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1 Cambridge Essentials Mathematis Core 7 S1.1 Answers S1.1 Answers 1 a 7 b 21 6 m d blue e ar 2 a 2 b 0 3 a 120 b Pizza 4 a Table 1 Number of people in vehile More than 4 Number of vehiles Table 2 Number of people in vehile More than 4 Number of vehiles b Table 1: 3 Table 2: 1 Table 1 represents vehiles approahing the Dover ferry. The higher value of the mode suggests more families and this would be expeted for holiday travel at the weekend. Table 2 fits the piture of people driving themselves to work and 55 6 a Pulse rate Frequeny b % 7 a 20 b No. The mode is also the maximum value of the data. Pupil s hoie, but should be a entral value, like a All of the values are different so the mode is meaningless. b Pupil s hoie, but should be a entral value, suh as 7. Original Material Cambridge University Press

2 Cambridge Essentials Mathematis Core 7 S1.1 Answers m 10 a 6 b d 28 e a 32 b d 51.5 e a 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4 b 2 hours 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5 d 2.5 hours 13 a 10 b No. The values above 10 are muh larger but this doesn t influene the median. The median doesn t hange. d The mode annot be used beause all of the values are different. 14 a 5 b d 23 e a 5.8 b a 2.4 b m 20 a 59 b m d 7.4 kg a 19.4 b a Goals sored per math G Number of mathes N G N Total = 12 Total = 24 total number of goals 24 b Mean number of goals per math = = = 2 total number of mathes 12 Original Material Cambridge University Press

3 Cambridge Essentials Mathematis Core 7 S1.1 Answers 24 total ost of tikets b Mean prie per tiket = = = total number of tikets sold a 29 b d Better e To the nearest whole number the mean would have been 2 in both weeks. 26 a 21 b 3.76 Sore Frequeny S F S F Total = 100 Total = a 10 b No. The mean has been heavily influened by the one exeptional value. It is too high. Median = 6.80; mode = The median is most typial of the data. 28 a 13 b m d 5 m m or a Any five numbers with range of 0.5 and median 16. b i... all of the numbers must be lose together. ii... not all of the numbers an be lose together. 34 a 4 b 6 9 Original Material Cambridge University Press

4 Cambridge Essentials Mathematis Core 7 S1.2 Answers S1.2 Answers 1 a i 250 ii b Friday 150 d a b Golf a The perentage of boys and girls who are regular smokers inreases eah year between the ages of 11 and 15. The inrease in the perentage of girls who are regular smokers is higher than the orresponding inrease for boys in eah year. 5 b Approximately 16% Approximately 25% Original Material Cambridge University Press

5 Cambridge Essentials Mathematis Core 7 S1.2 Answers 6 a Art, History and PE b Musi Art, PE, Maths, English, Design Teh., History, Musi, Siene d Art, PE, Maths, English, Design Teh., Siene, History, Musi e Siene 7 a Favourite subjets of 100 boys at primary and 100 boys at seondary level b Art and PE 8 a R&B b Rok Pop and R&B 9 a b sweets d = 85 e 25 Original Material Cambridge University Press

6 Cambridge Essentials Mathematis Core 7 S1.2 Answers 10 a b 6 10 tikets 11 a The range annot be found exatly beause the largest and smallest values are not given in the table. d 2 e 6; 20% b worms/m worms/m 2 d 15% 12 a 9% b Adventure a 25% b 36 Original Material Cambridge University Press

7 Cambridge Essentials Mathematis Core 7 S1.3 Answers S1.3 Answers 1 a Very unlikely b Unlikely Likely d Very likely 2 a Likely b Certain Unlikely d Even e Very unlikely f Very unlikely g Very likely h Impossible 3 A die is rolled to give a sore of 3. The spinner shown lands on green. A oin lands heads up. The spinner shown lands on blue. 4 a Less than even b Less than even Better than even d Better than even 5 a Asking for a volunteer would make some people suspet that the person hosen was an aomplie. b Faing the audiene would make it possible for Alfonso to throw the teddy bear to an aomplie. No. This method should make it lear to everyone that Alfonso has no ontrol over who is seleted. 6 a Writing eah name on a piee of paper and hoosing one without looking. b An extra preaution would be to make sure that all of the piees of paper were folded to the same size and shape. 7 a 1, 3, 5 b 2, 3, 5 1, 2, 3, 4 d 5, 6 e 6 f 2, 3, 4, 5, 6 8 a 3 b 3 5 d 2 e 2 f 1 9 a 6 b 2 i = ii = iii iv 2 1 = a = b d 2 1 = 6 3 Original Material Cambridge University Press

