While my sister has churned out her O Level A/E-Maths solutions with much fanfare, here’s my little contribution to all our A Level comrades this year.

Q6(iii) – amended working step n = lg1000/lg2 to compare 2^{9} = 512 and 2^{10} = 1024, in order to comply strictly with the “No Calculator” requirement in this question. Q11(i) – improved descriptions of the tangents (sorry couldn’t write straight that night *sigh*)

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, which was produced well after my last class at the end of my tiring day *rubs eyes*

Now go revise your

AP/GP

Integration by parts/substitution/ Volume of revolutions

@boo: Which "RJC's teacher" said that, may I ask? I'm from RJC myself, and if it's true that the grade boundary is 87, then even this school will have a ridiculously low distinction rate. Look at my below comment, and that of Carol.

Hi sir, just a few qns. for qn ten my method was correct of substituting h equals to something k, but the substitution was wrong. approximately how many marks for method will i get? additionally for the mi qn i put n is z and not z plus, is that ok,like will minus mark? and erm for the definite integral i just put =answer(in 3dp) without the longer answer than the curly equal sign, is that ok, like will minus mark? and uhm for the vectors qn 9 i got first aprt correct but cos of calculation error second and third aprt wrong but emthod correct, approx how many method marks? similarly for the intial vector qn ihad a calculation error at the final step the square root u etc last step, is that enuff for two method marks? and for the integration qn i didnt say c is a constant is that ok? and finally do u hv any duiea whats the grade range for a? any help would be sincerely appreciated thanks

and sorry one last one. for qn 8 i just said since the sign is negatiove its always less than zero. but i accidentally put min point. will is till get 1method mark? thank you

Here we go again, people asking about the grade boundary to get an A, as with every year. There is really no way anyone can give a good approximate, because SEAB is very opaque when it comes to their moderation procedure, so we can't really know. The worst thing anyone can do now is to give a high estimate (e.g. 85) since this was an 'easy' paper, then everyone who did NOT get that grade will start fearing, and have decreased morale.

Vector equation of the line AB: r = (7,8,9) + λ[ -(7,8,9) + (-1,-8,-1)] = (7,8,9) + λ(-8,-16,-8) , where λ is a parameter. (Can this be left as the final answer?)

@Jud: should be accepted. having factorised out the common factor doesnt change the answer. people usually factorise for sake of minimising careless mistakes when cal,

Hi, I would like to ask if answers that are not simplified will be accepted or penalized. For eg Q9iii, I didn't simplify my answer and left the Cartesian equation as over 2, -8 and 2 for the x y and z respectively. And for Q6iii also I left it as -10pie /3.

@T: For Q9(iii), you mean you left your equation of the line as a column vector? If this is the case then it's not in cartesian equation form leh.

For Q6(iii), generally it's a good idea to express your final answers for arguments as the principle argument but you may get away with leaving it as −10π/3 since the question did not specify requirement for the argument of z^{n} to be between −π and π in this case.

Hi may I ask if they asked you not to use a calculator in question 6 and you used lg1000/lg2 to compute n which is also stated in your solutions provided, what will happen?

@curious: For 6(iii), having yet to explore an alternative method, we'll all arrive at 2^{n} > 1000.

Hmmm ... maybe I should simply know that 2^{10} = 1024 and remove the lg1000/lg2 part just to strictly "comply". Heh. Alright amended the step to compare 2^{9} and 2^{10} in version 1.1 of the solutions.

hi to all who asked about mark gauges.. i would like to paraphrase a quote from a previous forum, and the quote was from the cambridge examiners themselves: the grading for a levels is comparable to judging a student's ability to swim 100 metres. if you're able to clear the 100 metres, you'll get the A regardless of the number of people who are able to swim around the world. so i guess don't worry if you aren't able to hit a high score, just aim for as high as possible for tmr's paper!

if you really want a gauge.. i think the RJ comment is not representative of wat is going on in SG la. over here at where i am the consensus is "ok but damn tedious", My estimate for my own score is 82 (provided got ecf..), but i've also seen ppl who couldn't do all the last three qns. so i guess this year the threshold will be lower..

