Edexcel GCSE Maths - Collins
Edexcel GCSEMathsHigher Student BookAnswers209732 Edexcel Higher Teacher Pack title page.indd 13/27/15 2:38 PM
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Exercise 1CChapter 1 – Number: Basic number1adgj50 0002000.31000b 90 000e 0.5h 10cfi30 0000.0060.052adgj56 0001.74.10.80b 80 000e 0.066h 8.0cfi31 0000.461.03a 60 000d 110g 0.3b 5300e 9h 0.7cf89.71.14ab 95, 149c950, 14995Elsecar 750, 849; Hoyland 1150, 1249; Barnsley164 500, 165 499618 to 23 inclusive71, because there could be 450 then 4498Donte has rounded to 2 significant figures ornearest 10 0009a Advantage – quick. Disadvantage – assumes3 penguins a square metre which may not beaccurateb Advantage. Quite accurate as 5 by 5 is a bigenough area to give a reliable estimate.Disadvantage – takes a long time.Exercise 1A1a 6000b 5 cans cost 1.95, so 6 cans cost 1.95.32 5 6 2. Cost is 10.53.2a 288b 163a 38b Coach price for adults 8, coach price forjuniors 4, money for coaches raised bytickets 12 400, cost of coaches 12 160,profit 2404(18.81.) Kirsty can buy 18 models. 8.40 per year, 70p per copy6 45071583 weeks9 250.7410 Gavin pays 2926.25 – 1840 1086.2511 a Col is correctb Abi has multiplied 30 50 as 150 instead of1500. Baz has lined up the columns wronglywhen adding. Instead of lining up the units hehas lined up the first digits. Des has forgottento add a zero on the second line of themultiplication, it should be 1530.Exercise 1D1adgj2a 5d 600g 400330 90 000 2 700 000600 8000 4 800 0005000 4000 20 000 000200 000 700 140 000 0004a 54 40051400 million6His answer is correct but he had one too manyzeros on each value, which cancel each otherout. Matt wrote 600,000 rather than 60,000 and2000 rather than 200. The two mistakescancelled themselves out due to the zerosinvolved.7a Value of the money is about 66 000 000 0.2 13 200 000, so it is enough to buy theyacht.b Weight is 66 000 000 5 330 000 000grams 330 tonnes, so they do not weigh asmuch as the yacht.81420 000 000 000 64 000 000 22 000, so theNational Debt per person is approximately 22000.Exercise 1B1adgj4.694.857.10.1behk0.08602.16.9044.0022a 0.0283a 35, 35.04, 0.04b 16, 18.24, 2.2c 60, 59.67, 0.33 d 140, 140.58, 0.584a 1856b 0.09b 140cfilc 50.9645.716671.7613.7860.0d 46.512c 1.4d12a 280 b 12c 240d450 e 0.62a 572b i 5.72ii1.43e 6.9iii 22.887a Incorrect as should end in the digit 2b Incorrect since 9 5 45, so answer must beless than 4583009a 27b i 27ii0.027iii 0.2710 Mark bought a DVD, some jeans and a pen.11 Headline A does not give the exact figure so doesnot convey any useful information. Headline B isaccurate and records should be given accurately.Headline C may be correct but without theprevious record does not convey any usefulinformation.Edexcel GCSE Maths (4th Edition)Higher Student Book – Answers65, 74160 0001520045b 120 000e 140h 0.08cfi10 0001000.09b 25e 2000h 8000cfi300050004 000 000b 16 000 HarperCollinsPublishers Ltd 2015
