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# GCE O Level Oct/Nov 2012 E-Maths 4016 Paper 2 Suggested Answers & Solutions

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Tuition given in the topic of Miss Loi the Tutor from the desk of at 9:04 pm (Singapore time)

Updated on

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My High Priestess 教主! …

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• 1.1: Q7(a) Corrected the value of p to 7.47.
• 1.2: Q7(b) Amended the y-axis to begin from −1 as required by the question.
Access it here if you’re having trouble accessing it on Facebook using your state-of-the-art smartphone 🙁

N.B. As usual, please, please leave a comment should you spot any mistake in the solution. After doing the paper at such a speed (admittedly, with some help along the way), the High Priestess is going to faint soon!

Meanwhile …

My High Priestess 教主! Mass dumping of EMaths books is being spotted across the state!

Post O Level fate of EMaths books
[source]

[EXEUNT]

### Revision Exercise

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

1. Erick commented in tuition class

2012
Oct
24
Wed
7:43pm

1

What would happen if my paper 2 graph question had a point plotted wrongly, and the subsequent parts had the wrong answers because the graph had the wrong shape. Will i get the whole graph question wrong? or can i still get some marks because of error carried forward?
Thankyou!

2. Rachel commented in tuition class

2012
Oct
24
Wed
8:29pm

2

My paper 2 was not tied in the qns order for the graph
qns, which is qns7. Instead, I tied it to the last page. Is it alright?? :/

3. wotagei commented in tuition class

2012
Oct
24
Wed
9:47pm

3

Hi.,. made a lot of careless mistakes T.T
How much do you think this year A1 and A2? T.T
For gradient of tangent, since scale is smaller, is it true that the range of accepted answer will be bigger than usual? My answer is 2.04. Then can explain to me about the probability qns last part?
Thanks T.T

• 2012
Oct
25
Thu
3:06am

3.1

@wotagei: Every year, Miss Loi has to say this:

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, you'd be fine 😉

4. Kester Tay  commented in tuition class

2012
Oct
24
Wed
9:49pm

4

Q10c)

Let the two people you pick be labeled A and B.

What's the probability of picking A, then a B (without replacement of the A)? (calculating only possible outcome: AB)

Ans: (11/16)(10/15) = 11/24

What's the probabilty of picking 2 people out of the lot, and having an end result of A and B in your selection, regardless of sequence? (calculating possible outcomes: AB, BA)

Ans: 11/24 + 11/24 = 11/12

Basically:

Probability of getting AB + Probability of getting BA = 11/12

Shouldn't this be the case, Ms Loi? :0

• 2012
Oct
25
Thu
2:32am

4.1

Q10(b)(ii)(b) requires us to find the probability that neither of two members selected at random is a right-handed female.

Do you first agree that both members selected die die cannot be right-handed females? This means that not even one of them can be a right-handed female.

So this translates simply into:

The first member you select from the group die die cannot be a right-handed female ⇒ probability = 11/16

AND

The second member you select from those remaining in the group die die cannot be a right-handed female ⇒ probability = 10/15

∴ P(neither is a right-handed female)
= (11/16)(10/15) = 11/24

If you still don't believe Miss Loi, you may work things out the long-winded way by considering all possibilities of not selecting any right-handed female as presented in the probability tree diagram below (note: we can't have even one right-handed female selected at any point):

So P(neither is a right-handed female)
= (6/16)(5/15 + 3/15 + 2/15) + (3/16)(6/15 + 2/15 + 2/15) + (2/16)(6/15 + 3/15 + 1/15)
= (6/16)(10/15) + (3/16)(10/15) + (2/16)(10/15)
= (11/16)(10/15)
= 11/24

*This reply was typed out by a left-handed female*

P.S. If Miss Loi understands the cases you've presented, you are labelling a person of "type A or B" but in actual fact for Q10(b)(ii) there should be only one "type" i.e. "not a right-handed female".

• Kester Tay  replied to Miss Loi’s comment

2012
Oct
25
Thu
11:24am

@Miss Loi: しまった！T_T

I did the 2010 TYS question, they had a similar question to the probability one (it's Q10c in the 2010 P2) a night before the paper.

