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- 1. 560 A n s w e r s answers CHAPTER 1 Earning money Skills check 1 75 2 12.6 3 3825 4 11.4% 5 400 km 6 20.8 days Exercise 1A — Calculating salary payments 1 $1700 2 $960 3 $4500 4 a $745 b $1490 c $3228.33 5 $1653.84 6 7 $23 920 8 $32 500 9 $69 600 10 C 11 $14.28 12 a $634.62 b $17.63 13 a $688 b Karina ($16.38 per hour) 14 45 hours Exercise 1B — Calculating wages 1 $518 2 3 a $424.80 b $566.40 c $501.50 4 a $432 b $499.50 c $600.75 5 a $17.34 b $225.42 6 D 7 $9.68 8 39 9 10 $12.54 11 C 12 D 13 $422.62 14 $548.80 15 a $349.65 b 43 hours 16 $11.78 10 Quick Questions 1 1 $344.16 2 $518.70 3 $218.40 4 $95.04 5 $12.87 6 $903.85 7 $2692.31 8 $4706.67 9 $846.15 10 $24.18 Exercise 1C — Commission and royalties 1 $ 2000 2 a $260 b $327 c $568.79 3 a $400 b $1200 c $1360 4 $1425 5 $4140 6 B 7 C 8 $8125 9 $800 10 a $4125 b $5375 c $16 875 11 $950 12 a $390 b $490 c $649 13 B 14 a $400 b $500 c $8000 d $8125 15 $625 16 a $300 b $345 c $406.80 17 D 18 $15 500 19 $510 20 $810 Exercise 1D — Payment by piece 1 $75.95 2 a $103.50 b $94.50 c $85.50 d $81 3 $175 4 $135 5 $325.50 6 $327 7 a $92 b $138 c $87.40 d $114.08 8 a $57.75 b $125.13 c $103.95 9 $22.80 10 a $11 b $27.80 c $19.32 11 a $134.40 b $16.80 12 a $174 b $21.75/h c $29.00/h 13 24 10 Quick Questions 2 1 $455.84 2 $346.15 3 $740.38 4 $3307.69 5 $32 406.40 6 $487.20 7 $570 8 $208.55 9 $60.30 10 $1840 Exercise 1E — Working overtime 1 $16.95 2 $22.84 3 $28.70 4 $142.56 5 $157.20 6 Answers Annual salary Weekly pay Fortnightly pay Monthly pay $30 000 $576.92 $1153.84 $2500.00 $39 500 $759.62 $1519.23 $3291.67 $42 250 $812.50 $1625.00 $3520.83 $54 350 $1045.19 $2090.38 $4529.17 $86 475 $1662.98 $3325.96 $7206.25 Name Hourly rate Hours worked Wage A. Smith $14.52 40.5 $580.80 B. Brown $16.45 38.5 $625.10 N. Tran $15.95 37.5 $598.13 A. Milo $20.10 41.5 $824.10 L. McTavish $18.04 36.5 $649.44 Name Wage Hours worked Hourly rate A. White $416.16 36 $11.56 B. Black $538.80 40 $13.47 C. Green $369.63 37 $9.99 D. Brown $813.96 42 $19.38 E. Scarlet $231.30 15 $15.42 F. Grey $776.72 38 $20.44 Name Ordinary rate Overtime rate Hours worked Pay A. Nguyen $8.90 Time and a half 4.5 $53.40 M. McDonnell $9.35 Double time 6.5 $112.20 F. Milosevic $11.56 Time and a half 7.5 $121.38 J. Carides $13.86 Time and a half 6.5 $135.14 Y. Robinson $22.60 Double time 5.5 $248.60 1A 1E MQ Maths A Yr 11 - Ans Page 560 Thursday, July 5, 2001 8:08 AM
- 2. A n s w e r s 561 answers ➔ 7 C 8 A 9 B 10 $543.52 11 $721.60 12 $596.25 13 14 C 15 A 16 $595.20 17 a $705.28 b $788.80 c $928 18 $455.78 19 $492 Exercise 1F — Additions to and deductions from gross pay 1 $385.20 2 3 $389.80 4 a $2519.23 b $1585.23 5 $7.58 6 $56.02 7 a $511.10 b $5.11 c $407.26 8 a $2153.85 b $44.84 c $1448.41 9 $18.71 10 $106.44 11 a $422.56 b $23.24 c $331.14 12 a $2884.62 b $137.02 c $69.60 d $1668.78 13 a $516.80 b $2428.96 14 a $880.77 b $4139.62 15 a $466.20 b $81.59 c $464.55 16 a $5269.23 b $922.12 c $96.15 d $4315.28 Chapter review 1 $761.54 2 $2592.31 3 $15 912 4 $22.29 5 a $522 b $594.70 c $588.24 6 a $442.80 b $220.80 7 $11.40 8 43 hours 9 $395.20 10 $798.50 11 $534 12 $340.75 13 $98 14 a $21.30 b $28.40 15 a $98.10 b $109 16 a $368.60 b $426.80 c $426.80 d $485 17 $590.24 18 $333.25 19 $4.05 20 a $1855.77 b $83.51 21 a $631.55 b $13.26 c $22.10 d $455.89 CHAPTER 2 Taxation Skills check 1 20.4 2 15% 3 $110 4 17.8 litres 5 4.05 hrs Exercise 2A — Calculating allowable deductions 1 $1153.90 2 $1624.55 3 $1070.10 4 $1540.36 5 a $914 b $1208.77 c $811.72 d $1560.20 6 a $1000 b $600 c $360 7 $3087.50 8 a i $30 000 ii $18 000 iii $10 800 b 2005–06 9 $960 10 $18 760 11 $712.27 12 $40 074.50 Exercise 2B — Taxable income 1 $43 754.25 2 a $16 879.20 b $15 736.50 3 $43 568.34 4 a $24 219.40 b $22 262.60 5 a $20 503.60 b $20 075.20 6 a $42 500 b $2600 c $39 900 7 a $34 262.30 b $498.24 c $32 204.06 8 a $74 280 b $8737.46 c $65 542.54 9 a $25 649 b $1470 c $1540 d $1349.40 e $21 289.60 10 A 10 Quick Questions 1 1 $2260 2 $1581.22 3 $1650 4 $1105.50 5 6 years 6 $36 520 7 $41 771 8 $22 660 9 $37 525.80 10 $24 570 Exercise 2C — Medicare levy 1 $598.05 2 a $648.75 b $851.18 c $1410 3 a $23 491 b $352.37 Exercise 2D — Calculating tax 1 $7015 2 a Nil b $2154.75 c $5755 d $9676 e $14 677 f $23 303.04 3 a $17 039.36 b $1876.63 4 $3897.40 5 a $7060 b $534.00 c $7594 6 a $2402.50 b $8646.10 c $18 662.50 7 $81.14 8 $230.69 9 B 10 B 11 D 12 a $38 674.10 b $8562.31 c $291.69 refund 13 a $38 942.80 b $166.28 c $8252.67 d $393.89 refund Name Ord. rate Normal hours Time and a half hours Double time hours Total pay W. Clark $8.60 38 4 $378.40 A. Hurst $9.85 37 .5 6 $482.65 S. Gannon $14.50 38 5 2 $717.75 G. Dymock $16.23 37.5 4 1.5 $754.70 D. Colley $24.90 36 6 8 $1518.90 Gross pay Deductions Net pay $345.00 $89.45 $255.55 $563.68 $165.40 $398.28 $765.90 $231.85 $534.05 $1175.60 $429.56 $746.04 $2500.00 $765.40 $1734.60 1A 2D MQ Maths A Yr 11 - Ans Page 561 Thursday, July 5, 2001 8:08 AM
- 3. 562 A n s w e r s answers 14 a Gross annual pay = $44 650, PAYG tax = $11 940.50 b $41 513.40 c $9456.72 d $2483.78 15 a $392.05 b $4751.14 debt 16 1590 17 Pay $180 10 Quick Questions 2 1 $600 2 $360 3 $442.01 4 $385.05 5 $502.62 6 Nil 7 $2305.20 8 $6130.00 9 $14 603.80 10 $25 920 Investigation — Tax offsets 1 The amount appears correct ($52.50) 2 $1115 Exercise 2E — Calculating GST and VAT 1 $3.56 2 a 23c b $6.89 c $9.85 d 13c e $8.99 3 a 80c b 48c c 9c d 63c e 34c 4 $123.75 5 a $126.39 b $32.89 c $16.17 d $5.45 e $6.47 6 a $30 b 94 cents c $47 d $2.94 e $9.86 7 $98.50 8 a $1.90 b 19c 9 $348.10 10 a $1.08 b $80.63 c $193.29 d $49.21 e $6.95 11 a $33 550 b $36 630 c $34 705 d $38 885 Chapter review 1 $2865 2 $2148.43 3 a $12 600 b $9072 c $6531.84 4 6 years 5 $27 057.35 6 $43 883 7 $70 420 8 a $28 483.60 b $26 465.60 9 a $34 409.30 b $32 366.15 10 $585 11 a $232.50 b $375 c $412.50 d $502.60 e $570 12 $9730 13 a Nil b $2270.69 c $7081 d $15 160 e $24 040 14 a $33 987.20 b $6576.16 c $509.81 d $7085.97 e $136.27 15 $291.66 16 a $40 255 b $9060.33 c $1100.93 17 $99 18 a $1.13 b $36.90 c 12c d $3.75 e $1.25 19 $22 20 $112.50 CHAPTER 3 Spending money Skills check 1 33.75 2 237.6 3 306 4 $360 5 $53.45 Exercise 3A — Discount 1 2 3 One item is discounted by just over 30% but the others range from a 10.00% to a 28.59% discount. 4 5 6 9 10 11 No, as the 12.5% is calculated from different amounts. For example, a $60.00 item reduced by 12.5% ($7.50) is $52.50. A $52.50 item increased by 12.5% ($6.56) is $59.06. Exercise 3B — Proﬁt and loss 1 2 5 Children’s $14.40; Adults’ $20.40; Extra large $22.80 a 25% b 49.3% c 27.7% d 28.8% e 11.5% f 26.5% g 25.2% h 28% i 10% j 20% a i $10.05 ii 25.16% b i $7.05 ii 23.54% c i $17.05 ii 42.68% d i $7.95 ii 19.90% a 25.02% b 11.12% c 10.00% d 28.59% e 22.23% f 20.01% g 30.78% a i $4.98 ii 19.88% b i $10.57 ii 9.46% c i $5.91 ii 7.78% d i $4.65 ii 14.19% e i $16.99 ii 11.77% f i $8.35 ii 10.30% Item Original price ($) % dis- count Discount ($) Sale price ($) a Microwave 300 10% 30 270 b Furniture set 2030 5% 101.50 1928.50 c Mirror 40 30% 12 28 d Necklace 1560 12.5% 195 1365 e Fridge 760 20% 152 608 f Stereo system 480 33 % 160 320 g Washing machine 564 25% 141 423 h Car 7500 50% 3750 3750 a $119 b $101.15 c $17.85 7 A 8 D a $11.94 b $1.79 a $175 b $8.75 a 74.94% b 40.63% c 80.08% d 50% e 55.26% f 197.5% g 45% h 63.64% a 80% b 78% c 85.71% d 92.48% e 85.71% f 70% g 75% h 95.83% 3 $70, 140% 4 $79.75; 53.26% 6 4 years 7 $150 8 $25 each 1 3 --- 1F 3B MQ Maths A Yr 11 - Ans Page 562 Monday, September 24, 2001 7:16 AM