Exercise 1E1a 35 000d 5b 15 000e 1200c 960f 5002a 39 700d 4.44b 17 000e 1130c 933f 5503a 1.74 md 83 Cg 14 m2b 6 minutese 35 000 people4a 10b 1c 35a 8.79b 1.03c 3.07682 F, 5 km, 110 min, 43 000 people, 6.2seconds, 67th, 1788, 15 practice walks, 5secondsThe answers will depend on the approximationsmade. Your answers should be to the same orderas these.7a 15 000b 18 0008 10009a 40 miles per hourc 240 gf 15 miles4 packs of sausages and 5 packs of buns (ormultiples of these)330 seconds412 minutes; Debbie will have run 4 laps; Fred willhave run 3 laps.51 3 5 7 9 25, 1 3 5 7 9 11 36, 1 3 5 7 9 11 13 49, 1 3 5 7 9 11 13 15 646a 2b 7c 12d 1e 307a 1b 3c 4d 2e 48a 400b 900c 2500d 0.25e 169a Student’s own explanationb 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91,105c Adding consecutive pairs gives you squarenumbers.c 17 50010b 10 gallonsc 7010 a 80 000e 5000b 2000f 2500c 1000g 75d 30 000h 10011 a 86 900e 3960b 1760f 2440c 1030g 84.8d 29 100h 163Cube numberMultiple of 713 a 0.2e 1.527.616.918 70016 a 37.5 48.6 40 50 2000 21.7 103.6 20 100 2000985 0.54 1000 0.5 2000b as both values are rounded down the actualanswer must be bigger than 2000. The othertwo must be less than 2000.c Pete is correct it is not possible to tell. 37.5 48.6 1822.5 985 0.54 1824.07419 Macau’s population density is approximately 710000 times the population density of Greenland.20 26.8 3.1 27 3 936.2 3.9 36 4 9. Second calculation must be biggest as firstis smaller than 27 3 and second is bigger than36 4.abcdefg2aceg31, 2, 3, 22, 5, 2 3, 7, 23, 32, 2 5, 11, 22 3,13, 2 7, 3 5, 24, 17, 2 32, 19, 22 5, 3 7,2 11, 23, 23 3, 52, 2 13, 33, 22 7, 29, 2 3 5, 31, 25, 3 11, 2 17, 5 7, 22 32, 37, 2 19, 3 13, 23 5, 41, 2 3 7, 43, 22 11,32 5, 2 23, 47, 24 3, 72, 2 524 abdeExercise 1F910c 6i 18d 13j 17Edexcel GCSE Maths (4th Edition)Higher Student Book – Answersd 0.9h 0.7118 a 58.9 4.8 60 5 300b Lower as both values are rounded up to getthe estimate.bhc 0.6g 0.8Exercise 1G17 149 000 000 300 000 496.67 500 secondsa 12g 16b 0.5f 2.114 The answers will depend on the approximationsmade. Your answers should be to the same orderas these.a 60b 1500c 18014 22.5 C – 18.2 C 4.3 Celsius degrees1Factor of 5682812 a 1, 64, 729, 4096, 15 625b 1, 8, 27, 64, 125c a3 a ad Square numbers13 1 million pounds is 20 million 5p coins. 20 000000 4.2 84 000 000 grams 84 tonnes, so 5lorries needed.27.571 428 57 ii16.896 516 39 ii18 672.586 16 iiSquare number644911 2, 3 and 1212 Approximately 50015 a ib ic i2e 15 f 14k 8 /16 l 21284 2 2 3 7100 2 2 5 5180 2 2 3 3 5220 2 2 5 11280 2 2 2 5 7128 2 2 2 2 2 2 250 2 5 584 22 3 7b 100 22 52180 22 32 5 d 220 22 5 11280 23 5 7 f 128 2750 2 522 is always the only prime factor64, 128c 81, 243, 729256, 1024, 40963, 32, 33, 34, 35, 36; 4, 42, 43, 44, 45, 46 HarperCollinsPublishers Ltd 2015
12 –460 F5a 2 2 3 5b 22 3 5c 120 23 3 5, 240 24 3 5,480 25 3 56a 72 112 132b 73 113 133c 710 1110 13107Because 3 is not a factor of 40 so it does notdivide exactly.8a 2, b 79a 2ab a2 4bExercise 1J1a 20e 10b 56f 152They are the two numbers multiplied together.3a 8c 6g 244No. The numbers have a common factor.Multiplying them together would mean using thisfactor twice, thus increasing the size of thecommon multiple. It would not be the leastcommon multiple.b 18a 168e 96d 28h 30c 12b 105f 54d 30c 84g 753 packs of cheese slices and 4 packs of breadrolls7a 88a918 and 24b 7c 4ii and iiid 16b10 a 6x2y2e 14iii3a 38g 253a (3 4) 1 11c ( 6 2) 1 4e (4 4) 4 0 f4a 49b 1c 5d 125a 40b 1c 78d 46Possible answer: 3 4 27Possible answer: (2 4) (7 3)8(–4)2 –4 –4 16, –(4)2 – (4 4) –169(5 6) (7 8) �1514–4–18bfjn–142316cgko–24–2–2436d 6h –8l –10aeim 9182013bfjn161816 13cgko 368 8d 32h 4l 48d 27– 118–504a 2b 30c155a –9b 3c16a 16b 2c 127 1 12, 1 12, 2 6, 2 6, 3 4, 3 4,8Any appropriate divisions9a 24b 24 degrees6f 6d –6ej 20 k 14f 2l 0b 6 ( 2 1) 6d 4 ( 4 4) 3(16 