UPDATE: Alright, to those who are still clinging on to their distant memories of that fateful opening day of last week’s Mathematical Armageddon, here’s the suggested worked solutions of E-Maths 4016 Paper 1:

O-Level October/November 2009 EMaths 4016 Paper I Solutions – click to download

This is in response to the 1 × 10^{n} missed calls (from these few days) that are currently residing in Miss Loi’s handphone now:

As Miss Loi is deeply embroiled in her Mega Jφss Sticks sessions during this week 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 (commencing December 2009), and she’ll get back to you when things have calmed down (around early November).

Thank You for your kind cooperation.

Once this morning’s Mega Jφss Sticks session had ended, and the last of her elite AMaths crack squad had left The Temple, Miss Loi feels the time is ripe again to quietly showcase her notorious handwriting once more:

O-Level October/November 2009 EMaths 4016 Paper II Solutions – click to download

P.S. As usual, please inform Miss Loi should you discover any mistake in her scribbling (if they are legible to you). Also, feel free to discuss in the comments below should you vehemently disagree with any of the answers/approaches described within.

P.P.S. If you happen to have the FULL set of questions for EMaths Paper 1 (and those from EMaths 4017), feel free to send them to Miss Loi’s arms, and the world may be rewarded with more glimpses of Miss Loi’s notorious handwriting and drawings 😉

To clarionx:hmm its not about rounding off and round off 9 min 58.5 seconds to 10 mins.the problem is 9 min and 58.5 seconds is the wrong ans. And i think there's a error the the ans.Question 9d)you shouldn't really reject the 45.82 at this part as the instruction is solve the equation.You should only do this at part e,where you write Diameter=.......(Since x=45.82 is rejected) Hmm this is just my opinion don't know is it right or not.

I have some reservations about Q5(b)(iv)(b). The 'suggested answers' lists it as 'F represents the total fare (in cents) collected from the adults and children respectively on a weekday.', however if we write down the working for the matrix multiplication, the first row is Look at the first row. The multiplication includes 10 and 30, which is the number of adults and children in the morning respectively, so how can 700 be exclusively adults when children are included? Likewise for the second row. The multiplication includes 20 and10, which is the number of adults and children in the afternoon respectively, so how can 650 be exclusively children when adults are included? Shouldn't the matrix represent the fare earned from both adults and children in the morning of a weekday and in the afternoon of a weekday respectively?

Plus I need to ask, for Question 6(d), how much allowance is given when finding the gradient?

And Q9(e). I agree with JH. I did not reject 45.82 at (d) since the part question only asks us to solve the equation. It is only at (e) when they ask us to use the answer from (d) to solve (e). So I think we should reject at (e)?

I understand you but I don't think you understood what I said... I am saying shouldn't we only reject it at (e) since we are only looking for the radius at (e)?

At (d) we are purely solving the quadratic equation, we are not looking for the radius yet in (d).

Yes JX you are right.My math teacher also stresses this to me.Many who reject at the solving part are falling for the trick as it only asks us to solve the equation.

Ahhh ... yes Jx for Q5(b)(iv)(b), the elements in F do indeed represent the total fare collected from both adults & children in the morning and afternoon respectively on each weekday.

Also for Q9(d), x = 45.82 should NOT be rejected since, even if one were to argue on the validity of rejecting the value at 9(d), the question puts this issue beyond doubt when it clearly states "giving both answers ...".

Thanks for pointing out the errors that Miss Loi had written in her haste, and this further emphasizes the need to read each question very, very carefully regardless of how kan cheong you are in the exam, as sometimes our tired minds can lapse into wrong assumptions after we have practiced too many standard questions.

In any case, the solution file has been updated. Let Miss Loi know if you find any more mistake.

mathslover: How Miss Loi wishes she can include the questions as well 😕

Ah Wei: Miss Loi doesn't have the 4017 paper here but if it follows the trend from last year, then 75% of the questions and answers should be similar, barring the few topics that are uncommon to the two syllabuses.

clarion: You're probably one of the many who did a 105% × 9.5 to get your 9 min 58.5 seconds. By doing this you're implying that the athlete's 2007 time is 105% of his 2008 time.