- 4. A n s w e r s 563 answers ➔ 10 Quick Questions 1 1 25% 2 $105 3 12.5% 4 $23.80 5 50% 6 $21.60 7 $40 8 236% 9 $780 10 $180 000 Investigation — Dealing in diaries 1 $2.40 2 $30 3 25% 4 58.3% 5 $50 6 41.7% 7 $130 8 $80 9 61.54% Exercise 3C — Budgeting 1 2 Answers will vary. 3 a b $34.83 4 5 a $320.83 b Income = $809.50 per month; New expenses = $677 per month, so she can afford to move out. 6 Answers will vary. 7 a b $600 c 2.36% Exercise 3D — Cost of services 1 a $348.50 b 1/3/01 c Previous $375.55, down $27.05 d 7/11/00, 7/02/01 e $3.79 f $26.60 g Tariff 11 up, Tariff 33 down 2 a 2253 b 52 964 c $24.13 d $241.31 e 10.7 cents 3 a 1904 b 1352 c $319.35 4 a $100.70 b $9.40 lower c Approx. same d $1.12 e $408.40 f $34.03 5 a 134 b × by MJ factor c $9.16 d 2.397c/MJ e $101.48 6 a 6370 b $106.26 c $10.63 d $116.89 7 $138.66 8 a $166.09 b $181.09 c Pensioner d $367.27 e $664.36 f $55.36 9 a 62 kL b $0.80 c 248 kL 10 $138.60 11 a $10 000 b 15% 12 a Call charges + Service and equipment charges − Flexi-Plan b 28.2% c Flexi-Plan d $144.15 13 a 404 @ 25c b 17.7% c 35.6 d 22.8c e 7 pm Exercise 3E — Credit cards 1 4 a 53 days, 48, 40, 34 and 26 days b Very beginning 5 $17.70 6 a 28 days b $22.10 c No, since it was paid on 29/4, which was less than 25 days from the end of the statement d The balance is over $25, but under $1000, so the minimum amount due is $25. e Credit limit − Closing balance: $1000 − $650 = $350 7 Exercise 3F — The exchange rate 1 a 58.29 b 38.27 c 119 900 d 406 2 a $373.83 b $821.14 c $630.32 d $74.57 3 a 50 504 yen b $784.59 c $15.41 4 a 800 b 320 c $257.82 5 $15.41 10 Quick Questions 2 1 Fixed, variable 2 $8.46 3 $46 800 4 3110 kWh 5 0.0493% 6 4th May 7 The total amount owing is $540.65. 8 Selling 9 7.81 Pounds 10 $150.28 a $1565 b $785 c $1450 d 2.07 months Monthly income ($) Monthly expenses ($) Austudy Birthday money 502.67 20.83 Board and food Transport Books and stationery Insurance Entertainment Enrolment fee Clothes 216.67 63 40 24 55 25 65 Total: 523.50 Total: 488.67 Item Cost ($ per week) Rent 138.46 Food 90 Electricity 32.31 Gas 4.62 Phone 27.69 Car registration 8.27 Car insurance 9.62 Health insurance 13.46 Contents insurance 2.40 Clothes 23.08 Entertainment 18.46 Total: 368.37 Income ($) Expenses ($) Government subsidy Membership fee Proﬁt from auction Proﬁt from stalls Proﬁt from concerts 4 200 16 250 400 920 3 600 Rent Newsletter Sunday School Bills Public liability and insurance Advertising Stationery Computer Unexpected 6 000 960 7 200 2 640 1 860 360 250 3 500 2 000 Total: 25 370 Total: 24 770 a $17.50 b $25 c $25 d $25 e $33 f $57 g $87 h $54 i $58 j $80 2 $4.95 3 $0.75 a $19.89 b $29.08 2E 3F MQ Maths A Yr 11 - Ans Page 563 Thursday, July 5, 2001 8:08 AM
- 5. 564 A n s w e r s answers Chapter review 1 $35 2 16.7% 3 $250 4 5 $256.20 6 $200 7 8 a Rent $100; Electricity $10; Gas $7; Phone $23; Car registration $8; Car insurance $9; Contents insurance $3; Health insurance $9; Food $100; Sport $30; Entertainment $20; Clothes $28; Holidays $23; Total $370 b $5200 9 $45.42 10 $400.97 11 $40 12 13 65.03 pounds CHAPTER 4 Length, area and volume Skills check 1 The shortest measured distance between two points. 2 mm, cm, m, km. 3 The distance around the boundary of an object. 4 a 24 cm b 28 m c 15 m d 18.85 m 5 The amount of space within the boundary of a two- dimensional closed ﬁgure. 6 mm2 , cm2 , m2 , km2 , ha 7 a 36 cm2 b 40 m2 c 10.83 m2 d 28.27 m2 8 a Square b Rectangle c Triangle d Trapezium/trapezoid e Parallelogram f Kite 9 a 2.13 b 1.75 c 79.51 d 3.06 10 ‘Volume’ is the amount of space within, or occupied by, a 3-D object. ‘Capacity’ is the quantity of liquid or gas which a 3-D container could hold. 11 a mm3 , cm3 , m3 b mL, L, kL, ML 12 a 0.6 cm b 250 mm c 0.004 m2 d 450 m e 0.3 L f 0.005 m3 g 0.025 kL h 5000 mm3 l 0.1 L j 25 m3 Exercise 4A — Changing units and calculating perimeters 1 a 7 cm b 6 m c 5 km d 90 mm e 1200 cm f 9000 m g 8.6 cm h 9200 m i 2.4 km j 64 mm k 1125 cm l 22 mm 2 5200 mm long 2400 mm wide 2500 mm high 3 a 28 m b 34 m c 84 cm d 42 mm e 24 m f 510 m 4 a 108 m b 12.1 m c 71.7 m d 334.3 mm e 79 cm f 139 m 5 E 6 C Exercise 4B — Calculating areas 1 a 0.7 cm2 b 0.6 m2 c 30 000 cm2 d 2 500 000 m2 e 45 000 m2 f 300 ha 2 a 64 cm2 b 841 mm2 c 12.96 km2 d 27 m2 e 1026 mm2 f 2914 cm2 g 20.37 m2 h 26.46 km2 i 6.845 m2 j 216.32 km2 k 3306 mm2 l 6.4 m2 m 60 m2 n 5.84 m2 o 26.82 cm2 p 161.2 cm2 q 26.9 mm2 r 438.7 m2 s 14.14 cm2 t 4.19 m2 u 65.45 mm2 3 a 140 m2 b 36 m2 c 104 m2 4 a 144 m2 b 68.5 cm2 c 10 m2 d 80 m2 5 B 6 A 7 B 8 a 34.56 m2 b $960.77 9 a b 180 m2 c 18 m long and 15 m wide d 90 m2 10 a C b E 11 107 cm2 12 30.6 cm2 13 a 2474 cm2 b 34.4% 10 Quick Questions 1 1 452.4 cm2 2 31.2 m2 3 184.3 cm2 4 13 939.2 mm2 5 306 cm2 6 625 cm2 7 1428.3 m2 8 1147.6 cm2 9 17 121.8 mm2 10 670.9 cm2 Investigation — Effect of scale factors on perimeter and area 1 Pentagon 2 All angles 108°. Figure is regular pentagon. 3 Larger knot has twice the side length of smaller knot 4 S = 2 5 Larger knot has twice perimeter of smaller knot 6 Area of larger knot is four times area of smaller knot 7 Perimeter is 3 times as long; area 9 times as large 8 Perimeter is ‘S’ times as long; area is ‘S2 ’ times as large 9 a Parallelogram b 4 trapeziums c Perimeter of larger knot twice as long and area 4 times as large as smaller knot. Supports conclusion in 8. Exercise 4C — Total surface area 1 a iii Triangular prism b iii Square-based pyramid c iii Triangle-based pyramid Item Cost price ($) Per- centage discount Discount ($) Selling price ($) a 200 12% 24 176 b 150 5% 7.50 142.50 c 98 10% 9.80 88.20 d 130 12.5% 16.25 113.75 e 416 20% 83.20 332.80 f 228 33 % 76 152 a 80% proﬁt b 124.14% proﬁt c 37.5% loss d 44.44% loss a $35 b $39.89 1 3 --- 1.5 m 15 m 12 m 3C 4C MQ Maths A Yr 11 - Ans Page 564 Thursday, July 5, 2001 8:08 AM
- 6. A n s w e r s 565 answers ➔ 2 a b c 3 a Square pyramid b Triangular prism c Cone 4 a 150 cm2 b 486 cm2 c 6144 cm2 d 95.98 cm2 e 1444 cm2 f 1274 mm2 5 11.92 m2 6 28 125 cm2 7 a 17.5 m2 b 70 c 42.5 m2 d 17.5 m2 e 5 L 8 a 4.9 m2 b 9148.3 mm2 c 2945 cm2 9 360 cm2 10 28 cm2 11 B 12 36 cm2 13 a 15.5 cm2 b 3267.3 cm2 c 879.6 cm2 14 a 58.1 cm2 b 39.3 m2 c 374 mm2 15 2 cm 16 No. If the side length was doubled, the area would be four times as large. 17 95.6 m2 18 50 m2 19 99 m2 20 C 21 B 22 E 23 A 24 a Cylindrical loaf b 108.7 cm2 10 Quick Questions 2 1 0.44 m2 2 29.52 m2 3 4224 m2 4 Triangular prism 5 Square pyramid 6 Triangular pyramid 7 486 cm2 8 236 cm2 9 568 cm2 10 160 cm2 Exercise 4D — Volume and capacity 1 a 350 mm3 b 0.0048 m3 c 56 litres d 1500 cm3 e 1600 litres f 2.3 mm3 g 570 cm3 h 0.14 litres i 250 cm3 2 a 750 mL b 0.8 L c 2500 mL d 40 L e 6 000 000 cm3 → 6 000 000 mL → 6000 L f 12 000 L g 4.2 kL h 7.5 kL → 7500 L i 5.2 cm3 j 6000 cm3 k 20 000 mL = 20 000 cm3 l 5.3 m3 3 a 125 cm3 , 125 mL b 13.824 m3 , 13.8 kL c 2197 m3 , 2197 kL d 56.448 m3 , 56.4 kL e 4050 mm3 , 4.1 mL f 4228.125 m3 , 4228.1 kL g 1357.2 cm3 , 1357.2 mL or 1.4 L h 339.3 m3 , 339.3 kL i 29 772.9 cm3 , 29.8 L 4 a i 12 cm2 ii 60 cm3 b i 24 cm2 ii 288 cm3 c i 4.59 m2 ii 6.885 m3 d i 12.48 m2 ii 156 m3 5 B 6 D 7 D 8 a 504 000 cm3 b 504 L 9 101.25 kL 10 a 150.796 m3 b 150 800 L 11 a 175 m2 b 17.5 m3 c $2546.25 12 a 2.8 m3 b 2800 L c 24 429 L d 27.5 cm 13 a 96 cm3 b 560 cm3 c 120 m3 d 100 cm3 14 a 262 cm3 b 1810 cm3 c 2212 mm3 d 77 585 cm3 15 254.5 cm3 16 a 904.8 cm3 b 2144.7 cm3 c 8181.2 m3 d 137.3 m3 17 6.37 cm3 18 A 19 C 20 D 21 a i 200 cm2 ii 2000 cm3 b i 99 m2 ii 792 m3 c i 204 cm2 ii 1224 cm3 d i 153 m2 ii 1836 m3 22 335.1 cm3 23 a 7 cm b 2144.7 cm3 c 1436.8 cm3 d 707.9 cm3 24 a 565.5 cm3 b 84.8 cm3 c 480.7 cm3 25 14.3 cm3 26 a 52.4 cm3 b 65.4 cm3 c 85.1 cm3 Chapter review 1 a 19 cm b 1.9 cm2 c 0.19 cm3 d 0.5 L e 0.0005 kL f 50 000 L g 200 000 cm3 h 2000 cm2 i 20 cm j 120 mL k 0.12 L l 300 000 cm3 2 3 4 5 a b c a i 97.98 mm2 ii 48 mm b i 8.55 cm2 ii 16.44 cm c i 168 cm2 ii 54 cm d i 32 cm2 ii 49.3 cm e i 8.8 m2 ii 13.4 m a i 540 cm2 ii 106 cm b i 60.7 m2 ii 45.7 m c i 29.7 cm2 ii 21.4 cm a C b E 4A 4D MQ Maths A Yr 11 - Ans Page 565 Thursday, July 5, 2001 8:08 AM
