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2012
Fri
9
Nov

GCE A Level 2012 Oct/Nov H2 Maths 9740 Paper 2 Suggested Answers & Solutions

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Tuition given in the topic of H1/H2 (A Level) Maths Tutor from the desk of The Higher Council at 9:41 pm (Singapore time)

Hello again everyone and I hope the first week of your A Levels has been good to you so far.

As for me, no thanks to my sister, my eyes are really, really popping out already o.O

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Latest version:

  • 1.1: Q6(ii) – rewritten final answer in set notation, since question asks for “the set of values of “.
GCE A Level 2012 H2 Maths 9740 Paper 2 solutions

2012 GCE A Level H2 Maths 9740 Paper 2 suggested solutions & answers
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As usual, all yim yim jim jim scrutinizers please leave a gentle comment should you spot any mistake in this set of suggested solutions.

Meanwhile, the work continues … *listens to Bon Jovi’s IT’S MY LIFE playing in the background*

All the best for the rest of your papers!

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62 Comments

  1. Emonemo's Avatar
    Emonemo commented in tuition class


    2012
    Nov
    9
    Fri
    9:55pm
     
    1

    Almost all marks lost are careless mistakes 🙁 the max mark I can get is 70 🙁 hopefully still alright!

  2. Student A (:'s Avatar
    Student A (: commented in tuition class


    2012
    Nov
    9
    Fri
    10:10pm
     
    2

    Hi Mr Loi, thanks for your quick update for the papers! Just wondering if marks would be awarded for Sketching of graphs if we do no label the intercepts?

  3. xyz's Avatar
    xyz commented in tuition class


    2012
    Nov
    9
    Fri
    10:26pm
     
    3

    Qn 1b, we should remove the modulus sign right(:

  4. j's Avatar
    j commented in tuition class


    2012
    Nov
    9
    Fri
    10:34pm
     
    4

    (80+74)/2,haiz.. btw i think q4 the interest rate one i got 1.90%,anyone got the same? i dun understand why solution is 4900+100

  5. Sharon's Avatar
    Sharon commented in tuition class


    2012
    Nov
    9
    Fri
    10:58pm
     
    5

    I think qn 6ii is wrong.

    If x bar is > 13.33 how can it be rounded to x bar > 13.3? This means to say x bar = 13.2 is accepted?
    Likewise for x bar < 15.66 it should be rounded off to x bar <15.7 right?

  6. NyoS's Avatar
    NyoS commented in tuition class


    2012
    Nov
    10
    Sat
    12:11am
     
    6

    With regards to question 7)iii) & iv), why is this solution inappropriate?

    7iii)
    P(sisters together, brother together)
    = (2/15)(1/35)
    =2/525

    7iv)
    P(either sisters together, or brothers together, or both)
    =1-P(sisters not together, brothers not together)
    =1-((34/35)(13/15))
    =83/525

    I would need this information for my upcoming H3 Mathematics examination. Thanks. 😛

    • Anon's Avatar
      Anon replied to NyoS’s comment


      2012
      Nov
      10
      Sat
      11:14am
       
      6.1

      @NyoS: I am not sure, but I am guessing it is because you can't multiply the two probabilities together. This is because they are not mutually exclusive. For instance, by letting the sisters be together, the probability of the brothers being together have changed since there are now fewer slots. Drawing a Venn diagram will help. Do correct me if I am wrong.

    • Anon's Avatar
      Anon replied to NyoS’s comment


      2012
      Nov
      10
      Sat
      11:17am
       
      6.2

      @NyoS: I mean independent, not mutually exclusive. My bad!

    • Jess's Avatar
      Jess replied to NyoS’s comment


      2012
      Nov
      10
      Sat
      6:33pm
       
      6.3

      @NyoS: Yup, I was thinking why that solution is inappropriate too. I did the way you did it too.

    • avid's Avatar
      avid replied to NyoS’s comment


      2012
      Nov
      10
      Sat
      10:30pm
       
      6.4

      @NyoS: erm i got the exact same answer for the entire qn7 expect for the last one mark hopefully not wrong



    • 2012
      Nov
      11
      Sun
      5:21pm
       
      6.5

      @NyoS: For simplicity's sake, lets denote "sisters next to each other" as SS and "brothers are all next to each other" as BBB.

      Q7(iii) caught numerous students out as many assumed P(SS and BBB) to be P(SS) × P(BBB) and concluded the result as the answer.

      As Anon tried to explained, however, you can only do this when SS and BBB are independent events i.e. P(SS ∩ BBB) = P(SS) × P(BBB)

      Without getting into an argument of whether/how SS affects BBB, the fact that we get different values when calculating P(SS ∩ BBB) via permutations vs simply P(SS) × P(BBB) is already proof that:

      P(SS ∩ BBB) ≠ P(SS) × P(BBB)
      ⇒ SS and BBB are NOT independent events.