4) 2 1010 weeks21632704a 32 5 75a 11.412 712 21b11.46a 412.603252b400.57a iii Prime numbers less than 20b i 252ii 3780iii 188a 10.663 418 7891200b 63b 1111 a 3.141 592 92b 0.000 009%12 a 7:25 pmb 4:00 pm on Tuesday13 a 15 120b 1214 a 90c 6b 24015 27 and 3616 a 2000b Higher as top values rounded down anddenominator rounded up.e 717 ap and q are 2 and 5. r is 3b 1518 m 5, n 3Chapter 2 – Number: Fractions, ratioand proportionc 3 6Exercise 2A1b –40 C –40 FEdexcel GCSE Maths (4th Edition)Higher Student Book – Answersc 3i0e10 510 13 6, 15 4, 72 4, 56 811 a 32 F and 212 Fd 451b xyExercise 1I22b 24h 25c 4Review questionsf 9aeImb 610 –6d 84h 14461a –4b 8a3b 4a3b2Exercise 1H513a 31b15c25d524 HarperCollinsPublishers Ltd 2015
2e 5212303154125 16f27ghgirls. 180 left-handed students altogether so 18013out of 900 15 .25930b 313510065 100 16and 25better mark.388112493710922adwhich is greater than 31 ,64 10058340which is greater than 1.of 80 50 women at least3833011 a 5 is 40 . 4 is 40 . Half-way between 8 and 30 is1919, so the mid-point fraction is 40 .b Yes as the mid-point of any two numbers a andb is (a b) 2 and adding the samedenominator is the same thing as dividing by2.Exercise 2C815110be71218cf1112112a4 4760b 724a16b 305No, one eighth is left, which is 12.5 cl, so enoughfor one cup but not two cups.41c 1 10912023d 1 30d3593 10h3 132a343a14b 5c83d454a 15b 2c 97d5353861874082597.denominator. Correct answer is 3 1210 ab 8c11f 2 12bg1151c 549de1 53of 6 12 10.40932b2566257111 After 1 day 8 of the water is left. On day 2, 8 778 6415641787is lost so total lost is 8 64 64 64 1549, so 1 – 64 is left 6412 50 1 12 75 kg. 120 – 75 45, 45 2 12 18, so18 of the 2 12 kg bags are packed.13 a 77% is about 43 . 243 is about 240, so 43 of 240 180.b Lower, as both estimates are lower than theoriginal values.11220 of 900 495, 11 of 495 90 left-handed boys.900 – 495 405 girls. 29 of 405 90 left-handedEdexcel GCSE Maths (4th Edition)Higher Student Book – Answers720eaHe has added the numerators and added thedenominators instead of using a commonPossible answer: The denominators are 4 and 5.I first find a common denominator. The lowestcommon denominator is 20 because 4 and 5 areboth factors of 20. So I am changing the fractionsto twentieths. One-quarter is the same as fivetwentieths (multiplying numerator anddenominator by 5). Two-fifths is the same aseight-twentieths (multiplying numerator anddenominator by 4). Five-twentieths plus eighttwentieths thirteen-twentieths.316512138of 200 80.1Three-quarters of 68725 1– 50 85 men at least 40. 5 of 200 120, so120 – 85 35 men under 40.so 13 out of 20 is the262540. 40 of 200 135 members at least 40. 135Exercise 2B11727720so Matt saves the greater proportion of hisearnings.71727Jon saves 90132023 8 40 , so 40 of the counters are yellow. 40of 600 25510 a because 40 Matt saves,63154 HarperCollinsPublishers Ltd 2015
Exercise 2D1a 1 1120b 1 14d 1130e6180f 167240a 12 14 miles3a 6 11208b 8 1563c 11 80d 3 113061e 7 80277f 4 396477a – 1591b Answer is negative5186512 (anticlockwise) or 7 (clockwise)127a 3527b 128d 5 179e 3 32fa 8 112091b 65 10059c 52 16017d 2 18522e 2 103881f 7 451289No, as the total is 101. She will save 20.20,which is less than the 25 it would cost to join theclub.7 29 425, 7% pay rise is an increase of 2425per year which is better than 150 12 18008a 6.125 ( 6.13)b x 0.025c y 1.175 1.29Offer A gives 360 grams for 