The answer told me 7/295 even though I thought it was 7/590. So I trusted the TYS answer, and x2 in the exam, and lost marks.

My working:

10)b)ii)a) 2(9/16 x 8/15) = 3/5 (when answer shld be 3/10)

10)b)ii)a) 2(11/16 x 10/15) = 11/12 (when answer shld be 11/24)

I multiplied by two for both the last part questions, will I still get any method marks out of 4m? Because I understand it's already logic error when I x2, so may not get it.

• 2012
Oct
25
Thu
8:49pm

Miss Loi just took this photo from a TYS at The Temple of the worked solutions for the question you mentioned:

... and it's answer & method is consistent with Miss Loi's leh. Which TYS are you using?

• Kester Tay  replied to Miss Loi’s comment

2012
Oct
25
Thu
9:50pm

@Miss Loi: I'd post a picture, but I don't know how to :/

It's the topical TYS, Nov 02 ~ Nov 10, published by Dyna, (C) 2010. No workings in the answer key, only the answer. Didn't cross-reference with other TYS answers at the time because I thought it was correct (and also bolui keep buying TYS T_T), so in the exam I just trusted the TYS answer (7/295), and thought that AB wasn't the 'same type', oh well... Maximum minus 4m ><

Anyway, 本当にありがとうございます 🙂

• Dot Diagram replied to Miss Loi’s comment

2012
Oct
25
Thu
10:29pm

@Miss Loi: Miss Lois's left-handed assistant highlighted incorrectly part of the probability tree diagram. The branch for RHF and the following branches should be all be hightlighted as RED.

• 2012
Oct
26
Fri
5:50pm

The left-handed female (who happens to be Miss Loi) initially highlighted the probabilities in red (for outcomes that resulted in selecting a RHF) in order to make it easy on her eyes when forming that long-winded expression at 2.30am in the morning *rubs eyes*

But yeah you're right - all branches following the first selection of the RHF should be highlighted as well to cover all possible outcomes that contain a RHF.

*image amended*

5. John commented in tuition class

2012
Oct
24
Wed
10:00pm

5

If I have an inaccurate "P" value for the graph question, however my tangent and x- coordinates are correct, do I still qualify for the marks for part C) onwards?

6. RY commented in tuition class

2012
Oct
24
Wed
10:02pm

6

1)For 9(c), i mistakenly wrote OM as 4cm instead of my calculated OM value. So my ans for part c is wrong, so will there be method marks given for part c, d and e and will there be 'error carry forward?'
2) for 4 ci) i did divide the 3.97x10^13 by 60k and then 12, will i get method mark for that?

• 2012
Oct
25
Thu
3:42am

6.1

@RY: 1) Apparently quite a number have used the wrong value of OM in Q9(c). You may still retain some marks in (d) & (e) if you've subbed the remaining values correctly into the appropriate formulae i.e. volume of pyramid, volumes of similar figures.

2) You mean 4(c)(ii)? Yes you should get a mark or two for the bulk of your workings if you missed out on only the year conversion or number of significant figures.

7. Denton  commented in tuition class

2012
Oct
24
Wed
10:55pm

7

For question 10a)i)a), can it be 37 instead of 37.4? Also, 10a)iii) can it be saying that the chem students had a lower median and higher upper quartile?

• 2012
Oct
25
Thu
3:50am

7.1

@Denton: IMHO, 37 is a bit off since the median point on the curve lies clearly between 37 and 38.

For Q10(iii) you should describe how each statistical parameter is used to compare the students' performances (i.e. a higher Physics median mark indicates that the students performed better in Physics) instead of simply stating them.

