2012
Wed
7
Nov

# GCE A Level 2012 Oct/Nov H2 Maths 9740 Paper 1 Suggested Answers & Solutions

(53)
Tuition given in the topic of H1/H2 (A Level) Maths Tutor from the tuition centre desk of at 9:09 pm (Singapore time)

It’s my annual hello to all of you again.

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.

Click the button and grab it here!

• 1.1:

Q6(iii) – amended working step n = lg1000/lg2 to compare 29 = 512 and 210 = 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
• Summatioon (Method of Difference)
• Complex Numbers (Argand diagram)

All the best for your Paper 2!

### Revision Exercise

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

1. pheng commented in tuition class

2012
Nov
7
Wed
9:33pm

1

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

• boo replied to pheng’s comment

2012
Nov
8
Thu
9:47am

1.1

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

• x replied to boo’s comment

2012
Nov
9
Fri
6:15pm

@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.

2. Michelle Lee commented in tuition class

2012
Nov
7
Wed
9:35pm

2

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

3. ck commented in tuition class

2012
Nov
7
Wed
9:41pm

3

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

4. ck commented in tuition class

2012
Nov
7
Wed
9:45pm

4

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

5. j commented in tuition class

2012
Nov
7
Wed
9:49pm

5

hi sir can u approximate the a for this year?

6. angstzx commented in tuition class

2012
Nov
7
Wed
9:53pm

6

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.. :/

• gr replied to angstzx’s comment

2012
Nov
7
Wed
10:05pm

6.1

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

• 2012
Nov
9
Fri
1:14am

6.2

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

Actually the question simply asked for the ratio AN : NB but you may obtain the same answer (1 : 3) via $\vec{NB}=3\vec{AN}$ too.

7. gr commented in tuition class

2012
Nov
7
Wed
9:59pm

7

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

8. Ang commented in tuition class

2012
Nov
7
Wed
10:53pm

8

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

• 2012
Nov
8
Thu
11:51pm

8.1

@Ang: Well in this question, the limits for x and θ happen to be the same since when sketching the curve in part (ii), we've already determined that:

x = 0 when θ = 0 at (0, 0)
x = 2π when θ = 2π at (2π, 0)

9. Wesley commented in tuition class

2012
Nov
7
Wed
11:18pm

9

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!

10. x commented in tuition class

2012
Nov
7
Wed
11:26pm

10

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.

11. cheryl commented in tuition class

2012
Nov
7
Wed
11:38pm

11

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

12. Jud commented in tuition class

2012
Nov
8
Thu
12:05am

12

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?)

• gr replied to Jud’s comment

2012
Nov
8
Thu
1:05am

12.1

@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,

• 2012
Nov
9
Fri
1:04am

12.2

@Jud: Yup not a problem

13. daniel zeng commented in tuition class

2012
Nov
8
Thu
2:20am

13

is 75 safe? can any1 estimate for me pls

14. T commented in tuition class

2012
Nov
8
Thu
7:39am

14

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

• 2012
Nov
9
Fri
1:04am

14.1

@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 zn to be between −π and π in this case.

15. curious commented in tuition class

2012
Nov
8
Thu
8:09am

15

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?

• 2012
Nov
9
Fri
1:32am

15.1

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

Hmmm ... maybe I should simply know that 210 = 1024 and remove the lg1000/lg2 part just to strictly "comply". Heh. Alright amended the step to compare 29 and 210 in version 1.1 of the solutions.

16. meme commented in tuition class

2012
Nov
8
Thu
1:17pm

16

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

17. Carol commented in tuition class

2012
Nov
8
Thu
6:55pm

17

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..

• meme replied to Carol’s comment

2012
Nov
8
Thu
7:23pm

17.1

@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

• Carol replied to meme’s comment

2012
Nov
9
Fri
3:08pm

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

• meme replied to Carol’s comment

2012
Nov
9
Fri
3:52pm

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

• Carol replied to meme’s comment

2012
Nov
9
Fri
5:28pm

@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 ><

• 2012
Nov
9
Fri
12:00am

17.2

@Carol: LIKE!

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

• Carol replied to Mr Loi’s comment

2012
Nov
9
Fri
3:18pm

@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?

• 2012
Nov
13
Tue
12:29am

@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?

• Carol replied to Mr Loi’s comment

2012
Nov
13
Tue
7:11pm

@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.

18. Adeline commented in tuition class

2012
Nov
8
Thu
9:59pm

18

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

• 2012
Nov
12
Mon
11:28pm
19. amos commented in tuition class

2012
Nov
9
Fri
5:49pm

19

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

• 2012
Nov
13
Tue
12:35am

19.1

@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 un rather than coming up with your own G.P. method.

• amos replied to Mr Loi’s comment

2012
Nov
13
Tue
10:12pm

@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 ><''

20. Ang commented in tuition class

2012
Nov
9
Fri
6:55pm

20

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

• 2012
Nov
12
Mon
11:29pm
21. Jess commented in tuition class

2012
Nov
10
Sat
1:08pm

21

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

• 2012
Nov
13
Tue
12:41am

21.1

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

• Jess replied to Mr Loi’s comment

2012
Nov
13
Tue
2:19pm

@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!

• 2012
Nov
14
Wed
12:09am

@Jess: Hmmm ...

$\frac{\sin (\frac{\theta}{2}+\frac{\theta}{2})}{1-\cos (\frac{\theta}{2}+\frac{\theta}{2})}$

$=\frac{\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})+\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{1-[\cos (\frac{\theta}{2})\cos (\frac{\theta}{2})-\sin(\frac{\theta}{2})\sin(\frac{\theta}{2})]}$

$=\frac{2\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{1-\cos^2 (\frac{\theta}{2})+\sin^2(\frac{\theta}{2})}$

$=\frac{2\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{\sin^2 (\frac{\theta}{2})+\sin^2(\frac{\theta}{2})}$

$=\frac{2\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{2\sin^2 (\frac{\theta}{2})}$

$=\frac{ \cos(\frac{\theta}{2})}{\sin (\frac{\theta}{2})}$

$= \cot (\frac{\theta}{2})$ (shown)

Did you steps tally?

22. Yak commented in tuition class

2012
Nov
15
Thu
10:44pm

22

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

23. Dudeail commented in tuition class

2012
Dec
3
Mon
10:26pm

23

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

24. Drea commented in tuition class

2013
Nov
18
Mon
10:43am

24

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!

### 5 Reactions

1. Miss Loi tweeted

2012
Nov
7
Wed
1:16pm

25

#alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

2. yen tweeted

2012
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#alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

3. Wee Keat tweeted

2012
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#alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

4. Lau Hui Ru tweeted

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Nov
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28

#alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

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