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2011
Fri
28
Oct

# GCE O Level Oct/Nov 2011 E-Maths 4016 Paper 2 Suggested Answers & Solutions

(56)
Tuition given in the topic of Miss Loi the Tutor from the desk of at 11:20 pm (Singapore time)

To the 1.0 × 10n (2 sig. fig.) missed calls & emails (from these few days) that are currently residing in Miss Lo’s handphone now:

As Miss Loi is deeply embroiled in her Mega Jφss Sticks sessions during this period of consecutive O Level A/E-Maths papers Please SMS or email your contact number if you’re interested in joining her maths classes for the new season, and she’ll get back to you when things have calmed down in early Novemberwhich starts this week!

Miss Loi is currently busy with her phone marathon to respond to all on new enquiries and those on the calling list. Will respond to the comments here in due time.

Thank You for your understanding and apologies for the slow response.

Meanwhile, do checkout the Jφss Sticks Facebook wall for the relentless updates 😉

Another big package just got air-dropped from Jφss Sticks Airways Flight JS296!

Click the button (if you haven’t yet done so) and grab it here!

• 1.1: To stem the horde of AMaths students who go “Miss Loi! Your gradient for Q9(d) is waaaaaaaaay off! My dy/dx says 3.2!”, the tangent has been ‘keeeeeewed‘ (bent) to a gradient of 3.2 to prevent any widespread panic. But seriously, read this.

As usual, please leave a comment should you spot any mistake in the solution – like yesterday, Miss Loi still had students to save at The Temple throughout this evening (including some who refused to leave)! tsk tsk

Now to turn the attention to The Temple’s crack elite AMaths Regiment over the weekend … *cracks whip!*

Meanwhile follow the Jφss Sticks Facebook wall to receive The Temple’s last-minute O Level air-drops cum tips. It’s all happening there!

Marching On! Maaarching ON!!!

### Revision Exercise

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

1. Hi commented in tuition class

2011
Oct
28
Fri
11:37pm

1

The gradient in 9(d) which I got was way off = 3.05
(dy/dx <x=4, it would be 3.2).

• Lala replied to Hi’s comment

2011
Oct
29
Sat
10:48am

1.1

@Hi: But what if I chose to use A-math too? I tried a lot of times to find the gradient which is 3.2, and I found 3.19...
I even used A-math to find the min point so it looks so accurate... ;(

• 2011
Oct
30
Sun
5:44pm

@Lala: While it's perfectly fine to use pagan AMaths techniques to double-check your answer, it's not really advisable to write stuff like dy/dx in your final workings.

Though Miss Loi isn't 100% sure of Cambridge's stand on this, why expose yourself to the possible risk of losing method marks for this?

*copy-and-pasted from Miss Loi's email response to someone who asked if it's possible to use Physics v = u + at formula in AMaths kinematics*

• 2011
Oct
30
Sun
5:35pm

1.2

@Hi: 3.05 isn't really considered "way off" IMHO.

In any case, as mentioned in the past years,

"... the gradients of these hand-drawn tangents will tend to vary a little among those who draw them, notwithstanding the lot of A-Maths students who adjust here adjust there till they fit their sneaky dy/dx calculations.

As long as you've demonstrated that you've obtained the gradient (within a tolerable range) at the point via calculating the gradient of your suitably-drawn tangent based on selected coordinates from your plot (and make sure you hide away all your sneaky dy/dx workings in the process), you'd be fine ;)"

2. Luchia Kiryu commented in tuition class

2011
Oct
28
Fri
11:46pm

2

Question 4 ~
Didn't get part one and part two. (Cannot get (b) equation)
So, will they be marks for part three and four?

3. Jolindaz commented in tuition class

2011
Oct
28
Fri
11:53pm

3

Can the gradient of the graph be 4? Mine turn out to be four..

• 2011
Oct
30
Sun
5:55pm
4. Lee Kian Boon commented in tuition class

2011
Oct
29
Sat
1:44am

4

Hi!

Its a year and a half since i last visited your 'virtual temple' at june last year.

