Hello again guys,

I’ve heard your little chorus of comments even as I was having my classes this afternoon.

So with whatever time I have at my disposal today, I’ve managed to squeeze this out (with a little help from my sister):

As usual please let me know via the comments should you spot any mistake in the H2 Maths Paper 1 solutions.

Meanwhile, here’s a list of topics which you might find it worthwhile to go through again before your Paper 2 tomorrow.

- Integration (by parts, by substitution, volume of revolution etc.)
- Summation
- Mathematical Induction
- Arithmetic & Geometric Progressions (AP/GP)
- Complex Numbers: Solving complex roots via simultaneous equations or de Moivre’s Theorem
- Composite Functions
- Statistics (this one no need to say)

All the best for your Paper 2!

## 77 Comments

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OMG MRLOI I DONT DARE TO LOOK NOW *hides* thanks for posting tho 😀

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Hi, may I ask, what's the estimated minimum marks that we should obtain for such a paper, if we want to secure an A? :X

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Hi, may I ask if we wrote the f(x) equation for question 5 wrongly, does it mean the whole question is wrongly and all the marks are lost?

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In qn 3, can be found by simply doing -

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@lolatyou: Yup for Q3(i),

u_{n}can indeed be straightforwardly obtained viaS_{n}−S_{n−1}but I've found through mycheong heilong-winded method that I managed to prove the sequence is an AP along them way. This made it easier for me to obtain the pattern in Q3(ii).In any case, I've updated the solutions to include the

u_{n}=S_{n}−S_{n−1}method for everyone's reference.曜

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Could you please post the H1 math paper? Thanks(:

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just wanna say thanks so much for your dedication as a tutor.

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hi mr loi! thanks so much for posting (:

anyway, for qn 9, what happens if I minus the surface area of the cover (i.e. - 2kxy - 6x^2 ) instead of adding it? My method should be correct though, because I obtained the negative version of all the answers. How many marks do you think I can get (as method marks)?

In addition, do you know the likely mark threshold for an A grade in this paper?

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Lol answers got imperfections. If Cambridge wants to discriminate, this answer cannot get 100. Cubic curve label (2,-6) but gradient at that point supposed to be 0. Also, for qn 11 area of triangle OAB, in the working, 0.5 (p sqrt8) (1/p sqrt8) is wrong, because p can be negative. Supposed to be 0.5 (absolute value of p times sqrt8) (1/(absolute value of p) times sqrt8). Because the sqaure root of p^2 is the absolute value of p, but just p itself ><

The first one not so serious. But the second one may lose a mark for working...?

From brian's blog: …And this is goodbye

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@brian: Haha oops sorry for that sketch in Q5 which I admit could be improved 😛 In any case, I've updated the solutions with a better 'high-tech' sketch 😉

Regarding that line of working in Q11(ii), the key purpose of the question is to show that the area is independent of

p.As the squared

ps will confirm lead to positive values ofOAandOB, coupled with the fact that theps will still cancel out each other (without affecting the final outcome) regardless of whether it's positive or negative, so I'm inclined to leave it as it is, unless there's a further chorus of protest on this (???)Anyone?

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@Mr Loi: yupp. It will cancel cause negative value divide by negative value will still be 1. I'm saying that if you write length of OA as 2psqrt2, it is not correct, cause a length cannot be negative. It's just mathematically not rigorous; just that it happens that cause the qn wants to prove independence, the two cancels and nothing goes wrong at the end of the day. But just cause it cancels out and still gives the correct ans doesnt mean the middle working is correct. Many times in H2 maths differentiation, there's sqrt (x^2) and must put (absolute value of x). but this time it wont change the ans. squaring makes it positive, which is why when you take the square root, you need to put the absolute sign because the square and square root process ensures that p becomes the positive value.

It depends on how picky Cambridge is. 🙂

From brian's blog: Exam Matters

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Thanks Mr Loi. 🙂

Here, I have simpler methods for a few of the questions, purely for your reference. Do let me know if any of them is wrong, thanks!

Q1ii

(a+b).(a-b)

= a.a - b.b

= |a|^2 - |b|^2

= 0 (since |a|=|b|)

Q3i

Un

= Sn - Sn-1

= n(2n+c) - (n-1)(2n-2+c)

= ...

= 4n+c-2

Q3ii

Un+1

= 4(n+1)+c-2

= 4n+c-2+4

= Un+4

Q11iii

x^2 = (t+1/t)^2 = t^2+2-1/t^2

y^2 = (t-1/t)^2 = t^2-2-1/t^2 = x^2-4

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can u upload the h2 maths paper 2 too!? thank you....

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Hi can upload paper 2 solutions ?

