Sorry to have kept everyone waiting, especially those who have been camping at the H2 Maths Paper 1 blog post.

Before that blog post’s comments section turns into a mini chit-chat lounge, here are the H2 Maths Paper 2 solutions that I’ve managed to get them done up despite my busy day (yesterday), with a little help from my siblings once again.

2010 ‘A’ Level October/November H2 Mathematics 9740 Paper 2 Suggested Solutions – click to download (Latest Version: 1.3)

Like students under exam pressure, I’ve done this under a bit of ‘pressure’ as well from the baying horde of “When will paper 2 be out?!”, “answers please!!!” etc. So, as with Paper 1, please leave a comment whenever you spot any mistake, typo and/or better/quicker/smarter methods (I really appreciate these! :)) and I’ll update the solutions as and when required.

Meanwhile, good luck for your remaining papers, and good morning to you if you’re seeing this the first thing on a bright Saturday morning!

just wondering if i calculate s^2 wrongly.. my p-value will be diff.. do we get heavily penalised??? as for e prob question got my 1st part wrong thus my subsequent parts.. do we get ecf on dat??

hi! thanks for the answers 🙂 but for question 10 (ii) the question asks for the answers to be corrected to 4 decimal places, but your answers are in 3 dp. yup just letting you know! 🙂

HEY! thank you SO MUCH for your efficiency! feel so relieved after seeing the solutions! anyway, for question 10, just want to point out a minor mistake in your solutions. 10(ii) they want us to leave the answer correct to 4 dp instead of 3. I just realise it too 🙁

thank you so much for uploading the solutions so fast! for the inequality question of 7v), shouldn't the lowest probability be 0 because there is a chance B and C are mutually exclusive?

@DD: For Q7, if P(B) and P(C) are mutually exclusive, then they would not intersect as shown in the following Venn Diagram:

From part (ii), P(A ∪ B) = 0.92 and from part (iv), we have P(A' ∩ C) = 0.15, which is the shaded region in the diagram.

However, in the diagram above, P(A ∪ B ∪ C) = 0.92 + 0.15 = 1.07 which is 0.07 greater than the expected total probability of 1.

Hence there must be at least a minimum intersection between B & C such that P(A' ∩ B ∩ C) is at least 0.07 as shown in the black region of the following diagram:

For 1ii), once we obtain the value of a and b, can we solve it using GC? Question did not specify that we couldn't >.<

For 4iii(, is it necessary to prove that fg(x) exists before going on to prove the ans?

For 11v), since the lowest possible number of busy days is 0 and will not be negative, should it be normalcdf(0,9.5 etc) instead of normalcdf(-e99 etc)? You get a slightly different answer: is that wrong?

Oh, for 10ii), it's to 4dp not 3sf. Thank you very much! (:

@Anon: For Q1(ii), using your G.C. to obtain your final roots should by and large be fine. However, for a 5-mark question, I would recommend at least indicating in your workings that the conjugate of −2 + i (i.e. −2 − i) is also a root.

Regarding Q4(iii), I believe that for this 2-mark question, you should be fine as long as you've demonstrated clearly in your workings how you've successfully derived fg(x). So don't worry about the additional proving of the existence of fg(x) (which is left there for our own checking only :P)

As for Q11(v), this has been amended since version 1.2 of the solutions.

just a small quibble but for the product moment correlation coefficient question, the paper asks for 4 d.p. instead of 3 s.f. heh 🙂 i almost made that mistake too...

Hi, my answer is almost the same as yours. +) question 3i) I proved that dy/dx always greater than 0 and thus it has only 1 turning point, that is the minimum. I wonder if the examiner will penalize me for this unnecessary working. Eventually i also get x= -4/3 like u. +) Question 8ii) My answer is 0.067 🙁 My working is (2x2x1x2!) 5! +) Question 10 iv) : Can i just say we cannot use both regression lines b/c we cannot use value of drag force to estimate the value of wind speeds. The rest should be okay!!! Thanks for ur solution !!!

@Daniel: For the 5 marks in Q3(i), I believe it should be OK if 1) you've differentiated correctly 2) expressed the answer as a single fraction 3) equated your differentiated expression to zero 4) shown that there's only one turning point and 5) finally obtained this value of x at the turning point.

Additional gey kiang workings should be fine unless you did them wrongly 😉

For Q10(iv), I believe it's more appropriate to enhance your statement by indicating the reason that v is the independent variable in your final answer.

hey! all's good! except that for qns 10 (ii), it's to 4 d.p., cnt correct it to 3 s.f. ~ anw, thanks for the neat and comprehensive solutions!

but there's sth troubling me really badly. i hope u can enlighten me though.

if for instance, i made an error in part (i) of a qns, and that caused me to have an incorrect ans for (i), which unfortunately is required in the subsequent parts. and of course, my other ans became terribly wrong as well.

i'd like to clarify, will i be awarded method marks? and if yes, is it going to be a pathetic mark, or are they like just going to minus 1 mark for my wrong ans, assuming that my method is sound?

@J: Yup, as amber and hello have both highlighted, in Q6's case we should use a t-test since its sample size is small (n < 30) and its population variance is not given.

if i calculated 11(iii) wrongly, does it means that for (iv) and (v) no matter whether my approach is correct i will still be wrong? or i will be marked down?

Hi, for qn 4 (iii), I don't think it is necessary to show that Rg is a subset of Df. Isn't it just substitution and simplifying the fraction to get the two marks?

Hi thanks for uploading the answers so efficiently! =) But I'm not sure if for question 10 (ii) the answers should be 0.9860 and 0.9907 instead because the question asked for answers to be corrected to 4 decimal places.

hmmmmm, i tink i spotted some error 10ii question say correct to 4dp not 3sf and if i am not wrong the C.C. are wrong, should be the other way round. thx a lot for this

@Audrey: When using a CC to approximate a discrete distribution, you'll need to consider whether the number(s) at the limit(s) of the probability interval need(s) to be accommodated ⇒ you need to be mindful of the inequality/equal sign(s) i.e.