      So in this question where you are unsure if Event A affects Event B, it may be worth to do a quick test to check if P(A ∩ B) = P(A) × P(B) to be sure.

      In Q7(iv): Having established in part (iii) that P(SS) & P(BBB) are dependent, P(SS' ∩ BBB') would not simply be P(SS') × P(BBB'), but instead involves some conditional probability which is not given.

  7. abcd's Avatar
    abcd commented in tuition class


    2012
    Nov
    10
    Sat
    1:46am
     
    7

    hi,wld appreciate it a lot if you could post the h1's answers as well (:

  8. Dudeail's Avatar
    Dudeail commented in tuition class


    2012
    Nov
    10
    Sat
    2:11am
     
    8

    Isn't qn 4 part i wrong?1 month bank money:$100
    2nd mth bank money:$100+$110

    And not 1 month: $100
    2nd mth : $110

  9. ChenZhiLiang's Avatar
    ChenZhiLiang commented in tuition class


    2012
    Nov
    10
    Sat
    8:44am
     
    9

    For the hypothesis testing question part (a) last step when you round the answers, shouldn't you be rounding the answer down instead of the usual up to 3SF since we are finding the range of x where the mean length hasn't changed?

  10. Renee's Avatar
    Renee commented in tuition class


    2012
    Nov
    10
    Sat
    9:20am
     
    10

    Im super disturbed for the last pure maths qns I put 1.05 instead of 1.005 cos it's 0.5% and not 5%. How much will the ecf be?

  11. Zong Han's Avatar
    Zong Han commented in tuition class


    2012
    Nov
    10
    Sat
    9:36am
     
    11

    hi for 3iv) shouldnt u include complex roots as well since they ask for all roots



    • 2012
      Nov
      11
      Sun
      9:27pm
       
      11.1

      @Zong Han: Yes I acknowledge that Q3(v) asks to find all roots which technically means all real and complex roots.

      However I've taken a long, hard, piercing look at Q4 and personally feel that only real roots are required since

      • There are only 4 marks allocated for writing down two cubic equations and calculating at least the four real roots.
      • There's no indication this question involves complex numbers (some of you will disagree I'm sure :\ )
      • Having proved that there's only one real solution in part (ii), it's a bit strange for the question to turn around and require you to use the (rejected) complex solutions for part (iv). (Again, some of you will disagree :\ )

      Again these just my personal opinions and it ultimately hinges on Cambridge's intention for this question.

  12. Xyz's Avatar
    Xyz commented in tuition class


    2012
    Nov
    10
    Sat
    9:54am
     
    12

    Actually, are there any ex students around who can confirm a rough gauge for an a based on ther experience in their year? Like is there anyone with a borderline a case (eg. Est 73 for both papers) and still got an a? Then this would quell all our worries about whether the mark boundary is really so ridiculously high.

  13. .'s Avatar
    . commented in tuition class


    2012
    Nov
    10
    Sat
    10:54am
     
    13

    Will internaliing the mod sign be necessary for Q1b and are complex roots also needed for Q3v?

    >Sharon: It's rounding-off error. You have to round-off to 3sf as given by the cover page, since it's non exact. Following ur argument, I can always say u will definitely miss out some values too.

    >NyoS: I think it's cuz they're not independent events. All the best for combinatorics!

  14. cjm's Avatar
    cjm commented in tuition class


    2012
    Nov
    10
    Sat
    11:47am
     
    14

    dear teacher,
    may i know why the answer to p2 qn 7 part 1 is 14!x2! /15! ?
    i tot it should be 13!x2! /15! since there are only left with 13 ppl after the 2 sisters are taken as one unit? thank you:)

  15. amos's Avatar
    amos commented in tuition class


    2012
    Nov
    10
    Sat
    11:59am
     
    15

    For the conditions of Binomial, I wrote

    (1)Who each voter supports is independent of who another voter supports and (2)the probability of a voter supporting Alliance party is the same for all voters.

    For the conditions of Poisson, I wrote

    (1)The number of gold coins found in a part of the area is independent of the number of gold coins found in another part of the area and (2)the number of gold coins found in a part of the area is proportional to the size of the part of area.