- 7. 566 A n s w e r s answers 6 Triangular prism 7 a 105.84 cm2 b 25.98 m2 c 19.44 m2 d 18.18 m2 8 a 54 m2 b 352 cm2 c 340 m2 9 a 301.6 cm2 b 23.1 m2 c 2670.4 cm2 10 a 247 m2 b 2463 mm2 c 879.6 cm2 11 a 452 cm2 b 763 mm2 c 157 cm2 12 a 75 m2 b 1650 m3 c 1 650 000 L d 1316.2 m2 13 37.5 m2 14 a 274.625 cm3 , 274.6 mL b 24 389 mm3 , 24.4 mL c 202.768 m3 , 202.8 kL d 984 cm3 , 984 mL e 368 cm3 , 368 mL f 57 906 mm3 , 57.9 mL 15 585 cm3 16 a 48 cm3 , 48 mL b 798 mm3 , 0.8 mL c 5.29 m3 , 5.29 kL 17 a 10 800 m3 b 10.95 m3 c 19 658 mm3 d 2339 mm3 e 50 965 mm3 f 179 594 cm3 18 a 6.1 m3 , 6.1 kL b 123 717.1 cm3 , 123.7 L c 2356.2 cm3 , 2.4 L 19 a 179.6 cm3 b 808.2 cm3 c 269.4 cm3 20 58.1 cm2 21 226.19 cm2 22 129.2 cm2 23 452 cm2 24 77.47 cm2 25 5.37 cm2 26 2073 cm2 27 21.237 cm2 28 2100.6895 cm3 29 536 cm3 CHAPTER 5 Right-angled triangles and trigonometry History of mathematics 1 Samos Island 2 Egypt and Babylonia 3 c2 = a2 + b2 or hypotenuse2 = base2 + height2 4 Patterns in music 5 Plimpton 322 6 A set of numbers that obeys Pythagoras’ theorem Skills check 1 a AB b DF c GI d No hypotenuse (as the triangle is not right- angled) 2 In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides hypotenuse2 = base2 + height2 3 a a = 10 m b b = 4.47 m c c = 14.14 cm 4 a 15 b 2 c 0.75 d 12.5 5 6 a a = 56° b b = 63° 7 a 35°30′ b 27°13′48″ c 68°7′30″ 8 a 45.45° b 84.59° c 64.01° 9 In a right-angled triangle a sine = b cosine = c tangent = 10 a b c 11 a 0.7071 b 0.8660 c 0.4142 d 0.9222 e 0.7871 12 a b c 13 a x = 2.08 b x = 1.56 Exercise 5A — Pythagoras’ theorem 1 a PR b YZ c AB 2 a 13 cm b 170 mm c 61 m 3 a 10.82 cm b 6.93 m c 14.20 km 4 a 10.4 cm b 1.9 m c 3.9 m 5 a 8.9 cm b 22.1 cm c 47.4 mm d 37.3 m 6 a Right b Right c Obtuse Angle of elevation Shadow opposite side length length of hypotenuse -------------------------------------------------- adjacent side length length of hypotenuse -------------------------------------------------- opposite side length adjacent side length ------------------------------------------------ Opposite Adjacent Hypotenuse Opposite Adjacent Hypotenuse Opposite Hypotenuse Adjacent Angle of elevation Angle of depression Angle of elevation 4D 5A MQ Maths A Yr 11 - Ans Page 566 Thursday, July 5, 2001 8:08 AM
- 8. A n s w e r s 567 answers ➔ 7 B 8 C 9 a Yes b No c Yes d No e Yes f Yes g No h No i Yes j Yes k Yes l No 10 a 9, 12, 15 b 7, 24, 25 c 1.5, 2.0, 2.5 d 3, 4, 5 e 11, 60, 61 f 10, 24, 26 g 9, 40, 41 h 0.7, 2.4, 2.5 11 a 15 c 50 e 1.0 f 25 i 61 j 26 k 20 12 E 13 B 14 13 m 15 3.23 m 16 3.73 m 17 2.2 m 18 7.5 m 19 7.07 cm Exercise 5B — Shadow sticks 1 a 5.7 m b 15.6 m c 5.3 m d 7.8 m 2 5.4 m 3 6.4 m 4 8.1 m 5 16 m 6 B 7 D Exercise 5C — Calculating trigonometric ratios 1 a 1.540 b 17.663 c 40.460 d 0.657 2 a 0.602 b 2.092 c 15.246 d 51.893 3 a 0.707 b 0.247 c 6.568 d 5.896 4 a 0.500 b 0.966 c 1 d 548.643 e 64 f 1.301 g 5.306 h 1.374 i 15.772 5 a 0.42 b 1.56 c 0.09 d 5.10 e 2.87 f 0.38 g 7.77 h 73.30 i 0.87 6 10° 7 a 44° b 80° c 57° 8 86°40′ 9 a 42°57′ b 31°21′ c 16°5′ Exercise 5D — Finding an unknown side 1 a b c 2 148.1 mm 3 5.08 m 4 30 cm 5 a 12.1 cm b 55.2 m c 9.4 km 6 a 12.5 m b 89.3 mm c 10.1 m 7 a 5.4 m b 1.4 km c 2.1 km d 18.4 mm e 3.2 cm f 66.5 m g 5.4 m h 5.4 km i 0.2 m j 41.6 km k 84.4 m l 13.2 cm 8 D 9 A 10 A 11 C 12 6 m 13 4.2 m 14 20 km 15 a b 6 m 16 a b 1.6 m 17 9.65 m 18 a b 58 m c 15.5 m 10 Quick Questions 1 1 17 cm 2 22.4 m 3 26.5 km 4 21.5 m 5 32.9 cm 6 25.3 m 7 12.5 mm 8 177.8 mm 9 97.5 m 10 17 m Exercise 5E — Finding angles 1 a 30° b 75° c 81° 2 a 32°48′ b 45°3′ c 35°16′ 3 a 53°8′ b 55°35′ c 45°27′ 4 a 50° b 32° c 33° d 21° e 81° f 34° 5 a 39°48′ b 80°59′ c 13°30′ d 79°6′ e 63°1′ f 19°28′ 6 A 7 B 8 C 9 37° 10 75°31′ 11 8°38′ 12 13° 13 4°35′ 10 Quick Questions 2 1 13 cm 2 17.0 cm 3 22.4 cm 4 6.409 m 5 0.8290 6 10.96 7 133.55 8 30° 9 73° 10 63°26′ Exercise 5F — Angles of elevation and depression 1 26.8 m 2 3984 m 3 190 m 4 39.2 m 5 42.1 m 6 100 m 7 15 km 8 Yes, the ladder needs to be only 28 m long. 9 a 914 m b 868 m 10 39° 11 21° 12 a b 85 m c 40° Chapter review 1 a 13.01 m b 18.65 cm c 3.58 m d 15.65 cm e 2.30 km f 2.47 m hyp opp adj θ hyp opp adj α hyp oppadj γ 24° 13.5 m 60° 1.4 m 15° 60 m 12° 400 m 5A 5F MQ Maths A Yr 11 - Ans Page 567 Thursday, July 5, 2001 8:08 AM
- 9. 568 A n s w e r s answers 2 98 km 3 66 m 4 a Right-angled b Right-angled c Obtuse d Acute 5 b and c 6 11.25 metres 7 a 0.7193 b 4.2303 c 2.7400 d 8.1955 e 21.9845 f 14.2998 8 a 54° b 51° c 53° 9 a 78°31′ b 26°34′ c 14°54′ 10 a 37.9 cm b 3.8 m c 13.6 cm d 11.7 cm e 14.7 cm f 14.6 m g 1.5 m h 4.9 cm i 15.6 mm j 7.5 m k 10.7 m l 5.3 km 11 8.5 m 12 2.5 km 13 63.9 m 14 a 57° b 27° c 68° 15 a 23°4′ b 61°37′ c 59°35′ 16 39° 17 24° 18 23 m 19 57° CHAPTER 6 Earth geometry Skills check 1 Latitude — imaginary lines which circle the Earth in an east–west direction parallel to the equator. Longitude — imaginary lines circling the Earth joining the North and South Poles and running perpendicular to the equator. 2 3 4 5 The shortest distance between two points on a sphere is represented by the length of an arc of a circle. 6 40 030 km 7 a Greenwich Mean Time (GMT) — the standard time in Greenwich (England) which is used as the basis for calculating the time in all other parts of the world. b The meridian of longitude 180° from the Greenwich Meridian. When we cross the International Date Line, the date will be different. c Eastern Standard Time — the time adopted by the eastern States of Australia (Qld, NSW, Vic and Tas) and the ACT. 8 Three — EST (Eastern Standard Time), CST (Central Standard Time), WST (Western Standard Time). 9 Clocks are put forward 1 hour during summer. 10 EST is 10 hours ahead of GMT. Exercise 6A — Latitude and longitude 1 a Cairo b Shanghai c Darwin d Montreal e London f Auckland g Tokyo h Beijing i Rio de Janeiro j Oslo 2 a (38°S, 145°E) b (40°N, 75°W) c (18°N, 76°W) d (26°S, 28°E) e (42°N, 12°E) f (35°S, 57°W) g (33°N, 44°E) h (55°N, 40°E) i (2°N, 104°E) j (18°S, 178°E) Exercise 6B — Distances on the Earth’s surface 1 50° 2 a 40° b 40° c 71° d 21° e 80° 3 60° 4 3336 km 5 a 3892 km b 15 012 km c 4337 km d 10 675 km 6 6672 km 7 5226 km 8 6600 km 9 a 4337 km b 4003 km c 3781 km 10 D 11 A 12 a 110° b 12 200 km 13 20 016 km 14 a 28° b 3114 km 15 3892 km 16 17 792 km 17 a 6894 km to South Pole b 4559 km to North Pole c 4893 km to North Pole d 8896 km to South Pole 18 a 2470 km b 3233 km c 2859 km d 425 km e 16 301 km f 6452 km Exercise 6C — Time zones 1 10 h 2 a 14 h b 7 h c 11 h d 22 h 3 11:00 pm Monday 1– 2 North Pole (90° N) South Pole (90° S) Tropic of Cancer (23 ° N) 1– 2Tropic of Capricorn (23 ° S) Equator (0°) S N 50° W 0° 20° E Equator Tropic of Capricorn N S 5B 6C MQ Maths A Yr 11 - Ans Page 568 Thursday, July 5, 2001 8:08 AM
- 10. A n s w e r s 569 answers ➔ 4 a 8:00 pm b 1:00 pm Friday c 5:00 pm Wednesday d 11:00 pm Tuesday e 3:45 pm Monday 5 5:00 am Saturday 6 11:00 pm Tuesday 7 10:00 am Monday 8 a 10:00 pm b GMT+11 c i 3:00 pm Monday ii 8:00 am Friday 9 a 18 h b 19 h c 17 h 10 7 h 11 a 10 h 20 min b 24 min c 2 h 48 min 12 C 13 D 14 2:00 pm Tuesday LAX local time 15 a 4:00 pm Wednesday b 8:00 am Sunday 16 a 1:00 am Wednesday b 3:00 am Wednesday Chapter review 1 a 207.3 cm b 44.0 cm c 57.8 m 2 56.5 km 3 71 cm 4 a Manila b Lima c Santiago 5 a (41°N, 3°W) b (1°N, 104°E) c (43°S, 147°E) 6 58° 7 a 16° b 1779 km 8 5671 km 9 a 14 481 km b 18 425 km 10 a 8 h b 11 h c 17 h 11 3:00 am Thursday 12 3:30 am Tuesday 13 a 11:00 am the same day b 11:00 am the same day 14 7:00 pm the same day CHAPTER 7 Basics of construction Skills check 1 a 1 : 0.75 b 1 : 4 c 1 : 25 d 1 : 40 2 a Enlargement b Reduction c Reduction d Reduction 3 a 1 m b 2.5 cm 4 a P = 40 m, A = 80 m2 b P = 56 m, A = 128 m2 5 a 0.6 m3 b 1 m3 6 a 3394 mm b 1.8 m 7 a 34.4° b 43.3° 8 a 3.46 m b 11.22 m 9 a 7.18 m b 2784 mm 10 a 76 m2 b 18.97 m2 Exercise 7A — Scale drawings 1 a 8.215 m b 3.5 m c 89 000 m d 0.026 m e 0.04 m f 6400 m 2 a 45 mm b 67 mm c 58 mm 3 a Reduction b Reduction c Enlargement d Reduction e Enlargement f Reduction 4 a 1 : 5000 b 1 : 200 000 c 10 : 1 5 a 1.8 m b 6.75 m c 22.5 m d 3.375 m 6 a 2.4 cm long × 1.4 cm wide b 3 cm × 1.8 cm c 4.4 cm × 2 cm 7 1 : 550 8 a 4.75 m b $3034 c 18.75 m 9 a Approx. 70 m b Approx. 1000 m c Approx. 2 km2 Exercise 7B — Building plans 1 a 630 m2 b 30 m, 21 m c Approx. 