P(k < X < k) becomes P(k+0.5 < X < k−0.5) ∵ k is not included in the interval P(k ≤ X ≤ k) becomes P(k−0.5 < X < k+0.5) ∵ k is included in the interval

Hi for qn 9 part i is it necessary to square thr variance (the 2 in front) because I thought it's just y-(x+x) so should be var(y-2x) = var(y) + var(x) + var(x)? Or am I wrong? I thought only price need to square for this qn...

@Kate: For Q9(i) and (ii), it's important to understand whether multiples or sums are being considered.

In part (i), we're dealing with twice the number of minutes of peak calls which is a multiple so you'll have to square its variance i.e. Var(2X) = 2^{2}Var(X).

@Keegan: The A grade hovers around 70 for all CIE/SEAB papers. If the paper is easy, they will be more picky and vice versa. That's why A for sch is 70. Don't worry. At most 75.

@meyeyumi: Really? I can't believe that you can be that confident about the student demographics and their performance... What a gross generalization...

@meyeyumi: Lol why you care whether the whole world get A/B or not? I mean, the A level is supp to just test proficiency and not "You-can't-answer-this-Math-Olympiad-question-so-you-deserve-a-D-HAHA" kind of thing. -.-

Sigh, after reading so many comments regarding the bell curve, i decided i would contribute my 10 cents worth. First thing to note is that the A levels is not to test your relative performance amongst other Singapore students. It is supposed to be an indicator/measure of your knowledge as an 18 year old and your preparedness to be able to continue higher education. From cambridge's perspective, the papers they set should be in line with those requirements. As what my GP tutor says, it would be unfair to use the bell curve if indeed the quality of this year's students are better than that of last years (meaning if many of you score 80 plus, so what? The A will still hover around 70) unless they feel that the paper quality has changed which will not be much comparing last years and this years and hence they might increase the requirement to say 75 for an A?). The approximate quote given by the cambridge markers were " If we require you to swim 100 metres to get the A and you have shown us that you are capable, you will get it regardless of whether a big group of students have proven themselves to be able to swim around the world"

@Anonymous: But still, even if the cut off is 75 and a whole bunch of people get A, we are competing with our batch for places in uni. So the "bell curve" actually exists, set up by ourselves.

I may be wrong, but for question 3(iii), isn't the graph of f^-1 supposed to be a reflection of the graph of f using the line y=x as a mirror? As for question 7(v), I would like to ask whether it is possible that there is a case where C notsubset B but there is a common area for A inter B inter C (3 separate circles like in case II but C also intersects B)? About question 11(iii) and 11(v), is the continuity correction supposed to be P(T>2199.5)cc and P(X<10.5) respectively? Thanks for uploading!

@anonymous: For Q3(iii), we're sketching the gradient function of f(x) i.e. f'(x) not the inverse function of f(x) i.e. f^{−1}(x)! You are not alone in this one *sigh*

But our fears are not unfounded because there are many ppl speculating that the min marks to get an A is 90. It seems ridiculous, but considering the difficulty of he paper again, it does seem plausible. ( which i hope not cos i'll be kissing gdbye to by A)....

Can i know if there's error carried forward in A levels maths? and to what extent is it given?

Guess what I can do now is to look forward and think positive. Gdluck to those taking As too this year! 🙂

@sh: This is what Cambridge wrote on their examiner's comments:

Marks are of the following three types: M: Method mark, awarded for a valid method applied to the problem. Method marks are not lost for numerical errors, algebraic slips or errors in units. However, it is not usually sufficient for a candidate just to indicate an intention of using some method or just to quote a formula; the formula or idea must be applied to the specific problem in hand, e.g. by substituting the relevant quantities into the formula. Correct application of a formula without the formula being quoted obviously earns the M mark and in some cases an M mark can be implied from a correct answer.

@sh: Like you pointed out those are merely speculations, honestly a 90 for an A looks highly unlikely and if so would certainly draw some amount of controversy

@David: For Q3(ii)(b), did you do this on your G.C.?

And sketched this?

Do note that to obtain the graph of y^{2} = x^{2}(x + 2), you'll need to plot y = ±x√(x + 2) which consists of the graph of y = x√(x + 2) AND the graph of y = −x√(x + 2).

The correct way of using your G.C. would be to plot the curves for y = x√(x + 2) and y = − x√(x + 2) as follows:

I think a million voices crying out "MR LOI!!! Q10(II) FINAL ANSWER MUST BE IN 4 D.P. NOT 3 SIG. FIG.!!!" have actually penetrated my dreams as I slept last night.

I've uploaded version 1.1 of the solutions simply to correct this, and so as to stem the tide of further comments on this issue. I'm having class now and will attend to the other comments later.

Hope to have your understanding and sorry about the 3 sig. fig. error.

@somebody: Unfortunately, as the sample size in Q6 is small, X does not strictly follow a normal distribution (z-test), so it's more appropriate to use a t-test in this case.

Hi Mr Loi, I don't think your answer to 5(i) is appropriate, because the question asks why it is difficult to use stratified sampling, not why it is difficult to get an unbiased/unrepresentative sample... So my interpretation is that the question asks for practical difficulty in carrying out the sampling?

And, after all, isn't a stratified sample meant to capture opinions from different strata for a more representative view? So what's wrong with Europeans having a rather biased opinion? >< It's the same as a stratified sample of boys and girls about the new ballet dance class. Probably girls will like it better than boys, yet this does not mean stratified sampling fails.

For Question 4v, it is ok if I just write the answer (-infinity to +infinity)? However, I took the range from the GC straight, would I still get the full three marks?

@justfate: If you check the graph, there is a region (-1 < y < 0) that is not within the range of fg. This is because there's an asymptote of y = -1. I'm not sure how many marks you'll get though.

sorry... can i ask you for qn 6?... the hypo testing question?... is it wrong? as in... they're asking you to calculate the mean time.. but you sub-ed the numbers inside. shouldnt you do this... x~N(mean,(variance/n))... because the data they gave you is the total. not the mean?