@Mr Loi: oh yes Mr Loi, just some question to ask: will there be method marks and ecf for question 10 if i forgot to include the base area. because i did everything else the same way and got an answer for r that differs by a digit..

and for question 11 i used parametric integration (the one where you differentiate y in terms of t and leave x as it is, then integrate in terms of t), and got 3pi (though with a negative sign so i took absolute value). would that be fine as well?

@Carol: As mentioned here, method marks and ECF are determined by the mark scheme, and that they are given when it was only the substitution of a wrong value in your appropriate steps that led to the wrong answer.

While I think there's a good chance they're allocated here with [7] & [5] marks in parts (i) & (ii), I'm really hoping they'll be lenient in your case since omitting the base area would have affected the expressions for the surface area, its derivative, r and h. (unless you've gotten some of the above right?)

For Q11, you seem to have done it the same way as me. If so, you shouldn't get −3π. Have you gotten your limits the other way round in the definite integral?

@Mr Loi: Sorry for the long hiatus. I found h in terms of r using the volume expression, so that part would be the same as the answer scheme. Yeah I do hope method marks will be given, since there is really no difference in the method other than the base area, and quite a lot of people from my school had left out the base area when calculating as well..

As for question 11, I realised I had unwittingly integrated x in terms of y, and it so happened that the answer was the same in magnitude. So I suppose I will lose the method marks and hopefully get one mark for the right answer...

Luckily paper 2 managed to pull me up, despite being a harder paper.

@amos: For Q3, though it wasn't explicitly stated, I really think Cambridge's intention is to test your concept in utilizing the given expression of u_{n} rather than coming up with your own G.P. method.

Hi, for the question that needs us to show that dy/dx = cot 0.5θ, could we do it this way? dy/dx=... = (sin θ)/(1-cosθ) = (sin 0.5θ+0.5θ) / ( 1- cos(0.5θ+0.5θ)) then we go on to solving the equation using these 2 formulas: sin( A+B) = sinAcosB+cosAsinB and cos(A+B)= cosAsinB-sinAcosB if not, then why is it wrong?

@Mr Loi: Hi Sir, but the problem is that when I continued to solve it using the additional formula, the final answer I get is 2 sin 0.5θ cos0.5θ. I am unable to get cot 0.5θ.

Hi Miss Loi, I know this is not the 2013 thread but I can't find it so can I ask you a general question regarding the grading system?

Does Cambridge give us our marks (based on score and/or ability) or do they simply write down our scores and give them to MOE who will moderate them and create the bell curve?

I am asking this because I am afraid I am scoring a low 70s due to a lot of careless mistakes 🙁

* 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]

Gratitudes

中三时，我对数学已经心灰意懒，认为那是难以捉摸的科目。但是，在Ms Loi 的耐心教导下，面对中四离校考试时，我对两棵树学以信心满满。而在稍早前的预考中，两课数学也拿了A1。… [read more]

## 48 Comments

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just wondering, how difficult do you think this year's H2 paper was?

曜

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@pheng: wa tis year's paper too easy.. RJC's tcher said to get A yall hav to score above 87 at least

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@boo: Which "RJC's teacher" said that, may I ask? I'm from RJC myself, and if it's true that the grade boundary is 87, then even this school will have a ridiculously low distinction rate. Look at my below comment, and that of Carol.

曜

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Hi hi, are you gonna share the solutions for H1 Math too?

曜

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Hi sir, just a few qns. for qn ten my method was correct of substituting h equals to something k, but the substitution was wrong. approximately how many marks for method will i get? additionally for the mi qn i put n is z and not z plus, is that ok,like will minus mark? and erm for the definite integral i just put =answer(in 3dp) without the longer answer than the curly equal sign, is that ok, like will minus mark? and uhm for the vectors qn 9 i got first aprt correct but cos of calculation error second and third aprt wrong but emthod correct, approx how many method marks? similarly for the intial vector qn ihad a calculation error at the final step the square root u etc last step, is that enuff for two method marks? and for the integration qn i didnt say c is a constant is that ok? and finally do u hv any duiea whats the grade range for a? any help would be sincerely appreciated thanks

曜

日

and sorry one last one. for qn 8 i just said since the sign is negatiove its always less than zero. but i accidentally put min point. will is till get 1method mark? thank you

曜

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hi sir can u approximate the a for this year?

