals2 a true b true c false d true e true

3 a true b false c false d false e false

4 a false b false c true d false e false

5 a false b true c false d true e false

6 a parallelogram, rhombus, rectangle, square

b parallelogram, rhombus, rectangle, square

7 a rectangle, square b kite, rhombus, square

c rectangle, square d rhombus, square, kite

e parallelogram, rhombus, rectangle, square

f rhombus, square g rhombus, square

h rhombus, square i rhombus, rectangle

j parallelogram, rhombus, rectangle, square

8 a rhombus b rectangle

c parallelogram d rhombus

e kite f rectangle

169ANSWERS

g parallelogram h parallelogram

i trapezium j rectangle

5-03 Investigating thegeometrical constructionsC Diagonals bisect each other

D Diagonals bisect the angles of the rhombus

E The axis of symmetry of an isosceles triangle isperpendicular to the unequal side

F Diagonals cross at right angles

G 1 The axis of symmetry is perpendicular to the unequalside

2 Opposite sides of a rhombus are parallel

3 ABC AFE 90 (corresponding angles,DE k BC)

5-04 Angles in polygons1 a 360 b 720 c 1080 d 1440

2 a 1980 b 2700 c 3240 d 7380

3 a 7 b 11 c 18 d 24

4 b all sides equal, all angles equal

5 a 540 b 108

6 a 90 b 135 c 60 d 120

7 a90

b

45

c

120d

60

8 All 360 9 All 360

10 a 72 b 40 c 36 d 22 12

11 a 15 b 156 c 360 d 24

e supplementary, angles on a straight line

12 a 9 b 1260 c 40

13 a 20 b 3240 c 162

14 a 10 b 12 c 30 d 16

5-05 Find the missing angle1 a 155 2 b 603 c 75, d 105, e 75 4 f 475 g 113, h 67 6 i 100, j 727 k 72 8 l 669 m 97, n 66 10 p 13511 q 130, r 50 12 s 72, t 48

13 u 67 14 v 4515 w 66, x 114 16 y 120, z 6017 a 112, b 68 18 c 13319 d 4520 e 63, f 27, g 2721 h 114, i 57 22 j 69, k 6923 l 122, m 58, n 5824 p 36

5-06 Congruent triangles proofs1 In DCBA and DCDE, BC = CD, AC = CE, ACB = DCE, [ DCBA DCDE.

2 In DOBA and DOBC, OA = OC, AB = BC, OBA = OBC = 90, [ DOBA DOBC.

3 In D ABD and D ACD, AB = AC (given), AD is common, ADB = ADC = 90 (AD BC),[ D ABD D ACD (SAS)

4 In DWZY and DWXY, WZ = WX (equal adjacent sides of akite), WY is common, ZY = XY (equal adjacent sides of akite), [ DWZY DWXY (SSS)

5 In DTRU and DTRQ, TRU = TRQ (TR bisects PRQ), U = Q = 90 (TU PR, Q angle of square), TR iscommon, [ DTRU DTRQ (AAS)

5-07 Congruent and similartriangle proofs1 a SSS b RHS

c AAS d SAS

2 SAS 3 SAS, x = 9 cm, y = 35

4 a AAS

b ML = 2 cm, KN = 6 cm

5 a AAS b GH

6 a SSS

b Z = X, ZOY = XOY, ZYO = XYOc 90

7 a SAS b RHS

c SSS d AA

8 a RHS, x = 24 b AA, x = 8

c AA, x = 5 d SAS, x = 11

5-08 Geometrical proofs orderactivity1 - 17 - 14 - 24 - 22 - 12 - 10, 2 - 23 - 8 - 9 - 18 - 15 - 7 - 14 -

19, 3 - 11 - 20, 6, 16 (in any order) - 5 - 13 - 21

5-09 Complete the proofs

1 a KML 180902

45angle sum of isosceles KML


b [ PMN = 180 45 = 135c N 180135

2 22:5

angle sum of isosceles PNM2 a (alternate angles, AC kDG)

c [ ABF = x yd [ BFG = ABF (alternate angles, AC k DG)e [ BFG = x yf [ BFG = BEF EBF

3 a DCAB b AC

c DB = BC d common

e [ D DAB D CAB (SSS)

f [ DAB = CAB (matching angles in congruenttriangles)

g [ BA bisects DAC

4 b 90 (angle sum of DWNP)

c TWN = 90 (90 ) =

d TWN e In DPWN and DWTN

f WNT = 90

g TWN

h DWTN (AA)

i4

WN(matching sides in similar triangles)

j 36 k 6

5-10 Geometry crosswordAcross:

3 ratio 8 nonagon

9 similar 12 quadrilateral

16 bisect 20 matching

25 enlargement 26 SSS

28 exterior 29 symmetry

30 dodecagon 31 interior

32 reduction 33 polygon

Down:

1 pentagon 2 rhombus

3 RHS 4 test

5 right 6 AAS

7 diagonal 10 parallelogram

11 trapezium 13 equilateral

14 obtuse 15 decagon

17 triangle 18 eighty

19 isosceles 21 congruent

22 rotational 23 rectangle

24 geometry 26 square

27 SAS (or SSS)

6-01 Brainstarters 61 33.909

2 a 64x6 b 827

3 10d 6 4 Volume of a cone5 x 46 a 2 : 7 b 6 : 5

7 SAS 8 5.4 L/hour

920

por 2

5

punits

10 65 cm2 11 No 12 r 6913 y 1514 a 30 b 130 c 3 d 16

e 0.75 f 1.75

15 a 325

b 18

16 a 0.09 b 0.065 c 0.015 d 0.008

17 23%

18 a $320 b $3.21 c $1725

19 $5382 20 $594 21 $144.45

22 $600 23 $86.50

24 a $2100.15 b $3254.86

25 $756 26 $2349

Challenge: At the end of 12 years

6-02 Percentage shortcuts1 a 0.12 b 0.73

c 0.05 d 0.4

e 0.186 f 0.08

g 0.031 h 1.22

i 0.0695 j 0.125

k 1.5 l 0.0825

2 a $14.40 b $397.71

c $2.52 d $15.46

e $142.40 f $11 926

g 74c h $4.53

i $53.28 j $130

k $63.72 l $3.83

3 a $90.85 b $37.50

c $179.20 d $360.40

171ANSWERS

e $24.75 f $414.75

g $82.94 h $255.20

i $408.62 j $47.60

k $572.47 l $91

4 a $27 b $69

c $760 d $152.15

e $77.88 f $377.20

g $5208 h $577.50

i $72.11 j $222.78

k $22.78 l $254.67

5 $437.50

6 a $65.65 b $11.26

c $33

7 $41 544.65

8 a 1.07 b $5350

c $5724.50 d $6125.22

e the size of the investment after n years

6-03 Simple interest1 a 72 b 108

c 30 d 39

2 a 260 b 416

c 234 d 117

3 a 0.06 b 0.085

c 0.1225 d 0.025

e 0.2 f 0.0505

g 0.035 h 0.0725

4 a 0.011 b 0.0175

c 0.006 875 d 0.0089

5 a 0.000 438 4 b 0.000 260 3

c 0.000 624 7 d 0.000 361 9

6 a $1687.50 b $1581.25

c $1033.60 d $2850

e $452.33 f $1629.36

7 a 6 years b 212

years

c 34

year 9 months d 10 months8 a $6900 b $10 700

c $22 000 d $34 500

9 a 5% b 4.5%

c 11.2% d 8.25%

10 a $3520 b $10 864.81

c $31 096.92 d $22 393.97

6-04 Compound interest1 a 48 b 84

c 42 d 15

2 a 0.04 b 0.065

c 0.1325 d 0.0803

e 0.075 f 0.0375

g 0.006 h 0.001 48

3 a 0.01125 b 0.015

c 0.002 625 d 0.009 225

4 a 0.000 411 0 b 0.000 205 5

c 0.000 591 8 d 0.000 458 1

5 a 0.045 b 0.0175

c 0.025 625 d 0.038 65

6 a $5832 b $6802.44

c $7346.64

7 a $4908.93 b $19 539.18

c $32 331.19 d $12 989.19

e $22 721.51 f $52 294.04

8 a $1049.91 b $13 928.37

c $6384.43 d $1084.20

9 a $2470.99 b $7166.79

c $12 860.09

10 a $7209.38, $1709.38

b $6372.75, $2927.25

c $31 013.83, $ 11 013.83

d $21 397.28, $ 42 02.72

e $8194.17, $4025.83

6-05 Compound interest table1 a $6043.20 b $7533.50

c $15 303.75 d $19 701

e $10 114.56 f $26 016.25

g $20 234.90 h $23 155.20

i $10 161.34 j $13 111.90

2 12 years

3 a $7529.40 b $3526.40

c $18 448.64 d $4958.53

e $588.15 f $4801.74

g $2700.84 h $9531.20

i $6174 j $751.53


6-06 Term payments spreadsheet1 a $673.35 b $3815.65

c $1030.23 d $4845.88

e $134.61 f $5519.23

6 a decrease b decrease

d $56.42, $3153.52

7 a increase c $140.97

8 c decreases to $108.11, increases to $5862.63

9 a Monthly repayment and total amount paid increase

b Zero repayments, zero interest

c Zero interest

d Monthly repayment decreases, total amount paidincreases

e Same as d f Impossible

6-07 Loan repayments table1 a $20.28 b $12.00

c $358 d $2969.40

e $443.45 f $165.22

2 a $201.59 b $24 190.80

c $5190.80

3 a $1511.80 b $3679

4 a 25 years b 7%

5 a $1 761.60 b $634 176

c $394 176 d 5.5% p.a.

6 Interest charged for 30 years

7 a No ($3357.50) b Yes ($2088.76)

c Yes ($1698.50)

8 a $2556.80 b 3.2% p.a.

9 DotCom Credit Union

6-08 Reducible interestspreadsheet2 $70.34

3 $7343.67, $67.32

17 $420, 22, $832.39; $500, 18, $691.31; $800, 11, $430.04;$330, 28, $1089.10

18 $372.87

20 10%, 22, $787.90; 8%, 22, $614.97; 15%, 24, $1263.57;3%, 21, $217.31

21 $600, 59, $8643.23; $650, 53, $7713.07; $1000, 31,$4442.44; $720, 47, $6710.01; $540, 68, $10 121.39

22 a $880.18 b $697.85

6-09 Credit card statement1 a 18 Dec b 7 Jan

c 29 Dec

2 a Home art b Myer

c Miranda

3 a $49.90 b $88.75

c $145.40

4 18 Dec, petrol

5 a 2 Jan, Ambarvale b $100

6 Wollongong, most purchases

7 a $2000

b maximum he can borrow on the card

c $1461.94 d 13 Jan

8 a 16.95%

b 0.046 438%

c 16.95 3659 a made payment on card

b credit

10 a $538.06

b amount owing

c opening balance + purchases payment11 a $16.14 b minimum amount he has to pay

c 3% d $521.92

12 a 32 days b 25 days

6-10 Saving and borrowingcrosswordAcross:

2 monthly 4 price

6 annum 7 deposit

11 term 12 quarterly

14 balance 15 lay by

17 discount 18 interest

22 investment 23 repayment

26 deferred 27 outstanding

31 compound 32 principal

Down:

1 credit 2 minimum

3 bank 5 simple

6 annual 8 purchase

9 reducible 10 depreciation

13 table 16 fortnight

19 statement 20 instalment

21 week 24 rate

25 period 28 loan

29 card 30 flat

173ANSWERS

7-01 Brainstarters 71 0.7

2

2 $1085 3 1000 4 irrational

5 33

p2

6 29.3 L 7 SA = 2r2 2rh

8 a 4.105 10-2 b 4

9 3(3y 1) (3y 1) 10 360

11 25u2 40u 16 12 4m5

13 d -1 13or 5 14 x = 16

15 12.5 units2 16 -3

17 a 45

punits b (0, 3) c - 1

2

18 a x 4 12

b y = -3 19 n = -2

20 y

x

54321

0-1-2-2-3-4

y = 0

y = -2

y = -2x

-4 -3 -2

-2

-1 1 2 3 4

1

21 a one pair of opposite sides parallel

b all sides equal c opposite sides equal andparallel

22 35

punits 23 y = - 4

24 a y= 2x 3 b y = 3x 1 c y = -2x 7

25

4321

0-1

-2

-3

-3 -2 -1 1 2 3

yy = 2x 3

x

Gradient 2,y-intercept -3

26 a 5 12

b 2 c 4

27 Yes

Challenge: circle

7-02 Intervals match-up

7-07 Linear equations match-upA 1, 13, 22, 29 B 15, 17, 25, 32

C 3, 12, 19, 33 D 4, 9, 18, 28

E 5, 8, 20, 30 F 10, 14, 23, 35

G 7, 24, 27, 34 H 6, 11, 26, 36

I 2, 16, 21, 31

7-08 Geometry problems usingcoordinates

Interval 1 2 3

Length29

p 32

p5

Gradient2

51 -

3

4

Midpoint (512, 3) (4, 7) (2, 21

2)

Interval 4 5 6

Length80

p8 13

Gradient -1

20

12

5

Midpoint (1, 4) (-1, 1) (-312, 4)

Interval 7 8 9 10

Length40

p10

72

p 117

p

Gradient -1

3

3

4-1 -

3

2

Midpoint (-1, -1) (0, -2) (4, 2) (0, - 12)

1 b AB 5, BC 90p , AC 5c isosceles d - 1

3

e y 3x 3 f - 12

, 1 12

g In an isosceles triangle, an interval drawn from the

midpoint of the uneven side to the opposite vertex is

perpendicular to the uneven side

h10

p2

2 b 12

,3 12

c S (2, 6)

3 b Diagonals are equal and bisect each other.

4 c Parallelogram

5 a 1 12

, 3 12

, -

1

2, 2

, -2, 4 1

2

f They intersect at the same point.


7-09 A page of lines and regions1 x = 4 2 y - x

2 2 3 y = -x 4

4 y = x 4 5 y x2 4 6 y 10 5x

27 y5 -3 8 y < 2 x

39 y5 2x 4

10 y >3x

2 7 11 y4 4x 12 y < 5 3x

13 y4 2x 7 14 y > -x 15 y4 x3

7-10 Graphing non-linearequations

7-11 Coordinate geometrycrossword


8-02 Trigonometry review1 6.62 cm 2 10.78 cm 3 72

4 14 5 9.97 cm 6 5.20 cm

7 13.16 cm 8 79 9 54

10 23 11 16 cm 12 6.13 cm

13 16 14 30 15 6.10 cm

6 b right-angled d 65 units

7 b rhombus c -1, 5d Diagonals bisect each other at right angles.

e80

p 4 5p , 20p 2 5p .f

20

p 2 5p , 5p g 20 units28 b P 1

2, 1 1

2

, Q 3 1

2, 1

2

c gradient - 1

3, LM 2 10p , PQ 10p .

x -3 -2 -1 0 1 2 3

1. y = x2 9 4 1 0 1 4 9

2. y = x2 2x 15 8 3 0 -1 0 3

3. y = x3 - 27 -8 -1 0 1 8 27

4. y = 2x 0.125 0.25 0.5 1 2 4 8

5. y = (12)x 8 4 2 1 0.5 0.25 0.125

6.y =

4

x2 2 0.36 0.67 1.33 2 1.33 0.67 0.36

Across:

1 parallel 4 cartesian

5 triangle 8 quadrilateral

10 gradient 12 isosceles

16 surd 20 RHS

22 rise 23 equilateral

25 constant 26 nonlinear

27 hypotenuse 29 Pythagoras

30 steepness 31 integer

32 exact

Down:

2 average 3 line

4 coordinates 6 parallelogram

7 interval 9 LHS

11 equation 13 length

14 vertical 15 distance

17 midpoint 18 point

19 horizontal 21 rectangle

24 intercept 28 plane

1 $250 2 8 3 1h 40 min

4 811

5 48 m 6 14 + 65

p

7 201.84 cm2 8 $9889.05 9 - 34

10

3

(1, 4)y = x2 + 3

11 d = 32 12 k4 13

13 4.5

14 x 11; y 4 15 y - 13x 16 ab

17 a 1.1276 b 5.7671 c 1d 0.3420 e 0.3420

18 a same b 40

19 a3

p2

b 13

p

20 a 30580 b 56260

c 60 d 61560

21 N

EW

S

200

22 a 15.43 b 26.46

23 a 86.24 b 6.47 c 15.17 d 2.30

24 502.51 m 25 20

26 a 10 km b 32380

Challenge: 45

175ANSWERS

16 9 cm 17 6 18 41

19 3.23 cm 20 12.29 cm 21 39

22 35 23 9.02 cm 24 37

8-03 Bearings match-up1 18 2 23 3 19 4 14 5 22 6 24

7 17 8 21 9 16 10 15 11 20 12 13

8-04 The exact ratios1 45 each 2

2

p

3 a12

p b 12

p c 14 F = G = 60, FEH = GEH = 305

3

p

6 a 12

b3

p2

c 13

p

d3

p2

e 12

f3

p

7

8 Teacher to check

9 a 60 b 60 c 45

10 true

11 a 13

p b 13

p c 1

d 1 e3

pf

3

p

12 true

13 ar

qb

p

qcr

p14 Teacher to check

15 a 12

p b - 12

c -3

p

d 12

e -3

p2

f -1

8-06 Trigonometric calculations

8-08 Finding a missing side1 3.36 cm 2 8.43 cm 3 6.59 cm

4 4.11 m 5 5.15 cm 6 20.08 cm

7 8.29 m 8 5.16 cm 9 8.84 cm

10 4.54 cm 11 10.44 m 12 3.63 cm

13 5.22 cm 14 9.83 cm 15 10.37 m

16 14.28 cm 17 3 m 18 19.27 cm

19 6.05 cm 20 10.16 km 21 7.58 m

8-09 Finding a missing angle1 33 2 68 3 58 4 80 5 115

6 124 7 26 8 66 9 17 10 27

11 136 12 137 13 83 14 63 15 125

16 117 17 90 18 90 19 60 20 70

21 88

8-10 Trigonometry crossword

Across:

6 second 9 negative 10 surd

12 theta 14 obtuse 16 minutes

18 supplementary 23 bearing 25 one

26 Pythagoras 27 west 30 WNW

33 elevation 34 degree 36 northwest

38 depression 39 southwest 40 alternate

Down:

1 ESE 2 included 3 half

4 south 5 sine 7 cosine

8 north 11 complementary 13 tangent

15 ENE 17 three 19 trigonometry

20 SSE 21 positive 22 NNW

24 northeast 28 hypotenuse 29 southeast

31 opposite 32 NNE 35 east

37 area

12

12

p3

p2

3

p2

12

p 12

13

p 13

p

1 a 144130 b 150230 c 123290

2 a 0.737 b -0.944 c 13.655

d 1.408 e -4.473 f -1.636

g -11.139 h -35.624 i -11.493

3 a 158 b 139 c 146

d 163 e 110 f 113

4 a 103

b 49

c 24

d - 32

e 3.328 f 5

5 a 0.215 b 67.899 c -0.042 d 3.907

e 0.999 f 102.641 g -0.520 h 2.360

6 a 11.485 b 98.339 c 606.660

Puzzle1 F 2 W 3 I 4 H 5 A

6 O 7 E 8 K 9 B 10 L

11 Y 12 N 13 G 14 T 15 R

16 S

Both are always looking for the right angles



1 1 000 000

2 11a15

3 Equal or bisect each other

4 $80 and $32

5 737:23 cm3 6 $916

7 y = 36 8 3

9 70

10 d 711 $24.50

12 $10 200

13 30

14 a 2.4 m b 34:56 m2

15 a 4.8 b 4.5 c 4

16 A census surveys whole population, a sample surveys apart of the population.

17 a 19 b 2

c 4 d 2.42

e

Freq

uenc

y

Number of TV sets

01

23456

7

1 2 3 4 5

18 a f: 2, 5, 6, 8, 5, 2, 1, 1; cf: 2, 7, 13, 21, 26, 28, 29, 30

b 4 c 4 d 7 e 13

f, g

1 2 3 4 5 6 7 80369

12151821242730

Cum

ulat

ive

frequ

ency

Median = 4No. of people

19 15%

20 64.5

21 a 21 b 64 c 24

d 64 e 11 f 64.62

Challenge: 63 matches, 6 rounds

9-02 Statistics review1 a discrete b continuous

c discrete d continuous

2 a 4 14

b 5 c 5

d 4 e 310

3 a 20 b 6.4 c 7

d 7 e 6 f 65%

4 a 24 b 19, 22, 24 c 24

d 26.1 e 48 f 12

5 a fx: 4, 12, 21, 32, 25, 36, 130 b 36

c 3.61 d 4

e 4 f 518

g 44.4%

6 a cf : 33, 83, 115, 137, 145, 150 b 150

c 2.58 d 2

e 5 f 2

g, h

0 1 2 3 4 5 6No. of people in car

Median = 2

15

30

45

60

75

90

105

120

135

150

Cum

ulat

ive

frequ

ency

177ANSWERS

9-03 Statistical match-up

9-04 Cumulative frequencygraphs

1 a

2

3

4

5

6

7

3

2

5

6

7

2

3

5

10

16

23

25

Score Tally f cf

b 25 c 6 d 5 e 5

f

2 3 4 5 6 70

2

4

6

8

10

12

14

16

18

20

22

2426

Cum

ulat

ive

frequ

ency

Hours of TVg i 5 ii 4 iii 6 iv 2

2 a

b 5 c 8 d 7.5

e

f i 7.5 ii 6 iii 8 iv 2

9-05 Interquartile range

A 1 2 3 4 5 6 7 8 9 10

B 10 7 6 3 5 4 1 9 8 2

C 7 3 1 9 4 8 6 2 5 10

D 1 3 10 9 2 8 7 4 6 5

5

6

7

8

9

10

2

6

6

9

4

1

2

8

14

23

27

28

Score Tally f cf

5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Cumu

lative

freq

uenc

y

Hours of sleep

Q Median Q1 Q3Interquartile

range

1 15 11 20 9

2 18 13 251

212

1

2

3 11 5 14 9

4 4 1 9 8


10-01 Brainstarters 101 $21 386.70 2 The most common score

3 1 : 5000 4 b 35 285 6 n = 3

7 x = 44 8 a 20.47 cm b 26.18 cm2

9-06 Box-and-whisker plots1 a i drivers ii passengers

iii drivers iv drivers

b 350 c 80

d 80 e 330

f 80 g consistent, smallest spread

2 a

12 J

12 R20 30 40 50

Exam marks60 70 80 90

b 12J did better; higher values in box plot.

c 12J has the greater range, while 12R has the greaterinterquartile range, and the greater range if the outlier in

12J is excluded.

d 12J, 28 e 12J

f False. Even if only the bottom 25% of each class areconsidered, 12J still outperforms 12R.