With regards to the hypothesis-testing question, if I keyed in s² [I forgot to square-root to obtain value s], and hence got the incorrect p-value and conclusion, would any marks awarded at all?

Question 10(iii), the question clearly asked for reference to 10(i) AND 10(ii)

So other than concluding it based on the r value alone, you need to state the observation that the scatter plot reveals a non-linear relation. because there is a concave outwards, thus a quadratic equation should be a more suitable model.

Hahas, I made the same mistake too... I wrote down on the paper s but i put in calculator s^2 n got 17%>sig lvl n happily "There's insufficient evident to reject Ho, bla bla bla..." T_T I think they give u 2 marks for the unbiased estimates... but i think mayb there's ECF for our s^2 if our working n our conclusion fits it... But thats my opinion.. At least u get 2 marks ^_^

@Anonymous: hey i accidentally calculated my s^2 wrongly!! rawr! i divided the whole load by 11 instead of 10 by accident!! will the subsequent marks be lost? arghh oh well...

just one question! my friends and I are rather confused about question 10(i). it says "DRAW" the scatter diagram not the usual "SKETCH" we see. does this mean we have to use the graph paper? or only when they "PLOT" then we have to use the graph paper?

I certainly hope my careless mistake doesn't screw me over. I lost 7 marks from reading qn 8, assuming no method marks, cos I thought it was no. of ways. 🙁 and I thought they wanted f inverse graph for 3iii, Instead of dy/dx. Sighhhh.

hi there. for question 11 (v), i believe if you approximate binomial to a normal, your lower limit for normalcdf should not be -E99 but -0.5 instead? since binomial values cannot take on negative values.

i accidentally used some correction tape during the exam..will they penalise me? :/ and for those who said they have to kiss A gdbye when they get 76-78 i think thats quite...zz.seriously.there is hope since 75 is the min.

@orangejuice: wont la, because they do not allow correction fluid only. i use correction tape for all the papers! in large amount. because if i do not, it would be so messy

@meyeyumi: hey that's very inconsiderate and may be a disadvantage to you, do you know why do they strictly disallow staples, correction fluid and highlighter? That's because when the paper is sent over to England, they will compress the whole stack of papers to minimise space and cost. Your correction fluid will stick itself strongly with the neighbour page under prolong period of time + humidity. This may tear and ruin other ppl's work, think about it.

Just stop visiting this page. You are putting extra burden on your remaining papers by being a paranoid and too aware of these competition, which is likely illusionary.

After the paper, you should be conditioning yourself for the remaining papers. Stay confident and don't discuss answers with peers and online =)

I merely look through the method briefly w/o even checking the final answer.just to know that I'm on the right track.

@untitled: Not to offend you in any way, but what can you do IF it's not an A? You're just going to lose hope and do badly for the rest of the papers. I suggest you let by gones be by gones, tell yourself you've done your best and continue to do the same for the rest of the papers. Cheers mate. All the best for the rest of your papers and hope you get your As.

I got about 60+ for Paper 1 and 70+ for Paper 2, this means getting an A is a no chance anymore right? And why are everyone here getting like 70-80+ on average for both papers! You guys are really smarty pants, should be from the top-end JCs?

Hmm I definitely agree that A should be 70~80. I mean you all are all worried bout getting As (including me)

But technically n logically speaking, the bulk and mean of the belt curve actually lies on B. So, if A hits 85... technically people who are weaker scoring 60+ would be getting C or D... Ouch~.. And people whu gets low 50+ would be scoring S == which seems a lil too extreme...

Ultimately, Cambridge should not be concern wif the large bulk of people getting As, ergo jusifying their actions to raise the bell curve to a 80+ to get As.. raising the bell curve would have detrimental to weaker students.. This seems largely unfair~

And for some whu argued that "My fren nvr do prelim papers or last year paper could get 85+" cannot make the assumption that this generalises over the whole of Singapore.

Our scope of argument only worries bout getting A... how bout the potential weakers student aiming to get B?

Bell curve aims to (most of the time) make grades equally distributed and to reward student for their ability, and not to largely compare whu made more mistakes then the other (which largely would be the reason for not having 100 marks right now, right?). So, try be a lil optimistic (and practical lols...) and dun worry so much of getting B if u had around 80 marks. Cambridge is not out to slaughter us...

Most likely though, there will be stricter marking to balance out~ Eg. -1 for not showing essential steps, statement or presentation seems too messy where workings are everywhere n ur arrows r flying left-right-top-bottom...

@Kidz: Already updated in version 1.3 of the solutions. Sorry to miss out your question earlier - it's not easy trawling through this pile of comments 🙁

@anon: You may confusing yourself. P(a<x<b) when using cc becomes P(a+0.5<x<b-0.5) because you don't want to include a and b. Unless it was P() then it becomes P(a-0.5<x<b+0.5)

@Joel: For Q11(iv), you'll obtain the same answer via the basic binomial distribution formula i.e. probability of obtaining 2 busy days (⇒ no. of successes r = 2) in 6 randomly selected days (⇒ no. of trials, n = 6),

As Min Han has kindly pointed out, using binompdf(6, 0.19176, 2) is basically the G.C.'s way of calculating the above, so the ^{6}C_{2} has already been taken into account.

Hey, i was just wondering about question 6. Since it's a two-tailed test, shouldn't the p-value we are comparing the obtained p-value against be 0.05 instead of 0.1? Anyway, thanks for the answers 😀

@Samantha: Yes as others have already mentioned, it's important to note that, regardless of whether it's a one-tail or two-tail test, your G.C. will always churn out the total p-value against the 'total' significant level.

So when you key in the following for your 2-tail test at 10% significance level as shown below

the calculated p-value of 0.09487 is compared against 10% significance level.