曜

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hello

for qn 9 (ii) is it possible to find the ratio of the lengths AN:NB using this method? or why is it not acceptable?

AN = ON - OA

NB = OB - ON

proceed to mod AN and NB, then compare the lengths? my answer was 1:5 if i didn't forget.. :/

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@angstzx: angstzx, the question requires to compare ratio of the vectors AN and NB. not the length. they dint mod the vectors

曜

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@angstzx: Errr ... I thought that's exactly what I did?

Actually the question simply asked for the ratio

AN:NBbut you may obtain the same answer (1 : 3) via too.曜

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i think the difficulty of p1 for this year as compared to last year was eazier

曜

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Hi I think qn 11iii) has a mistake, the limits weren't changed from x to teter?

曜

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@Ang: Well in this question, the limits for

xandθhappen to be the same since when sketching the curve in part (ii), we've already determined that:x= 0 whenθ= 0 at (0, 0)x= 2πwhenθ= 2πat (2π, 0)曜

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Hi, I would like to ask if there's likely to be ECF for QN 11, as I did not include the base surface area.

Thanks!

曜

日

Here we go again, people asking about the grade boundary to get an A, as with every year. There is really no way anyone can give a good approximate, because SEAB is very opaque when it comes to their moderation procedure, so we can't really know. The worst thing anyone can do now is to give a high estimate (e.g. 85) since this was an 'easy' paper, then everyone who did NOT get that grade will start fearing, and have decreased morale.

曜

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Hello! May I ask what is the estimated mark for an A this year?:)

曜

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For question 9(i),

Why shouldn't the solution be:

Vector equation of the line AB:

r = (7,8,9) + λ[ -(7,8,9) + (-1,-8,-1)]

= (7,8,9) + λ(-8,-16,-8) , where λ is a parameter.

(Can this be left as the final answer?)

曜

日

@Jud: should be accepted. having factorised out the common factor doesnt change the answer. people usually factorise for sake of minimising careless mistakes when cal,

曜

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@Jud: Yup not a problem 😉

曜

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is 75 safe? can any1 estimate for me pls

曜

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Hi, I would like to ask if answers that are not simplified will be accepted or penalized. For eg Q9iii, I didn't simplify my answer and left the Cartesian equation as over 2, -8 and 2 for the x y and z respectively. And for Q6iii also I left it as -10pie /3.

Thanks

曜

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@T: For Q9(iii), you mean you left your equation of the line as a column vector? If this is the case then it's not in cartesian equation form

leh.For Q6(iii), generally it's a good idea to express your final answers for arguments as the principle argument but you may get away with leaving it as −10π/3 since the question did not specify requirement for the argument of

z^{n}to be between −π and π in this case.曜

日

Hi may I ask if they asked you not to use a calculator in question 6 and you used lg1000/lg2 to compute n which is also stated in your solutions provided, what will happen?

曜

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@curious: For 6(iii), having yet to explore an alternative method, we'll all arrive at 2

^{n}> 1000.Hmmm ...

~~maybe I should simply~~Alright amended the step to compare 2knowthat 2^{10}= 1024 and remove the lg1000/lg2 part just to strictly "comply". Heh.^{9}and 2^{10}in version 1.1 of the solutions.曜

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I could guarentee 85 - 88 marks. Isit safe for an A ?

曜

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hi to all who asked about mark gauges..

i would like to paraphrase a quote from a previous forum, and the quote was from the cambridge examiners themselves: the grading for a levels is comparable to judging a student's ability to swim 100 metres. if you're able to clear the 100 metres, you'll get the A regardless of the number of people who are able to swim around the world. so i guess don't worry if you aren't able to hit a high score, just aim for as high as possible for tmr's paper!

if you really want a gauge.. i think the RJ comment is not representative of wat is going on in SG la. over here at where i am the consensus is "ok but damn tedious", My estimate for my own score is 82 (provided got ecf..), but i've also seen ppl who couldn't do all the last three qns. so i guess this year the threshold will be lower..