1 : 1750 e 632 m2 f i 1063 m2 , $58/m2 ii 850 m2 is larger g i Lot 110 ii Does it front a main road? Is it low lying? Slope of land, views, aspect. 2 a 2100 m2 , 83 perches b 104 m2 c Approx. 1 : 1000 d i Rising ii 1.4° 3 a 77.8 m2 b Approx. $265 c in order, 10.85 m2 , 11.25 m2 , 6.84 m2 , 5.04 m2 Exercise 7C — Floor plans and elevations 1 a No doors and 1 window b 9 (D4–D12) c Kitchen and dining room d 2400 mm (2.4 m) e At 4 corners of house, downpipes f 1490 mm (1.49 m) g 290 mm, 90 mm h Shower, bath, vanity unit, toilet i Refrigerator, pantry, oven, broom cupboard, hot plates, sink, benches j i No doors and 1 window, window is 310 mm wide ii 8990 mm, 7790 mm k 10 Quick questions 1 1 1 : 250 2 NE 3 20 m × 25 m 4 10 m × 15 m 5 4.4 m 6 1 :125 7 5.6 m × 3.75 m 8 Bed 1 9 3.75 m square 10 2.5 m Exercise 7D — Pegging out the perimeter 1 a 1697 mm b 45° 2 Acute angle 3 12 m square 4 No — it could be a parallelogram. 5 The shed could be rectangular or square. 6 17.7 m 7 The wall at X is 2 cm below horizontal level of wall at Y. Exercise 7E — Footings and slabs 1 a 8.855 m3 b 5.016 m3 c 20.832 m3 2 7.43 m3 3 a 10 lengths b 5.28 m3 2090 2400 4000 7990 8990 310 w 5 2 cm Wall Wall WaterX Y 6A 7E MQ Maths A Yr 11 - Ans Page 569 Thursday, July 5, 2001 8:08 AM
- 11. 570 A n s w e r s answers 4 8.6 m3 5 a i 12.579 m3 ii 24 lengths iii 12.75 m3 b i 14.679 m3 ii 28 lengths iii 16 m3 Exercise 7F — Bracing 1 a 6.46 m b Angle is 21.8° c 4 m 2 Yes, brace is at 45° to base. 3 a 1697 mm b 45° c Yes 4 3839 mm, 38.7° 5 a 40.6° and 43.8° b 3688 and 3467 mm = 7155 mm 6 a 34.18 m b 13.8 m Exercise 7G — The roof 1 2 3 a 13.4° b 16.9° c 36.9° d 36.9° 4 a 1 : 3, 18.4° b 1 : 1.67, 31° 5 a 43.8° b 33.6° Exercise 7H — Cladding the roof 1 2 a EF = 18 m, FH = 6 m b ∠CAB = 20° c AB = 3 m d AC = 3.2 m BC = 1.1 m e CD = 12 m f 48 m2 g 9.6 m2 h 115.2 m2 i $5184 (≈$5200) 3 a QR = 18 m, PQ = 6 m, ∠TQV = 20° b VQ = 3 m c TV = 1.1 m TQ = 3.2 m d 57.6 m2 , 115.2 m2 e $5184 4 5 6 a i There is no ridge — all faces meet at a point. ii 148.8 m2 b 148.8 m2 7 $3577.50 8 a and b c Exercise 7I — Brickwork 1 a 1680 b 3000 c 3000 d 1920 2 a 210 b 1955 3 a 50 b 25 c 19 4 a 43 cm b 1.892 m c 4.73 m 5 a 25 b 10 c 120 6 a 15 b 35 c 525 d 542 This is an estimate and allows for breakages. 7 4056 Chapter review 1 a 1 : 140 b 4 c 3.8 m × 3.6 m with ensuite containing shower, handbasin and toilet, walk-in wardrobe with hanging space and shelves d 5.8 m × 6.09 m e Living–dining room and hallway near bathroom f 231.45 m2 g Vanity basin, broom cupboard, washing machine, water closet, walk-in wardrobe, wall oven, range hood, hot plates, drain pipe Pitch ratio Pitch angle 1 : 22.9 2.5° 1 : 57.3 1° 1 : 7.6 7.5° 1 : 5.7 10° 1 : 1 45° 1 : 2.7 20° 1 : 1.43 35° 1 : 1.08 42.8° Roof pitch Building width King post height Rafter length 10° 8 m 705 mm 4062 mm 12° 10 m 1063 mm 5112 mm 18.4° 12 m 2 m 6325 mm 25° 27.19 m 6339 mm 15 m 10.8° 31.4 m 3 m 16 m 34.6° 14 m 4822 mm 8.5 m Hip roof Triangles Trapeziums Gable roof Rectangles 12 m 4 m 5.8 m 8 m 18° 8 m 4.2 m 18° 12 m 12 m 12 m 15° 15° 12 m 12 m 10 m 10 m 2.7 m 2.7 m 2.7 m 5 m 20° 20° 10 m 20° 20° 10 m 2.7 m 2.7m 2.7 m 2.7 m 2.7 m 5 m 5 m 2.7 m 7A 7I MQ Maths A Yr 11 - Ans Page 570 Thursday, July 5, 2001 8:08 AM
- 12. A n s w e r s 571 answers ➔ 4 a East b Rectangular c 21.3 m × 28.175 m d Sweetapple Crescent e 1.5 m f 4.5 m g 38.6% 5 a Garage b North c North-west d 1 e Panel lift f 4 g Concrete tiles h 21° i Gable j Brick k 1000 mm l 600 mm m 2400 mm n Standard Type A o 2.67 m × 3.6 m p 70 mm q 220 mm 6 a 200 mm b 100 mm c 900 mm d The ﬂoor of the garage falls 50 mm from back to front. e Internal footings f No, garage is 1 step down from house. g 40 mm h i Down western side of allotment, 600 mm 8 a 6.4 cm × 4 cm b 12.8 cm × 8 cm 9 4.48 m 10 $46.57 11 1.67 m3 12 6 13 $470 14 3988 mm 15 3042 mm 16 1 : 2.6 17 a No b 10.9° 18 1441 mm 19 $2880 20 $907.20 21 1000 22 11 23 28 24 a 308 b 312 Both methods give approximately the same number. CHAPTER 8 Construction: The ﬁnishing touches Skills check 1 a b c 2 a 37.5 m2 b 29.64 m2 3 a b 96 m2 c d 100 m2 e 4 m f 53° g h 4 a 11.847 m2 b 5.79 m2 5 a 471.24 m3 b 21.6 cm Exercise 8A — Painting and wallpapering 1 b 150 m2 c 25 L d 7 e $252 2 $243 3 1.3 L 4 3 tins 5 81.6 L 6 a 3.6 L white undercoat; 4.8 L blue enamel b 3.3 L white undercoat; 5 L acrylic c $198.40 7 a b 14 m c 28 d 2.4 m e 67.2 m f 7 8 9 9 Wallpaper $405 Paint $192 10 Wallpaper $4.50/m2 Painting $1.44/m2 So it is cheaper to paint. Exercise 8B — Tiling, carpeting and kitchen planning 1 $7380 2 a $234.78 b $123.12 3 a 24 m b 24 m 4 a b 116 tiles c 22.8 m d 21.6 m 5 $127.80/m 6 a i 1226 mm ii 820 high, 700 wide, 495 deep iii 720 high, 595 either side of corner b i 2135 high, 800 wide, 590 deep ii 875 mm iii Cabinet O — Deep corner ﬂoor cabinet 900 iii and narrow corner ﬂoor cabinet 750 iv 400 wide or 800 wide, 2135 high c 0.354 m2 d 590 mm e 315 mm 7 Check with your teacher 8 a 1.296 m2 b 1.0206 m2 c 0.567 m2 d 1.6686 m2 e 4.5522 m2 f 910 mL 3 m 6 m10 m 6 m10 m 10 m 5 m5 m 6 m 10 m 6 m 3 m 5 m 10 m 15 m 3.5 m 2.4 m 2.4 m 12 m 11.4 m 5.4 m 6 m Tiles (30cm × 30cm) Carpet 7F 8B MQ Maths A Yr 11 - Ans Page 571 Thursday, July 5, 2001 8:08 AM
- 13. 572 A n s w e r s answers 10 Quick questions 1 1 30 m × 34 m 2 128 m 3 $416 4 10.8 m × 14 m 5 151.2 m2 6 SW 7 42 m 8 43.2 m 9 85.68 kL 10 75 m2 Exercise 8C — Landscaping 1 a 2.4 m b 3 c 200 mm d 5 e 15 f $44.40 g $666 2 a 1.8 m b 4 c 100 mm d 10 e 40 f $9.45 g $378 3 a 1.8 m b 4 c 150 mm d 7 e 28 f $18.27 g $511.56 5 a i 75 mm wide and 38 mm thick 75 mm wide and 50 mm thick ii 75 × 50 mm iii 6 cm iv 10 m b i 100 × 38 mm and 100 × 50 mm ii 75 × 38 mm and 75 × 50 mm iii 2850 mm2 and 5000 mm2 iv 100 × 38 mm 6 a 20 PRP b or or other combinations c or or other combinations d 78.5% 7 a 0.288 m3 b 0.375 m3 c $86.19 d 16 m2 e 1.125 m2 f 3.99 m2 g 21.115 m2 h $253.38 i $339.57 Chapter review 1 a $32.60 b 1 : 25 c $42 d $210 2 a 32 m2 b $1216 c i $456 ii $850 laid horizontally $680 laid vertically 3 a Sink, oven and refrigerator arranged in triangle b 2 × 800 and 2 × 900 c 0.2 m3 d Approx. 356 mm 4 a 60 b $2664 c 57.6 m3 d $1728 5 a 600 b $990 c 450 m2 d No, 574 e 568 f The closer the rectangle approaches a square shape, the smaller the perimeter, and fewer palings would be required. 6 a Sand, clay b Compete with plants for water and nutrients c Makes them too thirsty d Thick grass requires too much water and water has difﬁculty reaching the roots. e Couch/kikuyu/buffalo — the broad leaf helps it absorb water. f Clay soil does not absorb as well, so requires a longer watering time. Once the clay is wet, it retains the water for a longer period of time than sandy soil does. g They sprinkle a further distance. h Water runs off surface. 7 a 0.1 m3 b $13 c 5.65 m2 d $84.75 e $97.75 f 1.13 m3 g 1.96 m CHAPTER 9 Collecting and entering data Skills check 1 Qualitative — some quality or feature (not involving numbers or measurements). Quantitative — involving some quantity or number which can be measured. 2 a −2, −1, 0, 1, 3, 6.5, 8, 12, 25 b −2, 25, 3 3 a b c 4 a 0.196 c/g b $0.88/L c 0.76 c/g 5 1 L for $2.50 Exercise 9A — Types of data 1 a Numerical b Categorical c Numerical d Categorical e Numerical f Numerical 2 a Continuous b Discrete c Continuous d Continuous e Discrete 4 6 4 6+ + + 4 4 4 4 4+ + + + 4 4 4 4 4+ + + + 4 4 3 3+ + + 3 3+ + 6 m 6 m Year Students 8 117 9 102 10 92 11 77 12 62 Year 9 Year 8 Year 12Year 10 Year 11 No.ofstudents Year level 8 9 10 11 12 0 10 20 30 40 50 60 70 80 90 100 110 120 8A 9A MQ Maths A Yr 11 - Ans Page 572 Thursday, July 5, 2001 8:08 AM