1.40, i.e. 0.388pence per gram.Offer B gives 300 grams for 1.12, i.e 0.373pence per gram, so Offer B is the better offer.Or Offer A is 360 for 1.40 2.6 g/p, offer B is 300for 1.12 2.7 g/p, so offer B is better.63c 1 802256b 3 14 milescm10 c Both the same as 1.05 1.03 1.03 1.0511 a Shop A as 1.04 1.04 1.0816, so an 8.16%increase.c 5 5212 425.25111813 0.9 1.1 0.99 (99%)14 Area of original circle 200.96Enlarged area 200.96 x 1.6 321.536Enlarged radius 321.536 3.14 10.1192885125% increase 2.11928/8 100 26.49%518 12m²15 a Let r 10. Approx formula gives V 4000,actual gives V 4188.79, 188.79 4188.79 0.045 which is 4.5%b The value is lower as 43 π is greater than 4as π is 3.14.10 33311 a 6 (1 4 )2 18 8 cm² 6 144b 34 142525 ,14425 125 2 52 cmExercise 2F7 227722112 22 (2 7 ) 2 , 7 2 2 38 2 cm²1aei232%36.5%433.7%5a64.9%790.5%8Stacey had the greater percentage increase.Stacey: (20 14) 100 14 42.9%Calum: (17 12) 100 12 41.7%9Yes, as 38 out of 46 is over 80% (82.6%)22422 1113 Volume cuboid 22 1124 cm³,24 ( 7 3 ) 34364,33 34364 1 4 cm14 After 1 dayis left, after two days343512three days15 120 4784964and afteris left1212 540. 175 1 262 . 540 – 2621212121212 277 . 277 2 111 bags.Exercise 2E25%41.7%1.9%49.2%b 60.6%f 60%j 8.3%c 46.3%g 20.8%k 45.5%b 64.5%cd 12.5%h 10%l 10.5%10.6%1a 1.1b 1.03c 1.2d 1.07e 1.122a 0.92b 0.85c 0.75d 0.91e 0.883a 391 kgd 143.50b 824.1 cme 736 mcf253.5 g 30.2410 Let z 100. y 75, x 0.6 75 45, so x is 45%of z4a 731 md 117 minb 83.52 ge 81.7 kgcf360 cm 37.7011 Let z be 100, x 60. If x is 75% of y, y 80, so yis 80% of z.5448Edexcel GCSE Maths (4th Edition)Higher Student Book – Answers12 30% of 4800 1440. 1.2 4800 5760. 70% of5760 4032. (4032 – 1440) 1440 1.8, so the5 HarperCollinsPublishers Ltd 2015
increase in numbers owning a mobile phone is180%.13 31 26 1.19 which is a 19% increase. 31% is5% more of the total votes cast than 26%2Pie charts with these angles:a 36 , 90 , 126 , 81 , 27 b 90 , 108 , 60 , 78 , 24 c 168 , 52 , 100 , 40 3abcd4a 36b Pie charts with these angles: 50 , 50 , 80 ,60 , 60 , 40 , 20 c Student’s bar chart.d Bar chart, because easier to makecomparisons.5a6a7a8Work out the angle for ‘Don’t know’ 40 , soReview questions1 5722a 36 secondsb i 25.2 secondsii Eve3 1204 5765a 9b 13.206a 0.875b 357 32281940914 1211iii Eve5 15c10 511 a22171,227,31299,5417b22712 28%13 77%14 25%Pictogram with suitable keyBar chart correctly labelledVertical line chart correctly labelledPie chart with these angles: 60 , 165 , 45 ,15 , 75 and correctly labellede Vertical line chart. It shows the frequencies,the easiest one to draw and comparisons canbe made.Pie charts with these angles: 124 , 132 , 76 ,28 b Split of total data seen at a glance.55 b 22%40360 19Exercise 3B16 13%117 a 150 men, 100 women13Pie charts with these angles:Strings: 36 , 118 , 126 , 72 , 8 Brass: 82 , 118 , 98 , 39 , 23 b Overall, the strings candidates did better, as asmaller proportion obtained lower grades. Ahigher proportion of Brass candidates scoredvery good grades.P(Don’t know) 15 For bag A P(red) 0.1875 and for bag B P(red) 0.186 so Tomas is wrong.c 33ab 12%Chapter 3 – Statistics: Statisticaldiagrams and averagesExercise 3A1ab About 328 millionc Between 1980 and 1985d Rising steeply at first, but then leveling off.Rise in living standards, cheaper flights, morepackage holidaysb 16c 42Edexcel GCSE Maths (4th Edition)Higher Student Book – Answers6 HarperCollinsPublishers Ltd 2015