As the distribution is symmetrical, you may also look at this as effectively comparing a p-value of 0.047 against 5% at each end as shown below:

Heyhey thankyou so much for uploading the answer! Anw i have a shorter method to the probablity question q7(iv) P(A' n C) = P(A n B') + P(B) = 0.32 + 0.60 = 0.92 Draw out the venn diagram and it is quite obvious. Anw iam so worried that the A standard would be like 90 omg. Else my A would be gone. Cos the most i can get is 80 overall. Everyone pray hard that it will be not be too high, perhaps 75. 75 is not v low right HAHA

oh dear how come everyone here's smart ): i seem to be the only one who found the math paper (1) tough because i got stumped by the differentiation qns. am ashamed for asking this but is there any rough gauge as to the passing mark thereabouts? yes i'm that terrible.

Hi, isn't the graph for 3 (b) (iii) wrong? I got the asymptote correct but I thought it should starting in the positive region then decreasing to touch x axis at turning pt of original graph then going into negative region and finally increasing to positive again? So end result would be something like U shape but not symmetrical?

@black: It's correct. If you think about it, its almost vertical and downward sloping, which means it's a highly negative gradient so it must start from negative. Alternatively, since you actually know the equation of the graph, just differentiate it and type it into your gc to see the shape.

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

About Miss Loi

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life’s calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over years she has been a savior to countless students … [read more]

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## 151 Comments

曜

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thanks for being efficient. could you estimate a threshold for getting an A for us?(:

曜

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just wondering if i calculate s^2 wrongly.. my p-value will be diff.. do we get heavily penalised??? as for e prob question got my 1st part wrong thus my subsequent parts.. do we get ecf on dat??

曜

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Q10i) says draw. do u use the graph paper?

Q10ii) says correct to 4d.p, i think u made a mistake.

曜

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q10ii) is wrong. the answer wants 4 dp (:

曜

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Thanks for the answers! Btw the answers for 10 (ii)(a) and (b) should be in 4 d.p not 3 s.f.

曜

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hi! thanks for the answers 🙂 but for question 10 (ii) the question asks for the answers to be corrected to 4 decimal places, but your answers are in 3 dp. yup just letting you know! 🙂

曜

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Thanks too!

曜

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ya.. what will be the minimum to get A? i think i only have 72% of it, will i fall short for an A, badly?

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HEY! thank you SO MUCH for your efficiency!

feel so relieved after seeing the solutions!

anyway, for question 10, just want to point out a minor mistake in your solutions.

10(ii) they want us to leave the answer correct to 4 dp instead of 3.

I just realise it too 🙁

曜

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thank you so much for uploading the solutions so fast! for the inequality question of 7v), shouldn't the lowest probability be 0 because there is a chance B and C are mutually exclusive?

曜

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@DD: For Q7, if P(

B) and P(C) are mutually exclusive, then they would not intersect as shown in the following Venn Diagram:From part (ii), P(

A∪B) = 0.92 and from part (iv), we have P(A' ∩C) = 0.15, which is the shaded region in the diagram.However, in the diagram above, P(

A∪B∪C) = 0.92 + 0.15 = 1.07 which is 0.07 greater than the expected total probability of 1.Hence there must be at least a minimum intersection between

B&Csuch that P(A' ∩B∩C) is at least 0.07 as shown in the black region of the following diagram:曜

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@Mr Loi: i get it now, thank you so much 🙂

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yeah thanks! but whats the gauge for A?

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My answer to 5(i) was:

It is difficult to obtain the exact number of spectators belonging to each stratum.

Izzit okay? Thanks. 🙂

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Thank you! 😀

I have 3 questions.

For 1ii), once we obtain the value of a and b, can we solve it using GC? Question did not specify that we couldn't >.<

For 4iii(, is it necessary to prove that fg(x) exists before going on to prove the ans?

For 11v), since the lowest possible number of busy days is 0 and will not be negative, should it be normalcdf(0,9.5 etc) instead of normalcdf(-e99 etc)? You get a slightly different answer: is that wrong?

Oh, for 10ii), it's to 4dp not 3sf. Thank you very much! (:

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@Anon: For Q1(ii), using your G.C. to obtain your final roots should by and large be fine. However, for a 5-mark question, I would recommend at least indicating in your workings that the conjugate of −2 + i (i.e. −2 − i) is also a root.

Regarding Q4(iii), I believe that for this 2-mark question, you should be fine as long as you've demonstrated clearly in your workings how you've successfully derived fg(x). So don't worry about the additional proving of the existence of fg(x) (which is left there for our own checking only :P)

As for Q11(v), this has been amended since version 1.2 of the solutions.

曜

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just a small quibble but for the product moment correlation coefficient question, the paper asks for 4 d.p. instead of 3 s.f. heh 🙂 i almost made that mistake too...

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Hi, my answer is almost the same as yours.

+) question 3i) I proved that dy/dx always greater than 0 and thus it has only 1 turning point, that is the minimum.

I wonder if the examiner will penalize me for this unnecessary working. Eventually i also get x= -4/3 like u.

+) Question 8ii) My answer is 0.067 🙁 My working is (2x2x1x2!) 5!

+) Question 10 iv) : Can i just say we cannot use both regression lines b/c we cannot use value of drag force to estimate the value of wind speeds.

The rest should be okay!!!

Thanks for ur solution !!!

曜

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@Daniel: Ey ey wrong wrong,

Question 3i) I proved d2y/dx2 always greater than 0. NOt dy/dx

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@Daniel: For the 5 marks in Q3(i), I believe it should be OK if 1) you've differentiated correctly 2) expressed the answer as a single fraction 3) equated your differentiated expression to zero 4) shown that there's only one turning point and 5) finally obtained this value of

xat the turning point.Additional

workings should be fine unless you did them wrongly 😉gey kiangFor Q10(iv), I believe it's more appropriate to enhance your statement by indicating the reason that

vis the independent variable in your final answer.曜

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hey! all's good! except that for qns 10 (ii), it's to 4 d.p., cnt correct it to 3 s.f. ~ anw, thanks for the neat and comprehensive solutions!

but there's sth troubling me really badly. i hope u can enlighten me though.

if for instance, i made an error in part (i) of a qns, and that caused me to have an incorrect ans for (i), which unfortunately is required in the subsequent parts. and of course, my other ans became terribly wrong as well.

i'd like to clarify, will i be awarded method marks? and if yes, is it going to be a pathetic mark, or are they like just going to minus 1 mark for my wrong ans, assuming that my method is sound?