- 14. A n s w e r s 573 answers ➔ 3 a Numerical and discrete b Categorical c Categorical d Numerical and continuous e Numerical and continuous f Numerical and discrete 4 Categorical, ordinal 5 Categorical, ordinal 6 Numerical and discrete 7 B 8 Categorical 9 Numerical and continuous Exercise 9B — Collecting data 1 Open questions — no boundaries for response. Closed questions — answer within category. 2 A variety of categorical responses suitable; check with your teacher. 3 A variety of categorical responses is suitable; check with your teacher. 4 a Vague — weekly? yearly? all jobs? b Vague — deﬁne ‘exercise’, ‘regularly’. c What do abbreviations stand for? d Emotional language. e Capable of being answered? What is the PM’s policy? g Double-barrelled question. h Leading question suggesting a particular response. i Emotive language. 5 Check with your teacher. Exercise 9C — Organising and displaying data using column and sector graphs 1 2 3 4 Check with your teacher. 5 6 7 8 9 Check with your teacher. 10 10 Quick Questions 1 1 Qualitative 2 Quantitative and discrete 3 Quantitative and discrete 4 Quantitative and continuous 5 40 6 Married 7 15 8 11 9 28 10 Make Tally Frequency Holden |||| ||| 8 Ford |||| ||| 8 Nissan || 2 Mazda ||| 3 Toyota |||| || 7 Mitsubishi || 2 Mark Tally Frequency 4 || 2 5 |||| 4 6 |||| | 6 7 |||| |||| 9 8 |||| 5 9 ||| 3 10 | 1 Mark Tally Frequency 40–49 | 1 50–59 || 2 60–69 |||| |||| 9 70–79 |||| ||| 8 80–89 ||| 3 90–99 || 2 H olden Ford N issan M azda Toyota M itsubishi Frequency Make of car 0 1 2 3 4 5 6 7 8 9 Holden Ford Nissan Mazda Toyota Mitsubishi Make of car 0 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 Numberofstudents Spelling test results 10 0 40–4950–5960–6970–7980–8990–99 1 2 3 4 5 6 7 8 9 Numberofstudents Maths exam mark 40–49 50–59 60–69 70–79 80–89 90–99 Marks on maths examNumber of students Married Widowed Separated Divorced Never married 8C 9C MQ Maths A Yr 11 - Ans Page 573 Thursday, July 5, 2001 8:08 AM
- 15. 574 A n s w e r s answers Exercise 9D — Graphical methods of misrepresenting data 1 Check with your teacher. 2 Horizontal axis uses same division for 5 and 7 year periods 3 a Check with your teacher b No 4 a 20.5 b 18.2, country schools have smaller class sizes 5 Check with your teacher 6 Check with your teacher 7 a 0.2 b 71.5° c 80° d The perspective appears to magnify some sections of the pie chart and diminish others. 8 a It is a circle viewed on an angle to produce an ellipse. b No, because it causes some angles to be larger and others to be smaller. Exercise 9E — Histograms and freauency polygons 1 2 3 4 a b 5 6 a b Exercise 9F — Stem-and-leaf plots 1 2 3 4 No. of matches in a box Frequency 47 3 48 5 49 10 50 15 51 7 52 5 53 4 54 1 0 0 2 4 6 1 2 3 4 5 Number of mistakes (score) Numberofdrivers (frequency) 8 10 12 14 1 0 1 2 3 2 3 4 5 6 No. of children in family Frequency 4 5 6 7 8 9 18 0 2 4 6 19 20 21 22 23 Age No.ofmembers 8 10 12 24 25 14 16 53 5447 0 2 4 6 48 49 50 51 52 No. of matches in a box Frequency 8 10 12 14 16 Time taken (seconds) Class centre Frequency 6 to <8 7 1 8 to <10 9 4 10 to <12 11 15 12 to <14 13 18 14 to <16 15 12 16 to <18 17 8 18 to <20 19 2 304.5 314.5 324.5 334.5 344.5 354.5 0 5 10 15 Length of fish (mm) Frequency 20 197 0 2 4 6 9 11 13 15 17 Time taken (s) Frequency 8 10 12 14 16 18 Key 0 | 6 = 6 errors Stem 0 1 2 3 4 Leaf 6 3 5 7 8 0 0 5 6 6 7 8 9 1 2 2 8 3 6 Key 3 | 6 = 36 min Stem 3 4 5 6 7 8 Leaf 6 7 8 8 9 9 0 0 1 2 2 2 2 2 3 5 6 7 7 8 8 8 0 2 2 2 3 4 5 7 8 9 6 8 8 1 2 5 2 Key 10 | 1 = 101 wpm 10* | 6 = 106 wpm Stem 8* 9* 9* 10* 10* 11* 11* 12* 12* 13* Leaf 6 8 2 5 5 5 6 6 6 8 9 2 2 2 3 7 7 7 8 8 0 1 2 5 0 1 1 4 0 Key 14 | 3 = 14.3 V 14* | 8 = 14.8 V Stem 13* 14* 14* 15* 15* Leaf 8 9 0 2 3 3 5 6 6 7 7 8 8 1 2 2 5 6 7 9 9B 9F MQ Maths A Yr 11 - Ans Page 574 Thursday, July 5, 2001 8:08 AM
- 16. A n s w e r s 575 answers ➔ 5 1.95 g 6 a 8.4 s b Lower quartile = 7.8 s, upper quartile = 8.85 s c 1.05 7 D 8 A 9 D 10 B 11 a b 22.9 cm c Lower quartile = 21.75 cm, upper quartile = 24.1 cm d 2.35 cm 12 a b 99.5 cm c Lower quartile = 92 cm, Upper quartile = 110 cm d 18 cm Exercise 9G — Five-number summaries and boxplots 1 8, 15, 16.5, 18, 25 2 a 23, 44, 81.5, 83.5, 92 b 1, 2, 4, 6, 7 c 8, 29, 45, 72, 93 3 a 13 b 5 c 26 4 a 122 b 6 c 27 5 6 a 147 b 56 c 90 d 91 e 28 7 a 58 b 31 c 43 d 27 e 8 8 B 9 C 10 D 11 a 22, 28, 35, 43, 48 b 12 a 10 mm, 13.5 mm, 22 mm, 33.5 mm, 45 mm b Chapter review 1 a Categorical b Numerical c Numerical d Numerical e Categorical 2 a Discrete b Continuous c Continuous d Discrete e Continuous 3 a Double-barrelled question b Double negative c Emotional language d Abbreviations e Leading question 4 5 6 7 Key 20 | 6 = 20.6 cm Stem 20 21 22 23 24 25 Leaf 2 7 4 6 7 8 2 8 8 8 0 1 2 6 6 6 6 7 8 1 Key 8 | 2 = 82 Stem 8 9 10 11 12 13 Leaf 2 4 5 5 8 0 1 2 3 4 6 6 7 8 9 1 1 3 3 7 8 0 0 1 4 5 7 6 6 2 35 40 45 50 55 60 20 25 30 35 Scales 40 45 50 10 15 20 25 Rainfall (mm) 30 35 40 45 Score Tally Frequency 1 ||| 3 2 |||| | 6 3 |||| | 6 4 |||| | 6 5 ||| 3 6 ||| 3 Number of CDs Tally Number of students 0–4 ||| 3 5–9 |||| |||| 9 10–14 |||| |||| 9 15–19 ||| 3 20–24 |||| 4 25–29 | 1 30–34 0 35–39 | 1 0 1 2 3 4 5 6 1 2 3 4 5 6 7 Frequency Number of people in a household 1 2 3 4 5 6 Number of people in a household 10 0 0–4 5–910–1415–1920–2425–2930–3435–39 1 2 3 4 5 6 7 8 9 Numberofstudents Number of CDs purchased 0–4 5–9 10–14 15–19 20–24 25–29 30–34 35–39 Number of CDs purchased 9D 9G MQ Maths A Yr 11 - Ans Page 575 Thursday, July 5, 2001 8:09 AM
- 17. 576 A n s w e r s answers 8 Check with your teacher 9 10 a b 11 12 a 28 b 38 c 12.5 13 6, 24, 41, 69, 91 14 a 43 b 43 c 14 15 16 20 17 11 18 7.5 19 7 20 21 45 22 15 23 35 24 7 25 Check with your teacher CHAPTER 10 Describing, exploring and comparing data Skills check 1 a 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9 b 11 c 6th d 5 e 3 to 9 or 6 f 5.55 g 6, 5 h 4 i Mean = 5.5, median = 5, mode = 4. The mean takes into account all scores, the median is the middle score (arranged in order), the mode is the most frequently occurring score. These values would only be the same for a symmetrical (or near symmetrical) distribution. j 4, 7 2 Central tendency is a measure of how the scores tend to be grouped around the centre of the data. The measure represents a typical score in the data set. 3 Range, interquartile range 4 The median is the second or middle quartile. 5 b, d 6 Consult your teacher. Exercise 10A — Calculating and interpreting the mean 1 Average, total, number, central, median, mode. 2 a 5 b 26.5 c 74.25 d 7.72 e 376 3 72.6, 3, 2 4 73.4 c/L, yes, 3 above and 4 below 5 1.81 m, 3 6 a Yes, mean mass is 45.035 g. b Both the same distance from the mean 7 a Mean is 10 greater; that is, 13 b Mean is 10 times as large; that is, 30. Exercise 10B — Mean, from frequency distribution tables 1 a b 131.36 mm 2 a b 7 c 10 Class Class centre Frequency 5000–9999 7 500 1 10 000–14 999 12 500 5 15 000–19 999 17 500 9 20 000–24 999 22 500 3 25 000–29 999 27 500 2 30 000–34 999 32 500 2 60 0 2 4 6 1 2 3 4 5 Number of sales Frequency 8 10 12 0 7500 12 500 17 500 22 500 27 500 32 500 2 4 6 No. of people at a football match Frequency 8 10 Key 2 | 1 = 21 Stem 2 3 4 Leaf 1 1 3 4 8 8 8 9 9 9 0 3 4 5 5 5 6 8 8 8 8 9 0 0 0 1 1 2 2 4 5 5 5 6 8 9 2 6 10 14 180 4 8 12 16 20 0 5 10 15 20 25 Score (x) Tally Frequency (f) fx 119 | 1 119 124 | 1 124 125 | | 2 250 126 | | 2 252 127 | 1 127 128 | | 2 256 129 | 1 129 130 | 1 130 131 | | | | 5 655 132 | | | 3 396 134 | | | 3 402 135 | | 2 270 136 | 1 136 138 | | 2 276 139 | | 2 278 141 | 1 141 Σ f = 30 Σ fx = 3941 Score Tally Frequency fx 4 | | 2 8 5 | | | | 4 20 6 | | | | 5 30 7 | | | | | | | | 9 63 8 | | | 3 24 9 | | | | 5 45 10 | | 2 20 Σ f = 30 Σ fx = 210 9G 10B MQ Maths A Yr 11 - Ans Page 576 Thursday, July 5, 2001 8:09 AM
