As the dice is fair all the outcomes are equally likely. In theory one in every six throws would be a 6, but this is unlikely to happen in reality.

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1 Camridge Essentials Mathematis Core 8 S. Answers S. Answers a 0 (unless you are answering this on a Saturday!) 2 Pupils own examples 3 a, 2, 3, 4, 5, 6 Yes As the die is fair all the outomes are equally likely. 4 a 6 0 d No e In theory one in every six throws would e a 6, ut this is unlikely to happen in reality. 5 a = = 0 5 d 0 e 6 3 = a d This method is fair as everyone has an equal hane of eing hosen, ut some may not want to e the rep. 7 a B There are the same total numer of squares on all three ards, ut there are five shaded squares on B whereas there are only four shaded squares on A and C. 8 Pupils own solutions 9 a No No, the oin would have to e thrown many times more Original Material Camridge University Press 2009

2 Camridge Essentials Mathematis Core 8 S.2 Answers S.2 Answers a i 2 = 8 4 ii 3 8 iii 8 3 iv 5 8 Proailities add to eause all possile outomes have een inluded 2 a d 0.5 e , a 3 2 5, 0.3 or 30% =, 0.2 or 20% =, 0.5 or 50% a = 6 5, or add together the proailities of soring, 2, 3, 4 or 5 6 a d 2 22 e 2 = 22 7 a 8 2 = d 7 8 e 6 3 = a 5 = = = 45 9 d a 26 = = = 52 4 d 26 = 52 2 e 48 2 = 52 3 f 40 0 = a 0.8 No, the us ould arrive early. 0.5 Original Material Camridge University Press 2009

3 Camridge Essentials Mathematis Core 8 S.2 Answers 2 a d 3 Seond oin a 4 2 H T First oin H HH HT T TH TT 4 Main ourse pasta ake pasta ake hiken korma hiken korma veggie urger veggie urger Pudding fruit salad sponge pudding fruit salad sponge pudding fruit salad sponge pudding 5 sausage and aon sausage and sramled eggs sausage and eans aon and eans aon and sramled eggs sramled eggs and eans 6 Window Window 2 red red red green green green lue lue lue red green lue red green lue red green lue Original Material Camridge University Press

4 Camridge Essentials Mathematis Core 8 S.2 Answers 7 a Die Coin H H, H, 2 H, 3 H, 4 H, 5 H, 6 T T, T, 2 T, 3 T, 4 T, 5 T, d 2 3 = 4 e 2 = a The most likely outome is 7 i 6 = 36 6 ii 30 5 = 36 6 iii 36 3 = 2 9 a i 2p 0p 20p 8 H H H H H T H T H ii 8 iii 8 7 H T T T H H T H T T T H T T T Original Material Camridge University Press

5 Camridge Essentials Mathematis Core 8 S.2 Answers 20 a i 2 3 = 6 4 ii 6 4 = 4 iii iv = 6 8 Original Material Camridge University Press

6 Camridge Essentials Mathematis Core 8 S.3 Answers / S.3 Answers 2 Repeating the experiment 50 times should give a more aurate predition. 3 5 = or a 24 4 d 3 = a 4 6 Results will usually e different eause they are experimental 7 a i 0.65 ii 0.24 iii 0. home win 0.48 away win 0.26 draw 0.25 Answers to will e more reliale eause proailities alulated from a larger numer of results will e more reliale. 8 Die Experimental results should eome similar to theoretial Die a 0 0 a i ii 49 8 iii 49 4 iv 49 Original Material Camridge University Press 2009

7 Camridge Essentials Mathematis Core 8 S2. Answers S2. Answers a Quantitative Qualitative Quantitative d Quantitative e Quantitative f Qualitative g Qualitative h Quantitative 2 Pupils may provide other examples of quantitative and qualitative measures a i How long it takes him to omplete i How muh the trainers ost ii How diffiult he found it ii The trainers olour i How long he spends playing it ii How muh he enjoys the game d i How long it takes him to yle ii How tired he feels on arrival e i How muh he spent ii How muh he enjoyed shopping f i The ost of the postage ii His exitement efore opening it g i How long they spent travelling h i The numer of alories in the ake ii How muh they learnt from the trip ii How full he felt after eating it 3 a Continuous Disrete Disrete d Continuous e Continuous f Disrete g Continuous h Continuous i Disrete (words per minute) 4 Pupils may provide a range of valid answers to these questions 5 a i The question is too diret and not easily quantifiale. ii Would you onsider yourself as overweight? (Yes, No, Not sure) i There are not enough hoies given. ii What is your favourite food? (Give a seletion of at least 6 varied foods + other ) i The ages overlap, e.g. whih ox does a 0-year-old tik? ii Make sure ages do not overlap. (e.g. 5, 6 0, 5, et.) Original Material Camridge University Press 2009