8. --- commented in tuition class

2012
Oct
24
Wed
11:14pm

8

10biib answer is it wrong? Cos for most of my friends and i get 11/24 for the answer

9. Navin  commented in tuition class

2012
Oct
25
Thu
12:28am

9

Hey wanted to ask whether the graphquestions 7'c) , 7d) and 7e) has a range of answers? If so, is answers to 7c) x= 2.4 ad x=3.3 , 7d) gradient = 1.51 and 7e) min pt. (2.8, -0.3) acceptable? Thank you for the solutions. Really appreciate it. 🙂

10. Ling commented in tuition class

2012
Oct
25
Thu
2:16am

10

Dear miss Loi , for qn 9d, if I got the height wrong and used it for other parts will I get carried forward marks ?

11. Ron commented in tuition class

2012
Oct
25
Thu
4:02am

11

Hi is question 1d (ii) confirmed correct? Cause just now I saw some other ans key something diff 🙁 thanks!

12. Angeline commented in tuition class

2012
Oct
25
Thu
7:37am

12

Miss Loi, can you predict what might be the A1 range?

13. Cat commented in tuition class

2012
Oct
25
Thu
7:37am

13

For 4(a)(i), can the answer be left as $420? 14. Ling commented in tuition class 2012 Oct 25 Thu 7:58am 14 Miss Loi , for qn 9d paper 2, if my height is wrong and I used it for other parts , is there error carried forward marks? 15. Mary commented in tuition class 2012 Oct 25 Thu 8:02am 15 For 6.(b)(v) I multiplied 1.05 to the original prices ($2.50/$3), then I found a new P and got a different total new fee. Is this method acceptable? • 2012 Oct 25 Thu 11:22pm 15.1 @Mary: By multiplying the prices i.e.$3 × 1.05 = $3.15 &$2.50 × 1.05 = $2.625, you should still arrive at the same answer albeit in a slightly longer way: New P = Total fees taken in a week after the increase =$525 + $708.75 =$1233.75 ≈ \$1234 (nearest dollar)

There must be a careless mistake somewhere within your workings 🙁

16. Ng Guan Zhi commented in tuition class

2012
Oct
25
Thu
9:41am

16

For the graph can I start with 1 on the x-axis and -1 on the y-axis.For part c can 2.35 and 3.55 be accepted and the gradient 1.73 be accepted. Can the min point be (3,-0.35)

17. Rayner commented in tuition class

2012
Oct
25
Thu
10:24am

17

Hi, just a question.

For example after i put P(Neither Blahblah)= 3/24

I rewrite the sentence : The probability of Neither Blah Blah is 3/24.

Accepted? Haha

18. April Lee commented in tuition class

2012
Oct
25
Thu
10:56am
19. Alicia commented in tuition class

2012
Oct
25
Thu
11:17am

19

Hi, I would like to ask, is there some mistake in qn 6aiii ?
Shouldnt the answer be only 5,7,9,10,11,13,14,15.
Why is there no. 3,6,12 ?
Can you explain? Thank you. (:

• 2012
Oct
26
Fri
1:07am

19.1

@Alicia: Since A = { 1, 2, 3, 4, 6, 8, 12 }
A′ = { 5, 7, 9, 10, 11, 13, 14, 15 }

B = { 3, 6, 9, 12, 15 }

Q6(a)(iii) asks for the union of sets A′ and B.

By definition, A′ ∪ B contains elements present in A′ or in B or in both A′ & B → basically putting all elements of A′ and B together.

So since 3, 6, 12 belongs to Set B they are contained in A′ ∪ B as shown in the diagram below:

20. Navin  commented in tuition class

2012
Oct
25
Thu
2:59pm

20

Hello. Just wanted to check that whether for Q3bib) the y intercept I can leave the answer in coordinate form like (0,-2)

21. Junwei commented in tuition class

2012
Oct
25
Thu
3:03pm

21

Hi, if I didn't put any curly wordy line for the equal sign but I stated (3sf) or (nearest dollars) etc. will I still be penalise?

22. Rachel commented in tuition class

2012
Oct
25
Thu
4:18pm

22

Hi. My friends told me thour ans script MUST be tied in order. But I tied my graph qns, which is qn 7 at the last page. Is is alright?

23. Xan commented in tuition class

2012
Oct
25
Thu
5:33pm

23

Hi!
If my Venn diagram already had a mistake from start, hence affecting all of my answers in the later parts of te Venn diagram question, will I get any working marks?