2a5abcdefb Smallest difference Wednesday and Saturday(7 ), greatest difference Friday (10 )3Median (mean could be unduly influenced byresults of very able and/or very poorcandidates)Median (mean could be unduly influenced bypocket money of students with very rich orgenerous parents)Mode (numerical value of shoe sizesirrelevant, just want most common size)Median (mean could be distorted by one ortwo extremely short or tall performers)Mode (the only way to get an ‘average’ ofnon-numerical values)Median (mean could be unduly influenced byvery low weights of premature babies)6a 20 b 25 c 46 d 43e The boys did better as they had a highermedian and their marks were less spread out.7a i 20 000ii 28 000iii 34 000b A 6% rise would increase the mean salary to 36 040, a 1500 pay increase wouldproduce a mean of 35 500.8a9Tom – mean, David – median, Mohammed –modeaMedianb ModecMean10 11.611 42.7 kg12 24b about 120c The same people keep coming back and tellothers, but new customers each weekbecome more difficult to find.Exercise 3D1ai 7bi 84No, you cannot extrapolate the data or the data islikely to change after 5 weeks2a12803a2.2, 1.7, 1.35All the temperatures were presumably higherthan 20 C.4a505a Roger 5, Brian 4c Roger 5, Brian 4 de Roger, smaller range6a 40 b 7c3f the mode, 3758The total frequency could be an even numberwhere the two middle numbers have an odddifference.9a 34b x 80 3y 104 266, so x 3y 82c x 10, y 24d 2.5Exercise 3C1a 472Modeb 53c 55d 653 ab 17c 154iii 6.4iii 8.2b 1.9c 0d 328b Better dental careb 2c 2.8b Roger 3, Brian 8Roger 5.4, Brian 4.5f Brian, better meand2e 2.5g 2.4Exercise 3E1Three possible answers: 12, 14, 14, 16, 18, 20,24; or 12, 14, 14, 16, 18, 22, 24; or 12, 14, 14,16, 20, 22, 242Edexcel GCSE Maths (4th Edition)Higher Student Book – Answersii 6ii 8.57aibicidi30 x 400 y 1005 z 107–9a100 m 120iiiiiiii 29.5158.39.438.41b 10.86 kgc 108.6 g HarperCollinsPublishers Ltd 2015
3a 175 h 200b 31%c 193.3 hoursd No the mean was under 200 and so was themode.4245a Yes, average distance is 11.7 miles per day.b Because shorter runs will be run at a fasterspeed, which will affect the average.c Yes, because the shortest could be 1 mile,the longest 25 miles.6Soundbuy; average increases are Soundbuy17.7p, Springfields 18.7p, Setco 18.2p7a 160c Modal group8The first 5 and the 10 are the wrong way round.9Find the midpoint of each group, multiply that bythe frequency and add those products. Dividethat total by the total frequency.3b 52.6 minutesd 65%a and bc Gretad about 70e about 704a10 aYes, as total in first two columns is 50, somedian is between 39 and 40.b He could be correct, as the biggest possiblerange is 69 – 20 49, and the lowest is 60 –29 31.Exercise 3F12agood positive correlation, time takenincreases with the number of press-upsb strong negative correlation, you complete acrossword more quickly as you get olderc No correlation, speed of cars on M1 is notrelated to the temperatured weak, positive correlation, older peoplegenerally have more money saved in thebankb Yes, as good positive correlation5aa and bb Little correlation, so cannot draw a line of bestfit or predict the value6a and bc about 19 cm/sd about 34 cmc about 2.4 kmd about 8 minutesEdexcel GCSE Maths (4th Edition)Higher Student Book – Answers8 HarperCollinsPublishers Ltd 2015
