AQA GCSE Maths - Collins
AQA GCSEMathsHigher Student BookAnswers209732 AQA Higher Teacher Pack title page.indd 13/27/15 2:37 PM
William Collins’ dream of knowledge for all began with the publication of his first book in 1819. A self-educated millworker, he not only enriched millions of lives, but also founded a flourishing publishing house. Today, staying true tothis spirit, Collins books are packed with inspiration, innovation and practical expertise. They place you at the centreof a world of possibility and give you exactly what you need to explore it.Collins. Freedom to teachPublished by CollinsAn imprint of HarperCollinsPublishersNews Building1 London Bridge StreetLondon SE1 9GFBrowse the complete Collins catalogue atwww.collins.co.uk HarperCollinsPublishers Limited 201510 9 8 7 6 5 4 3 2 1ISBN 978-0-00-814702-0A Catalogue record for this publication is available from the British LibraryCommissioned by Lucy Rowland and Katie SergeantProject managed by Elektra Media and Hart McLeod LtdProject edited by Jennifer YongAnswers checked by Amanda DicksonIllustrations by Ann PaganuzziCover design by We Are LauraCover photographs by Procy/Shutterstock (top) and joingate/Shutterstock (bottom)Production by Rachel WeaverAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in anyform or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior writtenpermission of the Publisher or a licence permitting restricted copying in the United Kingdom issued by the CopyrightLicensing Agency Ltd., 90 Tottenham Court Road, London W1T 4LP.AcknowledgementsThe publishers gratefully acknowledge the permissions granted to reproduce copyright material in this book. Everyeffort has been made to contact the holders of copyright material, but if any have been inadvertently overlooked, thepublisher will be pleased to make the necessary arrangements at the first opportunity.
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:32Exercise 1CAnswers1adgj50 0002000.31000b 90 000e 0.5h 10c 30 000f 0.006i 0.052adgj56 0001.74.10.80b 80 000e 0.066h 8.0c 31 000f 0.46i 1.03a 60 000d 110g 0.3b 5300e 9h 0.7c 89.7f 1.14a 65, 74b 95, 149c 950, 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 – assumes 3penguins 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.Chapter 1 – Number: Basic numberExercise 1A1a 6000b 5 cans cost 1.95, so 6 cans cost 1.95.32 5 6 2. Cost is 10.53.2a3a 38b Coach price for adults 8, coach price forjuniors 4, money for coaches raised bytickets 12 400, cost of coaches 12 160,profit 240288b 164(18.81.) Kirsty can buy 18 models.5 8.40 per year, 70p per copy6 45071583 weeks9 248.7510 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 forgotten toadd a zero on the second line of themultiplication, it should be 1530.Exercise 1B1adgj4.694.857.10.1behk0.08602.16.9044.0022a 0.028b 0.093a 35, 35.04, 0.04c 60, 59.67, 0.33cfilc 50.9645.716671.7613.7860.060 0001520045b 120 000e 140h 0.08c 10 000f 100i 0.092a 5d 600g 400b 25e 2000h 8000c 3000f 5000i 4 000 000330 90 000 2 700 000600 8000 4 800 0005000 4000 20 000 000200 000 700 140 000 0004a 54 400b 16 000e 6.951400 milliond 450e 0.626His answer is correct but he had one too manyzeros on each value, which cancel each other out.Matt wrote 600,000 rather than 60,000 and 2000rather than 200. The two mistakes cancelledthemselves out due to the zeros involved.7a Value of the money is about 66 000 000 0.2 13 200 000, so it is enough to buy the yacht.b Weight is 66 000 000 5 330 000 000 grams 330 tonnes, so they do not weigh as much asthe yacht.81420 000 000 000 64 000 000 22 200, so theNational Debt per person is approximately 22 200.a 185a 280 b 126a 572 b i 5.727a Incorrect as should end in the digit 2b Incorrect since 9 5 45, so answer must beless than 4583009a 27b i 27ii 1.43iiadgjd 124c 2401d 46.512b 16, 18.24, 2.24d 140, 140.58, 0.58b 140 c 1.4Exercise 1D0.027iii22.88iii 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 the previousrecord does not convey any useful information.718