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Wah lao! Is it okay if I just write my name on the yellow cover page :-s

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@Daniel: I don't think so centre number and index number required eh

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@Wee keat: No i wrote it. My name, centre number and index number. But I didnt write my name on my answer paper, except for the first one 🙁

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@Daniel: shouldn't go wrong as long as your scripts are tightly secured throughout their journey to UK.. so pray hard.

and make sure you write your name and index on all the scripts for following papers just in case.. besides, they give you extra time to do so at the start so why not 🙂

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@Xinzyl: Thanks! Seriously I was too nervous to think about writing my name b4 start the paper 🙁 OMG, cannot imagine if I suddenly get U for Maths 🙁

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@Daniel: Hmmmm pray that your papers wont get detached from your stack of answers during the flight to Cambridge, and before your script gets to the marker. Else it would be hard to trace your answers w no name nor index# on your answers.

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Please upload paper 2 answers too! Thanks a lot for being so efficient and dedicated. 🙂

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Hey, for question 11, are we able to do it by the vectors method? (1/2)|a x b| where a is coordinates of the first point, with k = 0, and likewise for b?

Also, please upload paper 2 answers too! Thanks! 😀

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@Lithilara: I also did the same way, using vector method 🙂 I think there should be no problem, because eventually i can show the area is independent of p.

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hi answers for p2 please?

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Heyhey thanks for uploading the paper 1 solutions. Can you upload the paper 2 solutions as well? HAHA many people are asking. Guess you should be working out the solutions using technology HAHA and what would be a safe mark for an A for this year's paper? Seems easier than last year's. Thanks!

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Hi is it possible for you to post the H1 math paper solutions please? Would appreciate it ALOT!

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Erm.... 90% abv A, 80% abv B, 70% abv C?

Generally cant tell, but most seem to be getting 80 n abv i think? But my math teacher seys that 50% of Sporean get A fer maths.. So well its hard imagining 50% of SG getting 80% n abv.... Scary...

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hello may i know is it ok if i dont state the axial intercepts or equations of assymptotes separately but i mention them in the graph?

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-.- 90% to get A ?

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answers please!!!

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love u for uploading paper 1...please do the same for paper 2 hahaha

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thx

sigh prepared not to get A already =( i onli eighty plus for this paper. few friends got almost hundred. bell curve will be push up. plus paper two i veri careless. paper2 ans plz ?=)

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@meyeyumi: meyeyumi: Which school are you from?

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@hi: AJC, u know mi?

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yo. think i have simpler method for Q11.

x = t + 1/t

y = t - 1/t

x + y = 2t

x - y = 2/t

t = (x+y)/2

x - y = 4/(x+y)

x^2 - y^2 = 4

there you go haha. tnks

btw mr loi, you rawk for putting up the ans so fast!

nice job!

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Hmmmm, at this point of time.. it seems -10 from paper 2 seems screwed up alrdy (cus of moderation n all) T_T

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hi. can you please upload paper 2 solutions?cant stop thinking abt it!

THANKS!!!

and,seriously,90 for As? dun lame la.

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any idea when would e paper 2 be out??

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getting only a c wit 70?? omg

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I think most likely 80+ n abv, I mean even if Cambridge moderate the paper they cant expect 90+ to be A... Most likely National Avg for A sky-rockets 😀 Either that or SG gonna face serious grade-inflations ==

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PLEASEEEEEEEEEEEEEEE post up the answers for H1 maths paper? why so biased? haha!

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i think people are making overbearing assumptions on what the A grade is based on their own perceptions of the paper and the small groups of people around them. I do not think that the minimum mark for A would be 80 or even worse, 90. It has been said that ~50% of S'poreans get A for math. Do you really expect half the JC population to get 80 and above? My personal opinion is that the A grade will always remain at ~70+ and will be moderated down if the paper is too tough. Even for this year, where the paper was 'considerably easy', it will remain at 70+, i mean just forget this 'bell curve' that people love to make reference to but know nothing much about, do you think that a person who gets 70+ does not deserve an A?

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@suphomies: Totally agree!!! 80 is the highest grade they can raise alr.

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@suphomies: hi suphomies

i hope you;re right (: your comment did make me feel better after seeing the others above. haha, 90 for A marks just made my heart sink./ Haa

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@suphomies: Yeap I agree with you! Cambridge has to be fair despite the paper being easier this year.. I think the min mark for A, at most, will be raised to a 75. (:

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last year's A was 80, but it was a significantly more difficult paper than this year's ridiculously elementary paper, if you're careless, that's it.

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If I scored 63 for p1, 76 for paper 2 thereabouts, is there a possibility of A? And I dont think they'll raise the bar for A so high hor, at most 75.

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@K: K, you know my most of my friends who constantly flunked their maths or didn't even practice a single prelim papers now score around 85 for each paper?

This is what happens when the paper was set so easy. Don't even have de Moire, connected rate of change, APGP, and volume of solid. What a joke.

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@lalala: @ Lalala how did you know that?! :O

I didn't bother attempting last year's paper but my classmates who did found this year's harder, oddly. But yes carelessness is the make or break factor.

