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

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• 1.1: Q6(ii) – rewritten final answer in set notation, since question asks for “the set of values of “.

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!

### Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

1. 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 (: 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?

• 2012
Nov
11
Sun
2:28pm

2.1

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 🙂

3. xyz commented in tuition class

2012
Nov
9
Fri
10:26pm

3

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

4. 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 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 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 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 replied to NyoS’s comment

2012
Nov
10
Sat
11:17am

6.2

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

• 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 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 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 (:

• 2012
Nov
13
Tue
12:46am
8. 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 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 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 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 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. . 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 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 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 🙂

• 2012
Nov
11
Sun
9:54pm

15.1

@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.

16. 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 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.

• 2012
Nov
11
Sun
10:18pm

17.1

@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.

18. 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.

• 2012
Nov
11
Sun
10:20pm
19. 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 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 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

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 commented in tuition class

2012
Nov
10
Sat
10:31pm
23. 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 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 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):

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 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 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 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

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