- 18. A n s w e r s 577 answers ➔ 3 a b 20.4 4 a b 2.3 c 31 below, 19 above — could be a better measure 5 a b 12 c Size 12 not available, perhaps a better measure could be used. 6 D 7 B 8 C Exercise 10C — Mean, from grouped data 1 a Mean = 131.6 mm b Slightly larger — scores not evenly spread around each class centre. 2 a b 68.17 c 61–70 class 3 a b 53.1 c 39 — remember faster is lower time 4 Check with your teacher. 5 a 14.1 b 3.4 c 44.4 No. of televisions sold No. of weeks fx 16 4 64 17 4 68 18 3 54 19 6 114 20 7 140 21 12 252 22 8 176 23 2 46 24 4 96 25 2 50 Σ f = 52 Σ fx = 1060 Score (x) Frequency (f) fx 0 4 0 1 9 9 2 18 36 3 10 30 4 5 20 5 4 20 Σ f = 50 Σ fx = 115 Score (x) Frequency (f) fx 8 2 16 10 7 70 12 11 132 14 6 84 16 2 32 18 2 36 Σ f = 30 Σ fx = 370 1 3 --- 1 3 --- Class Class centre (x) Tally Frequency (f) fx 119–121 120 | 1 120 122–124 123 | 1 123 125–127 126 | | | | 5 630 128–130 129 | | | | 4 516 131–133 132 | | | | | | | 8 1056 134–136 135 | | | | | 6 810 137–139 138 | | | | 4 552 140–142 141 | 1 141 Σ f = 30 Σ fx = 3948 Class Class centre (x) Tally Frequency (f) fx 31–40 35.5 | 1 35.5 41–50 45.5 | | | 3 136.5 51–60 55.5 | | | | 4 222.0 61–70 65.5 | | | | | | 7 458.5 71–80 75.5 | | | | | | | | | 11 830.5 81–90 85.5 | | 2 171.0 91–100 95.5 | | 2 191.0 Σ f = 30 Σ fx = 2045 Time Class centre No. of swimmers fx 50.01–51.00 50.5 4 202.0 51.01–52.00 51.5 12 618.0 52.01–53.00 52.5 23 1207.5 53.01–54.00 53.5 38 2033.0 54.01–55.00 54.5 15 817.5 55.01–56.00 55.5 3 166.5 Σ f = 95 Σ fx = 5044.5 10A 10C MQ Maths A Yr 11 - Ans Page 577 Thursday, July 5, 2001 8:09 AM
- 19. 578 A n s w e r s answers 6 a 6.6 b 30.67 7 166.25 8 a 12.5, 13.5, 14.5, 15.5, 16.5 b 14.4 9 a b 46.4 c 33 Exercise 10D — Median and mode 1 Middle, arranged in order, , average, cumulative frequency. 2 6 3 81 4 a 5 b 5.4 c 62 d 102 5 a 4 b 5.6 c The median is a better measure because one large score makes the mean larger than what is typical. 6 a b 20 7 3 8 1 9 C 10 C 11 A 12 a b 10–14 13 Most frequent, bimodal, modal class. 14 a 5 b 8 c 11 d 0.4 e 110 15 a 17 b 148, 151 c No mode d 72 e 2.6 16 a 4 b 8 c 42, 44 17 17 18 a 17–20 b 22–28 19 a b $350–$399 10 Quick Questions 1 1 5.5, 15.5, 25.5, 35.5, 45.5 2 5, 20, 49, 86, 97 3 48 4 86 5 Grouped 6 7 8 29 9 21–30 10 31–40 Exercise 10E — Best summary statistics 1 a $215 000 b $170 000 c $150 000 d The median, as the mean is inﬂated by one large score and the mode is the lowest price. 2 a 7.1 b 7 c 7 d The mode, as it is the size that sells the most. 3 a 23 550 b 20 000–30 000 c 10 000–20 000 d Median 4 B 5 a b 6.8 c 0–4 d 0–4 Class Class centre Frequency 1–10 5.5 12 11–20 15.5 6 21–30 25.5 5 31–40 35.5 7 41–50 45.5 9 51–60 55.5 9 61–70 65.5 5 71–80 75.5 5 81–90 85.5 5 91–100 95.5 7 Score Frequency Cumulative frequency 17 4 4 18 9 13 19 6 19 20 12 31 21 8 39 22 5 44 23 4 48 24 2 50 Days sickness Frequency Cumulative frequency 0–4 10 10 5–9 12 22 10–14 7 29 15–19 6 35 20–24 5 40 25–29 3 43 30–34 2 45 n 1+ 2 ------------ Class Class centre Frequency Cumulative frequency $200–$249 224.5 8 8 $250–$299 274.5 4 12 $300–$349 324.5 6 18 $350–$399 374.5 6 24 $400–$449 424.5 4 28 $450–$499 474.5 2 30 $500–$549 524.5 6 36 $550–$599 574.5 4 40 Class Class centre Frequency Cumulative frequency 0–4 2 16 16 5–9 7 6 22 10–14 12 4 26 15–19 17 2 28 20–24 22 1 29 25–29 27 1 30 5.515.525.535.545.5 0 5 10 15 Score Frequency 20 25 30 35 40 5.515.525.535.545.5 0 5 10 15 Score Frequency 20 25 30 35 40 10C 10E MQ Maths A Yr 11 - Ans Page 578 Thursday, July 5, 2001 8:09 AM
- 20. A n s w e r s 579 answers ➔ 6 Check with your teacher; answers depend on groupings used. 7 a b 42.2 c 16–30 d 16–30 e No f Check with your teacher. 8 a Player A: 34.3 Player B: 41.8 b Player B c Player A: 32.5 Player B: 0 d Player A e Check with your teacher. 9 a The statement is true but misleading as most employees earn $18 000. b Check with your teacher, but you should quote $18 000 as the median and the mode salary and that only 15 out of 80 (less than 20%) earn more than the mean. Exercise 10F — Range and interquartile range 1 Dispersion, spread, lowest, highest, outlying, interquartile, upper, lower, median, quarter, quarter, four, scores. 2 a 5 b 9 c 1 d 6.94 e 89 3 a 4 b 5 c 6 4 a 49 b 30 c 23 5 a Sydney — 120 Collingwood — 40 b Collingwood, because the range is lower. 6 a 9 b 8 c The range for machine A is large, only because of one extreme score. 7 a 5 b 25 c 53 d 15 e 74 8 a 5 b 9 c 2 d 4 e 32 9 A 10 B 11 D 12 B Exercise 10G — Standard deviation 1 Spread, mean, σn (or σx), σn – 1 or Sn, consistent/reliable, low. 2 a 2.29 b 2.19 c 20.17 d 3.07 e 42.44 3 a 26.94 b 2.14 c 57.51 d 0.26 e 96.04 4 a Sample b Population c Population d Sample e Population 5 a 616.6 b Sample c 270.97 6 a $1.44 million b Population c $0.48 million 7 a x– = 4.9, σ = 1.0 b x– = 48.3, σ = 1.2 c x– = 78.3, σ = 2.3 8 a x– = 17.45, σ = 3.69 b x– = 14.95, σ = 7.49 c x– = 56.02, σ = 14.26 9 a Brianna: x– = 75, σ = 3.69 Katie: x– = 74, σ = 18.28 b Brianna is more consistent because she has a lower standard deviation. 10 B 11 C 12 x– = $1825, sample SD = $797 13 a 500 hours b x– = 455.3 h, sample SD = 88.9 h 14 Crinkle, because the standard deviation in the weight of each pack is lower and therefore you are more likely to get the correct amount. 10 Quick Questions 2 1 23.3 2 21.5 3 16 4 29 5 19 6 24 7 5 8 7.93 9 Median, because the outlier inﬂates the mean. 10 The outlier makes the range very large. Exercise 10H — Comparing sets of data 1 2 a Text b Text c The ‘text’ group showed more variability. 3 4 a 5 a 6 a Smith: (0, 17.5, 57.5, 62, 85), Jones: (3, 31.5, 39, 46, 61) b 11 a Before: (20.3, 20.75, 21.1, 21.45, 21.8) After: (19.3, 19.7, 20.1, 20.95, 22.2) b 12 a Key: 2 1 = 21 fruit b Class Class centre Frequency Cumulative frequency 1–15 8 1 1 16–30 23 13 14 31–45 38 2 16 46–60 53 0 16 61–75 68 5 21 76–90 83 4 25 a Brand A b Brand A c Brand B d Brand A e Brand A f Brand B g Brand A 7 C 8 E 9 B 10 C Unsprayed Sprayed Leaf 9 9 8 7 5 9 7 5 4 3 2 1 0 8 6 2 1 0 8 8 5 3 2 2 1 Stem 2 3 4 5 6 7 8 Leaf 1 7 8 9 9 2 3 4 4 5 8 2 2 5 8 4 9 1 2 2 6 1 3 6 5 10 15 2520 30 35 Scale Group X Group Y 15 2520 30 35 40 Age Women Men 5 1510 20 25 30 Words per sentence Children's book Geography text Newspaper 0 4020 60 80100 Runs Smith Jones 19 20 21 22 Before kg After 20 40 60 80 Sprayed Fruit Unsprayed 10D 10H MQ Maths A Yr 11 - Ans Page 579 Thursday, July 5, 2001 8:09 AM
- 21. 580 A n s w e r s answers 13 a Key: 2 3 = 23 hours Key: 2* 5 = 25 hours b Chapter review 1 a 5.2 b 64.875 c 7.7 d 35.8 2 a 31.1 b 23.2 c 0.445 3 a 7.025 b 9.46 4 Mean = 38.2 5 a 29.9 b 26.4 c 18.6 6 a 27 b 6 c 3.2 d 5.5 e 128 7 a 2 b 56 c 68.5 8 a b 50–59 9 a 2 b 23, 27 c No mode 10 a 2 b 15, 18 11 46–49 12 a 27.8 b 24.5 c 28 d Median 13 Check with your teacher. 14 a 7 b 159 c 1.4 15 a Population b 17.3 16 a Sample b 0.89 17 a x– = 0.81, σ = 0.42 b x– = 67.25, σ = 75.3 c x– = 28.1, σ = 1.2 d x– = 27.5, σ = 7.03 18 C 19 D 20 a Key: 3* 9 = 3.9 b (3.9, 4.4, 4.9, 5.85, 6.8) c 21 a Elena: 2, 6, 11.5, 15, 25; Victoria: 3, 14, 20, 25, 35 b 22 a Key: 1 3 = 13 b Text A: (13, 35, 59, 82, 98); Text B: (37, 55, 63.5, 70, 82) c CHAPTER 11 Scatterplots and time series Skills check 1 An independent variable is one whose variation does not depend on changes in another variable. A dependent variable is one whose variation responds to changes in the independent variable. 2 Independent variable 3 a Height b Distance travelled c Temperature d Reaction time e Test results f Overtime pay g Value of car h Travelling time 4 a Increase b Increase c Decrease d Decrease e Increase f Increase g Decrease h Decrease Starlet Glow-worm Leaf 8 6 4 9 8 2 1 6 6 5 3 7 6 4 9 5 4 8 2 2 Stem 1* 2 2* 3 3* 4 4* 5 5* 6 6* 7 Leaf 3 3 7 8 1 5 5 8 9 1 1 2 5 7 8 8 9 0 2 4 Class Class centre Frequency fx 21–24 22.5 3 67.5 25–28 26.5 9 238.5 29–32 30.5 17 518.5 33–36 34.5 31 1069.5 37–40 38.5 29 1116.5 41–44 42.5 25 1062.5 45–48 46.5 19 883.5 49–52 50.5 10 505.0 Σ f = 143 Σ fx = 5461.5 Class Class centre Frequency Cumulative frequency 30–39 34.5 18 18 40–49 44.5 34 52 50–59 54.5 39 91 60–69 64.5 45 136 70–79 74.5 29 165 80–89 84.5 10 175 90–99 94.5 5 180 10 30 50 70 Glow-worm Hours Starlet Stem 3* 4 4* 5 5* 6 6* Leaf 9 0 0 2 3 5 6 7 8 8 0 3 5 8 8 9 1 2 2 8 Text B Text A Leaf 9 7 8 2 9 9 8 8 5 5 3 2 8 8 8 6 5 4 4 3 2 9 9 5 2 2 2 1 Stem 1 2 3 4 5 6 7 8 9 Leaf 3 1 2 5 8 5 5 4 8 2 5 6 9 4 9 2 2 6 1 3 4 4 4 5 8 3.5 4.5 6.55.5 kg 0 10 3020 Elena Number of lessons Victoria 0 20 40 60 80100 Text A Result Text B 10F 10H MQ Maths A Yr 11 - Ans Page 580 Thursday, July 5, 2001 8:09 AM