However, the question states that the athlete's time of 9 mins 30 secs in 2008 is 5% less than his time in 2007. In other words, his 2008 time is 95% of his 2007 time. This implies that the reference point (100%) should be his 2007 time instead of his 2008 time.

Jx: Regarding the tolerance of the gradient of the tangent in Q6(d), Miss Loi doesn't know the exact allowance (some say ±10%) but she believes they should be lenient here provided

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 😉

I got ze paper! you want? yup around 75% same questions, but still quite different to me, is it legal to like, send you the exam script? email me perhaps?

Miss Loi, do you mind making a prediction on the bell-curve for the A1 and A2 grade based on the response of this year's cohort? I found this paper moderate ba, neither hard nor easy =S.

Don't worry bout the moderation part =D. If you do a subject where there is a large cohort moderation is a good thing. Since sadly, in reality there are some that don't make it out alive at O-levels -bows heads and mourns-

Usually it will bring the marks for all grades lower since the mean mark will be lower made lower due to the sheer size the population. Unless of course the paper is SO easy that the mean mark is like 55- 60 then they wil push the grades up.

For subject with lower candidature the mean mark tend to be higher most of the time so you might worry about those instead.

You will learn all about this kind of stuff at JC level called normal distribution in statistics =D

Good luck and dont worry! >_< -goes back to studying stats-

Just in case you were wondering what the value of n is in the possible mean mark computation, recall your trip to the former National Stadium in P5, that no. of students + private candidates is your competition.

Don't count on other country people to further lower the mean (lots of countries subscribe for the easier june papers, even those in england)

Ok Miss Loi is back after a much-needed weekend of recovery 😀

Ah Wei + Nicholas: Will reply you via email 😉

zw: This is exactly the situation that Miss Loi has highlighted at the end of this blog post on approximation.

Well, strictly speaking your accuracy cannot be faulted as 12sin20° is exactly 4.10424172. Miss Loi's worry is whether the one who sets the question even realize in the first place that 12sin20° is exact with 8 decimal places.

zklim_1234: Full marks is unlikely as your 4 sig. fig. answer is in direct violation of the following Commandment:

If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.

pq: 0.1 more or less than the correct answer is usually due to rounding-off error at the final answer, or through the use of less-than-four-figure accuracy in your working, as decreed in your syllabus document:

Unless stated otherwise within a question, three-figure accuracy will be required for answers. This means that four-figure accuracy should be shown throughout the working, including cases where answers are used in subsequent parts of the question. Premature approximation will be penalised, where appropriate. Angles in degrees should be given to one decimal place.

Miss Loi made the same careless mistake too last year ... sigh ... 🙁

john + Alvin: Q4 in P2 asks you to "Find" instead of "State" and by right all necessary workings (and reasons) should be shown.

So it's a little baffling that only 1 mark is given for each part here, but Miss Loi thinks it's definitely good to write down your reason just in case they start deducting half a mark here and there.

mav: Sad to say (unless you've BOLDED them in an obvious manner), from what Miss Loi has seen in the markings of some prelim papers, what Zac has said seems to be ominously true. But we all pray that Cambridge markers are supposed to be more lenient that our own merciless school teachers cum markers.

X: You're referring to the last question of Paper 1 right? Umm ... how would you express it in matrix form (i.e. a column vector) when there isn't a cartesian grid of coordinates (with x and y-axes) defined in the question?

Nash: Umm ... in Singapore's context, other countries' people actually raises the mean further, no?

To those who are still worrying about moderation (which is LAST thing you should be worrying right now, since there are still two more weeks of your Os to go) Miss Loi can't really predict with deadly accuracy the A1 cut-off (after all, she only has limited feedback from her small sample population size) but in general, Miss Loi has always said that

85% for A-Maths and 90% for E-Maths

thereabouts should be the rough score you aim for (to cater for unexpected/undetected loss of marks).

Wow you all are fast wor...but solutions without questions a bit weird leh...can i have the Paper 1 questions? I just got the other maths papers from my cousin except for e.maths P1...