曜

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Sir!! For the hypo testing qn do we use Z-test or T-test since it is normally distributed?:)

PS thanks for working out the answers!

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@J: even though t is normally distributed, its variance isn't available (only unbiased estimate) and n is small. you need to use a t-test.

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@J: It should be t-test as n is small(11) 🙂

曜

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@J: Yup, as

amberandhellohave both highlighted, in Q6's case we should use at-test since its sample size is small (n< 30) and its population variance is not given.曜

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if i calculated 11(iii) wrongly, does it means that for (iv) and (v) no matter whether my approach is correct i will still be wrong? or i will be marked down?

曜

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Hey for question 10 (ii), the answers should be to 4 dp as required. No need to round off to 3 sf 🙂

曜

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Hi, for qn 4 (iii), I don't think it is necessary to show that Rg is a subset of Df. Isn't it just substitution and simplifying the fraction to get the two marks?

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@James: No worries 😉

曜

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Hi thanks for uploading the answers so efficiently! =) But I'm not sure if for question 10 (ii) the answers should be 0.9860 and 0.9907 instead because the question asked for answers to be corrected to 4 decimal places.

曜

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for the regression qn, it's 4dp, u read wrongly! the product moment part

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@Anon: haha, nice one

曜

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hi 10 ii should be in 4 dp

曜

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hmmmmm, i tink i spotted some error

10ii question say correct to 4dp not 3sf

and if i am not wrong the C.C. are wrong, should be the other way round.

thx a lot for this

曜

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sry my bad the C.C. are correct, i m wrong OMG!

曜

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@meyeyumi: i think the C.C are wrong ;o i thought P(k<x<k) = P(k-0.5<x<k+0.5)??

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@Audrey: When using a CC to approximate a discrete distribution, you'll need to consider whether the number(s) at the limit(s) of the probability interval need(s) to be accommodated ⇒ you need to be mindful of the inequality/equal sign(s) i.e.

P(

k<X<k) becomes P(k+0.5 <X<k−0.5) ∵kis not included in the intervalP(

k≤X≤k) becomes P(k−0.5 <X<k+0.5) ∵kis included in the intervalSimilarly,

P(

X>k) becomes P(X>k+0.5)P(

X≥k) becomes P(X>k−0.5)So for the CC in Q11(iii), P(

T> 2200) becomes P(T> 2200.5) ∵ 2200 isnotincluded in the interval.曜

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thanks mr loi(:

you may want to check q10(ii) answers. it's to 4dp, stipulated by qn.

anyway, i think if your answers are right, i'm getting my perfect score for the paper (:

thank you for making my day!

cheers!

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Erm, the r values for Q10ii are to be given in 4 d.p., not 3 s.f.

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Hi for qn 9 part i is it necessary to square thr variance (the 2 in front) because I thought it's just y-(x+x) so should be var(y-2x) = var(y) + var(x) + var(x)?

Or am I wrong?

I thought only price need to square for this qn...

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@Kate: For Q9(i) and (ii), it's important to understand whether multiples or sums are being considered.

In part (i), we're dealing with

twicethe number of minutes of peak calls which is amultipleso you'll have to square its variance i.e. Var(2X) = 2^{2}Var(X).曜

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ppl relax. Math a level maximum A grade floor in the past few years is 73. It's not a perfect bell curve.

Plus since it's an easy paper, they prolly will be more picky abt working and stuff to differentiate.

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@brian: Just wondering, how would you know that A grade floor in the past few years is 73

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@brian: How do you know that Brian?? Does it mean that if you got above 73 last year --> A?

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@Keegan: The A grade hovers around 70 for all CIE/SEAB papers. If the paper is easy, they will be more picky and vice versa. That's why A for sch is 70. Don't worry. At most 75.

And yeah, I have a friend who is an OCR assessor.

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@brian: hey brian, i'd like to ask if A is 75, would B be just -10 and range from 65-74?

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@brian: hmmmm, but i feel that if A is around 70+, for this paper, it sounds like the whole singapore will get A or B

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@meyeyumi: Really? I can't believe that you can be that confident about the student demographics and their performance... What a gross generalization...

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@Anonymous: but my friends are doing realli well, except for mi =(

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@meyeyumi: Lol why you care whether the whole world get A/B or not? I mean, the A level is supp to just test proficiency and not "You-can't-answer-this-Math-Olympiad-question-so-you-deserve-a-D-HAHA" kind of thing. -.-

Chill! Study for econ and chem!

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@brian: OMG really 73? Then i can be relieved man, hey btw how do you know haha.

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Sigh, after reading so many comments regarding the bell curve, i decided i would contribute my 10 cents worth. First thing to note is that the A levels is not to test your relative performance amongst other Singapore students. It is supposed to be an indicator/measure of your knowledge as an 18 year old and your preparedness to be able to continue higher education. From cambridge's perspective, the papers they set should be in line with those requirements. As what my GP tutor says, it would be unfair to use the bell curve if indeed the quality of this year's students are better than that of last years (meaning if many of you score 80 plus, so what? The A will still hover around 70) unless they feel that the paper quality has changed which will not be much comparing last years and this years and hence they might increase the requirement to say 75 for an A?). The approximate quote given by the cambridge markers were " If we require you to swim 100 metres to get the A and you have shown us that you are capable, you will get it regardless of whether a big group of students have proven themselves to be able to swim around the world"

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@Anonymous: nicely put. 😀

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@brian: Hey you make a lot of sense! Hmmmm then we all should be not be afraid becos we all surely are capable of swimming a 100m(analogy) HAHA ^^

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@Anonymous: But still, even if the cut off is 75 and a whole bunch of people get A, we are competing with our batch for places in uni. So the "bell curve" actually exists, set up by ourselves.