- 22. A n s w e r s 581 answers ➔ 5 a b c d e f g h Exercise 11A — Scatterplots 1 2 3 4 a b The greater the English mark, the greater the history mark, generally. However, as the points on the scatterplot do not form a straight line, the relationship is not linear. 5 a b The greater the temperature, the fewer pies are sold. The points on the scatterplot approximate a straight line and so the relationship can be said to be linear. 6 a b More workers on the team reduces the amount of time taken to unload the ship and, as the points on the scatterplot approximate a straight line, the relationship is linear. 7 D 8 A 9 Check with your teacher. Exercise 11B — Regression lines Note: Best fit lines are indicated as a guide only. 1 a b c d e 2 3 a y = 5x + 12 b y = 70 − 0.4x c y = 80x + 750 4 a b L = 0.05M + 220 5 a b V = 0.05T + 3.2 6 a b S = 1.25B + 21 7 a $17.40 b $8.40 c 20 km d 8.5 km 8 a 159.7 cm b 178 cm c 31.15 cm d 25.74 cm 9 a 755 b 295 c 20°C d 38°C Height Age Distance Time Temperature Elevation Reaction time Blood ale level Testresults IQ Overtime pay Hours worked Valueofcar Age Travelling time Speed 0 40 80 0 40 80 Geography History 0 200 400 0 20 40 Numberat cinema Temperature (°C) 0 0 100 200 200 400 600 800 Amountspenton entertainment($) Wages ($) 0 40 80 0 40 80 History English 0 80 0 20 40 Numberof piessold Temperature (°C) 0 10 20 30 0 10 20 30 Hourstaken Number in work team x y x y x y x y x y 0 40 80 0 40 80 Maths English 0 240 280 0 400 800 Lengthof spring(mm) Mass (g) 20–20–60 60 2 4 6 8 Temperature (°C) Volume (L) 0 20 40 60 0 10 20 30 40 Lifttest(kg) Circumference of biceps (cm) 11A 11B MQ Maths A Yr 11 - Ans Page 581 Thursday, July 5, 2001 8:09 AM
- 23. 582 A n s w e r s answers 10 a, b c C = 0.4d + 2100 d i $8100 ii $2500 iii 14 750 km iv 34 750 km 11 a, b c N = 135 − 20p d i 73 000 ii 43 000 e $2.75 f $1.75 12 a b A = 0.45d + 280 c i $582 ii $1236 iii $740 iv $1762 10 Quick Questions 1 1 $115 2 $235 3 $85 4 3 h 30 min 5 6 h 6 2 h 45 min 7 80 8 35 9 2 h 10 4 h 30 min Exercise 11C — Time series and trend lines Note: Your answers to questions 2 to 8 may vary slightly because you are using the ‘eye’ method. 1 a Seasonal b Random c Secular, upwards d Random or cyclical e Cyclical 2 Deﬁnite secular trend downward 3 Although there are some random variations, the trend could also be secular. 4 Prediction is about $5.40 (see dotted line at right). This price is an extrapolated value (outside the plotted values) and can only be treated as an approximate value at best. 5 Impossible to ﬁt a trend line, given cyclical nature of the data. 6 a b Prediction for t = 25 is about $92. 7 Difﬁcult to ﬁt an accurate trend line, due to likely cyclical nature of software sales business. 8 At current rate (about 300/month), bank will have no employees in another year! Although not likely, there is a clear downward trend. Chapter review 1 2 a b There appears to be a positive relationship which is linear. 3 a b There is no apparent relationship. 4 D 5 D 6 C 7 a, b c y = 99 − 5x 8 a $242 400 b $73 000 9 a b F = 107 − 8I c 73 d 13.4 mg 0 0 8000 16000 100002000030000 Annualcost($) Distance (km) 0 80 160 0.00 2.00 4.00 Weeklysales (×1000) Price ($) 0 800 1400 0 1000 2000 3000 Price($) Distance (km) Days Temp.(°C) 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 t 0 10 20 0 2 4 6 8 10 12 t y 2 3 4 5 6 0 2 4 6 8 10 Price($) 12 t y Price(cents) 20 40 60 80 100 0 5 10 15 20 25 t Sales(×1000) 240 220 200 180 160 140 120 100 1999 2000 2001 Numberofemployees 7000 6000 5000 4000 3000 2000 1000 0 1086 Months 420 t 0 10 20 0 20 40 Maximum temperature (°C) Minimum temperature(°C) 0 4 8 12 0 2 4 6 Number of children Numberofsickdays 0 2 4 0 2 Number of cars Numberof televisions 0 40 80 0 8 16 y x 0 40 80 120 0 4 8 12 Amount of insecticide (µg) Numberofblowflies 11A 11C MQ Maths A Yr 11 - Ans Page 582 Thursday, July 5, 2001 8:09 AM
- 24. A n s w e r s 583 answers ➔ 10 C 11 Impossible to ﬁt a trend line as trend is seasonal. Summer uniform bought at the end of the year and then the beginning of the year. Winter uniform bought near winter. CHAPTER 12 Introduction to probability Skills check 1 a 50-50 b Almost impossible c Almost certain d Not very likely e 50-50 f Impossible 2 a 6 b 1, 2, 3, 4, 5, 6 c 1 in 6 d 3 e 3 in 6 f 3 (2, 3 and 5) g 3 in 6 3 a b 8 c 2 d 3 4 a 0.833 b 0.667 c 0.167 d 0.077 e 0.417 5 a 83.3% b 66.7% c 16.7% d 7.7% e 41.7% 6 a , 0.125 b , 0.444 c , 0.875 d , 0.938 e , 0.875 f , 0.009 Exercise 12A — Informal description of chance 1 a Probable b Unlikely c Impossible d Fifty-ﬁfty 2 a Impossible b Certain c Even chance d Even chance e Probable f Unlikely g Impossible h Even chance 3 Check with your teacher. 4 More likely during school term 5 a More likely b Equally likely c Less likely d More likely e Less likely 6 Rolling a 6 Rolling a number less than 3 Rolling an even number Rolling a number greater than 2 7 Winning a rafﬂe with 5 tickets out of 30 Selecting a court card from a standard deck Drawing a green marble from a bag containing 4 red, 5 green and 7 blue marbles Rolling a die and getting a number less than 3 Tossing a coin and having it land Heads 8 Australia 9 Carl Bailey because he has better past performances. 10 A 11 B 12 C 13 Probable 14 Unlikely 15 Fifty-ﬁfty Exercise 12B — Sample space 1 S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 2 a S = {Heads, Tails} b S = {1, 2, 3, 4, 5, 6} c S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} d S = {a, b, c, d, …, y, z} e S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat} f S = {Jan, Feb, Mar, …, Dec} 3 a 52 b 15 c 45 d 1500 e 901 f 11 4 a S = {M, I, S, S, I, S, S, I, P, P, I} b 11 c 4 5 a 52 b i 4 ii 2 iii 13 6 a S = {1, 2, 3, 4, 5, 6} b E = {5, 6} 7 a 100 b 40 8 D 9 B 10 D 11 a S = {NSW win, Qld win, draw} b 3 c No, because the teams may not be of equal ability. 12 a S = {20, 20, 20, 20, 20, 10, 10, 10, 10, 5}, 10 b S = {20, 20, 20, 20, 10, 10, 10, 10, 5} c S = {20, 20, 20, 20, 20, 10, 10, 10, 5} d S = {20, 20, 20, 20, 20, 10, 10, 10, 10} 13 Check with your teacher. 14 Check with your teacher. 10 Quick Questions 1 1 Unlikely 2 Fifty-ﬁfty 3 Probable 4 100 5 18 6 3 7 10 8 1 9 0 10 4 Exercise 12C — Tree diagrams 1 S = {HH, HT, TH, TT} 2 S = {11, 12, 13, 21, 22, 23, 31, 32, 33} Child 1 Child 2 Child 3 Boy Girl Girl Boy Boy Girl Boy Girl Boy Boy Boy Boy Girl Boy Boy Girl Boy Girl Girl Girl Boy Girl Girl Girl 6 Month 42 12108 50 30 110 90 70 10 Numberofuniformssold Impossible b d a c e f Certain 1 8 --- 4 9 --- 7 8 --- 15 16 ------ 7 8 --- 9 1024 ------------ 11C 12C MQ Maths A Yr 11 - Ans Page 583 Thursday, July 5, 2001 8:09 AM
- 25. 584 A n s w e r s answers 3 S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} 4 a 12 b No 5 S = {13, 14, 18, 31, 34, 38, 41, 43, 48, 81, 83, 84} 6 S = {DZ, DM, DK, DS, ZD, ZM, ZK, ZS, MD, MZ, MK, MS, KD, KZ, KM, KS, SD, SZ, SM, SK} 7 S = {AM, AS, AL, PM, PS, PL, YM, YS, YL} 8 S = {CA, CR, CL, CK, AR, AL, AK, RL, RK, LK} 9 a Check with your teacher. b S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT} c 6 10 C 11 D 12 B 13 The statement is not correct because there are 4 elements to the sample space. The one Head and one Tail can occur in either order. 14 a S = {22, 25, 27, 28, 52, 55, 57, 58, 72, 75, 77, 78, 82, 85, 87, 88} b S = {25, 27, 28, 52, 57, 58, 72, 75, 78, 82, 85, 87} 15 a 12 b 24 c 24 16 a S = {TJ, TS, TR, TM, JT, JS, JR, JM, ST, SJ, SR, SM, RT, RJ, RS, RM, MT, MJ, MS, MR} b 20 c 2 d 6 e 12 17 a 36 b c 6 Exercise 12D — Equally likely outcomes 1 No. The players are not of equal ability. 2 No. The runners are not of equal ability. 3 Yes. The number is chosen randomly. 4 a Yes b No c No d Yes 5 a True. The letter is chosen randomly. b False. On a page of writing, each letter of the alphabet does not occur equally often. 6 B 7 No, there are two chances of a boy and a girl, as they could be born in either order. 8 a S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} b No 9 a 24 b No. The chance of each combination depends on people’s taste. 10 a 10 b No. Each horse has a different rider and ability. c Yes. Yes. The selection of horse is made randomly. 