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:32Exercise 1E1a 35 000d 5b 15 000e 1200c 960f 5002a 39 700d 4.44b 17 000e 1130c 933f 5503a 1.74 md 83 C2g 14 mb 6 minutese 35 000 people4a 10b 1c35a 8.79b 1.03c3.07682 F, 5 km, 110 min, 43 000 people, 6.2 seconds,67th, 1788, 15 practice walks, 5 secondsThe 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 15.5 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 16312 Approximately 50013 1 million pounds is 20 million 5p coins. 20 000 000 4.2 84 000 000 grams 84 tonnes, so 5 lorriesneeded.14 22.5 C – 18.2 C 4.3 Celsius degrees15 a ib ic i227.571 428 57 ii16.896 516 39 ii18 672.586 16 ii27.616.918 70016 a 37.5 48.6 40 50 2000 21.7 103.6 20 100 2000 985 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 1824.07417 149 000 000 300 000 496.67 500 seconds20 26.8 3.1 27 3 936.2 3.9 36 4 9. Second calculation must be biggest as first issmaller than 27 3 and second is bigger than36 4.Exercise 1F1a 12g 16b 9h 10c 6i 18d 13j 17e 15f 14k 8 or 16 l 21Factor of 5682811 2, 3 and 1212 a 1, 64, 729, 4096, 15 625b 1, 8, 27, 64, 125c a3 a ad Square numbers13 a 0.2e 1.5b 0.5f 2.1c 0.6g 0.8d 0.9h 0.714 The answers will depend on the approximationsmade. Your answers should be to the same orderas these.a 60b 1500c 150Exercise 1G1abcdefg2aceg31, 2, 3, 2 , 5, 2 3, 7, 2 , 3 , 2 5, 11, 2 3, 13,4222 7, 3 5, 2 , 17, 2 3 , 19, 2 5, 3 7, 2 11,323223, 2 3, 5 , 2 13, 3 , 2 7, 29, 2 3 5, 31,5222 , 3 11, 2 17, 5 7, 2 3 , 37, 2 19, 3 13,3222 5, 41, 2 3 7, 43, 2 11, 3 5, 2 23, 47,4222 3, 7 , 2 518 a 58.9 4.8 60 5 300b Lower as both values are rounded up to get theestimate.19 Macau’s population density is approximately 710000 times the population density of Greenland.Square number6449Cube numberMultiple of 74 abde71984 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 5284 2 3 722180 2 3 53280 2 5 7250 2 522b 100 22 52d 220 2 5 117f 128 2322 is always the only prime factor64, 128c 81, 243, 729256, 1024, 409623456234563, 3 , 3 , 3 , 3 , 3 ; 4, 4 , 4 , 4 , 4 , 42
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:32512 –460 F2a 2 2 3 5b 2 3 534c 120 2 3 5, 240 2 3 5,5480 2 3 52223Exercise 1J36a 7 11 13101010c 7 11 137Because 3 is not a factor of 40 so it does not divideexactly.8a 2, b 79a 2ab a 4b2b 7 11 1333Exercise 1H1a 20e 10c 6g 242They are the two numbers multiplied together.3a 84No. 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 least commonmultiple.b 18d 28h 30c 12b 105f 54d 305a 168e 9663 packs of cheese slices and 4 packs of bread rolls7a 88a918 and 24b 7c 84g 75c 4ii and iii2 2d 84h 144d 16b10 a 6x ye 14f 9iiib xyExercise 1I12a –42a 38g 253a (3 4) 1 11c ( 6 2) 1 4e (4 4) 4 04a 49b 1c 5d 125a 40b 1c 78d 46Possible answer: 3 4 27Possible answer: (2 4) (7 3)8(–4) –4 –4 16, –(4) – (4 4) –169(5 6) (7 8) 93 2b 8a b 4a bb 56f 151– 118–50b 24h 25c 4d 45c 3i 0e6f 6d –6ej 20 k 14f 2l 0b 6 ( 2 1) 6d 4 ( 4 4) 3f (16 4) 2 102210 –6Review questions110 weeks21632704a 3 5 75a 11.412 712 21b11.46a 412.603252b400.57a iii Prime numbers less than 20b i 252ii 3780iii 188a 10.663 418 78912002b 63b 36d 6h –8l –1012 a 7:30 pm Monday (7:45 pm on Town Hall Clock)aeim 9182013bfjn161816 13cgko 368 8d 32h 4l 4813 a 2 3 5 5b 2 314 a 90c 610 511 a 3.141 592 92b 0.000 009%b 6:00 pm on Tuesday (7:00 pm on Town Hallclock)43b 63b 240215 27 and 364a 2b 30c155a –9b 3c116 a 2000b Higher as top values rounded down anddenominator rounded up.6a 16b 2c 1217 a p and q are 2 and 5. r is 37 1 12, 1 12, 2 6, 2 6, 3 4, 3 4,8Any appropriate divisions9a 24b 24 degreesd 27e 718 m 5, n 3c 3 610 56 8, 72 4, 15 4, 13 611 a 32 F and 212 Fb –40 C –40 F720b 15