Q Median Q1 Q3Interquartile

range

5 221

220 31 11

6 30 19 40 21

7 64 57 68 11

8 3 2 5 3

9 85 83 88 5

10 30 15 45 30

11 4 3 6 3

12 17 16 19 3

13 7 61

28

1

22

14 20 17 22 5

15 9 8 10 2

16 221

221 23

1

22

1

2

17 50 48 51 3

18 9 9 9 0

19 2 1 3 2

20 6 4 71

23

1

2

9-08 Statistical calculations

9-10 Analysing data crosswordAcross:

3 number 5 outlier

9 fifty 10 distribution

13 five-point 14 continuous

16 cluster 19 average

20 discrete 21 categorical

22 quartiles 28 plot

29 deviation 30 middle

31 whisker 32 stem

33 range

Down:

1 lower 2 centre

4 mean 6 statistics

7 quantitative 8 cumulative

11 interquartile 12 histogram

13 frequency 15 location

17 symmetrical 18 standard

23 upper 24 skewed

25 ogive 26 order

27 mode 29 data

Mean Mode Median RangeIQ

rangeSD

14.07 14 14 7 2 1.84

37.83 35 57 19.5 14.84

9.24 9 9 5 2 1.24

2.42 2 2 4 1 1.09

14.512, 14,16, 17

14 5 3 1.83

2.19 2 2 5 2 1.33

74.9253, 71,76, 84

76 45 21.5 13.04

4.75 5 5 8 3 2.33

9.75 10 10 8 3 2.33

14.25 15 15 24 9 7.00

6.44 5 5 20 4 5.27

1

2

3

4

5

6

7

8

9

10

11

179ANSWERS

9 m1m2 = -1 or m2 = -1

m1

10 x = 5 11 17 units 12 $145.11

13 a 12

b 3 14 64%

15 a 25

b 15

c 310

16 a 16

b 23

c 56

17 14 18 Teacher to check

19 a 0.55 b 16

20 Certain, must happen 21 0.5

22 Reds win, blues win, draw 23 25

24 0.02 25 58

26 55%

27 a 14 b13

c 313

d 513

28 19.2%

Challenge: 24

10-02 Games of chance1 a 1

52b 1

2c 1

4d 1

13

e 213

f 313

g 34

h 513

i 713

2 a 124

b 124

c 112

d 1112

3 a 14

b 316

c 16

d 124

4 a 1351

b 417

c 117

d 151

5 a 16

b 0 c 12

d 12

e 56

f 13

6 a 17

b 27

c 17

d 27

e 47

f 57

7 36

8 CASH in any six sectors

10 a 137

b 1837

c 1837

d 1837

11 a 1237

b 337

c 1237

d 637

e 437

f 2437

12 1037

13 1437

14 2837

10-03 Coins probability

1

2

3 Each event is not equally likely there are two ways ofgetting 1 head.

7

8

9 a 1 and 2 b 0 and 3

15 a 16 b 2

i

ii

iii

iv

1st coin 2nd coin No. of heads

H H 2

H T 1

T H 1

T T 0

No. of heads Probability Probability (%)

0 1

4

25

1 1

2

50

2 1

4

25

1st coin 2nd coin 3rd coinNo. ofheads

H H H 3

H H T 2

H T H 2

H T T 1

T T T 0

T H T 1

T T H 1

T H H 2

i

ii

iii

iv

v

vi

vii

viii

No. of heads Probability Probability (%)

0 1

812.5

13

837.5

23

837.5

31

812.5


10-04 Dice probability

1

2

10-06 Matching probabilities1 P 2 A 3 I

4 Z 5 M 6 N

7 O 8 T 9 R

10 Y 11 E 12 K

13 D 14 J 15 U

16 F 17 L 18 A

19 G 20 H 21 Q

22 S 23 U 24 N

25 V 26 X 27 B

28 W 29 E 30 C

No chance at all. Its an Australian slang term, a pun on the

name of an old Melbourne firm Buckleys and Nunn (none).

10-07 Probability review1 no chance at all

2 413

3 a 14

b 512

c 23

4 a 126

b 313

c 513

d 713

5 12

6 a 310

b 15

c 1340

7 a 920

b 11100

c 950

8 1320

9 a 4 b 14

c 12

10 2125

11 16

12 a 15

b 35

c 35

13 a 12: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

b 112

c 14

14 a

b 16

c 5, 118

15 a 36% b 48 12%

16 a BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG

b 37 12%

17 37

10-08 Tree diagrams1 All possible arrangements of boys and girls.

a 14

b 14

c 12

2 3 4 5 6 7

3 4 5 6 7 8

4 5 6 7 8 9

5 6 7 8 9 10

6 7 8 9 10 11

7 8 9 10 11 12

+

Sum Probability Probability (%)

21

362.78

31

185.56

41

128.33

51

911.11

65

3613.89

71

616.67

85

3613.89

91

911.11

101

128.33

111

185.56

121

362.78

1 2 3 4 5 6

1 0 1 2 3 4 5

2 1 0 1 2 3 4

3 2 1 0 1 2 3

4 3 2 1 0 1 2

5 4 3 2 1 0 1

6 5 4 3 2 1 0

1stdie

2nd die

181ANSWERS

2 Science History

0.85

0.15

a 0.595 b 0.045

P

FF

P

F

P0.7

0.3

0.7

0.3

PP

PF

FP

FF

Outcomes

338

38

38

58

P(1 rainy day) = 58

58

1st day 2nd day Outcomes

RR

RR

RR

RR

RR

1532

R RR

R

4 Adrain Pete Outcomes

H

M

H HH

HM

MH

MM

M

H

M

P(at least one scores) = 1415

45

23

13

15

45

15

5

RR RR

RS

SR

SS

S

R

SS

Outcomes1st student 2nd student

1025

1525

1424

1024

1524

924

P(SS) = 720

6S

S

P P

TS

P

T

T

TT

TP

TSPT

PP

SS

SPP

T STPSS

1st 2nd Outcomes5

19 619

619

619 6

19

719

820

620

620

519

819

819

P(neither are teachers) = 3395

7 a 11225

b 961225

c 971225

8 B

9 a 13

b 23

c 12

10-09 Investigating combinations1 20 2 60 3 160

4 a 17 576 b 1000 c 17 576 000

5 1024 6 120 7 720 8 6

9 30 10 20 11 1320 12 10

13 56 14 56 15 3003 16 2 598 960

17 210 18 8 145 060

10-10 Probability crosswordAcross:

1 clubs 4 trial

5 decimal or certain 7 sum

11 multiple 13 outcome

14 event 15 probability

18 random 19 not

21 certain or decimal 22 die

23 spinner 25 head

26 favourable 28 simulation

29 experiment 31 occurring

33 percentage 35 cards

36 unlikely 37 chance

Down:

1 coin 2 sample

3 relative 4 tally

6 even 8 likelihood

9 impossible 10 complementary

12 hearts 16 theoretical

17 one 20 frequency

24 diamonds 27 fraction

30 predict 32 spades

34 tail


2p 2 1

83 3

3

p

4 198 5 17.05 6 5y


7 4190 cm3 8 6150 9 rectangle

10 108 11 310

12 124

13 $1300, $650, $2600 14 360

15 y = -x 4 16 a 3 b -2 c 23

17 a 113 b 22 c 64 d 4

18 C 19 a 36 b 8 c 120

20 a x = -1 or 5 b x = -5 or 1 13

21 a 0 b 1 c 19

d -17

22 a 60 km/h b 12:30 pm c 150 km

23 a 1 b -2 c - 12

24 -1

525 d = 3, h = 6

Challenge: 16 m

11-02 Graphs of change1 a slowing down b not moving c fast

d going backwards e speeding up f slow

2 a steep b shallow c flat

3 a C b B c A

4

Hei

ght

Time

steeper than 3C 5 D

6 a C b D c E

d B e A

7 a i E ii A iii C iv D

b

8 rapidly at first, then slows to a constant rate

Hei

ght

Time

9

TimeTem

pera

ture

10 a slowing down then stopping

b slowing down

c speeding up (in opposite direction)

d constant speed, stopped, then constant slower speed

11-05 Matching parabolas1 D 2 A 3 I 4 E 5 H 6 L

7 B 8 P 9 G 10 C 11 F 12 N

13 M 14 K 15 J 16 O

11-06 Features of a parabola

1 1 or 3 9 2 (2, -3) H

2 -1 or -3 -6 -2 (-2, 2) C

3 None 5 2 (2, 1) I

4 2 or -3 -12 - 12

- 1

2, -12 1

2 D

5 -1 1 -1 (-1, 0) B

6 0 or 3 0 32

1 1

2, 2 1

4 E

7 2 or -2 -4 0 (0, -4) A

8 None -2 -1 (-1, -1) G

11-07 A page of parabolasPossible answers:

1 y = 2x2 2 y = x2 23 y = x2 3x 4 y = 4x2 8x 35 y = -

x2

26 y = -x2 5x

7 y = 3x2 6x 8 y = -x2 2x 159 y = 2x2 4x 4 10 y = x2 2x 111 y = x2 2x 8 12 y = -4x2 24x 3213 y = -x2 4x 4 14 y = x2 2x 215 y = x2 6x 8

11-11 Matching graphs1 B 2 I 3 D 4 P 5 L 6 O

7 F 8 C 9 E 10 M 11 K 12 H

13 J 14 G 15 A 16 N

11-12 Graphs crosswordAcross:

1 equation 4 radius 5 constant

6 symmetry 7 coordinates 10 intercept

12 horizontal 14 speed 15 variable

16 centre 17 vertical 20 asymptote

21 dependent 22 line 24 concave

25 parabola 26 curve 27 gradient

183ANSWERS

Down:

2 quadratic 3 origin 6 steepness

7 coefficient 8 exponential 9 quadrant

11 vertex 13 reciprocal 18 cubic

19 hyperbola 23 rate


22 -

3

p

3 SSS, SAS, AA, RHS 4 r -2 47

5 a 251.33 cm2 b 3.75 c 38.26 cm2

6 1.6% 7d3

8c6

8

x

y

21-1-2-1

12

456

3

9 $864 10 x = 4, y = - 1

11 x 3y 9 = 0 12 9 : 25

13 $24 112

14

segment

tangent

15 a a = 78 b w = 154

c m = 35, n = 145 d p = 65, r = 85

16 a SSS or SAS

b In DOCA and DOCB, OA = OB (equal radii), OC iscommon, AC = CB (given), [ DOCA DOCB (SSS)

c OCA = OCB = 90 (matching angles in congruenttriangles), [ OC AB

17 17 cm 18 3.85 cm2

19 a Equal angles in isosceles DOAB

b 2x 2y = 180c ABC = x y = 90

20 a x = 5 35

b d = 28

c y = 12

d n = - 9 or 4

21 a SAS

b In D AOB and D DOC, OA = OD (equal radii),OB = OC (equal radii), AOB = DOC (verticallyopposite angles), [ DAOB DDOC (SAS)

c AB = DC (matching sides in congruent triangles)