ee you cannot extrapolate values from a scatterdiagram or the data may change for longerjourneys7about 23 mph8Points showing a line of best fit sloping downfrom top left to bottom rightReview questions1c i 48iii 216d e.g. pie charts show proportions or they arepercentages, not actual numbers or do notknow how many students, etc.43.7 matches3a 10 t 20b 10 t 20c 19 minutes4aMargot’s tomatoes50 m 100100 m 150150 m 200200 m 250250 m 300300 m 3501223342452fa Grade 75b 100or 183602mass, m (grams)mass, mMargot’smid(grams)tomatoespoint x50 m 100100 m 150150 m 200200 m 250250 m 300300 m 350totals122334245210075125175225275325x m900287559505400137565017150estimate for the mean 171.5 gg on average Tom’s tomatoes were generallysmaller, but more consistentbecause over half the students have morethan 10 pocket money, so the mean must bemore than 10b 11.178a i Diagram Cii Diagram A iii Diagram Bb Diagram A: strong negative correlation,diagram B: no correlation, diagram C: strongpositive correlation8a/b Student’s graph as follows: Time onhorizontal axis from 0 to 20 and Distance(km) on vertical axis from 0 to 10 with thefollowing points plotted: (3, 1.7) (17, 8.3) (11,5.1) (13, 6.7) (9, 4.7) (15, 7.3) (8, 3.8) (11,5.7) (16, 8.7) (10, 5.3) and with line of best fitdrawn.c/d answers depend on student’s line of best fit5Chapter 4 – Algebra: Number andsequences6a 100 m 150b 150 m 200c 159 gdEdexcel GCSE Maths (4th Edition)Higher Student Book – AnswersExercise 4A91a 11111 11111 123 454 321,111111 111111 12 345 654 321b 99999 99999 9 999 800 001,999999 999999 999 998 000 0012a 7 8 72 7, 8 9 82 8b 50 51 2550, 60 61 36603a 1 2 3 4 5 4 3 2 1 25 52,1 2 3 4 5 6 5 4 3 2 1 36 62b 21 23 25 27 29 125 53,31 33 35 37 39 41 216 634a 1 6 15 20 15 6 1 64,1 7 21 35 35 21 7 1 128b 12 345 679 45 555 555 555,12 345 679 54 666 666 6665a 13 23 33 1 43 (1 2 3 4)2 100,13 23 33 43 53 (1 2 3 4 5)2 225 HarperCollinsPublishers Ltd 2015
b 362 372 382 392 402 412 422 432 442,552 562 572 582 592 602 612 622 632 642 6526abcdefghi71 500 501, 2 499 501, . 250 251 501, 250 501 1252503a 33rd4a i 4n 1ii 401b i 2n 1ii 201iii 99 or 101, 49th and 50thc i 3n 1ii 301d i 2n 6ii 206e i 4n 5ii 405f i 5n 1ii 501g i 3n 3ii 297h i 6n 4ii 596i i 205 – 8nii –595j i 227 – 2nii 2764th and 63rd12 345 678 987 654 321999 999 998 000 000 001122 12819081 92512 83512999 999 999(1 2 3 4 5 6 7 8 9)2 20255c 100th 499iii 101, 25thiiiiiiiiiiiiiiiiiiiiiiii100, 33rd100, 47th101, 24th101, 20th99, 34th98, 17th101, 13th99 or 101,2n 13n 1 b Getting closer to 2 (0. 6 )3Exercise 4B1ab 30thc i 0.667 774 (6dp)ii0.666 778 (6dp)d 0.666 678 (6dp), 0.666 667 (6dp)a 21, 34: add previous 2 termsb 49, 64: next square numberc 47, 76: add previous 2 terms6a 4n 15n 1215, 21, 28, 36b Getting closer to 4 (0.8)361, 91, 12741 3 2 5 3, , , ,2 5 3 7 4c i 0.796 407 (6dp)ii0.799 640 (6dp)d 0.799 964 (6dp), 0.799 9996 (7dp)55a 6, 10, 15, 21, 28b It is the sums of the natural numbers, or thenumbers in Pascal’s triangle or the triangularnumbers.6a 2, 6, 24, 7207364: Daily totals are 1, 3, 6, 10, 15, 21, 28, 36,45, 55, 66, 78 (these are the triangular numbers).Cumulative totals are: 1, 4, 10, 20, 35, 56, 84,120, 165, 220, 286, 364.897a 3058a 3 , 5, 7479a 8n 210 abcdadgj3n 1, 1514n 3, 1975n 1, 2513n 18, 168359behkEdexcel GCSE Maths (4th Edition)Higher Student Book – Answerscfil3nb 8n 13c 8nd 812 Difference is 19 – 10 9. 9 3 3 so A 3. 