24. Jim Li commented in tuition class

2012
Oct
25
Thu
8:57pm

24

For Question 5, if one of the angles is proven wrongly does it mean that all my subsequent answers will be incorrect even if the methods used or angle is correct?

25. Raymond commented in tuition class

2012
Oct
25
Thu
10:45pm

25

Hi miss loi. If I put units inside the matrices for qn 5aii and 5aiii, will I be given the marks?

26. Raymond commented in tuition class

2012
Oct
25
Thu
10:50pm

26

Oh and I thought for the median marks should be only to accuracy of 0.5? cos this is the case in actual...

27. Jason commented in tuition class

2012
Oct
25
Thu
11:10pm

27

Sorry Ms Loi >.< For question 3), is it okay to put (0,-2) as the y-intercept instead of -2?

28. Navin  commented in tuition class

2012
Oct
25
Thu
11:35pm

28

Hi just wanna ask, whether Q3bib) the y interct I could leave the answer in coordinate form like (0,-2). Thnks!

• 2012
Oct
26
Fri
6:21pm

28.1

@Navin: It appears that a significant number of students are asking this with regards to the format of the y-intercept answer in Q3(b)(i)(b).

Strictly speaking, the y-intercept should be the y-value (i.e. −2) of the coordinates of the intercept point.

Leaving the answer in coordinate form (0, −2) will really depend on whether this is condoned in the mark scheme (something which an eternally optimistic Miss Loi thinks they will 🙂 )

• 2012
Oct
28
Sun
12:28pm

@Miss Loi: One last question, for the graph in part (b)where we are told to draw the graph, it is 3 marks. How are the 3 marks allocated. My graph wasn't drawn neatly . Will they penalize marks? Though my answers in parts (c) (d) and (e) were correct.

• 2012
Nov
2
Fri
2:55am

@Navin: Please note that the mark scheme isn't set by Miss Loi so no way she can be 100% sure about marks allocation.

For Q7(b), however, an educated guess could be 2 marks for all points plotted correctly and joined by a smooth curve + 1 mark for correctly drawing and labeling the axes to the required scale.

So your "wasn't drawn neatly" could fall under the "smooth curve" part but it's kinda hard for Miss Loi to objectively gauge how badly drawn your graph is.

29. Jsn commented in tuition class

2012
Oct
26
Fri
6:14pm

29

Hi,

Im very worried about qn 2d. I got my a) b) and c) right. Just that i somehow got 2d wrong. I used cosine rule for triangle ECD... So i may have gotten some values wrong. Ended up getting DE = 12.9 or something. So would i get 0/3m for this? Or would i get method mark for using cosine rule?

8e) I showed my working : 2000/161.8, somehow i evaluated it wrongly cause i may have typed it in cal wrongly. Would i be given 1m for this?

10a)i)a) Median i put as 37.5?

10b)ii)b) Probability of getting neither right handed female, if i got my ans as 11/12, would i get 0/2m? Or is there any chance of 1m?

• 2012
Oct
28
Sun
1:04am

29.1

@Jsn: For Q2(d), if you read through how method marks are awarded, they are awarded based on the correct application of the formula rather simply stating the use of the formula.

From your description, you appear to have used the cosine rule on the wrong triangle so, strictly speaking, no method mark will be awarded if this is the case 🙁 (Miss Loi hopes she's wrong here for your sake)

For Q8(e), it depends on the mark scheme but since there are 2 marks in this part, there's a chance to for a 1 mark redemption here.

For Q10(a)(i)(a), 37.5 should be fine ^^

For Q10(b)(ii)(b), again it ultimately depends on the mark scheme but for probability questions like this one where you need to get the concept right from the start, it's often a case of 0 or full marks 🙁

30. Hari commented in tuition class

2012
Oct
26
Fri
9:35pm

30

Hi Ms Loi ,

For qn 4c i) I wrote my ans as 8.14X10^13 instead of 8.1356x10^13. minus marks for that ?

Qn 10b) i counted the total group of students as 17 instead of 16 , thus i got all the answers wrong for 10b , will i get any marks for that qn ?