8 Cambridge Essentials Mathematis Core 7 S1.3 Answers 11 a 5 b 3 3/5 d 5 e 5 0 = 1 f 0 g = a 1 b No. There are 3 outomes, but they are not equally likely beause the sides of the triangle do not all have the same length. 15 a i 3 5 ii 0.6 iii 60% b 100% 0 16 a 2 out of 5 outomes are hoolate = = 40% John isn t right beause the outomes are not equally likely. b 100% 17 75% 18 a 20 1 = b % Original Material Cambridge University Press

9 Cambridge Essentials Mathematis Core 7 S2.1 Answers S2.1 Answers 1 Additional questions might be based around opening days/times, ost, safety and onerns about older hildren bullying the younger ones. 2 It would be important to onsult hildren of different ages who might want to attend and loal residents who may be affeted. 3 a The question gives a suggested response. b, Many people might be offended by these questions as they are too personal. d e f g h i The phrasing of the question learly indiates an expeted response. This question is too omplex for a survey. The question is too vague. This is another question that people might regard as too personal. The question makes an assumption that not everyone would agree with. The responses are likely to be so varied that it would be diffiult to analyse them. 4 The hoies should allow for all possibilities without being too omplex. 5 It doesn t allow for the possibility that the person responding may not eat any meat. 6 There are too many possible resorts to list. 9 b The frequenies of the sores should be roughly the same. e For a lokwise spin, the position favours the numbers 2 and 3. f For an antilokwise spin the position favours the numbers 1 and a Seondary b Primary Seondary d Experimental Original Material Cambridge University Press

10 Cambridge Essentials Mathematis Core 7 S2.2 Answers S2.2 Answers 1 a i 5 heads, 5 tails ii 25 heads, 25 tails iii 50 heads, 50 tails d The perentages should all work out at around 50%, on average, but it is likely that the results for 100 trials will be more onsistent than for 10 trials. In a lass, it is quite likely that someone will obtain results of 70%, 30% or even 80%, 20% for 10 trials but this is extremely unlikely for 100 trials. 2 a 38% b 46% 16% 3 a 74% b 19% 6% d 1% 4 a No. The game is fair. b 6 No. d This ould take any integer value greater than or equal to 6. e In theory, the probability that the game will be won after 6 turns is 1/64 1.5%. If about 200 games are played in total, estimates are likely to be in the range 0.5 4%. f The atual answer is approximately 62%. Estimates from the lass results should be approximately in the range 60 70%. g The player with the advantage will not always win, unless it is impossible for the other player to win. Original Material Cambridge University Press

11 Cambridge Essentials Mathematis Core 7 S3.1 Answers S3.1 Answers 1 a The main differenes relate to the 6 10 and lasses, whih have muh higher proportions in the first hart than in the seond. As a result, most of the other proportions are smaller in the first hart, with the 65+ lass onsiderably redued. b The first hart represents July. The higher proportion of the 6 10 and lasses orresponds to shool age hildren who will be on holiday in July. There are more people at the resort aged than sine the proportion is higher. d No. The smaller angle orresponds to a smaller proportion. However, it is likely that the resort will be busier in July than in May, so it ould be a smaller proportion of a muh larger group of people. 2 a Some possible figures are: Lowest Median Highest Sarah Rifat b The lowest and highest figures are only estimates, so we annot be ertain who had the lower pulse rate at the end of the run. However it is more likely to be Rifat, beause we estimated that her highest pulse rate was lower than Sarah s. The reovery rate is shown by the range. The larger value for Sarah indiates that her pulse rate is returning to normal quiker than Rifat s, so she is showing the greater rate of reovery. 3 a In the seond test, the frequeny of low sores (< 40%) is less than in the first test, and the frequeny of high sores (> 60%) is greater. So, on average, the perentage sores are higher for the seond test. The mean will be higher for the seond test. b The modal lass is the same (41 60) for both tests. The mean is more sensitive to the hange in the marks than the modal lass and so the mean is a more aurate way to measure the differene between the two sets of sores. Yes. The lowest and highest marks ould atually be the same in both tests, or they ould both have hanged by the same amount. Original Material Cambridge University Press

12 Cambridge Essentials Mathematis Core 7 S3.1 Answers 4 a The effet will have been to redue the higher speeds to near the speed limit. b The new mean is likely to be lose to 40 mph but slightly less beause some ars will be slowing down to turn into the side roads. The range will be smaller due to the redution in the higher speeds. The mode is likely to be 40 mph beause most motorists will drive at the speed limit. 5 a 30% b 2 20% d 30% e Number of 4s in ten spins Perentage of 4s Frequeny Perentage Frequeny f Mean = 20.3% to 1 d.p. Total: 30 Total: 610 g Range = 50%. h Number of 4s in twenty spins Perentage of 4s Frequeny Perentage Frequeny i Mean = 20.2% to 1 d.p. Total: 30 Total: 605 j Range = 30%. k The mean will get loser to 20%. The range will get loser to 0%. Original Material Cambridge University Press