3 5 b 10, b –5Exercise 4D125, 29, 4n 132, 38, 6n – 437, 44, 7n 523, 27, 4n – 1–8, –18, 42 – 10n–1, –6, 29 – 5n2n 5, 1058n 6, 3948n 5, 39547 – 7n, –30323Sequence goes up in 2s; first term is 2 29n 108Because it ends up as 2n n79tha Even,Exercise 4C2ii11 If there was a common term then for some valueof n the expressions would be equal i.e. 2n 2n –1, Subtracting 2n from both sides gives 0 – 1,which is impossible.11 4n 2 3n 7 rearranges as 4n – 3n 7 2, son 9bdfhjl103n 129 and 4113, 15, 2n 133, 38, 5n 320, 23, 3n 221, 25, 4n 317, 20, 3n – 14, 0, 24 – 4nd 5c For n, 2n 1 2n 2b 69!X. There are 351 (1 2 . 25 26) lettersfrom A to Z. 3 351 1053. 1053 26 1027,1027 25 1002, so, as Z and Y are eliminated,the 1000th letter must be X.acegikc 3b i 0.666 666 777 810 No, because in the first sequence, the terms arealways one less than in the 2nd sequence1b 600 OddEvenOddEvenOddEvenOddEven OddEvenOddOddEvenEvenEvenEvenb Odd,5n 2, 248n 4, 543n 2, 14841 – 8n, –102a1 3 5 7 16 42, 1 3 5 7 9 25 52b i 100ii 563a 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 HarperCollinsPublishers Ltd 2015
b because odd odd even, odd plus even odd and even odd odd.c i a 2b, 2a 3b, 3a 5b, 5a 8b, 8a 13bii coefficient of a odd and b even, a evenand b odd, both odd4a Evend Oddg Even5ace6a i Oddii Evenb Any valid answer, e.g. x(y z)789Odd or evenOdd or evenOdd or evenb Odde Oddh OddcfiExercise 4E1OddOddOddb Odd or evend Oddf Evena 64, 128, 256, 512, 1024b i 2n 1ii 2n 1iii Evenb 4n 3c 97d 50th diagramiii 3 2na The number of zeros equals the power.b 6c i 10n – 1ii 2 10n2a 125, 216b 1 8 9, 1 8 27 36, 1 8 27 64 100 the answers are square numbers10 a 28, 36, 45, 55, 66b i 210ii 5050c You get the square numbers.11 aIf n is odd, n 1 is even.If n is even, n 1 is odd.Even times odd is always even.ii 2n must be even, so 2n 1 must be odd.b OddOddEvenEvenOddc (2n 1)2 4n2 4n 1or (2n)2 4n24n2 4n is even so adding 1 makes it odd4n2 is 2 2n2 which is even13 a 36, 49, 64, 81, 100b i n2 1ii 2n215 acded49th seta 18b 4n 2 c4a i 24b 255a 5, 8, 11, 14b i 20 cmiic 33212ii 5n 1iii 224(3n 2) cm iii 152 cm6a i 20ii 162b 79.8 km7a i 14b 668ai 5ii n iiib 20 tins9a 2nb i 100 2n–1 ml ii 1600 mlc Next sizes after super giant are 3.2l, 6.4l and12.8l with weights of 3.2 kg, 6.4 kg and 12.8kg, so the largest size is 6.4 litres.ii 3n 2iii 4118n10 The nth term is 3 , so as n gets very large, the 4 iii n2 – 1unshaded area gets smaller and smaller andeventually it will be zero; so the shaded area willeventually cover the triangle.6, 24, 96, 384, 153621, 147, 1029, 7203, 50 4212, 10, 50, 250, 12506, 60, 600, 6000, 60 00054, 162, 486, 1458, 437411 Yes, as the number of matches is 12, 21, 30, 39, which is 9n 3; so he will need 9 20 3 183 matches for the 20th step and he has 5 42 210 matches.3 2n – 1b 5 4n – 120 5n –1 or 4 5n21 3n – 1 or 7 3n24 8n – 1 or 3 8n12 a 20b 12013 Alex’s answer gives 4(n 2) 4n 8Colin’s method gives 4n 4Ed’s method gives 4(n 1) 4n 4Gail’s method gives 2 n 2(n 2) 2n 2n 4 4n 4Linear sequence is 8 12 16 20 . Which hasan nth term of 4n 4 so they are all validmethods except for Alex who forgot that thecorners overlap and should have taken the 4overlapping corners away to get 4n 8 – 4 4n 416 2 as all other primes are odd, so the sum of twoof them will be even, so could not be a prime.17 a There are many answers, 5 31 36, 7 29 36, 2 47 49 etc.b There are many answers, 49 – 36 13, 81 –64 17Edexcel GCSE Maths (4th Edition)Higher Student Book – Answersab 2n 1c 1213i12 11th triangular number is 66, 18th triangularnumber is 17114 abcdea11 HarperCollinsPublishers Ltd 2015
