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2008
Wed
29
Oct

# Just A Few More Steps To Enlightenment (Updated With O-Level Oct/Nov 2008 E-Maths Solutions)

(28)
Tuition given in the topic of Miss Loi the Tutor from the tuition centre desk of at 10:16 pm (Singapore time)

FRONTLINE UPDATE:

It was a rare windless day when Miss Loi made her way to the salon.

Miss Loi! The paper was OK!

She felt as if the weight of the world was lifted from her little shoulders as she settled down on the comfy bed.

The paper was very easy but scared of moderation.

After agreeing to use the ‘latest’ brand of collagen mask whom her favourite facial aunty just recommended, she relaxed and closed her eyes …

Hey! OMG it was alright. I’m kinda happy I managed to prove my quadratic equation, a lot of my friends couldn’t 🙂

At this moment, a gentle breeze blew through a window that was unintentionally left opened, carrying with it two pieces of paper that eventually landed flat on Miss Loi’s face.

Under the illusion that the ‘latest’ collagen mask had just been applied on her face, Miss Loi fell into deep sleep and began answering the questions contained within the papers, with the same notorious handwriting even in her dream:

O-Level October/November 2008 EMaths Paper II Solutions

The shift in the wind was discernible as many now begin to sense the imminence of their Mathematical Salvation, as we gaze upon the twilight of this long campaign.

Already, those who bothered to look up during that dark Day of Mathematical Armageddon claimed to have seen a sliver of light from the sky, from whence the clouds parted momentarily to reveal a vision …

A vision of endless bonfires of burning ShingLee textbooks. A vision of you on a date with the guy/gal you like. A vision of you shopping without a care in the world. A vision of you resuming you saved computer game. A vision of Miss Loi frolicking in some remote beach.

A vision that revealed itself differently to the different ones who had seen it.

Did I forget to remove those price tags?

But before these visions become reality, a couple of E-Maths topics (plus the small matter of your Humans and Science papers) stand before you and your post-O-Level Paradise, and now’s the worst possible time for complacency to creep in.

As the last mathematical joss stick (Science ones are still burning BTW) is extinguished for the season and the last of those fluffy piggy-headed farewell gifts gets snapped up, as students exchange hugs, camwhore and run amok on their last day at The Temple, Miss Loi, like last year, shall leave you with some last-minute pointers amid a cheong hei list of topics that you’ll expect to face at dawn tomorrow:

• Algebra – Factorization, normal solving of equations & changing the subject of a formula e.g.

Given that , express g in terms of π, T and L.
• Quadratic Equations – the kind where you need to form a quadratic equation from a ‘story’ e.g.

A boat can travel at a speed of 12km/h in still water. If it takes 3 hours to go 15km upstream and back, find the speed of the current.
• Don’t give up the entire question just because you can’t form/prove the quadratic equation! Skip and plug the ‘proven’ equation directly in the next part and solve using if needed!
• Trigonometry (Sine/Cosine Rule, angles of depression/elevation (3D diagrams) etc.

• Know the difference between angle of elevation (looking up) and angle of depression (looking down).

If you really can’t ‘see’, trying holding a ruler upright on the relevant spot in the diagram!

• The largest angle of elevation/depression occurs when the distance between the two points is the shortest.
• The ONLY time you need to change your calculator to RADIAN MODE is when you’re performing a , or on an angle that’s given in radians e.g. in your sine/cosine rule or area of triangle calculation.
• Geometric Properties of Circles

• You DON’T NEED to change your calculator to RADIAN MODE when calculating your arc length, area of sector etc.
• Mensuration (Arc length, area of sector, volume/surface area of sphere, pyramid, cones etc. etc.)

• 1 m3 ≠ 1000 cm3!
1 m3 = 100 cm x 100 cm x 100 cm = 106 cm3
• 1 litre ≠ 1 m3!
1 litre = 1000 ml = 1000 cm3
• 19.2 mins ≠ 19 min 20 sec (DUH!)
• Always double-check the unit the question requires you to express your final answer in. Is it m2? Or cm2? etc.
• Don’t leave blank if you really can’t prove! Miss Loi shouldn’t say this but marks may be given even if you just write something that ‘looks’ logical e.g. ∠x = ∠y 😛
• Number Pattern (anything can come out – 听天由命吧!)
• Graphs (don’t forget your curve ruler!)