I did not put the curly sign or (3.sf) for most of the qns . Will i still get penalised for that ?

Thanks 😀

31. Tom commented in tuition class

2012
Oct
26
Fri
9:53pm

31

Hi Ms Loi, for question 4ciii) is it okay to write "Assume one month has 31 days" and divide the value by (31x12) instead of 365?

And for question 7c), will marks be deducted for not showing "Hence y=0"?

Lastly, what do you think this year A1 mark will be?

• 2012
Oct
28
Sun
1:28am

31.1

@Tom: Q4(c)(iii): Miss Loi have come across some arguing that 1 year should be 365.25 days, but by assuming 1 month = 31 days ⇒ 1 year = 31 × 12 = 372 days you are committing a seditious act of Monthistism in discriminating against the lesser months of Feb/April/June/Sep/Nov!!! 😮

Q7(c): Would think the 2 marks here goes towards the correct values for x obtain directly from the graph, rather than anything else.

32. Cindy commented in tuition class

2012
Oct
26
Fri
10:37pm

32

Will there be error carried forward marks? For example, for the venn diagram, if I drew it wrongly.

33. Lim commented in tuition class

2012
Oct
28
Sun
10:14am

33

For last probability qn, i thought it meant it cannot be both right handed female. The qn is phrased such that it is actually trying to convey that cannot have AT LEAST ONE right handed female....... 🙁

34. weng commented in tuition class

2012
Oct
29
Mon
8:24pm

34

wow thanks miss loi for the answers, are the qn paper available to be posted too for easy x ref thanks for the great work

• 2012
Nov
2
Fri
3:16am
35. Serene commented in tuition class

2012
Nov
5
Mon
5:51pm

35

Hey, just wondering if I did not add units for most of my answers, will they minus 1 mark for all? What if for those "prove" questions?

36. rush13 commented in tuition class

2016
Apr
15
Fri
12:35am

36

hey if i draw my venn diagram wrong..like if it was written D={factors of 6} and i wrote the multiples and drew it and there were in total 5 parts each carrying 1.5 marks expect one which was carrying 1.... i knew exactly what to do... but silly mistakes T.T

### 23 Reactions

1. Miss Loi tweeted

2012
Oct
24
Wed
1:12pm

37

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2012
Oct
24
Wed
1:18pm

38

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2012
Oct
24
Wed
1:20pm

39

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2012
Oct
24
Wed
1:21pm

40

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5. WAH(: tweeted

2012
Oct
24
Wed
1:22pm

41

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6. 2012
Oct
24
Wed
1:25pm
7. DELEEE!✨ tweeted

2012
Oct
24
Wed
1:28pm

43

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8. Fuquan tweeted

2012
Oct
24
Wed
1:30pm

44

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9. Zenneth Lim tweeted

2012
Oct
24
Wed
1:38pm

45

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10. 2012
Oct
24
Wed
1:44pm

46

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11. Joel Chua tweeted

2012
Oct
24
Wed
1:46pm

47

RT @MissLoi #Olevel #emath paper 2 full answers & suggested solutions: http://t.co/HIBhqcfm (cont) http://t.co/VOKUFBuH

12. 2012
Oct
24
Wed
1:53pm

13. 2012
Oct
24
Wed
1:53pm

14. 2012
Oct
24
Wed
2:04pm

50

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15. 2012
Oct
24
Wed
2:04pm

51

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16. 2012
Oct
24
Wed
2:04pm

52

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Oct
24
Wed
2:04pm

53

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Oct
24
Wed
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54

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Oct
24
Wed
2:04pm

55

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20. Yew Siang tweeted

2012
Oct
24
Wed
2:07pm

56

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21. 2012
Oct
24
Wed
2:16pm

57

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22. Fazly Rafi tweeted

2012
Oct
24
Wed
3:18pm

23. 2012
Oct
24
Wed
11:47pm

59

Gessians checking EMP2 sols should use link at http://t.co/5DHA9GqV cos the other typed written version circulating around has a wrong ans

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