Missed the "joss sticks" that you'd given in your posts

Anyway, now i'm back, i realised a few improvements made on your 'temple', like that facebook connect button 😛

• 2011
Oct
30
Sun
6:09pm

4.1

Oh dear it was sooooo waaaaaaaaaaaaaay off! As such, Miss Loi has uploaded v1.1 of the solutions after hiring an AMaths-capable robot to redraw the tangent to a gradient of 3.2 ± 1 × 10−12 using the latest Japanese technology capable of up to pico precision 😀

Wah you're so free to do your own answers, instead of studying for your AMaths, Science etc? You suddenly remind Miss Loi of someone though ... hmmmmmmmmm ...

5. vic commented in tuition class

2011
Oct
29
Sat
1:51am

5

Hi ms loi!:) for qn1d, the ans is (2x-y)/x... is it ok if i put 2 - (y/x)? 🙂 thx...

• 2011
Oct
30
Sun
6:53pm
6. surian commented in tuition class

2011
Oct
29
Sat
2:14am
7. commented in tuition class

2011
Oct
29
Sat
2:31am

7

For qn no 10 why is the x=multiple of 5? shouldnt the number used be 4.5,14.5,24.5 ....etc. There are 10 numbers being: 0,1,2,3,4,5,6,7,8,9 . shouldnt it be the centre terms added then divide by 2? (4+5)/2=4.5?

• 2011
Oct
30
Sun
8:03pm

7.1

@MathA1: The mid-values are simply the physical middle point of each class interval in the histogram.

If we employ the way we use to find the median to obtain 4.5, 14.5 ... etc then these mid-points will no longer be at the center of each bar in the given histogram, unless there are gaps between the bars which don't exist in the given diagram.

P.S. Actually a histogram represents a frequency distribution so there can never, ever be gaps between bars (else it would be just a bar chart). You may consider the purpose of the ≤ and < signs in the data ranges is to determine which frequency bar the data belongs to.

8. arvind :) commented in tuition class

2011
Oct
29
Sat
4:57am

8

10(aiia) Shouldn't the middle points be 4.5, 14.5, 24.5 etc?
Because the given parameters are 0 ≤ x < 10, so the possibilities should be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

So shouldn't the median be 4.5 to be used in calculation?

9. passer-by commented in tuition class

2011
Oct
29
Sat
5:45am

9

Hi， Ms Loi. There are a few qns I'd like to ask for this paper. (actually, is a lot !!! ><' )

1. For Qn 5b(i), is it possible if we say that because p is multiplied by 2 and that makes it an even number, so the addition of 1 made it an odd no. ?
2. For Qn 6a(iv), a friend of mine said that bearings should be rounded off to 3s.f. ...
3. For Qn 7a. if we did not use the proportion method (meaning make an eqn like how you did), would they deduct marks ?
4. For Qn 8,
a,
ii. they would give method marks even if we do not get the answer right ?
b,
i&ii. if we did not put the wave under the letters, would they deduct marks ?
iii. can we say that line OX & OY are parallel, since they are collinear ?

Thanks a thousand !! 😀
and for the answers too ! ^^

• 2011
Nov
3
Thu
1:37am

9.1

Q5(b)(i): You definition should be fine for this 1-mark part. Miss Loi left it this way as the primary definition of an odd number is an integer that is not wholly divisible by 2.

Q6(a)(iv): Umm ... bearings should always contain 3 digits, and since they are in degrees, they should be rounded off to one decimal place for non-exact answers (as stated in the instructions)

Q7(a): You used ratios? i.e. If so, they're basically similar so should be fine 😀

Q8(a)(ii): Method marks are not a myth! More apparently so in a 2-mark question!

Q8(b)(i)(ii): Unfortunately yes. Hence this tip. Unless you somehow managed to bold the vector letters to a point that it became obvious (without causing a hole in the paper :P) - but that's quite a waste of time.

Q8(b)(iii): All collinear vectors are parallel (but not all parallel vectors are collinear!) so you should be OK - though a paranoid Miss Loi feels that since the question asks for two facts about the points O, X and Y, your facts should at least mention directly some of the points rather than base them purely on lines or vectors e.g. X is the mid-point of OY.

10. Rachel commented in tuition class

2011
Oct
29
Sat
7:32am

10

For 7(b)(ii), the surface area of the pot should not include the surface area of the circle because it is an open pot.