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:32Chapter 2 – Number: Fractions, ratioand proportionFive-twentieths plus eight-twentieths thirteentwentieths.8Exercise 2A1a13e 522123031541251120b15f16c25d524g27h13315231717 8 40 , so 40 of the counters are yellow. 40 of600 2552710 a because 40 52 1which is greater than 1.5230902740 3135100 651003 and1625of 200 135 members at least 40. 135 – 50 720which is greater than1385 men at least 40. 5 of 200 120, so 120 – 85 35 men under 40., so 641008133011 a 5 is 40 . 4 is 40 . Half-way between 8 and 30 isso 13 out of 20 is the1919, so the mid-point fraction is 40 .b Yes as the mid-point of any two numbers a and bis (a b) 2 and adding the same denominatoris the same thing as dividing by 2.73881124Exercise 2C937131d 10bc1112e18f1122Three-quarters of 683a4 4760b 724a16b 305No, one eighth is left, which is 12.5 cl, so enoughfor one cup but not two cups.6He has added the numerators and added thedenominators instead of using a common41c 1 109120denominator. Correct answer is23d 1 3073 123593 10h3 13e2a341b 1 153a14b 5c83d454a 15b 2c 97d53538618740825ac11f 2 12gc 5Exercise 2B712db 898157201651210 227340b 5 of 200 80. 8 of 80 50 women at least 40.better mark.aof 405 90 left-handedout of 900 15 .Matt saves the greater proportion of his earnings.129girls. 180 left-handed students altogether so 1809Matt saves,6of 495 90 left-handed boys.900 – 495 405 girls. 52Jon saves1320211of 900 495,949de 1 53of 6 12 10.4010 a932b256625.7Possible answer: The denominators are 4 and 5. Ifirst find a common denominator. The lowestcommon denominator is 20 because 4 and 5 areboth factors of 20. So I am changing the fractions totwentieths. One-quarter is the same as fivetwentieths (multiplying numerator and denominatorby 5). Two-fifths is the same as eight-twentieths(multiplying numerator and denominator by 4).7111 After 1 day 8 of the water is left. On day 2, 8 8 764178715is lost so total lost is 8 64 64 64 64 , so15491 – 64 is left 6412 50 1 12 75 kg. 120 – 75 45, 45 2 12 18, so72118 of the 2 12 kg bags are packed.
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:333413 a 77% is about. 243 is about 240, so34of240 180.b Lower, as both estimates are lower than theoriginal values.4a 731 md 117 min54486No, as the total is 101. She will save 20.20,which is less than the 25 it would cost to join theclub.77% pay rise is an increase of 1925 per year whichis 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. 0.388 penceper gram.Offer B gives 300 grams for 1.12, i.e 0.373 penceper 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.Exercise 2D1a 1 1120b 1 14d 1130e63c 1 806180167240f2a 12 14 milesb 3 14 miles3a 6 11208b 8 1563c 11 80d 3 113061e 7 80277f 4 396477a – 1591b Answer is negative51118 12cm657(anticlockwise) or 12(clockwise)127a 5327b 128c 5 52d 5 179e 3 3211f 18a 8 112091b 65 10059c 52 16017d 2 18522e 2 103881f 7 4512b 83.52 ge 81.7 kgc 360 cmf 37.7010 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.12 425.258913 0.9 1.1 0.99 (99%)14 Area of original circle 200.96Enlarged area 200.96 1.6 321.536Enlarged radius 321.536 3.14 10.1192885125% increase 2.11928/8 100 26.49%15 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 4 asπ is 3.14.518 12m²10 33 2311 a 6 (1 4 ) 18 8 cm² 6 144b 34 14,25251442572222Exercise 2F 125 2 52 cm771a 25%e 41.7%i 1.9%232%36.5%433.7%5a 49.2%64.9%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%)112 22 (2 7 ) 2 , 7 2 2 38 2 cm²22413 Volume cuboid 22 11cm³, 22 11 ( 7 3) 242434364,3 3436414 After 1 daythree days3 1 4 cm78343512is left, after two days4964and afteris left15 120 4 12 540. 