d Matching angles in congruent triangles, equal angles inisosceles triangles

e alternate angles equal

Challenge: 12

12-02 Parts of a circle2 a diameter b segment c arc

d secant e chord f tangent

g radius h sector i semi-circle

j segment k sector l circumference

12-04 Circle geometry cards

1 E 2 F 3 I 4 J 5 N 6 A

7 C 8 B 9 H 10 G 11 P 12 D

13 O 14 K 15 L 16 M

12-05 Circle geometry review

1 a = 65, b = 90 2 u = 52 3 k = 49

4 x = 65, y = 25 5 m = 72 6 d = 105, e = 105

7 p = 14 8 h = 6 9 69

10 v = 220, w = 70, x = 110 11 d = 92

12 c = 45 13 n = 15, y = 7 14 a = 60, b = 60, c = 30

15 v = 3 13

16 w = 103 17 a = 46

18 r = 30, p = 50 19 x = 5, y = z = 38

20 d = 60, e = 30 21 t = 50 22 k = 5

23 x = 3 24 r = 2


1 -5 2 $18 000 3 45 4 2 h 40 mins

5 0.000313 6 5 7 rectangle


8 14

9 235.62

10

0-2 -1 1 2 43

-1

1

y

x

234

-2-3-4

-3

11 SAS 12 a =v2 u2

2s13 $45

14 a 38130 b 17.3 cm2 15 1, 3, 5, 15

16 x 2 y2 = 16

17 a parabola b -10 c -5 and 1

18 a 14m 12 b 2x3 x2 15x

19 24, remainder 3 20 195

21 a -8 b 0 c 10

22 a (3b 7) (b 2) b 2y (y 3) (y 4)

23 a 3 b 2 c 6 24 25, 5

25

y = -x3

x

y

(-1, 1)

yy = x2 + 5

x

5

a b

26 a x = -8 or 7 b p = 2 23

27 x = -2 25

, y = 6 1925

or x = 2, y = 5

Challenge: 100

13-03 Circle equations orderactivity22 - 11 - 21 - 25 - 1, 24 - 14 - 13 - 27 - 12,

6 - 2 - 19 - 3 - 7, 8 - 23 - 26 - 4 - 18 - 9,

20 - 17 - 5 - 15 - 10 - 16

13-04 Simultaneous equationsorder activity1 - 11 - 31- 18 - 26 - 19 - 12 - 25 - 24,

8 - 10 - 3 - 29 - 16 - 2 - 20 - 30 - 17 - 7 - 5,

15 - 4 - 13 - 6 - 21 - 14 - 22 - 9 - 23 - 27 - 28

13-05 Polynomials review

1 a yes b yes

c no, power of x in1

xis negative d yes

e no, power of x inx

pis a fraction f yes

2 a yes b -15 c no d 5e 1 f 9

3 3 4 a 7x3 x b 7x3 4x 3c 14x4 14x3 6x2 10x 4d -104

5 3x3 2x2 4x 5 = (x 2) (3x2 4x 4) 36 a 20 b -175 c 0

7 a P (-2) = 0 b (x 2) (x 3) (2x 5)8 (x 3)(x 3)(x 4)9 y

x

a

y = x (x + 2) (x + 3)

0-1-2-3

b

y = (x + 4)(x 1)(x 2)2

y

x-1 0 1 2-2-3-4

-4 4-3 -2 -1 1 2

y = -2(x 3)3(x + 1)54

c y

x30

y

x

1 (1, )y = 2-x

12

c

185ANSWERS

10 a x = -2, -1 or 4

6

b

-3 -2 -1 0 1 2 3 4 x

y

-8

y = x3 x2 10x 8

11

-4-5-6-7 -3 -2 -1 x

49

y

y = x3 + 15x2 + 63x + 49

12

a

y = P(x) 3

y

x-3

b y

x

y = 3P(x)

c y

x

y = P(x)

d y

x

y = P(-x)

13-06 Advanced graphs

1 E 2 H 3 J 4 D 5 G 6 I

7 B 8 K 9 C 10 L 11 F

12 P, (-3, 4), (4, -3) 13 O, (-2, -4), (1, -1)

14 M, (-1, -2), (4, 12) 15 N, (-3, 2 1

2), (2, 0)


1 3.34

2

30

N

3 a 9 p2 64 b 21 8 5p4 6 200 000 5 x = - b

b2 4ac

p2a

6 2000 7 SA = 3r2 8 76

9 pentagon 10 x4 2 113

11 136

12 a (3, -2) b 42

punits

13 circle

14 a 343 b 64 c 17

d 19

e 4 f 8

15 x = 6


16ya

x

(-1, 1)

x

y

-1 1

1

b

x

y

1

c

(1, 3)

17 a x = y 43

b x = y5

qc x = - 2y

18 16a2 8a 519 a 3k9 b 2m

6

9c 16 d16 d 2y2

e 2 f 4n23

por 4

n3

p 2

20y

y = x

x

(1, 1)

a

x

(1, 1)

b y y = x3

21 a n = 9 b r = 5 c x = 6

Challenge: x = 13

14-02 Inverse functions codepuzzle1 J 2 V 3 B 4 G 5 L 6 M

7 Y 8 A 9 R 10 E 11 T 12 K

13 O 14 C 15 I 16 N 17 P 18 S

19 D 20 X 21 H 22 Q 23 W 24 U

What do lumberjacks sing while they are chopping down

trees? Logarithms.