• replied to Rachel’s comment

2011
Oct
29
Sat
12:09pm

10.1

@Rachel: The pot has a base. its top is open but its base has a radius of 24 cm (not 36 cm). The qn clearly states that the base end of the pot has a radius of 24cm.

• 2011
Nov
3
Thu
2:47am

10.2

@Rachel: As quoted from the Jφss Sticks Facebook wall:

… just for comparison's sake …

Total surface area of a cone = curved surface area + base area
Total surface area of a pyramid = area of all triangular faces + base area

In this case, Q7(b)(ii) asks us to calculate the *total* surface area (not just the curved surface area) of the pot which is clearly stated to contain a base with an open end at the top.

Thus total surface area of the pot = curved surfaced area + circular base area (i.e. the π24²).

The reason they put "outside of the pot" is so that students would not go on to add the inner curved surface area + the base on the inside of the pot.

So the pot is only open at the top. If its base is taken away as well, then it's not really a pot anymore isn't it? More like something we use to bake cookies 😛

11. Peace commented in tuition class

2011
Oct
29
Sat
10:28am

11

hi was wondering why the bearing we were asked to find could be left in 4sf? since bearing is always only 3 numbers?

12. mini commented in tuition class

2011
Oct
29
Sat
11:04am

12

how many marks would be deducted if the significant figure is wrong??

13. Anonymous commented in tuition class

2011
Oct
29
Sat
11:53am

13

Miss loi, will I get two mark if I plot the graph wrongly? My P value is correct but I accidentally plot the point (-2,4.8) . The other four point I plotted correctly. And my gradient is 2.8. Does that mean my gradient is wrong?

14. Discuss commented in tuition class

2011
Oct
29
Sat
12:37pm

14

Is it necessary to write down the workings for 10(a)(ii)-mean and standard deviation to get the marks? I used my calculator to get the answers.

• 2011
Nov
10
Thu
5:11pm

14.1

@Discuss: From Miss Loi's experience with the mark schemes of Singapore's schools, it should be fine to simply state the final answer after arriving at it by the calculator method - provided you got it right.

HOWEVER, by doing so you'll have no method mark(s) to fall back on should you somehow get it wrong through punching the wrong key(s) etc. so it's definitely a good idea to at least show your workings like what's written in the solutions - especially so for that 2-mark part (ii)!

15. Hilda commented in tuition class

2011
Oct
29
Sat
1:04pm

15

1) Question 2(a)(i) If i leave the answer as 6.3 l (Short form for litre) and not litre/100km, i will only get 1 mark right?

2) Question 5(ii) Is it a must to write 'The n'th term is 11 term'? I just leave my answer as 11.

3) Question 7(b)(Ii) If i never add the base area, i will get 2 marks?

4) Question 8(b)(iii) Can i write ' O,X and Y are collinear. OX=1/2OY'

5) Question 9(d) My gradient is 2.56, is it acceptable?

6) Question 10(a)(ii)(b) If i just use calculator to get S.D, i will only get 1 mark?

Thank you (:

16. Celeste commented in tuition class

2011
Oct
29
Sat
2:22pm

16

Hi

Do you think 90% will be enough for an A1.

17. chamberlain commented in tuition class

2011
Oct
29
Sat
3:45pm

17

MISS LOI ，i honestly want to ask you : A1 must be above 90%? if above 85% ,can i get A1 ?how much possibility if i get 85% above to get A1. THX ,begging for your reply.........

18. Desperato commented in tuition class

2011
Oct
29
Sat
7:05pm

18

I didn't state my reasons for the angle question3b because it is only 1 mark each. Will i still get it correct?
And for question 5a(ii) i wrote T11. will i be marked down as well?

• 2011
Nov
10
Thu
7:01pm

18.1

Strictly speaking, reasons should be stated as part of your workings in Q3(b)(i) but since they only carry a mark each, it'll depend on how particular Cambridge is on this.

As for Q5(a)(ii), opinions might vary but Miss Loi feels that T11 is a clear enough reference to the 11th term. This, after all, is a maths paper.