Ya...are we allowed to leave our answer in improper fraction? Oh and yes, i know we are asked to rationalise our answers...but i heard trigo can have exception. Is it true?

Improper fractions are still fractions O_o, should be ok since im usually leave them as they are, and my O's did fine..Unless they became a little stricter. Rationalisation is a must, for trigo it would end up as a special angle like π/3 or π/4 or something. but u should rationalise the no. within the trigo anyways, keeps the marker happy =D

Oh btw Miss Loi I meant other country ppl taking the paper in other countries. The ones we have here, well we can always count on them to make our A1s so close yet so far.. =D

JOYL, HXJ & Nash: Miss Loi hasn't come across any specific requirement from Cambridge that penalizes final answers that are in improper fractions (improper fractions are good for checking answers!) or un-rationalized surds (in AMaths), though she'll be extremely grateful if any one can point her to the relevant literature that says otherwise.

However, it's important to note instead that surds in final answers should be reduced to their simplest forms i.e. 3√2 instead of √18.

Perhaps that's the reason for the perception of trigo ratios of special angles (e.g. 1/√2) being 'excused' from rationalization?

Sasori: For P2 Q1a, don't think there's any problem leaving it in 3/8 hrs, since we can even find a 1½ hour within the question itself!

For P2 Q6d, as mentioned in an earlier reply to Jx, the key is to demonstrate that you’ve obtained the gradient (within a tolerable range) from calculating the gradient of your suitably-drawn tangent based on selected coordinates from your plot.

As to what constitutes 'a tolerable range', some say ±10% of the actual answer. Even though your 2.8 is just a weeeeee bit outside this 10% of 3.26 (the exact gradient if you differentiate), Miss Loi still thinks you're fine as long as you've shown the ample workings within your graph.

16 (a)(ii) Angle ABC should be 40 degrees; there was an error when the final answer was transferred because you wrote it as 26 degrees.

19 (b) "Sue is trying to estimate the distance ..." and "giving your answer to a reasonable degree of accuracy". Noting that the figures provided (280m and 30 degrees) could be estimates as provided by her, it is likely that the question is intended as an estimation question. In addition, part (a) of question 19 is testing the ability of candidates to estimate. So 162m (to 3 sf) may be a little to accurate since Sue only requires an estimated distance. Would 160m be a better answer?

@Aaron: Many thanks and your help in pointing out the typos in 1(a) and 16(a)(ii) is really appreciated (must've been those cramped fingers from countless ctrl-c-ctrl-v's). They have been amended accordingly.

Regarding 19(b), while your argument sounds ok initially, Miss Loi feels it's pretty dangerous in this case to assume (based on a subjective interpretation of "a reasonable degree of accuracy") that a less accurate answer is a better answer, especially when no specific instruction is given to round it to the nearest 10.

Furthermore, 280m and 30 degrees are what Sue estimated directly while the final answer is what needs to be calculated based on these estimated values. Just something that suddenly comes mind - what if she needed this to find a rope long enough to cross the river?

I think your last answer for probability is incorrect. To get the answer, you should use the concept of complement... When you do it the way you had done, you miss out 2 other scenarios. Correct me if I'm wrong. 🙂

* 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

Thanks for helping my Math improve! from like C5 to A1! I never thought I will do well, but thanks to you, I did! … [read more]

## 49 Comments

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solutions without questions.. a bit weird..

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hey miss loi! u have the 4017 paper 2 answers?

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Hey, for question 1biii), can leave answer as 9 min 58.5 seconds not? Thanks.

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To clarionx:hmm its not about rounding off and round off 9 min 58.5 seconds to 10 mins.the problem is 9 min and 58.5 seconds is the wrong ans.

And i think there's a error the the ans.Question 9d)you shouldn't really reject the 45.82 at this part as the instruction is solve the equation.You should only do this at part e,where you write Diameter=.......(Since x=45.82 is rejected)

Hmm this is just my opinion don't know is it right or not.