175 1 12 262 12 . 540 – 262 12 277 12 . 277 12 2 12 111 bags.Exercise 2E1a 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 mc 253.5 gf 30.24b 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%10 Let z 100. y 75, x 0.6 75 45, so x is 45%of z11 Let z be 100, x 60. If x is 75% of y, y 80, so y is80% of z.722
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:3312 30% of 4800 1440. 1.2 4800 5760. 70% of5760 4032. (4032 – 1440) 1440 1.8, so theincrease in numbers owning a mobile phone is180%.13 31 26 1.19 which is a 19% increase. 31% is 5%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 0.875b7 32281940914 121135iii Eve5 15c10 511 a5417,31299,227,22171b22712 28%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, theeasiest one to draw and comparisons can bemade.Pie charts with these angles: 124 , 132 , 76 ,28 b Split of total data seen at a glance.55 b 2213%Pie 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) 13 77%c 3340360 1914 25%15 For bag A P(red) 0.1875 and for bag B P(red) 0.186 so Tomas is wrong.Exercise 3B1a16 13%17 a 150 men, 100 womenb 12%Chapter 3 – Statistics: Statisticaldiagrams and averagesExercise 3A1ab About 328 millionc Between 1980 and 1985d Rising steeply at first, but then leveling off. Risein living standards, cheaper flights, morepackage holidaysb 16c 42723
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:332a5a i 20 000ii 28 000iii 34 000b A 6% rise would increase the mean salary to 36 040, a 1500 pay increase would producea mean of 35 500.6a Median7Tom – mean, David – median, Mohammed – mode811.6942.7 kgb Modec Mean10 24Exercise 3Db Smallest difference Wednesday and Saturday(7 ), greatest difference Friday (10 )3ab about 120c The same people keep coming back and tellothers, but new customers each week becomemore difficult to find.4No, you cannot extrapolate the data or the data islikely to change after 5 weeks5All the temperatures were presumably higher than20 C.1aibi2a12803a2.2, 1.7, 1.34a505a Roger 5, Brian 4c Roger 5, Brian 4e Roger, smaller range6a 40e 2.5758The 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 2.5a 472Mode3Three possible answers: 12, 14, 14, 16, 18, 20, 24;or 12, 14, 14, 16, 18, 22, 24; or 12, 14, 14, 16, 20,22, 244abcdefb 53c 55d 65Median (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 sizes irrelevant,just want most common size)Median (mean could be distorted by one or twoextremely short or tall performers)Mode (the only way to get an ‘average’ of nonnumerical values)Median (mean could be unduly influenced byvery low weights of premature babies)ii 6ii 8.5iiiiiib 1.96.48.2c 0d 328b Better dental careb 2c 2.8b Roger 3, Brian 8d Roger 5.4, Brian 4.5f Brian, better meanb 7c 3f the mode, 3d 2g 2.4Exercise 3E1aibicidi30 x 400 y 1005 z 107–92a100 m 1203a 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, thelongest 25 miles.6Soundbuy; average increases are Soundbuy 17.7p,Springfields 18.7p, Setco 18.2p7a 160c Modal group8The first 5 and the 10 are the wrong way round.Exercise 3C178724iiiiiiii29.5158.39.438.41b 10.86 kgc 108.6 gb 52.6 minutesd 65%