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I may be wrong, but for question 3(iii), isn't the graph of f^-1 supposed to be a reflection of the graph of f using the line y=x as a mirror?

As for question 7(v), I would like to ask whether it is possible that there is a case where C notsubset B but there is a common area for A inter B inter C (3 separate circles like in case II but C also intersects B)?

About question 11(iii) and 11(v), is the continuity correction supposed to be P(T>2199.5)cc and P(X<10.5) respectively?

Thanks for uploading!

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@anonymous: For Q3(iii), we're sketching the gradient function of f(

x) i.e. f'(x)notthe inverse function of f(x) i.e. f^{−1}(x)! You are not alone in this one *sigh*For Q7(v), would these diagrams help?

For Q11(iii) & (iv), have a look at this comment.

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Thanks for the answers(:. But do you mind explaining why for 7(v) the lower limit is 0.03? I got 0.07 though.

My working was

From part ii, and part iv,

as

Sorry, can't type in the last part. Having troubles with the texts but subbing in the values and I get 0.07 as the lower limit.

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@anonymous: Oh thinking about it again, I think what your working was finding was the minimum P(AnBnC) instead of P(A'nBnC)

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@anonymous: The solutions for Q7(v) has been amended since version 1.2. Thanks for pointing this out 😉

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For 11 (v), it should be from -0.5 to 9.5 cos it cannot be negative. qn 3 also need to label y-intercept and max-min coordinates.

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10 (ii) should be 4 d.p!! XD

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But our fears are not unfounded because there are many ppl speculating that the min marks to get an A is 90. It seems ridiculous, but considering the difficulty of he paper again, it does seem plausible. ( which i hope not cos i'll be kissing gdbye to by A)....

Can i know if there's error carried forward in A levels maths? and to what extent is it given?

Guess what I can do now is to look forward and think positive. Gdluck to those taking As too this year! 🙂

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@sh: ECF is given only if everybody screws up the question. I reckon question 9 will have ecf if you took into account the lid volume into 300.

That's just my thoughts tho.

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@sh: This is what Cambridge wrote on their examiner's comments:

Marks are of the following three types:

M: Method mark, awarded for a valid method applied to the problem. Method marks are not lost for numerical errors, algebraic slips or errors in units. However, it is not usually sufficient for a candidate just to indicate an intention of using some method or just to quote a formula; the formula or idea must be applied to the specific problem in hand, e.g. by substituting the relevant quantities into the formula. Correct application of a formula without the formula being quoted obviously earns the M mark and in some cases an M mark can be implied from a correct answer.

... which should mean that there's ecf for As.

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@sh: Like you pointed out those are merely speculations, honestly a 90 for an A looks highly unlikely and if so would certainly draw some amount of controversy

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Graph of 3(ii) (b) looks incorrect - Gradient should be positive initially, becomes negative, go back to zero and then increase once more.

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@David: For Q3(ii)(b), did you do this on your G.C.?

And sketched this?

Do note that to obtain the graph of

y^{2}=x^{2}(x+ 2), you'll need to ploty= ±x√(x+ 2) which consists of the graph ofy=x√(x+ 2) AND the graph ofy= −x√(x+ 2).The correct way of using your G.C. would be to plot the curves for

y=x√(x+ 2) andy= −x√(x+ 2) as follows:曜

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10 (ii) is to 4 d.p rather than 3 s.f.

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Hi there,

The answers for 10(ii) should be left as 4 decimal places, instead for 3SF.

:]

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For 8(i) you can do it even faster by only considering the first number. Everything else looks fine.

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Good morning! And thanks a lot for the answer.. (: what a relief.

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Thanks for uploading! But for question 10 (ii), aren't the r values supposed to be correct to 4 decimal places?

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Hey thanks so much for yur hard work;

Qn 10 partii its supposed to be in 4dp ;D

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thanks for the answers!

just one small error i've found, the answers for q10(ii) should be to 4dp as specified by the question and not 3sf.

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Please upload the H1 math paper solutions ):

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Good morning (or rather good afternoon everyone).

I think a million voices crying out "MR LOI!!! Q10(II) FINAL ANSWER MUST BE IN 4 D.P. NOT 3 SIG. FIG.!!!" have actually penetrated my dreams as I slept last night.

I've uploaded version 1.1 of the solutions simply to correct this, and so as to stem the tide of further comments on this issue. I'm having class now and will attend to the other comments later.

Hope to have your understanding and sorry about the 3 sig. fig. error.

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omgawd I got careless mistakes ahhhhhhhhh 🙁

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hmmm if i used z test instead of t test will i be wrong?...cos i still got the same conclusion...i'll prolly get atleast some marks righttt

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@somebody: Unfortunately, as the sample size in Q6 is small,

Xdoes not strictly follow a normal distribution (z-test), so it's more appropriate to use at-test in this case.曜

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Hi Mr Loi, I don't think your answer to 5(i) is appropriate, because the question asks why it is difficult to use stratified sampling, not why it is difficult to get an unbiased/unrepresentative sample... So my interpretation is that the question asks for practical difficulty in carrying out the sampling?

And, after all, isn't a stratified sample meant to capture opinions from different strata for a more representative view? So what's wrong with Europeans having a rather biased opinion? >< It's the same as a stratified sample of boys and girls about the new ballet dance class. Probably girls will like it better than boys, yet this does not mean stratified sampling fails.

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For Question 4v, it is ok if I just write the answer (-infinity to +infinity)?

However, I took the range from the GC straight, would I still get the full three marks?

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@justfate: If you check the graph, there is a region (-1 < y < 0) that is not within the range of fg. This is because there's an asymptote of y = -1. I'm not sure how many marks you'll get though.