    Are these correct? Please comment. Thanks 🙂

  16. daniel tan's Avatar
    daniel tan commented in tuition class


    2012
    Nov
    10
    Sat
    12:55pm
     
    16

    err i can confirm i am from vjc and last year the teacher from a class which i cannot reveal because it wasnt suppose to be said said the mark for A was (73+ and minus 2) this year they said is 75+- 2, so if your score is 77 and above you should be fine don'tworry cambridge dont expect u all to be gods and score 80+ (national distinction rate for h2 math is 45%

  17. Jess's Avatar
    Jess commented in tuition class


    2012
    Nov
    10
    Sat
    1:45pm
     
    17

    Hi, I have some questions.

    For 1b) can't we solve it this way?
    ∫ ( 1/ 16-9u^2) dx = ∫ (1)/( 4^2 -(3u)^2 dx
    = and we continue to solve using the formula from MF15 which is ∫ 1/( a^2 -x^2) where a= 4 and x=3u?

    As for qn4, part (a) I made a careless mistake of thinking that it is 100, 210 ,220,230… I went on to solve the qn using sum of AP. For part (b), I read it wrongly as 5% instead of 0.5%. I continued solving the qn using the normal method. How many method marks do you think I can get for this whole question?

    For qn8, I did not know how to do (iv), so my (iv) answer is wrong. But I went on solving the remaining parts using this wrong (r) value. How many method marks do you think I can get?

    Thank you so much for your help.

  18. j's Avatar
    j commented in tuition class


    2012
    Nov
    10
    Sat
    3:26pm
     
    18

    Hi for one of the questions the one where they said to sketch the graph. Is it ok not to state when they cross the axis? And the max point?? Since they didn't specifically state that you have to.

  19. j's Avatar
    j commented in tuition class


    2012
    Nov
    10
    Sat
    8:27pm
     
    19

    for qn 1 asking us to find t in terms of u, I din read properly and found u in terms of t, out of 5 issit possible to get 3 or 4 marks?I mean it isn't really a bad thing right? I did extra steps bcos I tot 5 marks usually ask us to do the hard way in prelim papers..

  20. avid's Avatar
    avid commented in tuition class


    2012
    Nov
    10
    Sat
    10:22pm
     
    20

    argh 2iii i wrote sin (4/sqrt 58) instead of sin inverse (4/sqrt 58) instant lost 3 marks after all the time wasted thinking.

    also, 1b i thought can use MF15 de

  21. ilovemath's Avatar
    ilovemath commented in tuition class


    2012
    Nov
    10
    Sat
    10:31pm
     
    21

    3(i) and (iv) - are axial intercepts required? considering only 1m and question does not specify.
    3(iii) - are complex roots required? since "real roots" was not specified.
    4(ii) - is it necessary to state the exact month (Sep 04) or is 45th month sufficient? what if wrong month is stated despite correct number (e.g. 45th month, Aug 04)?
    8(iii) - is it acceptable to say that since an extrapolation will be required in order to predict future marks, neither model will be appropriate? in fact, isn't the question invalid because the prediction of which week she will get >90% will be unreliable?
    8(vii) - could this simply refer to the maximum possible score Amy will ever get on the test? there seems to be no information given that the actual exam will only be taken after infinite practice papers have been taken.
    9(iv) - what does "suitable degree of accuracy" mean? why have you chosen 2 d.p. as suitable? should the answer be anything related to the fact that a 5 d.p. value was provided in the question?
    10(i) - is it correct to say that occurrences of gold coins must occur independently i.e. finding one gold coin does not affect finding another gold coin?
    10(iv) - question asks to "state the parameter(s) of the distribution that you use". what does this require?



    • 2012
      Nov
      12
      Mon
      1:27am
       
      21.1

      @ilovemath: 3(i)/(iv) Since they carry only 1 mark each, you should be fine.

      3(iii) See here.

      4(ii) 45th month should be sufficient actually. Describing the wrong month despite obtaining n = 45 would depend on the examiner's leniency (at most one mark for loss of accuracy).

      8(iii) The question requires you to explain how the nature of the data renders it unsuitable to be modeled using a linear or quadratic model.

      Saying that extrapolation is unreliable is moot since the intention to predict Amy's future marks has already been declared. So we are looking for the best model to predict her marks, though we are aware to an extent of the inherent unreliability of extrapolation (as with all future predictions :P).

      8(vii) I wrote the way it was in the solutions because, in the context of the question, Amy takes her exam after all her practice papers (regardless of how many weeks she takes) as x → ∞.

      Also I said L represents the likely mark instead of the maximum mark Amy will score since, again in context/reality, she might get something like L±1 but the prediction is that she will score L marks as x → ∞.

      Having said that, 1-mark comments like these are commonly open to more than one interpretations so your description is most likely fine as well 😀

      9(iv) 2 d.p. for p was chosen to be in line with values of p given earlier in the question.