d ie if iExercise 4F12abcdiiii34, 4324, 3154, 6557, 53iiiiiiiia 4, 7, 12, 19, 28c 2, 6, 12, 20, 30e 2, 8, 16, 26, 38goes up 3, 4, 5, 6, etc.goes up 1, 2, 3, 4, etc.goes up 5, 6, 7, 8, etc.goes down 10, 9, 8, 7, etc.43a 2n 1b nc n(2n 1) 2n2 nd 2n2 n 14a nc n(n 1)5a Yes, constant difference is 1c Yes, constant difference is 2e Yes, constant difference is 16a 4n 4b n22c n 4n 4d n2 4n 4e The sides of the large squares are of length n 2 so the total number of squares is (n 2)2which is the same answer as c.a Table 10, 15, 21; 6, 10, 15; 16, 25, 36b i 45ii 1008n2 2n – 3 n2 n 3, gives n 6. Substitutinggives 45 for both expressions.9a Sequences are 4, 7, 14, 25, 40, 59, 82, and4, 11, 20, 31, 44, 59, 76, so 59 is the nextcommon term.b 59 is the 6th term in each sequence sosubstitute 6 into each expression. This will give59 in both cases.n2 52b 3n2 2n – 3n 1n2 1 21 n 656n26a 267a 45b nth term isb 1 21 n2 1227002502246n2 1212df12n12n son2 4 21 n – 2n2 1 21 n 2c128475 15 15 12 15 120, so no.b Nod Nof No71212eb n 1d 9900 square unitsiiiiiia 2n2 – 3n 2cb 2, 8, 18, 32, 50d 4, 9, 16, 25, 36f 4, 7, 14, 25, 40n(n 4)n2 25n – 48Front face is n2, sides faces are n (n 1) n2 n so total surface area is2 n2 4 (n2 n) 6n2 4n.9Sequence is 1, 7, 19, 37. nth term is 3n2 – 3n 1so the 100th hexagonal number is 29 701.10 a Taking the height first. There are n 1 strips mfeet long. That is m(n 1) in total.Taking the width. There are m 1 strips n feetlong. That is n(m 1) in totalm(n 1) n(m 1) mn m mn n 2mn m nb Taking the nails across a width strip. There aren 1 lots of 2 nails which is 2(n 1).There are m 1 width strips, so the total is 2(n 1)(m 1).Review questions10 a There are many answers, for example a –3and b 1.b The only solution is c 2 and d – 31No. Sequence is 7, 10, 13, 16, 19, 22, 25, 28, so the first 3 odd terms are prime but 25 is notprime.11 All values of n from 1 to 39 give a prime number.n 40 gives 1681 which equals 41 412a 4n 1b Not oddc 28th term is 1133nth term is 5n 1. 5 150 1 7514a 6n 3b No, 3n 2 generates the sequence 5, 8, 11,14, 17, 20, 23, so the even terms of thissequence are always 1 less than the terms ofthe original sequence5a 2 3n– 16a 5 6n– 17a This misprint will be corrected at reprint. Thefirst five terms in the sequence are –27, –21, –11, 3, 21. Of these terms, 3 is a prime number.b When n2 29, the expression can befactorised as 29(2 29 – 1) so is not a primenumber8a 4, 9, 18, 31, 489n 1 (n – 1) 0, n 2 (n – 2) 0, n 31)(3 – 2) 5 2 2 1 5 0.812 a (n 1)(n – 1) n2 n – n – 1 n2 – 1b n2 – 1 as 50 50 – 1 is easy to work out but 51 49 isn’tc (n 1)(n – 1) as 100 98 is easy to work outbut 992 – 1 isn’t.Exercise 4G123abcdefiiiiii36, 4935, 48
Edexcel GCSE Maths 209732 Edexcel Higher Teacher Pack title page.indd 1 3/27/15 2:38 PM Higher Student Book Answers. Browse the complete Collins catalogue at www.collins.co.uk William Collins’ dream of knowledge for all began with the pu
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aliments contenant un additif alimentaire des dispositions des alinéas a) et d) du paragraphe 4(1) ainsi que du paragraphe 6(1) de la Loi sur les aliments et drogues de même que, s'il y a lieu, des articles B.01.042, B.01.043 et B.16.007 du Règlement sur les aliments et drogues uniquement en ce qui a trait