Thanks for posting the solutions to P1: Eagerly waiting for P2! (:

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@Anon: @Anon

My senior told me that, he counted his marks with his teacher immediately after the exam and got around 80±2

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@lalala: Lalala, did your snr get an A? If he did, it doesn't necessarily mean 78 is the lower limit of an A grade, just that 78 = A.

If he got a B.... Ouch!

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@Anon: yes, i actually found this year's paper to be harder than '09. ><

From brian's blog: All the best for A levels!

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@lalala: May I know which sch r u from?

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@K: Dont worry!! I dont think they can raise the bar to above 80. Yet 75 does not ensure an A 🙁

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@K: You are right abt that. 73 was max in the history of math.

From brian's blog: Exam Matters

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@brian: How do you know that 73 is the max in the history of math? it seems pretty low...

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Don't think they will raise the bar so high also, maybe around 75 to 80? From the % of As in schools, its hard to think that there are so many students achieving like such high scores after careless mistakes etc...

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is the total number of As fixed? or is there a chance that they will increase the As if the whole cohort performed well.

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I think it will be likely that % As increase rather than decrease... look at pw haha

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Hey ma'am, are you going to post the paper 2 answers? Please do!

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Oh yes. by the way will there be method marks? Lets say part(i) wrong but (ii) method 100% correct only answer wrong...

So will I get the full marks for part (ii) still?

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@Shermz: Oh boy there are still people camping here at this hour. Wondering if I should just go ahead and publish it now ...

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@Shermz: yes, there are method marks in As. in your case you'll get at least partial credit for part (ii). my senior says you'll get full marks for part ii if your method is correct (:

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@amber: Hi thanks amber... saw your posts in the previous threads... all quality posts supported with cambridge evidence as well. Thanks a lot!

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Alright everyone, break your camps and move over here 😀

I'll try to catch up with some of the comments here once I get the time to do so. Meanwhile sweet dreams everyone ... zzzzz ....

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For Q2 i) Paper 1: Is it possible for me to use McLaurin to expand 1+sin2x instead using MF15?

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@Daniel: No worries, but expanding sin 2

xvia Maclaurin would be a little more tedious though.曜

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erm, may I know which sch r u from?

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please tell me 80 plus minus two is enough to get an A.... anyway not to discriminate but not every jc is like ri or hci

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hey just to make sure.

wad happens if i get 4 coordinates for qn4(ii) by subbing it into the original eqn? will i still be penalized even tho i got the 2 values correct???

also for qn3, will my method hold?

n(2n+c)

= n/2(4n +2c)

= n/2(c+2+c+2+4(n-1))

therefore, it is an AP since it follows the general formula.

Tn = c+2+4(n-1)

Tn = 4n+c-2

some help here pls!!!

tnks

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@thecarz: The outcome to both your questions will really depend on the marker, as I've always felt that it's more important to demonstrate your understanding of essential concepts rather than the correctness of your final answer as far as A Level Maths go.

For Q4(ii), usually it's method marks awarded for correct workings but wrong answer. However in this case it's likely something has gone awry in your working/approach but yet you've somehow obtained the 'correct' answers so .... hmmmm ...

For Q3(i), you appeared to have made a somewhat bold assumption at the start that the sequence

isan A.P., before working backwards to 'confirm' it. So it's really up to the marker to be convinced that you've "demonstrated your understanding of the concept involved in finding the general term of the sequence".曜

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Hmm I definitely agree that A should be 75~80. 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...

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how did people from other jcs do? i'm from vj and so far i've only heard of roughly 3-4 people doing not so good...

even our arts students are getting near full marks wts

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im from hci and the majority of people think that this paper is easy but that doesnt mean most of us will do well (90 and above). In fact, alot of us made a lot of careless mistakes so for a safe estimate, the majority of the school will score between 78~82 for the overall grade. So that perhaps shall determine the cutoff point for an 'A'.

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Hi i would just like to comment on the ans given for 2010 H2 maths 9740 paper 1 solutions

For qn 8i) i think there is a mistake i spotted.

Qouting frm the solution u gave: arg (z

_{2})=-Shldnt it be =- ???

Hence the next few ans are diff bcos of the ans fr arg (z

_{2})Im taking my H2 alevel maths this year so im just a random visitor to this site cos i was practicing the 2010 maths paper and was checking my ans with the solutions given here , if im wrong pls correct me thank you.

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@Random user:

I've shifted your comment over to this post to keep everything on topic.

The principal argument of

z_{2}= −1−i is always , since it lies in the 3rd quadrant as shown in the Argand diagram.What I've missed out in the workings is the

−π +to reflect this which probably led to a bit of confusion there.Anyway this change will be reflected on our final cleaned-up H1/H2 maths solutions which are going to be released very very very soon!

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hi can you do the solutions for this year's h1 math paper? would really like to know how i did.... thank you

## 4 Reactions

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