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I have some reservations about Q5(b)(iv)(b). The 'suggested answers' lists it as 'F represents the total fare (in cents) collected from the adults and children respectively on a weekday.', however if we write down the working for the matrix multiplication, the first row is

Look at the first row. The multiplication includes

10and30, which is the number of adults and children in the morning respectively, so how can 700 be exclusively adults when children are included?Likewise for the second row. The multiplication includes

20 and10, which is the number of adults and children in the afternoon respectively, so how can 650 be exclusively children when adults are included?Shouldn't the matrix represent the fare earned from both adults and children in the morning of a weekday and in the afternoon of a weekday respectively?

Plus I need to ask, for Question 6(d), how much allowance is given when finding the gradient?

And Q9(e). I agree with

JH. I did not reject 45.82 at (d) since the part question only asks us to solve the equation. It is only at (e) when they ask us to use the answer from (d) to solve (e). So I think we should reject at (e)?曜

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To JX

I can only answer the Q9(e)

Must reject 45.82. If not this means the radius is longer then the length or the rectangle. Hope you understand me.

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To

lolwtfisthis:I understand you but I don't think you understood what I said... I am saying shouldn't we only reject it at (e) since we are only looking for the radius at (e)?

At (d) we are purely solving the quadratic equation,

we are not looking for the radius yet in (d).曜

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Yes JX you are right.My math teacher also stresses this to me.Many who reject at the solving part are falling for the trick as it only asks us to solve the equation.

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To Jx

Oops sorry never read your comment properly, my bad.

Does this thing really matter? If i rejected on part (d) will i loose mark?

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Ahhh ... yes

Jxfor Q5(b)(iv)(b), the elements inFdo indeed represent the total fare collected from both adults & children in the morning and afternoon respectively on each weekday.Also for Q9(d),

x= 45.82 should NOT be rejected since, even if one were to argue on the validity of rejecting the value at 9(d), the question puts this issue beyond doubt when it clearly states "givingbothanswers ...".Thanks for pointing out the errors that Miss Loi had written in her haste, and this further emphasizes the need to

read each question very, very carefullyregardless of howkan cheongyou are in the exam, as sometimes our tired minds can lapse into wrong assumptions after we have practiced too manystandardquestions.In any case, the solution file has been updated. Let Miss Loi know if you find any more mistake.

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can i see the answer for maths paper 1 ?

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Answers for a math p1?

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mathslover:How Miss Loiwishesshe can include the questions as well 😕Ah Wei:Miss Loi doesn't have the 4017 paper here but if it follows the trend from last year, then 75% of the questions and answers should be similar, barring the few topics that are uncommon to the two syllabuses.clarion:You're probably one of the many who did a 105% × 9.5 to get your 9 min 58.5 seconds. By doing this you're implying that the athlete's 2007 time is 105% of his 2008 time.However, the question states that the athlete's time of 9 mins 30 secs in 2008 is 5%

lessthan his time in 2007. In other words, his 2008 time is 95% of his 2007 time. This implies that the reference point (100%) should be his 2007 time instead of his 2008 time.Jx:Regarding the tolerance of the gradient of the tangent in Q6(d), Miss Loi doesn't know the exact allowance (some say ±10%) but she believes they should be lenient hereprovided[source]

sha:Miss Loi doesn't have the question paper for Paper 1 since all of you have submitted it to Cambridge!J:It's been a hectic day 🙁曜

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Ah Loi

I got ze paper! you want? yup around 75% same questions, but still quite different to me, is it legal to like, send you the exam script? email me perhaps?

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for Qn(3)

what if i did not convert to 3 sig fig?

coz i thought 12sin20 is exact so dont need to round off.

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Miss loi, for question 89ai i put the answer 399.3m, can i still get the full marks?

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i mean ques 8ai

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hey miss loi is it possible to give the solution for this year's N level maths? I have the paper and can send it in

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hey miss loi is it okay if my ans is 0.1 more or less than e correct answer???

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Miss Loi, do you mind making a prediction on the bell-curve for the A1 and A2 grade based on the response of this year's cohort? I found this paper moderate ba, neither hard nor easy =S.

Thanks in advance.

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i didnt state reason for qns 4 as it was a 1 mark qns, will they deduct marks from it?