• Please check your value again if you discover that your plotted graph has a ‘kink’ and is not smooth.
• Remember to label your y-axis, x-axis and the equation of the curve itself – they carry marks.
• The ‘tangent’ that you draw to find the gradient of a curve only cuts the curve at one point (not two -_-)
• Don’t blindly plot your histogram against class frequency (WRONG!), you need to plot it against your frequency density – especially when you see data with unequal class widths.
• Know thy difference between a histogram and a frequency polygon – you can draw the latter only after drawing the histogram!
• Be prepared to calculate mean, median, mode and/or probability anytime in your statistics/data analysis question.
• Probabilities (this may appear as a standalone or within a statistics question)
• Coordinate Geometry

The maybes (since they have already appeared in Paper I but in very small parts):

• Vectors
• Matrices – those questions where you may be required to form matrices from a table of data e.g.

The table shows the daily production of two types of sweets X and Y, and the percentages of ingredients A, B and C required to produce them.

Sweet TypeABCDaily Production (kg)
X603010300
Y504010240

Given that the costs per kilogram of A, B and C are \$4, \$6 and \$8 respectively, use matrix multiplication to obtain the total cost of daily production.

• Sets & Venn Diagrams (Note: a very minor ‘shading’ qn has already appeared in Paper I)
• Simple interest/compound interest, taxes/GST etc.

• Know how to compute interest that’s compounded monthly i.e. monthly rate = (p.a. rate)/12 etc.

Missed out anything?

Rest well tonight and fight well tomorrow 😉 Once again, for the very last time this year,

Ganbatte!!! FTW!!!

*Pulls the lever to shut the Temple Gates*

### Revision Exercise

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

1. Anoneemers commented in tuition class

2008
Oct
29
Wed
10:44pm

1

Geometric Properties of Circles
You DON’T change your calculator to RADIAN MODE when calculating your arc length, area of sector etc

Huh? I thought the formula Arc length=rθ and
area of sector=(1/2)²θ the θ must be in radian mode?

2. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Oct
29
Wed
10:59pm

2

Anoneemers: Yes the θ must be in radians but you only need to change to RAD mode in your calculator when you need to do a sin/cos/tan θ, else there's NO NEED to switch to RAD mode for rθ or (1/2)²θ cases 🙂

P.S. Changed the relevant phrase to "DON'T NEED" for better clarity. Do let Miss Loi know if you've spotted anything that requires clarification.

3. zzz commented in tuition class

2008
Oct
31
Fri
11:11am

3

hey i think ur answers to Emaths p2(4016) are not very accurate cause u never use exact answers? & my probability answers are all diff from u except the 0 haha!

4. koen commented in tuition class

2008
Oct
31
Fri
11:33am

4

hey zzz the probability answers are correct.

but miss loi, the probability question ask for possibility diagram, not tree diagram. so it should be something like this :

 1 2 3 4 5 6 1 * * * * * 2 * * * * * 3 * * * * * 4 * * * * * 5 * * * * * 6 * * * * *

Each asterisk represents a possible outcome. There is no outcome at (1,1), (2,2), (3,3), (4,4), (5,5) & (6,6) as this is done without replacement.

5. koen commented in tuition class

2008
Oct
31
Fri
11:36am

5

pardon my possibility diagram. not sure why my table is posted as such 😛

(Miss Loi: Edited on your behalf 😉 )

6. jasmine lim commented in tuition class

2008
Oct
31
Fri
12:49pm

6

i can't believe i'm doing it all over again. the paper 2 is right in front of me and i'm calculating the marks again. sian. i calculated : 69 /100. round off 50. *prays hard i pass*

anyway, 7aii should be 766cmsquare, no?

7. Anoneemers commented in tuition class

2008
Oct
31
Fri
1:50pm

7

yup...the 1.35 in the working is supposed to be 1.349.
Even though its difference of 0.001, when multiplied by 2100, it gives a different answer =)

8. zzz commented in tuition class

2008
Oct
31
Fri
6:43pm

8

yeah should be 766 i gt that also! sian my whole cumilative frequency is wrong cause i just read from the graph never minus now i think i minus around 10 marks... T.T

9. Lisa commented in tuition class

2008
Oct
31
Fri
9:37pm

9

Hi Miss Loi, do you know how I can get a copy of the O Level A & E Maths Paper 1 & 2 (questions)? I know there's some book called the Ten Year Series with past exam papers... but where can you find those? and how do you know if it's certified? Please help, much thanks to you.

10. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Nov
1
Sat
11:32am

10

Alright folks, thanks to your feedback the following has been amended in the solutions:

1. 4016 Qn 1c(ii) - changed the approach to use the completing square solution obtained in part 1c(i) since this is a HENCE question.

The original answer was 1st done on the corresponding question in the 4017 paper and was copied over - but Miss Loi didn't see that the question in 4016 has a HENCE contained within.

Sneaky people. Tsk.

2. 4016 Qn 10b(i) / 4017 Qn 9b(i) - added the tabulated possibility diagram. (though Miss Loi personally believe the 1 mark would still be given if the tree diagram had been used - but can't argue the fact that the question specifically stated possibility diagram ... oh well )
3. 4016 Qn 7a(ii) / 4017 Qn 7a(ii) - answer changed to 766cm2.

As Anoneemers mentioned, one of the angles in the working should've been 1.349 instead of 1.35, while normally this won't matter too much in the final answer, the huge √41002 multiplying term before it caused the deviation in the final answer.

This is a good demonstration of the following point in the 圣旨 aka Imperial Edict (kindly brought up by Michael):

*All to kneel down now!*
*Blaring of trumpets*

奉天承運，皇帝詔曰!

6. 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 penalized, where appropriate. Angles in degrees should be given to one decimal place.”

"萬歲！萬歲！萬萬歲！"

Miss Loi's last words before she was being led away by soldiers for her careless mistake were "Keep those feedback coming!"

11. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Nov
1
Sat
9:24pm

11

Li-sa: If it's the Ten-Year Series (TYS) you're looking for, in general the main ones (all certified by SEAB) are shown below:

1. The Shing Lee Pass Series with past O-Level questions arranged by topics:

 Click to enlarge AMathsClick to enlarge

These are used widely by students in Singapore, as being grouped by topics allow them to quickly zoom-in on the relevant topics that they wish to practice. Charmingly-summarized notes are also provided at the start of each topic for easy reference.

P.S. This being the inaugural year of the A/E-Maths new syllabus, you won't be able to find actual past-year questions on some of the newly-introduced topics within this series of TYS.

P.P.S. Do not be confused by ShingLee's other series like Pass with Distinction Series etc. - you'll be faced with many different ShingLee books on the shelves!

2. The Dyna Publisher Series with past O-Level questions arranged by paper & year (as in the actual June/November papers):

 Click to enlarge AMathsClick to enlarge

Students usually move to this format after they've already covered all the topics - this is when they need to start getting used to solving questions quickly from one topic to the next as per actual exam conditions.

There's also another series by SAP but Miss Loi seldom use those. In fact, she usually supplements these TYS questions with slightly harder ones selected from the textbooks/workbooks and of course her Exam Papers! *SHAMELESS PLUG* 😀

Having said these, you might still be able purchase them at the BIG branches of Popular Bookstores in Singapore, bearing in mind that they're probably sold-out at the smaller outlets since we're now at the end of the academic year - when current editions end their run and we await the new editions to be published sometime in Jan-March 2009.

12. Lisa commented in tuition class

2008
Nov
2
Sun
10:31am

12

Misss Loi <333333333333333333333333333
thank you so much =]
I'll go look for those books soon, I'm currently using the SAP + yellowreef ones to review the topics but there aren't enough past examination questions that I want to try ^^
yippee tytytytyvm.

13. Li-sa commented in tuition class

2008
Nov
3
Mon
10:00pm

13

Look, Miss Loi, the one that's called "Lisa" (no hyphen) is from US while the one that has a hyphen and have sent the CE questions from HK and is a 香港人 is "Li-sa".

14. Li-sa commented in tuition class

2008
Nov
3
Mon
10:13pm

14

順帶一提，古裝片多以「奉天承運，皇帝詔曰：……欽此！」為聖旨的格式。
其實我想專心考好會考，不過也不希望有太多「聊齋」風言風話哩。

15. Li-sa commented in tuition class

2008
Nov
3
Mon
10:14pm
16. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Nov
4
Tue
1:15am

16

參見 Li-sa 娘娘!