10 Quick Questions 2 1 Unlikely 2 8 3 3 4 1 5 Yes 6 S = {BB, BG, GB, GG} 7 S = {AL, AM, AJ, SL, SM, SJ} 8 9 9 6 10 No Exercise 12E — Using the fundamental counting principle 1 50 625 2 a 4 b 36 c 12 3 1000 4 7776 5 6 760 000 6 D 7 B 8 1833 9 72 10 a 64 b 144 c 168 d 112 e 384 11 a 3 200 000 b 240 12 a 5408 b 676 13 36 14 a 100 000 000 b 80 000 000 c 1 000 000 d 2 000 000 15 96 16 C 17 a 1200 b 550 18 20 000 19 307 328 000 Investigation — Q-lotto: frequencies 1 Unlikely 2 Almost impossible 3 Less likely 4 No 5 {1, 2, 3, 4, . . . 44, 45}, 45 6 {4, 5, 8, 15, 22, 30, 23, 35} 7 8, no 8 No, at least 3, plus either bonus 9 {4, 5, 8, 15, 22, 30} 10 Yes, they occur only once each 11 No 12 60 13 3 14 28, 76 15 6, 43 16 {10, 20, 21, 25, 38, 40, 41, 43} 2 supplementary or bonus numbers 17 {9, 11, 27, 28, 29, 38, 43} 6 of these 18 {2, 5, 8, 12, 15, 37} Exercise 12F — Relative frequency 1 0.74 2 0.79 3 0.375 4 a 0.45 b 0.55 5 4% 6 a 0.03 b 0.97 7 a 0.96 b 0.04 8 A 9 A 10 a 0.525 b 0.4375 c 0.0375 11 a 6.67% b 80 12 a 0.02 b $400 13 Yes, the relative requency is 27%. 14 a 2.5% b 51.5% c 17.5% 15 40 000 km 16 a b Win = 0.375, Loss = 0.35, Draw = 0.275 Total 2 3 4 5 6 7 8 9 10 11 12 No. of elements 1 2 3 4 5 6 5 4 3 2 1 Result Number Win Loss Draw 15 14 11 12A 12F MQ Maths A Yr 11 - Ans Page 584 Thursday, July 5, 2001 8:09 AM
- 26. A n s w e r s 585 answers ➔ Exercise 12G — Single event probability 1 S = {Heads, Tails}, 1 2 a S = {1, 2, 3, 4, 5, 6}, 1 b S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, 3 c S = {a, b, c, d, e, … y, z}, 5 d S = {Sun, Mon, Tue, Wed, Thu, Fri, Sat}, 2 e S = {Jan, Feb, Mar, … Nov, Dec}, 3 3 a 26, 52 b 1, 15 c 1, 45 d 5, 1500 e 3, 11 4 5 a b c d e f 6 a b c d e f g g i 7 a b c d e f 8 a b c 9 a b c d e f 10 11 a b c d e 12 C 13 C 14 C 15 D 16 a b 17 a b c 18 a b c d e f 19 Check with your teacher. 20 a Because there are two numbers which could go in the last place. b A number greater than 400 10 Quick Questions 3 1 2 3 4 5 6 True 7 False 8 0.2 9 0.75 10 0.5% Exercise 12H — Writing probabilities as decimals and percentages 1 0.5 2 37.5% 3 a 0.5 b 50% 4 a 0.17 b 0.5 c 0.33 5 a 16.7% b 50% c 83.3% 6 a 0.02 b 0.25 c 0.08 d 0.5 e 0.23 7 a 1.9% b 25% c 7.7% d 50% e 23.1% 8 A 9 D 10 B 11 a 0.2 b 0.4 c 0.6 d 0.8 12 a 20% b 40% c 40% Exercise 12I — Range of probabilities 1 a Even chance b Probable c Unlikely d Certain e Probable f Unlikely g Probable h Impossible i Unlikely 2 a 0, impossible b 1, certain c , even chance d , even chance e , unlikely f 0, impossible g , even chance 3 Check with your teacher. 4 , , , , 5 A, D, C, B, E 6 D 7 B 8 D 9 a b Unlikely 10 , very probable 11 a Very unlikely b Even chance c Probable d Unlikely 12 a True, as there are 4 Aces from 52 cards in the deck. b False, as each letter does not occur equally often. c False, as each student is not of equal ability. d True, as the name is chosen randomly. 10 Quick Questions 4 1 2 3 , , 4 62.5% 5 0.375 6 0.154 7 23.1% 8 1 9 0 10 Probable Exercise 12J — Complementary events 1 a S = {1, 2, 3, 4, 5, 6} b c 1 2 a i ii iii b 1 3 a Losing a race b Failing a test c Your birthday not falling on a Monday 4 A coin landing Heads A coin landing Tails An odd number on a die An even number on a die A picture card from a A non-picture card from a standard deck standard deck A red card from a A black card from a standard deck standard deck Winning 1st prize in a Not winning 1st prize in rafﬂe with 100 tickets the rafﬂe Making the last 4 teams A team not making the in a 20-team last four tournament 1 2 --- 1 6 --- 1 6 --- 1 2 --- 1 2 --- 2 3 --- 1 3 --- 1 45 ------ 1 45 ------ 22 45 ------ 23 45 ------ 1 5 --- 1 3 --- 19 45 ------ 2 9 --- 2 15 ------ 1 52 ------ 1 13 ------ 1 4 --- 1 2 --- 3 13 ------ 3 13 ------ 1 12 ------ 1 3 --- 7 12 ------ 1 4 --- 1 4 --- 1 4 --- 3 4 --- 1 2 --- 3 4 --- 5 6 --- 1 4 --- 3 4 --- 1 4 --- 1 4 --- 1 2 --- 1 200 --------- 4 999 --------- 3384 160 000 ------------------- 6768 160 000 ------------------- 10 152 160 000 ------------------- 1 5 --- 1 5 --- 4 5 --- 1 5 --- 4 5 --- 1 5 --- 1 6 --- 1 13 ------ 7 11 ------ 33 100 --------- 5 9 --- 3 6 --- 26 52 ------ 4 52 ------ 6 12 ------ 13 20 ------ 7 13 ------ 9 18 ------ 8 19 ------ 6 25 ------ 50 2000 ------------ 98 100 --------- 1 2 --- 1 4 --- 4 9 --- 1 2 --- 10 19 ------ 1 6 --- 7 20 ------ 8 20 ------ 5 20 ------ 12D 12J MQ Maths A Yr 11 - Ans Page 585 Thursday, July 5, 2001 8:09 AM
- 27. 586 A n s w e r s answers 5 a , , , , , b , , , , , c 1 6 a Rolling an odd number b Rolling a number less than 4 c Rolling a number greater than 2 d Not rolling a 6 e Rolling a 1 7 a Choosing an even-numbered ball b Choosing a ball numbered greater than 19 c Choosing a ball that has a number less than 24 d Choosing a ball that is not a multiple of 5 8 a Selecting a coloured ball b Selecting a black ball c Not selecting a pink ball; that is, selecting a black or orange ball 9 A 10 C 11 a b 12 a b 13 a b c d e f 14 a b c d e 15 a b 16 a b c 17 0.3 18 a 91% b 9% 10 Quick Questions 5 1 S = {heart, club, diamond, spade} 2 3 4 5 6 7 8 9 10 Investigation — Q-lotto: conclusion 1 45 × 44 × 43 × 42 × 41 × 40 = 5 864 443 200 2 6 × 5 × 4 × 3 × 2 × 1 = 720 3 5 864 443 200 ÷ 720 = 8 145 060 4 Chapter review 1 Marcia will probably get a higher card. 2 a Probable b Impossible c Even chance d Unlikely e Unlikely 3 Check with your teacher. 4 Hot weather 5 Rolling a die and getting a number greater than 1 Selecting a blue marble from a bag containing 14 blue, 15 red and 21 green marbles Selecting a picture card from a standard deck Winning the lottery with 1 ticket out of 100 000 tickets sold 6 Mark is most likely to win based on past performances. 7 S = {S, A, M, P, L, E} 8 a S = {Heads, Tails} b S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18} c S = {ace club, ace spade, ace diamond, ace heart} d S = {black, black, black, black, white, white, white, green, green, green, green, green} 9 a S = {1, 2, 3, 4, 5, 6} b E = {5, 6} 10 a i 2 ii 1 b i 52 ii 32 c i 15 ii 11 11 S = {HH, HT, TH, TT} 12 36 13 a S = {56, 57, 59, 65, 67, 69, 75, 76, 79, 95, 96, 97} b 9 14 a S = {MN, MP, MR, MS, NM, NP, NR, NS, PM, PN, PR, PS, RM, RN, RP, RS, SM, SN, SP, SR} b 8 15 a S = {TCB, TCM, TCZ, TDB, TDM, TDZ, THB, THM, THZ, TIB, TIM, TIZ, KCB, KCM, KCZ, KDB, KDM, KDZ, KHB, KHM, KHZ, KIB, KIM, KIZ} b 15 16 a 8 b No. Each greyhound is not of equal ability. 17 a Each is equally likely, as the winning ticket is selected randomly. b Each outcome is not equally likely, as the teams have different abilities. c Each letter is not equally likely, as each letter is not used equally often. 18 759 375 19 20 20 272 21 160 22 a 10 000 b 500 23 a 100 000 000 b 94 109 400 24 0.02 25 a 0.15 b $750 26 S = {1, 2, 3, 4, 5}, E = {3, 4, 5} 27 a b c d e f 28 a b c d e f 29 a b c 1 2 --- 1 2 --- 3 13 ------ 1 2 --- 1 100 --------- 1 5 --- 1 2 --- 1 2 --- 10 13 ------ 1 2 --- 99 100 --------- 4 5 --- 1 8 --- 7 8 --- 1 5 --- 4 5 --- 9 20 ------ 11 20 ------ 3 20 ------ 17 20 ------ 3 5 --- 2 5 --- 2 5 --- 3 10 ------ 3 5 --- 7 10 ------ 3 10 ------ 7 20 ------ 13 20 ------ 3 25 ------ 21 50 ------ 29 50 ------ 1 10 ------ 1 8 --- 1 10 000 ---------------- 8 15 ------ 7 15 ------ 3 10 ------ 1 5 --- 4 5 --- 4 5 --- 1 8 145 060 ----------------------- 1 25 ------ 1 25 ------ 13 25 ------ 1 5 --- 9 25 ------ 16 25 ------ 1 52 ------ 1 13 ------ 1 4 --- 1 2 --- 4 13 ------ 10 13 ------ 7 20 ------ 1 10 ------ 3 4 --- 12G 12J MQ Maths A Yr 11 - Ans Page 586 Thursday, July 5, 2001 8:09 AM
- 28. A n s w e r s 587 answers ➔ 30 a b c d e 31 a b 32 a 0.025 b 0.5 c 0.75 33 a 50% b 33 % c 66 % 34 Probable 35 . It is probable that the car will have a defect. 36 a Tossing a coin that lands Heads b Rolling a die and getting a number greater than 4 c Not choosing a blue ball 37 a b 38 39 1 24 ------ 3 4 --- 1 4 --- 3 4 --- 1 2 --- 1 400 --------- 4 1999 ------------ 1 3 --- 2 3 --- 7 8 --- 3 10 ------ 7 10 ------ 5 12 ------ 18 25 ------ MQ Maths A Yr 11 - Ans Page 587 Thursday, July 5, 2001 8:09 AM

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