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@amber: what i wrote was (-infinity,infinity), x ≠ 2, 3 4. is that alright?

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@amber: Oh yea. Thanks for the clarification. There goes my 3 marks. 🙁

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Hello, im wondering the continuity correction for the last question last part should be P(x > 2199.5) instead of 2200.5.

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@Audrey: SOrry so typo there, i meant P(X > 2199.5) instead of 2200.5 for one of the previous part (:

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@Audrey: See my little write-up on continuity correction.

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what if i just insert the numbers into the gc for question 1a? do i still get the marks?

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@sl: hey me tooo!! but i'm sure they won't penalize cos they didn't ask for algebraic method right? right?!?

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@thecarz: hahaha... i guess not! which school are u from?

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sorry... can i ask you for qn 6?... the hypo testing question?... is it wrong? as in... they're asking you to calculate the mean time.. but you sub-ed the numbers inside. shouldnt you do this... x~N(mean,(variance/n))... because the data they gave you is the total. not the mean?

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Hello, for qn4(iv), is it alright if I put my answer as 2<x<4 , x≠3?

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@Yohanes: No worries! There are many roads to Rome!

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I was just wondering..

With regards to the hypothesis-testing question, if I keyed in s² [I forgot to square-root to obtain value s], and hence got the incorrect p-value and conclusion, would any marks awarded at all?

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Question 10(iii), the question clearly asked for reference to 10(i) AND 10(ii)

So other than concluding it based on the r value alone, you need to state the observation that the scatter plot reveals a non-linear relation.

because there is a concave outwards, thus a quadratic equation should be a more suitable model.

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@Kidz: Thanks for your feedback! I've added a reference to the non-linear relationship from part (i) for Q10(iii) in version 1.3 of the solutions!

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Hahas, I made the same mistake too... I wrote down on the paper s but i put in calculator s^2 n got 17%>sig lvl n happily "There's insufficient evident to reject Ho, bla bla bla..." T_T I think they give u 2 marks for the unbiased estimates... but i think mayb there's ECF for our s^2 if our working n our conclusion fits it... But thats my opinion.. At least u get 2 marks ^_^

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@Anonymous: haha me too!!! i guess we still got mark for showing them we noe which test to use???

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@Anonymous: hey i accidentally calculated my s^2 wrongly!! rawr! i divided the whole load by 11 instead of 10 by accident!! will the subsequent marks

be lost? arghh

oh well...

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hello thanks for uploading the answers! (:

just one question! my friends and I are rather confused about question 10(i). it says "DRAW" the scatter diagram not the usual "SKETCH" we see. does this mean we have to use the graph paper? or only when they "PLOT" then we have to use the graph paper?

thanks!!

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I barely scraped a 70% on average for both paper.Guess I shall kiss my A goodbye 🙁

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I certainly hope my careless mistake doesn't screw me over. I lost 7 marks from reading qn 8, assuming no method marks, cos I thought it was no. of ways. 🙁 and I thought they wanted f inverse graph for 3iii, Instead of dy/dx. Sighhhh.

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@Lithilara: lol. if youre who i think you are, full marks for paper 1 not enough ah?

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@Lithilara: OMG HI FIVE! we can be best friends

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For 11 (v), it should be from -0.5 to 9.5 cos it cannot be negative. qn 3 also need to label y-intercept and max-min coordinates.

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For Q11(v), since days cannot be negative I feel that the lower limit for normalcdf should be 0 and not -E99. what do you think?

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Omg i only scored an average of 76 to 77 overall for both papers. theres goes my A and B. next need to retake already. D:

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i lost marks for question 8 too): haha but if your paper 1 is good, you'll do fine luh. no worries((:

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hi there. for question 11 (v), i believe if you approximate binomial to a normal, your lower limit for normalcdf should not be -E99 but -0.5 instead? since binomial values cannot take on negative values.

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H1 Math solutions please ):

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i accidentally used some correction tape during the exam..will they penalise me? :/

and for those who said they have to kiss A gdbye when they get 76-78 i think thats quite...zz.seriously.there is hope since 75 is the min.

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@orangejuice: wont la, because they do not allow correction fluid only. i use correction tape for all the papers! in large amount. because if i do not, it would be so messy

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@meyeyumi: hey that's very inconsiderate and may be a disadvantage to you, do you know why do they strictly disallow staples, correction fluid and highlighter? That's because when the paper is sent over to England, they will compress the whole stack of papers to minimise space and cost. Your correction fluid will stick itself strongly with the neighbour page under prolong period of time + humidity. This may tear and ruin other ppl's work, think about it.

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@lalala: omg die i should go kill myself. i use all three that u state!

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Hope seems bleak at times like this.

Competitiveness its at its peak and the implementation of the bell curve and paranoia seems hard to ignore.

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Just stop visiting this page. You are putting extra burden on your remaining papers by being a paranoid and too aware of these competition, which is likely illusionary.

After the paper, you should be conditioning yourself for the remaining papers. Stay confident and don't discuss answers with peers and online =)

I merely look through the method briefly w/o even checking the final answer.just to know that I'm on the right track.

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@Kidz: haha yeah. i am subscribed to the comments here ><

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why are there no answers for h1 math?!?????????????????????????????????????????????????????????????????????????????????????????????

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opps, i meant extrapolating the competition you see here to the rest of the cohort hahaha.

You know extrapolation is bad 😀

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hi if i get ard 80 plus on average, would i still b able to get an A?

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can someone pls enlighten me? i'm really scared that i cannot get an A.

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@untitled: Not to offend you in any way, but what can you do IF it's not an A? You're just going to lose hope and do badly for the rest of the papers. I suggest you let by gones be by gones, tell yourself you've done your best and continue to do the same for the rest of the papers. Cheers mate. All the best for the rest of your papers and hope you get your As.

