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# GCE ‘A’ Level 2010 Oct/Nov H2 Maths 9740 Paper 1 Suggested Answers & Solutions

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Tuition given in the topic of H1/H2 (A Level) Maths Tutor from the desk of at 5:26 pm (Singapore time)

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):

2010 ‘A’ Level October/November H2 Mathematics 9740 Paper 1 Suggested Solutions

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!

### Revision Exercise

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

1. unicorn commented in tuition class

2010
Nov
11
Thu
7:32pm

1

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

2. :D commented in tuition class

2010
Nov
11
Thu
7:43pm

2

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

3. digi commented in tuition class

2010
Nov
11
Thu
7:58pm

3

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?

4. lolatyou commented in tuition class

2010
Nov
11
Thu
8:20pm

• 2010
Nov
12
Fri
2:03pm

4.1

@lolatyou: Yup for Q3(i), un can indeed be straightforwardly obtained via SnSn−1 but I've found through my cheong hei long-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 un = SnSn−1 method for everyone's reference.

5. james commented in tuition class

2010
Nov
11
Thu
8:33pm

5

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

6. kris commented in tuition class

2010
Nov
11
Thu
10:06pm

6

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

7. emma commented in tuition class

2010
Nov
11
Thu
10:29pm

7

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?

8. commented in tuition class

2010
Nov
12
Fri
11:40am

8

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

• 2010
Nov
12
Fri
1:56pm

8.1

@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 of OA and OB, coupled with the fact that the ps 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?

• replied to Mr Loi’s comment

2010
Nov
13
Sat
10:31am

@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

9. Otto commented in tuition class

2010
Nov
12
Fri
12:58pm

9

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

10. tim commented in tuition class

2010
Nov
12
Fri
3:19pm

10

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

11. Wee keat commented in tuition class

2010
Nov
12
Fri
3:40pm
12. Daniel commented in tuition class

2010
Nov
12
Fri
3:44pm

12

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

13. banana commented in tuition class

2010
Nov
12
Fri
4:08pm

13

14. Lithilara commented in tuition class

2010
Nov
12
Fri
5:23pm

14

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?

15. candice commented in tuition class

2010
Nov
12
Fri
5:41pm
16. hello commented in tuition class

2010
Nov
12
Fri
5:57pm

16

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!

17. Nick commented in tuition class

2010
Nov
12
Fri
6:45pm

17

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

18. Anonymous commented in tuition class

2010
Nov
12
Fri
6:50pm

18

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...

19. alex commented in tuition class

2010
Nov
12
Fri
7:53pm

19

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?

20. m commented in tuition class

2010
Nov
12
Fri
8:37pm
21. hi commented in tuition class

2010
Nov
12
Fri
8:44pm
22. arjun commented in tuition class

2010
Nov
12
Fri
9:08pm

22

23. meyeyumi commented in tuition class

2010
Nov
12
Fri
9:11pm

23

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 ?=)

24. thecarz commented in tuition class

2010
Nov
12
Fri
9:26pm

24

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!

25. Anonymous commented in tuition class

2010
Nov
12
Fri
9:45pm

25

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

26. orangejuice commented in tuition class

2010
Nov
12
Fri
9:46pm

26

hi. can you please upload paper 2 solutions?cant stop thinking abt it!
THANKS!!!
and,seriously,90 for As? dun lame la.

27. guy commented in tuition class

2010
Nov
12
Fri
9:58pm
28. guy commented in tuition class

2010
Nov
12
Fri
10:00pm
29. Anonymous commented in tuition class

2010
Nov
12
Fri
10:02pm

29

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 ==

30. ohno commented in tuition class

2010
Nov
12
Fri
10:08pm

30

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

31. suphomies commented in tuition class

2010
Nov
12
Fri
10:23pm

31

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?

32. lalala commented in tuition class

2010
Nov
12
Fri
10:33pm

32

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.

33. K commented in tuition class

2010
Nov
12
Fri
10:38pm

33

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.

34. Shermz commented in tuition class

2010
Nov
12
Fri
11:06pm

34

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...

35. celine commented in tuition class

2010
Nov
12
Fri
11:07pm

35

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

36. Shermz commented in tuition class

2010
Nov
12
Fri
11:32pm

36

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

37. Tak commented in tuition class

2010
Nov
12
Fri
11:53pm

37

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

38. Shermz commented in tuition class

2010
Nov
13
Sat
3:49am

38

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?

39. Mr Loi Friend Mr Loi on Facebook commented in tuition class

2010
Nov
13
Sat
4:44am

39

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 ....

40. Daniel commented in tuition class

2010
Nov
13
Sat
9:26am

40

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

41. Anon commented in tuition class

2010
Nov
13
Sat
9:48am
42. kim commented in tuition class

2010
Nov
13
Sat
7:51pm

42

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

43. thecarz commented in tuition class

2010
Nov
13
Sat
8:15pm

43

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

• 2010
Nov
16
Tue
8:54pm

43.1

@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 is an 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".

44. Anonymous commented in tuition class

2010
Nov
13
Sat
11:07pm

44

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...

45. kim commented in tuition class

2010
Nov
14
Sun
4:17pm

45

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

46. jqw commented in tuition class

2010
Nov
14
Sun
7:55pm

46

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'.

47. Random user commented in tuition class

2011
Sep
8
Thu
11:23am

47

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 (z2)=-
Shldnt it be =- ???
Hence the next few ans are diff bcos of the ans fr arg (z2)
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.

• 2011
Sep
8
Thu
9:20pm

47.1

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

The principal argument of z2 = −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!

48. marie commented in tuition class

2011
Nov
10
Thu
5:52pm

48

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

1. akagitenpai tweeted

2010
Nov
11
Thu
12:50pm

49

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2. T. Jonathan tweeted

2010
Nov
11
Thu
1:12pm

50

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3. Ben Lim tweeted

2010
Nov
11
Thu
1:20pm

51

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4. 2010
Nov
11
Thu
1:42pm
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