19. yoyo commented in tuition class

2011
Oct
29
Sat
8:09pm

19

hope tis year , dey dont glgl go anyhw adjust moderation till we emo la =.=

20. Greg commented in tuition class

2011
Oct
30
Sun
1:10am

20

Hi Miss Loi,

First of all, thanks for the answers to both paper 1 and paper 2! They have been a great help to me and my classmates.

I have a couple of questions regarding the answer(s) to the papers.

1) Question 2a (ii) (a), should the answer be rounded up or down? Since the question asks for the distance that she can travel, I thought that it should be rounded down instead of up.

2) Question 9, would I be penalised for writing the answers on a piece of foolscap paper?

3) Question 10b (i), I was told by my teacher that if you are asked to complete the probability tree, the answers on the tree must be in it's simplest form. Was I supposed to leave it in it's x/9 and x/10 form or change it to it's simplest form?

Thank you.

• yoyo replied to Greg’s comment

2011
Oct
30
Sun
12:52pm

20.1

@Greg: graph ans write on foolscape of cuz will penalize la =.=

• 2011
Nov
21
Mon
3:06pm

20.2

@Greg: *rubs eyes at yet another missed comment!*

1) This kinda thing huh ... we (and most others) have rounded up since, technically, we've been instructed to give all non-exact answers to 3 sf when the degree of accuracy isn't specified. In this aspect, it's perfectly fine to say she can travel approximately 732 km (make sure you use the ≈ sign).

But if you round down, logically you're not wrong in this context but Miss Loi is just worried that a 'robotic' marker may not see it your way - so you'd be wise to state your reason clearly in order to to cover yourself.

2) For Q9 - on the contrary Miss Loi would like to believe that Cambridge markers are kindly, compassionate folks who are not particular about such things as long as they can see your workings!

3) No need lah - even the probabilities on the question paper are not in the simplest form!

21. Randomness commented in tuition class

2011
Oct
30
Sun
6:51pm

21

Hello, Miss Loi

Would I be penalized for using the equal sign when rounding off my answer instead of the rounding off sign?

And would I be penalized for using calculator to get the standard deviation for question 10?

22. hannah commented in tuition class

2011
Oct
31
Mon
2:15pm

22

i'm very scared that i'll fail my maths. i usually get D7s. i found the o level maths papers easy but when i look at the solutions, i made soooo many careless mistakes & now i'm worrying like crazy. i wonder how the moderation will be like since most the peeps around me are scoring as high as 90, some even getting full marks. i don't want to end up failing T.T i really put in a lot of hard work, i don't mind getting a C6 cos i never passed math since sec 2. ughhh

23. Nigel Woon commented in tuition class

2011
Nov
1
Tue
11:32pm

23

Hi, erm im not a student here & im not sure if this will be answered, but I would like to ask you what is ur view on the A1 mark for this year? Taking into consideration the good schools& the neighbourhood ones. Much appreciated. Thanks

24. Random commented in tuition class

2011
Dec
11
Sun
3:08pm

24

Hi ms Loi,i know this is a VERY late comment but i just want to ask you if we will get penalised if we use 3.sf numbers in workings but got the coorect answer in the end as i used stored numbers?

### 5 Reactions

1. Miss Loi tweeted

2011
Oct
28
Fri
3:22pm

25

2011 Emaths Paper 2 solutions air-dropped: http://t.co/yfrjT4FS #emath #olevel Please be gentle with me on all those little sig. fig. etc ..

2. Racchel tweeted

2011
Oct
28
Fri
3:41pm
3. Janelle tweeted

2011
Oct
28
Fri
3:51pm

27

2011 Emaths Paper 2 solutions air-dropped: http://t.co/yfrjT4FS #emath #olevel Please be gentle with me on all those little sig. fig. etc ..

4. Racchel tweeted

2011
Oct
28
Fri
3:58pm

28

2011 Emaths Paper 2 solutions air-dropped: http://t.co/yfrjT4FS #emath #olevel Please be gentle with me on all those little sig. fig. etc ..

5. Winnie ✿ tweeted

2011
Oct
28
Fri
4:48pm

29

@JOSEOBISM RT @xoInfinite: For clearer EM p2 solutions & answers: http://t.co/SDMVSTUw