      10(i) Not a problem. In fact "independent" is one of the keywords for Poisson conditions.

      10(iv) The parameters in this case are the mean and variance (both λ = 80) of the Normal distribution used to approximate the Poisson distribution, and are indicated in:

      X100 ~ N (80, 80)

  22. avid's Avatar
    avid commented in tuition class


    2012
    Nov
    10
    Sat
    10:31pm
  23. avid's Avatar
    avid commented in tuition class


    2012
    Nov
    10
    Sat
    10:36pm
     
    23

    anyways is 70 plus without any method marks for both papers considered A cuz im worried sick of all the careless mistake ive done in p1 and p2

  24. cz's Avatar
    cz commented in tuition class


    2012
    Nov
    11
    Sun
    9:18am
     
    24

    Hmm, should'nt question 6's working consider the sample deviation given in the question to be that of a sample, cause the question said the sample deviation of the squirrels of the island, and not the species known to her what!

  25. cz's Avatar
    cz commented in tuition class


    2012
    Nov
    11
    Sun
    2:21pm
     
    25

    Hi, shouldnt the standard deviation in question 6 be that of a sample, since the question stated that the SD given is that of squirrels of the island, which is a sample.



    • 2012
      Nov
      11
      Sun
      4:32pm
       
      25.1

      @cz: There's quite a number of queries as to whether the standard deviation in Q6 belongs to the sample set or the population.

      If you look at the question again (click to enlarge):

      2012 GCE A Level H2 Maths Paper 2 Q6 Question

      The zoologist is simply testing if the mean tail lengths of the population of squirrels on the island is 14.0 cm. This "14.0 cm" should be considered merely as a value known to her from her knowledge of the species, and you should not take the entire species as the population.

      As such, she assumes the tail lengths, X, of the island population are normally distributed with standard deviation 3.8 cm i.e.

      X ~ N (14, 3.8²).

      So the population refers to the population of squirrels on the island (NOT the entire species) and the sample set is simply her group of 20 randomly selected cute little squirrels.

  26. John's Avatar
    John commented in tuition class


    2012
    Nov
    12
    Mon
    1:00pm
     
    26

    Hey, anyone know if an overall score of 57/100 would probably fetch what grade?

  27. Harvey's Avatar
    Harvey commented in tuition class


    2012
    Nov
    13
    Tue
    2:54am
     
    27

    For qn8 part 3, is it ok if i wrote that her marks need not depend on the number of weeks she practise since the difficulty of papers varies? Do i get at least 1 mark or none for that? And for 8 part 7, i wrote the L means the mark that she predicts she will score? Is it ok? Lastly for the condition for poisson qn, one of my conditions is that the number of something (cant remember exactly) occurs randomly and independently. I think it's a rather awkward answer but is it wrong?

    Assuming that i got the qns asked above wrong, along with some other qns wrong that ive checked. I scored around 80% (+/- 1) i hope it's safe enough for an A, really afraid that an A is greater than 75% or 80% 🙁

  28. Brendan's Avatar
    Brendan commented in tuition class


    2012
    Nov
    14
    Wed
    2:50pm
     
    28

    Hi, for H2 P2, qn 10(vi), i thought we shouldnt use continuity correction since we changed each poisson distribution to normal distribution before combining them?
    but other than that, 95/100. lol

6 Reactions

  1. Tweetback
    Miss Loi tweeted


    2012
    Nov
    9
    Fri
    1:51pm
     
    29

    #ALevel #H2 #Maths Paper 2 answers & solutions: http://t.co/tuqqM5td Note: It's Jφss Sticks' solutions NOT Miss Loi's solutions 😛 #math



  2. 2012
    Nov
    9
    Fri
    1:52pm
     
    30

    @einnaeg wtf i screwed up damn badly. even though my p1 was good http://t.co/aqFlAOop



  3. 2012
    Nov
    9
    Fri
    1:52pm
     
    31

    @einnaeg wtf i screwed up damn badly. even though my p1 was good http://t.co/aqFlAOop

  4. Tweetback
    Jess Neo tweeted


    2012
    Nov
    9
    Fri
    2:13pm
     
    32

    Lol in the midst of xfactor, im here to say the alvl maths paper 2 solutions are out. http://t.co/Ib3M2gm8

  5. Tweetback
    Miss Loi tweeted


    2012
    Nov
    9
    Fri
    2:21pm
     
    33

    @weeeekeatt The answer to the mystery of Amy's marks in Week 5 is revealed: http://t.co/tuqqM5td 😛 #alevel #H2 #maths #math Paper 2

  6. Tweetback
    Sean Lim tweeted


    2012
    Nov
    9
    Fri
    2:25pm

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