祝 Li-sa 娘娘會考考出好成绩！

萬歲！萬歲！萬萬歲！

17. DK commented in tuition class

2008
Nov
4
Tue
3:30am

17

Temple close for holiday? When reopen? Ms Loi must be very free nowadays right? 😀

18. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Nov
4
Tue
10:46pm

18

DK: Shhh ... there're other joss sticks still burning at The Temple, and Miss Loi's still bz bz bz.

19. cendrine commented in tuition class

2008
Nov
5
Wed
1:06pm

19

hmm i have forgotten about the x and y axis liao...so where's x and where's y ?

20. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Nov
7
Fri
7:26pm

20

y↑→x ... do memories of those innocent days come flooding back now? 😀

21. Jac commented in tuition class

2008
Nov
26
Wed
3:11pm

21

Hi, for the E maths 4016 paper 2, question 3c, why is it not 20? I got the other parts of question 3 correct though

22. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Nov
27
Thu
7:01pm

22

Jac: Your comment has been moved here since you're talking about E-Maths Paper 2.

To recap the key parts of the question 3:

3. The cost of making a souvenir was 90 cents. The cost of making each souvenir was divided between materials, wages and other expenses in the ratio 5:4:6 respectively.

...

(b) Find the cost of materials and the cost of wages needed to make each souvenir.

3(c) John worked 7 hours per day for 5 days making souvenirs. He received a wage of \$630 for this work.

Calculate the number of souvenirs that he made in one hour.

...

In part 3(b), you would've calculated that the cost of wage needed to make each souvenir = \$0.90 x 4/15 = \$0.24

This means \$0.24 of wages went into making one souvenir.

In part 3(c), John worked a total of 7 hours x 5 days = 35 hours and received \$630 in total ⇒ he earns \$630/35 = \$18 per hour.

Since it cost \$0.24 in wages to make one souvenir, and John 'cost' a total of \$18 in an hour ⇒ he made a total of \$18/\$0.24 = 75 souvenirs in one hour.

You cannot divide \$18/\$0.90 to get 20 souvenirs in an hour, as this would mean that the entire cost (\$0.90) of making a souvenir is 100% due to wages - which isn't true since it has been stated in 3(b) that materials and other expenses were also involved (i.e. the 5:4:6 ratio).

23. CAROLYN! commented in tuition class

2008
Dec
9
Tue
2:18pm

23

Hi! You tagged on my blog once. XD

Anyway, I checked my answers for the Emaths paper 2 (4016) answers with mine and I was looking at the graph question when I got really confused because for the gradient question, I differentiated the graph equation to get the gradient I should get (without putting the working in the graph paper :P), which was -3, and I managed to tweak my tangent to get -3, but in you answer the gradient's -2.22 so now I just want to check whether I'm safe or not.

Paiseh luh, such a long comment for one silly question 😛

24. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Dec
10
Wed
12:59am

24

Don't worry my little A-Maths student 😉

As you know, 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 😉

25. CAROLYN! commented in tuition class

2008
Dec
10
Wed
2:02pm

25

Hahah, thanks! : D
My Maths teacher taught us how to cheat for tangent questions which explains the dy/dx bits in my E Maths question paper : P

P.S: I checked my A Maths answers with yours and I scored 83% (actually 82.7777777...%), do you think I'll manage to get an A1 from the bell curve? XP

26. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2009
Jan
26
Mon
2:19pm

26

Alright folks, as part of Miss Loi's Chinese New Year spring cleaning efforts, the O Level Oct/Nov 2008 Maths suggested solutions have finally been rid of her horrible handwriting, minor typos here and there, and are now more *ahem* student-friendly.

Do check them out (and pass them to your younger peers, where applicable):

P.S. Yeah yeah the exact same announcement has been made here.

27. Sabrina commented in tuition class

2012
Oct
16
Tue
10:55pm

27

I would like to know question 6a, when we comparing similar triangle.. do we compare AAA or AA when comparing angle... Im confused

• 2012
Oct
17
Wed
12:56am

27.1

@Sabrina: Strictly speaking, there's no AA or AAA "property" for proving similarity so for Q6(a), it'll be sufficient as long as you are able show that any two of the associated angles are equal (which would automatically imply the third angles are equal as well).

*Wonders why the "AAA" was left there way back in 2008* 😕