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John, I don't think need to state reasons, they did not ask for it. Otherwise, should be needed right? xD

Causee.. I didn't put as well. 😡

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me too i didnt put cuz they didnt asked

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hey guys ! im afraid that the moderation will bring down my marks ? can it ever happen ? 🙁

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Don't worry bout the moderation part =D.

If you do a subject where there is a large cohort moderation is a good thing. Since sadly, in reality there are some that don't make it out alive at O-levels -bows heads and mourns-

Usually it will bring the marks for all grades lower since the mean mark will be lower made lower due to the sheer size the population. Unless of course the paper is SO easy that the mean mark is like 55- 60 then they wil push the grades up.

For subject with lower candidature the mean mark tend to be higher most of the time so you might worry about those instead.

You will learn all about this kind of stuff at JC level called normal distribution in statistics =D

Good luck and dont worry! >_<

-goes back to studying stats-

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Just in case you were wondering what the value of n is in the possible mean mark computation, recall your trip to the former National Stadium in P5, that no. of students + private candidates is your competition.

Don't count on other country people to further lower the mean (lots of countries subscribe for the easier june papers, even those in england)

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Miss Loi seems to have gone MIA-ed here.

Though she can't see me, I saw her shopping away at ION Orchard just now. And she seems to be on the phone all the time ... poor thing ...

Oh, and I see that the EMaths Paper 1 solutions are up!

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hey what would happen if i didn't put the wavy lines for the vector question? o.o anyone?

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Sorry to tell you but you would be penalised and the whole qn would be marked wrong... It's a pity!

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But maybe if the marker was lenient enough, you might still get half the marks!

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hey for paper 2 last parts, the qn say leave in position vectors. then it should be in like the matrix form right?

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Ok Miss Loi is back after a much-needed weekend of recovery 😀

Ah Wei + Nicholas:Will reply you via email 😉zw:This is exactly the situation that Miss Loi has highlighted at the end of this blog post on approximation.Well, strictly speaking your accuracy cannot be faulted as 12sin20° is

exactly4.10424172. Miss Loi's worry is whether the one who sets the question even realize in the first place that 12sin20° is exact with 8 decimal places.zklim_1234:Full marks is unlikely as your 4 sig. fig. answer is in direct violation of the following Commandment:pq:0.1 more or less than the correct answer is usually due to rounding-off error at the final answer, or through the use of less-than-four-figure accuracy in your working, as decreed in your syllabus document:Miss Loi made the same careless mistake too last year ... sigh ... 🙁

john + Alvin:Q4 in P2 asks you to "Find" instead of "State" and by right all necessary workings (and reasons) should be shown.So it's a little baffling that only 1 mark is given for each part here, but Miss Loi thinks it's definitely good to write down your reason just in case they start deducting

half a markhere and there.mav:Sad to say (unless you'veBOLDEDthem in an obvious manner), from what Miss Loi has seen in the markings of some prelim papers, whatZachas said seems to be ominously true. But we all pray that Cambridge markers are supposed to be more lenient that our own merciless school teachers cum markers.X:You're referring to the last question of Paper 1 right? Umm ... how would you express it in matrix form (i.e. a column vector) when there isn't a cartesian grid of coordinates (with x and y-axes) defined in the question?Nash:Umm ... in Singapore's context, other countries' people actuallyraisesthe mean further, no?To those who are still worrying about moderation (which is LAST thing you should be worrying right now, since there are still two more weeks of your Os to go) Miss Loi can't really predict with deadly accuracy the A1 cut-off (after all, she only has limited feedback from her small sample population size) but in general, Miss Loi has always said that

thereabouts should be the rough score you aim for (to cater for unexpected/undetected loss of marks).

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Wow you all are fast wor...but solutions without questions a bit weird leh...can i have the Paper 1 questions? I just got the other maths papers from my cousin except for e.maths P1...

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Hello, are we allowed to leave our answers in IMPROPER fractions? I heard that Cambridge penalises. Is it true?

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Ya...are we allowed to leave our answer in improper fraction? Oh and yes, i know we are asked to rationalise our answers...but i heard trigo can have exception. Is it true?

