“NOOOOOOOOOOOOOOO ….“
The despairing cry made its way from dream to reality as a distraught Miss Loi sat up in bed in the middle of the night, with her heart still rapidly beating from a nightmare that had felt so frighteningly real.
That vivid scene from the dream continued to play out over and over again in her head as she drove along the PIE the following morning, causing a train of frustrated cars to form behind hers, as she was in no mood to notice the incessant horning and flashing of headlights when her speed dropped from 90 km/h to 70 km/h to 50 km/h …
Recognizing the futility of trying to shake off the recurring images in her mind, she decided to turn off the expressway and head towards the scene of the nightmare, for if the terrible dream was true, life would have lost some of its meaning, and a part of her future would be in grave jeopardy.
At her favourite boutique in Far East Plaza, Miss Loi asked the regular salesgirl who has always served her in all her visits
Hey you know what? I dreamt of you quitting the shop last night! Must be just a dream right? Coz if it’s real, who’s gonna give me my regular discount next time???
The salesgirl’s eyes widened.
小姐, this kind of things cannot anyhow say! My boss over there can hear!
She then leaned forward, smiled and said,
“But since I know that my boss didn’t pass her O-Level EMaths, I can tell you this …”
Let y be my salary, and x be the time that has passed since I’ve joined this shop.
Before I joined this shop, my previous pay was represented by y=a−x+c, where a=2 and c=580.
After I joined this shop, my salary over time is represented by y=axn+c.
Initially I humbly asked for a=20, n=2 and c=500. But my boss was kind enough to offer me a=15, n=1 and c=550, which I accepted.
A couple of years later, when I charted my salary records using what I’ve learnt from this website, I was pleasantly surprised to find that it was actually a=−100, n=−2 and c=600.
Furthermore, after a review, a became 550, n became 0 and c became 0 for a long period of time.
And now my friendly boss has even decided to give me a bonus by making a=−1, n=3 and c=600!
So do you think there is any chance that I will quit?
While your question on Graphs won’t exactly appear in this form in your O-Level E-Maths Paper 1, Miss Loi thinks that sketching out all the graphs described by the salesgirl above will give E-Maths students some practice to familiarise themselves with some of the shapes of the 12 Graphs of Functions and, at the same time, convince Miss Loi that it was, after all, just a bad dream.
P.S. Please just focus on the shapes of the graphs more than anything else.
, 
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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 21 years she has been a savior to countless students ... 
曜
日
Of Approximation And That Granny On A Trishaw
(8)As if the world hasn’t had enough of the geek calendar, today (being 22 July) (Edit: Actually it was yesterday – couldn’t post this in time
) happens to be Pi Approximation Day – a day to honour that often-used 
fraction to approximate the value of π, though in reality 
etc. are actually better approximations.
Speaking of approximation, Miss Loi would like to pay a little homage on this day to this most primal and basic of mathematical topics. A topic that many of us first may have first grasped from the Granny of that classic folk song:
『三轮车，跑得快，上面坐個老太太。
要五毛，給一块，你说奇怪不奇怪！』
A topic that resurfaced later in life when a mean taxi uncle (who knew you haven’t been taught approximation in school yet) asked for $10 when the meter showed $9.70.
Or when you somehow instinctively brought along $50 to a sale to grab five items at $9.90 each, for nothing would be left if you had to return home to get more money.
Or that Miss Loi’s weight will always be 50 kg (correct to the nearest 10 kg) everytime you asked her …
In any case, do take a moment today to reflect on the following rules which are, well, supposedly so simple it’s laughable for anyone old enough not to be cheated by mean taxi uncles.
Rounding Off A Number
If digit < 5, drop this digit/replace with zeros to keep place value.If digit ≥ 5, add 1 to digit on the left before dropping/replace with zeros to keep place value.要五毛，給一塊, and the 三輪車 Granny is always right!
ALWAYS use/show at least 1 more decimal place/sig. fig. in your intermediate workings and only round off to the required decimal places/sig. fig. in your final answer.
CASE-IN-POINT: See Miss Loi’s O-Level ‘significant’ careless mistake
Rules of Significant Figures
e.g. 12 (2 sig. fig.), 12.5 (3 sig. fig.), 1.025 (4 sig. fig.)
Zeros ARE significant UNLESS
e.g. 0.007 (1 sig. fig.), 0.071 (2 sig. fig.), 1.007 (4 sig. fig.)
e.g. *87 000 (2, 3, 4 or 5 sig. fig.), 8.7000 (5 sig. fig.)
*Depends on how estimation is made e.g.
86 999.5 ≈ 87 000 (correct to 5 sig. fig.)
86 995 ≈ 87 000 (correct to 4 sig. fig.)
86 990 ≈ 87 000 (correct to 3 sig. fig.)
86 900 ≈ 87 000 (correct to 2 sig. fig.)
86 000 ≈ 90 000 (correct to 1 sig. fig.)
Note how we round off the digit to the right of the required no. of significant figures.
Ultimately, however, do be aware that this seemingly-innocuous topic actually harvests itself in more than half of the questions in any O-Level exam that require numerical answers, as pre-warned on the cover page of every paper (which some of you never ever read
):
Also do note the following additional note 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.”
And in this era of foreign cyborgs and “90% to get A1!” moderation, failure to adhere to the above Commandment has often led to minor loss of marks here and there that could sadly mean the difference between grades, euphoria and despair.
But having said this, Miss Loi and some of her students have always wondered what exactly is a “non-exact numerical” answer?
What if an answer showed exactly 1.2345678 in your calculator – should you leave as such or round it off to 1.23 (3 sig. fig.)?
Hmmm … 你说奇怪不奇怪?