8 Camridge Essentials Mathematis Core 8 S2. Answers d i The question is amiguous. What if someone likes fruit ut not vegetales? ii The question should e split. Do you like most fruit? (Yes, No) Do you like most vegetales? (Yes, No) e i The question is not relevant to this survey. ii Do not ask this question in the survey. f i This question is iased. The wording disourages people from answering yes. ii Do you like fried food? (Yes, No, Some) g i People are unlikely to know aurately, the numer of alories they eat. ii Possily give people a omprehensive list of foods and ask them to tik the sort of things they would eat on a typial day. Calories ould then e alulated from this. 6,7 There are many valid ways of sampling the people. Eah suggested method should give a representative sample of the population. 8 There are several valid ways to sample the populations. a i All pupils in shool i All passengers on train i All rail passengers that day d i All shoppers e f i All loal people i All ar uyers g i All your friends h i All dogs in loal dog home 0 a With all the heights listed, most will have either no frequeny or a frequeny of. The heights overlap, e.g. 40 m is in two groups. The data is grouped and the groups do not overlap. a The seond tale is est as the groups are equally spaed and do not overlap. Original Material Camridge University Press

9 Camridge Essentials Mathematis Core 8 S2.2 Answers S2.2 Answers a 7 3 d 2 a 37 kg 95 kg and 00 kg 99.9 kg (to d.p.) d 00 kg 3 a 0.89 s none s d s 4 a 300 kg 60 kg 366 kg d 66 kg 5 Peter Amelia a i 8.4 (to d.p.) ii 5.5 iii 20 This is true if you take the mode as the average sore. The mean and median are etter indiators than the mode as only two of the results are aove 0. 7 a i 4 h 3 min ii 6 h 36 min iii 3 h 8 min If the mode is used as the average, then the statement is true. The median appears to e the most reliale as the mean value is affeted y the two very low results. The mode is the least reliale value as all the other results are higher than the modal result. 8 a (to d.p.) 7 d 7 9 a (to d.p.) d 4 e 4 0 a shortest 9 mm, longest 4 mm 36 mm 27 mm Original Material Camridge University Press 2009

10 Camridge Essentials Mathematis Core 8 S2.2 Answers a Mode: girls 33 marks; oys 32 and 36 marks Median: girls 28 marks; oys 3.5 marks d Range: girls 43 marks; oys 35 marks e f Mean: girls 28 marks; oys 25 marks Pupils will make different oservations. These are some possiilities: The girls results are more spread out The averages indiate that the results were roadly similar The girls mean is higher than the oys, ut the girls median is lower Original Material Camridge University Press

11 Camridge Essentials Mathematis Core 8 S2.3 Answers S2.3 Answers a 0 d a 2 d a a 60 people d The ar hart is learer eause it shows the numer of people who liked eah type of offee. Original Material Camridge University Press 2009

12 Camridge Essentials Mathematis Core 8 S2.3 Answers 5 a The modal time group is 6 T < 8 6 a The time 90 T < 00 means the time was at least 90 s ut less than 00 s. 7 a Height Frequeny 8000 T < T < T < T < T < T < 8200 Original Material Camridge University Press

13 Camridge Essentials Mathematis Core 8 S2.3 Answers 8 a 28 C 6 C Yes, eause although the highest reorded temperature was 32 C, it may have een higher at other times whih weren t reorded. 9 a i There was no rain in weeks 2, 5 and 6. ii The line graph is horizontal i Week 7 ii The line graph is steepest or the inrease in the total was greatest d 2.8 mm e 6mm 0 a 9.3 kg heavier Original Material Camridge University Press

14 Camridge Essentials Mathematis Core 8 S2.3 Answers a 60.9 million 960s d It is where the line is steepest 2 a i disagree ii agree iii agree Siene % 4 Original Material Camridge University Press

15 Camridge Essentials Mathematis Core 8 S2.3 Answers 3 a Point 5 is inorretly plotted Yes, the greater the distane travelled, the less petrol is left in the tank. Original Material Camridge University Press