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Improper fractions are still fractions O_o, should be ok since im usually leave them as they are, and my O's did fine..Unless they became a little stricter. Rationalisation is a must, for trigo it would end up as a special angle like π/3 or π/4 or something. but u should rationalise the no. within the trigo anyways, keeps the marker happy =D

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Oh btw Miss Loi I meant other country ppl taking the paper in other countries. The ones we have here, well we can always count on them to make our A1s so close yet so far.. =D

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Miss Loi, for Paper 2 Q1a, can I leave my ans as 3/8 hrs ? & my gradient for Q6d) is 2.8, acceptable?

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JOYL,HXJ&Nash: Miss Loi hasn't come across any specific requirement from Cambridge that penalizes final answers that are in improper fractions (improper fractions are good for checking answers!) or un-rationalized surds (in AMaths), though she'll be extremely grateful if any one can point her to the relevant literature that says otherwise.However, it's important to note instead that surds in final answers should be reduced to their simplest forms i.e. 3√2 instead of √18.

Perhaps that's the reason for the perception of trigo ratios of special angles (e.g. 1/√2) being 'excused' from rationalization?

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Sasori:For P2 Q1a, don't think there's any problem leaving it in 3/8 hrs, since we can even find a 1½ hour within the question itself!For P2 Q6d, as mentioned in an earlier reply to

Jx, the key is to demonstrate that you’ve obtained the gradient (within a tolerable range) from calculating the gradient of your suitably-drawn tangent based on selected coordinates from your plot.As to what constitutes 'a tolerable range', some say ±10% of the actual answer. Even though your 2.8 is just a weeeeee bit outside this 10% of 3.26 (the exact gradient if you differentiate), Miss Loi

stillthinks you're fine as long as you've shown the ample workings within your graph.曜

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Ok...understand...thanks...

Oh...anyone have the emaths paper 1? I downloaded the solutions but a lot of it I dun understand without the questions...

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do you have the answers to combined science phys/chem??

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Hello

KH, looking for these? 😛曜

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hey plz nybody get me 0ct/nov 09 english O level cambridge paper.....

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i have it.

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Oh ya, Miss Loi, regarding the 2009 E Math P1 Solutions:

https://www.exampaper.com.sg/blog/wp-content/uploads/gce-o-level-2009-emaths-4016-paper-1-solutions.pdf

1 (a) p = 5y(4x - 1)

There should'nt be a 'p'.

16 (a)(ii) Angle ABC should be 40 degrees; there was an error when the final answer was transferred because you wrote it as 26 degrees.

19 (b) "Sue is trying to estimate the distance ..." and "giving your answer to a reasonable degree of accuracy". Noting that the figures provided (280m and 30 degrees) could be estimates as provided by her, it is likely that the question is intended as an estimation question. In addition, part (a) of question 19 is testing the ability of candidates to estimate. So 162m (to 3 sf) may be a little to accurate since Sue only requires an estimated distance. Would 160m be a better answer?

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@Aaron: Many thanks and your help in pointing out the typos in 1(a) and 16(a)(ii) is really appreciated (must've been those cramped fingers from countless ctrl-c-ctrl-v's). They have been amended accordingly.

Regarding 19(b), while your argument sounds ok initially, Miss Loi feels it's pretty dangerous in this case to assume (based on a

subjectiveinterpretation of "a reasonable degree of accuracy") that alessaccurate answer is a better answer, especially when no specific instruction is given to round it to the nearest 10.Furthermore, 280m and 30 degrees are what Sue estimated directly while the final answer is what needs to be

calculatedbased on these estimated values. Just something that suddenly comes mind - what if she needed this to find a rope long enough to cross the river?曜

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I think your last answer for probability is incorrect. To get the answer, you should use the concept of complement... When you do it the way you had done, you miss out 2 other scenarios. Correct me if I'm wrong. 🙂

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@Phoebe: Are you referring to the probability question in the 2012 EMaths Paper 2 (this being the 2009 thread)?

If so, Miss Loi's explanation for

thatquestion is here.