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:339Find the midpoint of each group, multiply that bythe frequency and add those products. Divide thattotal by the total frequency.4a10 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 taken increaseswith 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 the bankb 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 cm3a and bc about 2.4 kmd about 8 minutese you cannot extrapolate values from a scatterdiagram or the data may change for longerjourneysc Gretad about 70e about 707about 23 mph8Points showing a line of best fit sloping down fromtop left to bottom right725
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:33eReview questionsmass, m (grams)Margot’s tomatoes150 m 100100 m 150150 m 200200 m 250250 m 300300 m 3501223342452a Grade 75b 100or 18360c i 48iii 216d e.g. pie charts show proportions or they arepercentages, not actual numbers or do notknow how many students, etc.243.7 matches3a 10 t 20b 10 t 20c 19 minutes4afbecause over half the students have more than 10 pocket money, so the mean must be morethan 10b 11.135mass, 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 had a smaller massand were therefore probably smaller in size6a 100 m 150b 150 m 200c 159 gd7a i Diagram Cii Diagram Aiii Diagram Bb Diagram A: strong negative correlation, diagramB: no correlation, diagram C: strong positivecorrelation8a/b Student’s graph as follows: Time on horizontalaxis from 0 to 20 and Distance (km) on verticalaxis from 0 to 10 with the following pointsplotted: (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 fit drawn.c/d answers depend on student’s line of best fitChapter 4 – Algebra: Number andsequencesExercise 4A1a 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 7 7, 8 9 8 8b 50 51 2550, 60 61 36603a 1 2 3 4 5 4 3 2 1 25 5 ,1 2 3 4 5 6 5 4 3 2 1 36 263b 21 23 25 27 29 125 5 ,331 33 35 37 39 41 216 64a 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 1 2 3 4 (1 2 3 4) 100,3333321 2 3 4 5 (1 2 3 4 5) 225222222222b 36 37 38 39 40 41 42 43 44 ,72622233332
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:3322222222b 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 63rd55 56 57 58 59 60 61 62 22263 64 656abcdefghi12 345 678 987 654 321999 999 998 000 000 001212 128190281 93512 8512999 999 9992(1 2 3 4 5 6 7 8 9) 202571 500 501, 2 499 501, . 250 251 501,250 501 1252505iiiiiiiiiiiiiiiiiiiiiiii100, 33rd100, 47th101, 24th101, 20th99, 34th98, 17th101, 13th99 or 101,a 2n 13n 1 b Getting closer to 2 (0. 6 )3c i 0.667 774 (6dp)ii 0.666 778 (6dp)d 0.666 678 (6dp), 0.666 667 (6dp)Exercise 4B12a 21, 34: add previous 2 termsb 49, 64: next square numberc 47, 76: add previous 2 terms61, 91, 12741 3 2 5 3, , , ,2 5 3 7 4a 4n 15n 1b Getting closer to 4 (0.8)15, 21, 28, 363565c i 0.796 407 (6dp)ii 0.799 640 (6dp)d 0.799 964 (6dp), 0.799 9996 (7dp)a 6, 10, 15, 21, 28b It is the sums of the natural numbers, or thenumbers in Pascal’s triangle or the triangularnumbers.7a 3058a 3 , 5, 747a 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.b i 0.666 666 777 8X. There are 351 (1 2 . 25 26) letters fromA to Z. 3 351 1053. 1053 26 1027, 1027 25 1002, so, as Z and Y are eliminated, the1000th letter must be X.929 and 4110 No, because in the first sequence, the terms arealways one less than in the 2nd sequence11 4n 2 3n 7 rearranges as 4n – 3n 7 2, son 99a 8n 210 abcd213, 15, 2n 133, 38, 5n 320, 23, 3n 221, 25, 4n 317, 20, 3n – 14, 0, 24 – 4nadgj3n 1, 1514n 3, 1975n 1, 2513n 18, 1683a 33rd4ai4n 1bdfhjlbehkb 30thii 401cfil5n 2, 248n 4, 543n 2, 14841 – 8n, –359233nb 8n 13c 8nd 811 If there was a common term then for some value ofn the expressions would be equal i.e. 2n 2n – 1,Subtracting 2n from both sides gives 0 – 1, whichis impossible.12 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, –303iiSequence goes up in 2s; first term is 2 29n 108Because it ends up as 2n n79tha Even,Exercise 4Cacegikd 5c For n, 2n 1 2n 2b 69!8c 3103n 161b 600 OddEvenOddEvenOddEvenOddEven OddEvenOddOddEvenEvenEvenEvenb Odd,22a3a 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144b because odd odd even, odd plus even oddand even odd odd.c i a 2b, 2a 3b, 3a 5b, 5a 8b, 8a 13bc 100th 499iii 101, 25th7271 3 5 7 16 4 , 1 3 5 7 9 252 5b i 100ii 56
