CAMBRIDGE IGCSETM MATHEMATICS:CORE EXTENDED COURSEBOOKAnswersThe questions and example answers that appear in this resource were written by the author In examination,the way marks wouldbe awarded to answers like these may be differentChapter 1Getting startedExercise 1.11 a Student answers will vary based on what1a{3,4,6,11,16,19,25}they already know and feel confidentb{46,16doing.{3,11,19,25}b Some students will select the things theyare less confident in,but other may selectthings they enjoy doing or are good at.e{-4,-1}Encourage them to say why they havefmade each selection.2 a There are many possible answers for each{416,25}value.For example,(a)could be 92orh{3,11,19}9(2+7)or 8 x 10+1.Let students useicalculators to check that each other's clueswork.a{109,111,113,115}b Twenty-one thousand,eight hundred and6Various,e.g.{2010,2012,2014,2016)orthirty-seven{2020,2022,2024,2026}etc.{995,997,999,1001,1003.10053a93d{1,4,9,16,25}b122eVarious,e.g.{0.49,048,0.47,0.46,0.45}c75or{0.40.3,02,0.1}f.137211137a EvenbEvenOdd14000010019OddaAny real-world measurement problemsEveninvolve a level of approximation,as doEvenproblems where you have to work out ifyou have enough money,or have catered4aA perfect number is one where the sum ofenough food,estimated times of arrivals,its factors,including 1,but excluding theestimates for building materials and costsnumber itself,is that number.6 is perfectof doing different jobs.number because 1 +2 +3=6.b Encourage students to share ideas andbA palindromic number is a'symmetrical'discuss their own methods of decidingnumber like 16461 that remains the sameAnswers will vary,but could include thatwhen its digits are reversed.estimating allows you find errors andA narcissistic number is one that is thejudge the size an answer should be,avoidsum of its own digits each raised to themistakes due to button push or placepower of the number of digits,value errors.eg.371=33+73+13Cambridge IGCSETM Mathematics-Morrison,Hamshaw Cambridge University Press Assessment 2023CAMBRIDGE IGCSETM MATHEMATICS:CORE EXTENDED COURSEBOOKExercise 1.2c75,150,225,300,375,450,525,600,675,7501a19<45d114,228,342,456,570,684,798,912,b12+18=301026.1140e299,598,897,1196,1495,1794,2093,d0.8≠8.02392,2691,2990e-34<2×-16千350,700,1050,1400,1750,2100,2450，2800,3150,350091012,2024,3036,4048,5060,6072,7084,9x≤-458096.9108.10120h is approximately equal to 3.14h9123,18246,27369,36492,45615,i5.1>5.0154738,63861,72984,82107,91230j3+4≠3×4k12--12)>12b50,100,150,200,250,300,350c4100,4200,4300,4400,4500,4600,4700,m 12x is approximately equal to-404800.49002 a False4576,396,792,1164b True5816and1116c Trued TrueExercise 1.4e True1a10f Trueb40g Falsec12h Trued 9i Truee385j Truek False2 No-the common multiples are infinite.I Falsem TrueExercise 1.5n False1aF4=1,2,43 Students'own discussions.Exercise 1.3cFg=1,2,4,8dF1=1,111a2,4,6,8,10b3,69,12,15fF12=1,2,3,4,6129F35=1,5,7,35d8,16,24,32,40hF40=1,2,4,5,8,10,20,401F52=1,3,19,57f10,20,30,40,50jFg0=1,2,3,5,6,9,10,15,18,30,45,90912,24,36,4860kF1m=1,2,4,5,10,20,25,50100h100,200,300,400,5001F12=1,2,3,4,6,11,12,22,33,44,66,132mF16o=1,2,4,5,8,10,16,20,32,40,80,160290nF1ss=1,3,9,17,51,153b44,88,132,176,220,264308.352.396.0F60=1,2,3,4,5,68,9,10,12,15,18,20,44024,30,36,40,45,60,72,90,120,180,360Cambridge IGCSETM Mathematics-Morrison,Hamshaw Cambridge University Press Assessment 2023CAMBRIDGE IGCSETM MATHEMATICS:CORE EXTENDED COURSEBOOKa 4conjecture is much more difficult to proveb45and that the method used to prove theweak conjecture won't work for the strongc14one.d22e 82 a The prime number theorem shows thatprime numbers become less common as3 a falsethey get bigger using the rate at whichb trueprime numbers occur.c truebYes.Euclid (325-265BCE)proved thered trueare infinitely many prime numbers.Thisproof is known as Euclid's theorem.e truef true3 If you write prime backwards you get emirp.An emirp is a prime number that when youg truewrite it backwards gives you a different prime.h falseFor example,17 and 71.The first few emirps4 The smallest factor is 1 and the largest factorare:13,17,31,37,71,73,79,97,107,113,149.157.is the number itselfExercise 1.7Exercise 1.6121a32143a6,8,9,1012,14,15,16,18,20,21,22,c 524,25,26,27,28d14b6=3+3,8=3+5,9=2+7,10=5+5,12=5+7,14=3+11,92215=2+13,16=5+11,h 618=5+13,20=3+17,2 a Any two from:4,6,10,1421=2+19,22=5+17.b 12 and 18 are the only possible two,less24=5+19or17+7,25=2+23,than 2026=3 23 or 13 13,27 not possible,28=5+233I because each prime number has only 1 anditself as factors4 3 and 5,5 and 7,11 and 13,17 and 19,29 and418m31,41and43,59and61,71and735 20 students149 is prime.Determined by trial division byall integers from 2 to 1496 150 braceletsWhy do mathematicians find prime numbersExercise 1.8exciting?1a30=2×3×51 a Every even integer greater than 2 can beb24=2×2×2×3written as the sum of two prime numbersc100=2×2×5×5b The weak conjecture is that every oddd225=3×3×5×5integer greater than 5 can be written ase360=2×2×2×3×3×5the sum of three odd prime numbers.f504=2×2×2×3×3×7Harald Helfgott's proof uses complicatedmathematics to prove that this is correct.g650=2×5×5×13His proof is largely accepted by theh1125=3×3×5×5×5mathematics community but they alsoi756=2×2×3×3×3×79240=2×2×2×3×5×7×11Cambridge IGCSETM Mathematics-Morrison,Hamshaw Cambridge University Press Assessment 2023