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 x̄“.
2012 GCE A Level H2 Maths 9740 Paper 2 suggested solutions & answers
Access it here if you’re having trouble accessing it on Facebook using your state-of-the-art smartphone 🙁
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!
62 Comments
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Almost all marks lost are careless mistakes 🙁 the max mark I can get is 70 🙁 hopefully still alright!
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@Emonemo: But if your p1 is strong, I think it should be ok? Most people keep saying p2 is much tougher.
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@Meow: u sure? my sch ppl thinks otherwise. i feel p2 was harder but many in my sch said p2 was eazier.
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@Meow: i personally feel p2 was harder. but according to the majority of my sch, p2 was dam eazy lol
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@meme: I got 82 for P1 and 71 for P2. No prizes for guessing which one I found more difficult.
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@meme: Um for myself, I found p2 easier! (probably because I did better at stats) :p However almost everyone around me felt p1 is much easier. What school are you from though?
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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?
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@Student A (:: Normally it's always good to label the intercepts but as only 1 mark is allocated to each graph in Q3, it's probably safe to assume they are looking for the appropriate shape of the curve more than anything else.
So I think you're fine in this case 🙂
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Qn 1b, we should remove the modulus sign right(:
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@xyz: Actually you'll need the modulus sign, as u can be negative.
If you are referring to the integral
with no modulus sign described in MF15, note that there's already a restriction in the form of |x| < a stated next to it.
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(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
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@j: You add 100 because they asked for the amount he has on 2 Dec 2003 to be $5000, meaning that on 30 Nov 2003 he got his interest and on 1 Dec he topped up $100. So the amount he has on 30 Nov 2003 should be $4900 while the amount he has on 2 Dec 2003 should be $5000 since he has topped up $100 on 1 Dec 2003.
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@Student A: Cheers for your help!
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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?
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@Sharon: You mean 12.33? See here.
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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. 😛
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@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.
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@NyoS: I mean independent, not mutually exclusive. My bad!
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@NyoS: Yup, I was thinking why that solution is inappropriate too. I did the way you did it too.
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@NyoS: erm i got the exact same answer for the entire qn7 expect for the last one mark hopefully not wrong
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@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.
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hi,wld appreciate it a lot if you could post the h1's answers as well (:
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@abcd: Here.
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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
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@Dudeail: The table above Q4(i) refers to the deposit made each month not the bank balance. This is indicated by the word "Deposit" in the table in case you've missed it.
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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?
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@ChenZhiLiang: AGREE, that's what I've been wondering about too...
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@ChenZhiLiang: As mentioned by here, this is a case of allowable rounding error as part of the 3 sig. fig. accuracy requirements of the paper.
It is more important that we don't round off prematurely in intermediate calculations which will reduce the accuracy of our final answers.
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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?
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hi for 3iv) shouldnt u include complex roots as well since they ask for all roots
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@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
Again these just my personal opinions and it ultimately hinges on Cambridge's intention for this question.
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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.
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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!
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@.: See here for the mod sign.
See here for the curious case of complex roots for Q3(v).
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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:)
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@cjm: first treat 2 sisters as one unit, then there will be left with 13 other ppl, together with the one unit of sisters, there will be 14 'groups'...^^
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@0.0: Thanks for your help in our effort to answer the comments! 😀
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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 🙂
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@amos: Hmmm ... while your first three conditions are legit, your last one sounds like you are using a property of the Poisson Distribution as a prerequisite condition which I think it may not be appropriate since conditions for Poisson are almost always about the events being independent, random, occurring singly at a constant rate.
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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%
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@daniel tan: i thought national distinction rate is more than 50%
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@avid: Hi all, the national distinction rate for H2 math is about 50% (50.8% to be exact, based on KiasuParents lolol). And based on what I hear the A rate is somewhere near our usual school A rate (i.e. 70). And given that this year's paper is already considered harder than previous years', the A rate will not deviate too much from there. So don't worry too much about it (:
My paper 1 is approx. 78 (accounting for some variance cos of careless mistakes), and my paper 2 is in the 85+ range. (ironic enough, I find paper 2 harder tho...)
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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.
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@Jess: For 1(b), nothing wrong with your method just that you should sub x = u instead of 3u into the MF15 formula since you are integrating with respect to u,
else your constant term outside of the integral may be affected.
As for the method marks, I can't determine exactly how many marks you'll get but generally they are only awarded in parts with multiple marks (with ECF catered for that part) and only when it's crystal clear that it was only the substitution of a wrong value in your appropriate steps that led to the wrong answer.
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@Mr Loi: Hi Mr Loi,
thank you for the explanation 🙂 I understand your explanation.
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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.
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@j: You should be fine 😀
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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..
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@j: wads ecf?
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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
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@avid: You may use the MF15 formula in Q1(b) but just be careful.
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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?
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@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)
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anyways if MF15 still same answer
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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
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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!
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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.
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@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):
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.
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Hey, anyone know if an overall score of 57/100 would probably fetch what grade?
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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% 🙁
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@Harvey: You will be fine (: (based on what I know, the A rate does not deviate much from the school A rate i.e. 70, so max. is 75)
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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