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@Yohanes: ok thx(= all best for your remainning paper too(=

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I got about 60+ for Paper 1 and 70+ for Paper 2, this means getting an A is a no chance anymore right? And why are everyone here getting like 70-80+ on average for both papers! You guys are really smarty pants, should be from the top-end JCs?

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@Anonymous: Jurong JC here. What about you friend? 😛

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@Yohanes: Pioneer JC!

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Hmm I definitely agree that A should be 70~80. I mean you all are all worried bout getting As (including me)

But technically n logically speaking, the bulk and mean of the belt curve actually lies on B. So, if A hits 85... technically people who are weaker scoring 60+ would be getting C or D... Ouch~.. And people whu gets low 50+ would be scoring S == which seems a lil too extreme...

Ultimately, Cambridge should not be concern wif the large bulk of people getting As, ergo jusifying their actions to raise the bell curve to a 80+ to get As.. raising the bell curve would have detrimental to weaker students.. This seems largely unfair~

And for some whu argued that "My fren nvr do prelim papers or last year paper could get 85+" cannot make the assumption that this generalises over the whole of Singapore.

Our scope of argument only worries bout getting A... how bout the potential weakers student aiming to get B?

Bell curve aims to (most of the time) make grades equally distributed and to reward student for their ability, and not to largely compare whu made more mistakes then the other (which largely would be the reason for not having 100 marks right now, right?). So, try be a lil optimistic (and practical lols...) and dun worry so much of getting B if u had around 80 marks. Cambridge is not out to slaughter us...

Most likely though, there will be stricter marking to balance out~ Eg. -1 for not showing essential steps, statement or presentation seems too messy where workings are everywhere n ur arrows r flying left-right-top-bottom...

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How do people know the average marks for getting an A for the past few years? Does Cambridge reveal it?

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Alright everyone I've just uploaded version 1.2 of the H2 Maths Paper 2 solutions in respond to some of the feedback here, namely

X< 10) with P(0 ≤X< 10) as the probability to consider, since the lower limit of the number of daysXcannot be < 0.Good night everyone for now!

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@Mr Loi: You didn't read #55 for my response to question 10(iii) 🙁

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@Kidz: Already updated in version 1.3 of the solutions. Sorry to miss out your question earlier - it's not easy trawling through this pile of comments 🙁

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@Mr Loi: I still think the C.C. is wrong D: shouldnt it be

P(k<x<k) continuity correction to P(k-0.5<x<k+0.5)? that's what i learnt.

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@anon: You may confusing yourself. P(a<x<b) when using cc becomes P(a+0.5<x<b-0.5) because you don't want to include a and b. Unless it was P() then it becomes P(a-0.5<x<b+0.5)

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@anon:

Min Hanis right. See my little write-up on continuity correction.曜

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@Mr Loi: mr loi.... can i ask you abt the hypo testing?.... shouldnt we calculate mean for t test first then sub in?... they asked for mean you know..

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Hi I was just wondering if you need to times 6C2 for qn11iv because it might be any 2 of the 6 days?

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@Joel: When you use binompdf(6,0.192,2), it already takes into account 6c2.

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@Joel: For Q11(iv), you'll obtain the same answer via the basic binomial distribution formula i.e. probability of obtaining 2 busy days (⇒ no. of successes

r= 2) in 6 randomly selected days (⇒ no. of trials,n= 6),P(W = 2) = (0.192)

^{2}(1−0.192)^{6−2}×^{6}C_{2}≈ 0.235 (3 sig. fig.)As

Min Hanhas kindly pointed out, using`binompdf(6, 0.19176, 2)`

is basically the G.C.'s way of calculating the above, so the^{6}C_{2}has already been taken into account.曜

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Hey, i was just wondering about question 6. Since it's a two-tailed test, shouldn't the p-value we are comparing the obtained p-value against be 0.05 instead of 0.1?

Anyway, thanks for the answers 😀

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@Samantha: It's not, you still compare it with 0.1. P-value includes the region of both ends already for a 2 tail test.

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@Samantha: i think the G.C already took into account the two-tailed test.

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@Samantha: Yes as others have already mentioned, it's important to note that, regardless of whether it's a one-tail or two-tail test, your G.C. will always churn out the

totalp-value against the 'total' significant level.So when you key in the following for your 2-tail test at 10% significance level as shown below

the calculated p-value of 0.09487 is compared against 10% significance level.

As the distribution is symmetrical, you may also look at this as effectively comparing a p-value of 0.047 against 5% at each end as shown below:

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Heyhey thankyou so much for uploading the answer! Anw i have a shorter method to the probablity question q7(iv)

P(A' n C) = P(A n B') + P(B) = 0.32 + 0.60 = 0.92

Draw out the venn diagram and it is quite obvious. Anw iam so worried that the A standard would be like 90 omg. Else my A would be gone. Cos the most i can get is 80 overall. Everyone pray hard that it will be not be too high, perhaps 75. 75 is not v low right HAHA

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@hello: It's not as obvious as you say it is, possibly even wrong. That and P(A'nC) is actually 0.15 and not 0.92.

Anyway I'd say A won't go past 75 tops, don't think they are that evil.

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@hello: Oh unless you meant 7(ii) for P(AuB).

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oh dear how come everyone here's smart ): i seem to be the only one who found the math paper (1) tough because i got stumped by the differentiation qns. am ashamed for asking this but is there any rough gauge as to the passing mark thereabouts? yes i'm that terrible.

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Hi, isn't the graph for 3 (b) (iii) wrong? I got the asymptote correct but I thought it should starting in the positive region then decreasing to touch x axis at turning pt of original graph then going into negative region and finally increasing to positive again? So end result would be something like U shape but not symmetrical?

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@black: It's correct. If you think about it, its almost vertical and downward sloping, which means it's a highly negative gradient so it must start from negative. Alternatively, since you actually know the equation of the graph, just differentiate it and type it into your gc to see the shape.

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@black: Have a look at my comment here. You used

y= √[x^{2}(x+2)] to sketch your f'(x)?曜

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Is there any ecf for 10iii and iv??