16 Camridge Essentials Mathematis Core 8 S2.4 Answers S2.4 Answers a and 995 Vehile theft rose etween 98 and 993. It fell again etween 995 and d Pupil s own reasons. Perhaps ars have eome more seure. 2 a d Pupil s interpretations. e.g. Crime is elow the national average in Region B and well aove the national average in Region A. In oth regions, rime figures have remained relatively onstant during the period April 2005 to Marh e Pupil s opinion and reasons 3 a 20 million 3.3 million 0 9 years d years e Pupil s might inlude these omments. In the Asian ountry, the numer of people dereases as people get older. In the European ountry, the numers in eah age group rise up to years and then derease steadily. Both graphs are roadly symmetrial, i.e. there are roughly equal numers of males and females in eah age group. 4 a % d 50% e Pupil s might inlude these omments. The perentage of those employed who are women has inreased y aout 20%. The perentage of the total workfore who are unemployed has dereased. Original Material Camridge University Press 2009

17 Camridge Essentials Mathematis Core 8 S3. Answers S3. Answers a Mass (kg) Frequeny 30 M < M < M < M < M < 80 2 Height (m) Frequeny 00 H < H < H < H < H < H < a Time (s) Frequeny Mass (g) Frequeny 2 T < M < T < M < T < M < T < M < T < M < a Distane (km) Frequeny 0 D < D < D < D < D < Class intervals of 3000 km would also e appropriate Split into 5 groups with equal lass size of 4000 km. Class sizes smaller than 3000 would produe too many groups. Original Material Camridge University Press 2009

18 Camridge Essentials Mathematis Core 8 S3.2 Answers S3.2 Answers a i 6 min 27 s ii 5 min 7 s iii 5 min 55 s iv 4 min 40 s Time (mins) Frequeny 0.00 T < T < T < T < T < i 6 min 48 s ii 4.00 T < 8.00 d The mean values are similar. The mode of the raw data falls within the modal lass for the grouped data. 2 a 75 m Length (m) Mid-interval value Frequeny 0 L < L < L < L < L < L < 00 d 20 m Original Material Camridge University Press 2009

19 Camridge Essentials Mathematis Core 8 S3.2 Answers 3 a i 23 min 47 s ii 23 min iii 25 and 38 min iv 67 min Time (mins) Frequeny 90 T < T < 0 0 T < T < T < T < T < 60 i 23 min 53 s ii 20 T < 30 4 a i 38 km ii 309 km iii No mode iv 50 km Distane (km) Frequeny 0 D < D < D < D < D < D < i 36.7 km ii 300 D < 400 d The mean values are very similar. The modes annot e ompared as the raw data has no mode. Original Material Camridge University Press

20 Camridge Essentials Mathematis Core 8 S3.3 Answers S3.3 Answers a 2 a Mean duration attery A = 8 h 40 min Mean duration attery B = 6 h 30 min Although attery B has a shorter mean duration, the distriution is less spread out, therefore atteries are more reliale. d They should hoose attery A, eause 9 of the sample lasted at least 25 hours, whereas only of the sample of attery B did. However there is a greater risk that the atteries will run out early on. (They ould just uy more atteries!!) Original Material Camridge University Press 2009

21 Camridge Essentials Mathematis Core 8 S3.3 Answers years 3.6 years 3 a d Country A has a more even distriution with modal lasses of 20 A < 40. The modal lass for ountry B is 0 A < 20 and the numers in eah lass interval derease with age. e B is likely to e the developing ountry. f Developing ountries tend to have a younger population. Developed nations tend to have an ageing population. i Mean A = 30.9 C ii Median A = 3 C Mean B = 24.7 C Median B = 24.5 C iii Mode A = 3 C Mode B = 24 C iv Range A = 9 C Range B = 3 C Resort B is likely to e England as all three average temperatures are lower for resort B. The smaller range in temperature for resort A shows that temperatures there are more onsistent, whih is why people go for holidays there. 4 Pupils reports will vary, ut may inlude the following oservations: House pries have generally inreased steadily throughout the UK. Region 3 saw a very steep rise from mid-2006 to mid-2007, when pries started to fall. Mean house pries in Region have een the higher than in the other three ountries throughout, exept in 2007 when Region 3 pries were higher. Mean house pries in Region 2 have een the lowest throughout most of the period. Original Material Camridge University Press