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:33ii4a Evend Oddg Even5aceb Odde Oddh OddOdd or evenOdd or evenOdd or evencfia i Oddii Evenb Any valid answer, e.g. x(y z)7a 64, 128, 256, 512, 1024nnb i 2 1ii 2 19OddOddOdd2b Odd or evend Oddf Even68iii Eveniii 3 2na The number of zeros equals the power.b 6nnc i 10 – 1ii 2 10a 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 OddOddEvenEvenOdd22c (2n 1) 4n 4n 122or (2n) 4n24n 4n is even so adding 1 makes it odd224n is 2 2n which is evend49th set3a 18b4n 24a i 24b 25ii5n 15a 5, 8, 11, 14b i 20 cm ii (3n 2) cm iii 152 cmc 3326a i 20ii 162b 79.8 km7a i 14b 668ai 5ii nb 20 tins9a 2n–1b i 100 2 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 12.8 kg,so the largest size is 6.4 litres.n–1n–1iii41iii18n 4 unshaded area gets smaller and smaller andeventually it will be zero; so the shaded area willeventually cover the triangle.11 Yes, as the number of matches is 12, 21, 30, 39, which is 9n 3; so he will need 9 20 3 183matches for the 20th step and he has 5 42 210matches.iii n – 1nc 20 5or 4 5n–1ne 24 8or 3 816 2 as all other primes are odd, so the sum of two ofthem 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 17Exercise 4Eiii 224n2n–1c 1210 The nth term is 3 , so as n gets very large, the6, 24, 96, 384, 153621, 147, 1029, 7203, 50 4212, 10, 50, 250, 12506, 60, 600, 6000, 60 00054, 162, 486, 1458, 437415 a 3 2b 5 4n–1nd 21 3or 7 3ii 3n 212 a 2013 a 36, 49, 64, 81, 10022b i n 1ii 2n1ab 2n 1c 121i12 11th triangular number is 66, 18th triangularnumber is 17114 abcdeb 4n 3c 97d 50th diagramcoefficient of a odd and b even, a even andb odd, both oddb 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 valid methodsexcept for Alex who forgot that the corners overlapand should have taken the 4 overlapping cornersaway to get 4n 8 – 4 4n 4Exercise 4F1abcd2a 4, 7, 12, 19, 28c 2, 6, 12, 20, 30e 2, 8, 16, 26, 383a 2n 1b n2c n(2n 1) 2n n2d 2n n 1a728iiii34, 4324, 3154, 6557, 53iiiiiiiigoes 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.b 2, 8, 18, 32, 50d 4, 9, 16, 25, 36f 4, 7, 14, 25, 40
AQA GCSE Maths Higher SB Answers.pdf March 22, 2017 13:30:334a nc n(n 1)b n 1d 9900 square units5a Yes, constant difference is 1c Yes, constant difference is 2e Yes, constant difference is 16a 4n 4b n22c n 4n 4d n 4n 4e The sides of the large squares are of length n 22so the total number of squares is (n 2) whichis the same answer as c.b nth term isb Nod Nof No7a Table 10, 15, 21; 6, 10, 15; 16, 25, 36b i 45ii 1008n 2n – 3 n n 3, gives n 6. Substitutinggives 45 for both expressions.9a Sequences are 4, 7, 14, 25, 40, 59, 82, and 4,11, 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.210 a There are many answers, for example a –3and b 1.b The only solution is c 2 and d – 322Exercise 4G12342abcdefi 36, 49i 35, 48i 38, 51i 39, 52i 34, 47i 35, 46iiiiiiiiiiiin2n –12n 22n 32n –22n 10abcdei 37, 50i 35, 48i 41, 54i 50, 65i 48, 63iiiiiiiiii(n 1) 12(n 1) – 12(n 1) 52(n 2) 12(n 2) – 1abcdefi n 4i 3n 22i (n 1) – 1i n(n 4)2i n 2i 5n – 4iiiiiiiiiiii2504152260027002502246221212ce2n 521212d2n 1 21 n 66n6a 267a 45b 1122n 15 15 12 1522Front face is n , sides faces are n (n 1) n nso total surface area is2222 n 4 (n n) 6n 4n.9Sequence is 1, 7, 19, 37. nth term is 3n – 3n 1 sothe 100th hexagonal number is 29 