14-03 Logarithm tables1 a 0.8129 b 0.3010 c 1.3010

d 0 e 1.7243 f 2.8451 g 1.5798

h 2.7853 i 2.9542

2 a 7.8 b 6.2 c 2.0 d 50 e 34

f 280 g 210 h 13 i 2600

3 a 14 b 47 c 2.2 d 1.4 e 220

f 5 200 000 g 17 h 390 000 i 1.9

4 a 32 b 16 c 810 d 2.7 e 16

f 2.7 g 7.7 h 11 000 i 14 j 4.1

14-04 Logarithms review1 a 3 b 8 c 3 d 2 e -1

f -2 g 12

h 0

2 a log4 64 = 3 b log5 25 = 2

c log2 32 = r d logy z = 6

3 a 102 = 100 b 23 = 8 c 37 = b

d a2 = 16

4 a 5 b 3 c 2 d 3 e 1 f 3

g 12 h 6

5 a loga 30 b loga 5 c loga 12

f loga 4 2 e 0 f loga 3 2g loga 4 12 h loga 3c

d3

pe2

6 a loga x loga y b n loga xc loga p loga q loga rd loga 4 2 loga 5e 1

2loga x 12 logay

f loga c 2 loga d7 a x z b 1

2x c 2x z

d y z x8 a 1.5564 b -0.7782 c 1.7782

d -0.2218 e 2.5564 f 1.8891

9 a x = 6 b x = 8 c xJ 2.97

d xJ 9.67 e xJ 8.48 f xJ -1.19

10 a x = 81 b x = 3125 c x = 2

d x = 6 e x = 10 f x = 4

187ANSWERS

ContentsPrefaceSyllabus reference grid1 Working with number1-01 Brainstarters1-02 Fractions without calculators1-03 Wheres the point?1-04 Significant figures1-05 Percentages without calculators1-06 No calculators1-07 Scientific notation1-08 Ratio problems1-09 Rates problems1-10 Number crossword

2 Surface area and volume2-01 Brainstarters 22-02 Area ID 2-03 A page of prisms and cylinders 2-04 Formula matching game 2-05 A page of solid shapes 2-06 Back-to-front problems 1 2-07 Back-to-front problems 2 2-08 Investigating paper sizes 2-09 Areas and volumes of similar figures2-10 Surface area and volume crossword

3 Surds and indices3-01 Brainstarters 3 3-02 Surds 3-03 Surds on the number line 3-04 Newtons method 3-05 Simplifying surds 3-06 Surds code puzzle 3-07 Multiplying and dividing surds 3-08 Rationalising the denominator 3-09 Indices squaresaw 3-10 Surds and indices crossword

4 Equations and inequalities4-01 Brainstarters 4 4-02 Equations code puzzle 4-03 Getting the right formula 4-04 Testing simultaneous equations 4-05 Intersection of lines 4-06 Simultaneous equations order activity 14-07 Investigating quadratic equations 4-08 Quadratic equations puzzle 4-09 Problems involving quadratic equations4-10 Equations and inequalities crossword4-11 Equations and inequalities review

5 Deductive geometry5-01 Brainstarters 5 5-02 Naming quadrilaterals 5-03 Investigating the geometrical constructions5-04 Angles in polygons 5-05 Find the missing angle 5-06 Congruent triangles proofs 5-07 Congruent and similar triangle proofs5-08 Geometrical proofs order activity 5-09 Complete the proofs 5-10 Geometry crossword 5-11 Geometry summary poster

6 Saving and borrowing6-01 Brainstarters 6 6-02 Percentage shortcuts 6-03 Simple interest 6-04 Compound interest 6-05 Compound interest table 6-06 Term payments spreadsheet 6-07 Loan repayments table 6-08 Reducible interest spreadsheet 6-09 Credit card statement 6-10 Saving and borrowing crossword

7 Coordinate geometry7-01 Brainstarters 7 7-02 Intervals match-up 7-03 Coordinate geometry: open-ended problems7-04 Using a graphics calculator 7-05 Graphing linear equations 7-06 Linear equations code puzzle 7-07 Linear equations match-up 7-08 Geometry problems using coordinates7-09 A page of lines and regions 7-10 Graphing non-linear equations 7-11 Coordinate geometry crossword

8 Trigonometry8-01 Brainstarters 8 8-02 Trigonometry review 8-03 Bearings match-up 8-04 The exact ratios 8-05 sine and cosine curves 8-06 Trigonometric calculations 8-07 Discovering the sine rule 8-08 Finding a missing side 8-09 Finding a missing angle 8-10 Trigonometry crossword

9 Analysing data9-01 Brainstarters 9 9-02 Statistics review 9-03 Statistical match-up 9-04 Cumulative frequency graphs 9-05 Interquartile range 9-06 Box-and-whisker plots 9-07 Statistics mode (calculator) 9-08 Statistical calculations 9-09 Comparing word lengths 9-10 Analysing data crossword

10 Probability10-01 Brainstarters 10 10-02 Games of chance 10-03 Coins probability 10-04 Dice probability 10-05 Greedy pig game 10-06 Matching probabilities 10-07 Probability review 10-08 Tree diagrams 10-09 Investigating combinations 10-10 Probability crossword

11 Graphs11-01 Brainstarters 11 11-02 Graphs of change 11-03 Graphing parabolas 11-04 Graphing curves (graphics calculator)11-05 Matching parabolas 11-06 Features of a parabola 11-07 A page of parabolas 11-08 Graphing cubics 1 11-09 Graphing hyperbolas 11-10 Graphing exponentials 11-11 Matching graphs 11-12 Graphs crossword

12 Circle geometry12-01 Brainstarters 12 12-02 Parts of a circle 12-03 A page of circles 12-04 Circle geometry cards 12-05 Circle geometry review

13 Curve sketching and polynomials13-01 Brainstarters 13 13-02 Graphing cubics 2 13-03 Circle equations order activity 13-04 Simultaneous equations order activity13-05 Polynomials review 13-06 Advanced graphs

14 Functions and logarithms14-01 Brainstarters 14 14-02 Inverse functions code puzzle 14-03 Logarithm tables 14-04 Logarithms review

AppendicesA1 Teaching schedule A2 Teaching schedule blank A3 Teaching program register A4 Number plane grid paper A5 2 mm grid paper A6 5 mm grid paper A7 1 cm grid paper A8 Square dot paper A9 Isometric dot paper

Worksheet answers Topic test answers

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WORKSHEET ANSWERS FOR NEW CENTURY MATHS