曜

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@Carol: True. If its 87 for an A, all the people taking h2 math in rj and hci sure A then people of yjc and mi get D? Lol

曜

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@meme: ...i'm from hci btw haha.

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@Carol: im from yjc. practically half of the school said that p1 was difficult lol.

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@meme: well for me i was ridiculously careless.. at first i put the correct ans for smth and then changed it. 3 marks down the drain ><

曜

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@Carol:

LIKE!This quote really brings back memories of that long list of comments in 2010!

曜

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@Mr Loi: oh yes Mr Loi, just some question to ask: will there be method marks and ecf for question 10 if i forgot to include the base area. because i did everything else the same way and got an answer for r that differs by a digit..

and for question 11 i used parametric integration (the one where you differentiate y in terms of t and leave x as it is, then integrate in terms of t), and got 3pi (though with a negative sign so i took absolute value). would that be fine as well?

曜

日

@Carol: As mentioned here, method marks and ECF are determined by the mark scheme, and that they are given when it was only the substitution of a wrong value in your appropriate steps that led to the wrong answer.

While I think there's a good chance they're allocated here with [7] & [5] marks in parts (i) & (ii), I'm really hoping they'll be lenient in your case since omitting the base area would have affected the expressions for the surface area, its derivative,

randh. (unless you've gotten some of the above right?)For Q11, you seem to have done it the same way as me. If so, you shouldn't get −3π. Have you gotten your limits the other way round in the definite integral?

曜

日

@Mr Loi: Sorry for the long hiatus. I found h in terms of r using the volume expression, so that part would be the same as the answer scheme. Yeah I do hope method marks will be given, since there is really no difference in the method other than the base area, and quite a lot of people from my school had left out the base area when calculating as well..

As for question 11, I realised I had unwittingly integrated x in terms of y, and it so happened that the answer was the same in magnitude. So I suppose I will lose the method marks and hopefully get one mark for the right answer...

Luckily paper 2 managed to pull me up, despite being a harder paper.

曜

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Hi, will there be solutions for the Math H1 paper as well?

曜

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@Adeline: Here.

曜

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Will it be penalised if l = -1/3 is found using GP method instead of the usual way?

曜

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@amos: For Q3, though it wasn't explicitly stated, I really think Cambridge's intention is to test your concept in utilizing the given expression of

u_{n}rather than coming up with your own G.P. method.曜

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@Mr Loi: For some reasons I did it using the GP way but ended up with the same answer. Is there a likelihood that marks will be deducted ><''

曜

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Hi Sir, may I know if today maths paper 2 solutions will be up?

曜

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@Ang: Here.

曜

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Hi, for the question that needs us to show that dy/dx = cot 0.5θ, could we do it this way?

dy/dx=...

= (sin θ)/(1-cosθ)

= (sin 0.5θ+0.5θ) / ( 1- cos(0.5θ+0.5θ))

then we go on to solving the equation using these 2 formulas:

sin( A+B) = sinAcosB+cosAsinB and

cos(A+B)= cosAsinB-sinAcosB

if not, then why is it wrong?

thanks 🙂

曜

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@Jess: Q11(i) Using Additional Formulae is perfectly fine, though it looks a bit tedious 😉

曜

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@Mr Loi: Hi Sir, but the problem is that when I continued to solve it using the additional formula, the final answer I get is 2 sin 0.5θ cos0.5θ. I am unable to get cot 0.5θ.

thanks!

曜

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@Jess: Hmmm ...

(shown)

Did you steps tally?

曜

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Are we really expected to do 2^10 without calculators? =\

曜

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Hi ,I know it's kind of late haha but my friend wanna ask whether can switch step1 with step 3 for qn7:)

曜

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Hi Miss Loi, I know this is not the 2013 thread but I can't find it so can I ask you a general question regarding the grading system?

Does Cambridge give us our marks (based on score and/or ability) or do they simply write down our scores and give them to MOE who will moderate them and create the bell curve?

I am asking this because I am afraid I am scoring a low 70s due to a lot of careless mistakes 🙁

Thanks!