701.210 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 is2(n 1)(m 1).Review questions1No. Sequence is 7, 10, 13, 16, 19, 22, 25, 28, sothe first 3 odd terms are prime but 25 is not prime.2 a 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 The first five terms in the sequence are –27, –21, –11, 3, 21. Of these terms, 3 is a primenumber.2b When n 29, the expression can be factorisedas 29(2 29 – 1) so is not a prime number8a 4, 9, 18, 31, 489n 1 (n – 1) 0, n 2 (n – 2) 0, n 3(3 – 2) 5 2 2 1 5 0.8b Not an even numberb 8th term is 1 399 680f12nb 2, 2, 3, 5, 82(3 – 1)2211 a nth term is n 2n, 12 12 2 12 168, soyes enough squaresb 40 40 2 40 16802212 2n – n, 2 20 – 20 7802n 4 21 n – 213 The sequence of dots is5, 15, 30, 50, nca b2a2n 1 21 n 2251210 2n – 2n 3b 3n 2n – 3n 1n so22a 2n – 3n 212811 All values of n from 1 to 39 give a prime number.n 40 gives 1681 which equals 41 4112 a (n 1)(n – 1) n n – n – 1 n – 12b n –
AQA GCSE Maths 209732 AQA Higher Teacher Pack title page.indd 1 3/27/15 2:37 PM Higher Student Book Answers Higher Student Book Answers. Browse the complete Collins catalogue at www.collins.co.uk William Collins' dream of knowledge for all began with the publication of his first book in 1819. A self-educated mill
GCSE AQA Revision † Biology GCSE AQA Revision † Biology GCSE AQA Revision † Biology GCSE AQA Revision † Biology GCSE AQA Revision † Biology . Digestion Blood and the Circulation Non-Communicable Diseases Transport in Plants Pathogens and Disease What are the three main types of digestive enzymes? What are the three different types of blood vessel? What two treatments can be used for .
GCSE AQA Revision † French GCSE AQA Revision † French GCSE AQA Revision † French GCSE AQA Revision † French GCSE AQA Revision † French. Music Cinema and TV Food Eating Out Sport What tense is used in this sentence? J’ai t
KWM-2, Collins KWM-2A, Collins 30L-I, Collins 75S1, Collins 75A3, Collins 75 S 3C, Collins 7552, Collins 75S3A, Collins 75A2, Collins 32S2, Collins 32S3, Collins PM-2. flammarlund SP-600, Hammarlund HQ-140XA, Hammarlund
GCSE Computer Science - OCR GCSE Geography - AQA GCSE History - AQA GCSE Triple Science [Biology, Chemistry & Physics] - AQA. Computer Science OCR GCSE For More Information Contact: Mrs Roche at the Academy. This GCSE specification encourages candidates to explore how
AQA Maths GCSE GCSE Mathematics: 90 maths problem solving questions The new Maths GCSE has an increased focus on problem solving. So that you can help your students practice this type of question, we’ve refreshed our 90 maths problems resource so that it’s relevant to the new GCSE.
(CGP GCSE Maths 9-1 Revision) 4 GCSE Maths Edexcel Exam Practice Workbook: Foundation – for the Grade 9-1 Course (with Answers) (CGP GCSE Maths 9-1 Revision) 4 Psychology GCSE AQA Book Image Book Name Price AQA GCSE 9-1 Psychology All-in-One Revision and Practice (Collin
14 GCSE Maths in a Week (Foundation) GCSE MATHS EXAM STRUCTURE Your GCSE Maths (Foundation) examination is comprised ofthree sections: Paper 1: Non-Calculator 1 hour and 30 minutes 33.3% of GCSE Marks out of 80 Paper 2: Calculator 1 hour and 30 minutes 33.3% of GCSE Marks out of 80 Paper 3: Calculator 1 hour and 30 minutes 33.3% of GCSE Marks .
Anatomy 2-5 Indications 5 Contra-indications 5 General preparation 6 Landmarks 6-7 Performing the block 7-8 Complications 8 Trouble shooting 9 Summary 9 References 10 Appendix 1 11. 6/10/2016 Fascia Iliaca Compartment Block: Landmark Approach 2 FASCIA ILIACA COMPARTMENT BLOCK: LANDMARK APPROACH INTRODUCTION Neck of femur fracture affect an estimated 65,000 patients per annum in England in .
