Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths. Her life's calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over 17 years she has been a savior to countless students ... [read more]
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Songs to keep you awake while studying!
*You'll need to login with an Imeem account to listen to the full tracks.
*Sits down with a lone glass of oren juice at the top of Platinum Fashion Mall and looks around*
Don’t think there’s gonna be any Ping.sg gathering here today :P.
Like starving rabbits freed from the shackles of their little cages, they bounded past the Temple Gates towards the vast open meadows of freedom beyond, where they hope to pick up where they left off a month ago: be it restarting a saved computer game, salvaging a once-decent figure ruined by junk food, or finally mustering enough courage to ask that chick out for a movie.
As they bask in the glorious sunshine that envelops the plains, few, however, notice the cluster of brooding storm clouds gathering on the horizon.
But notice them Miss Loi (with her geeky 450o glasses supernatural eyesight) did.
And as thoughts of The Cause is never far from her mind, even as the Temple Gates creak to a close in preparation for the holy dates (13-23 May) of her annual shopping pilgrimage, the High Priestess has decreed, on this Day of Love, the following schedule for the imminent salvation of the growing ranks of LMBFH Syndrome sufferers:
| Lesson Times: | |
| Mondays to Thursdays |
3.00-5.00pm (E-Maths) 5.00-7.00pm (A-Maths) |
| Fridays |
3.00-5.00pm (E-Maths) 5.00-7.00pm (A-Maths) 7.00-9.00pm (A-Maths) |
| Saturdays |
10.30am-12.30pm - Full (blocked for existing students) 1.00-3.00pm (Subject TBC - pending enquiries) 3.00-5.00pm (Subject TBC - pending enquiries) 5.00-7.00pm - Full (blocked for existing students) |
| Sundays |
1.00-3.00pm (Subject TBC - pending enquiries) 3.00-5.00pm (Subject TBC- pending enquiries) 5.00-7.00pm - Full (blocked for existing students) |
| Venue: | Miss Loi’s Temple |
| Class Size: | Exclusive to 4-6 students/class |
| Duration/Session: | 2 hours |
| Included: |
Drinks and light snacks Miss Loi’s fabled Exam Papers School uniform is optional (but still must wear something okay!) |
As per last year, these intensive tuition sessions are designed to cover the entire O-Level Mathematics syllabus within this June holidays. To ensure that every single participant will receive Miss Loi’s maximum tender loving care, each session is limited to a maximum of six students.
Lastly, history has shown that a major schedule announcement like this is usually followed by a chaotic tremendous surge in spiritual fervour.
As such, Miss Loi implores you to contact her at your earliest convenience to confirm your early salvation, for it’ll be too late when you see pot-bellied beer-drinking security guards deployed for crowd control at the Temple Gates to ensure that no one (not even a limping terrorist) sneaks in!
Miss Loi will be on her overseas pilgrimage trail from 13-23 May.
Please email missloi [at] exampaper [dot] com [dot] sg during this period as her mobile phone might not be reachable at times, and she will try to get back to you as soon as she can find the next internet access point.
One more time …
*Puts on helmet*
*SHOWS STERN & MEAN & TIRED FACE*
*Sounds bugle* EVERYBODY FALL IN!
Most of you would’ve started your Mid-Year Exams by now - a series of no-holds-barred trials to determine once and for all if indeed a wind tunnel exists between your ears to test your understanding of topics taught in Semester 1.
For some, this could also be a time for your ‘chers to avenge all the tortures you’ve subjected them to throughout the term. As such, the Mids always tend to be a little on the sadistic side, and strewn with devious tricks around every turn and corner.
That’s why Miss Sergeant Loi (whose Teresa Teng voice is now hoarse from all the shouting) is here - to hopefully help save you a mark or two, to give you that little bit of edge from being pwned by your ‘chers.
So let’s do this one more time (to complete the chapter on Polynomials) … for now …
e.g. Find the remainder when 4x3 - 5x + 1 is divided by:
i. x-2, ii. x+3, iii. 2x-1
Ans: Let f(x) = 4x3 - 5x + 1. Remainder, R =
DON’T waste time doing long division in remainder theorem questions!!!
From your Sec Two Expansion & Factorisation chapter:
e.g. Factorise x2 - 5x + 6
Ans via Trial & Error (try getting this under 10 sec 
):
Choose 2 factors of the constant 6
try: 1 x 6 → 1x + 6x ≠ -5x (reject)
try: 2 x 3 → 2x + 3x ≠ -5x (reject)
try: (-2) x (-3) → -2x + (-3)x = -5x (YAY!)
⇒ cross-check: f(3) = f(2) = 0 (YAY!)
⇒ x2 - 5x + 6 = (x - 3)(x - 2)
When you see the keyword Factorise, final answer must be in (brackets) i.e. don’t try to be funny and write x = 3, 2 → minus marks!
When you spot the keywords Solve and/or = 0 in your exam question, it means you’ll normally have to:
e.g. Solve 3x3 - 10x2 + 9x - 2 = 0
Ans: Let f(x) = 3x3 - 10x2 + 9x - 2.
Try x=1: f(1) = 3(1)3 - 10(1)2 + 9(1) - 2 = 0 (YAY!)
⇒ (x-1) is a factor
OR LONG DIVISION (if you’re a long division aficionado)
You should get the SAME expression either way - use which ever method you’re more comfortable with (use one method to cross check the other if you’re one of those with lotsa free time left in your exam).
Choose 2 factors of the constant 2
try: (-2) x (-1) → (3)(-2)x + (-1)x = -7x (YAY!)
→ Note the coefficient of 3 of the x2 term
⇒ 3x2 - 7x + 2 = (3x - 1)(x - 2)
→ Note it’s NOT (3x - 2)(x - 1) coz you need to corss-multiply
⇒ cross-check: f(⅓) = f(2) = 0 (YAY!)
⇒ 3x3 - 10x2 + 9x - 2 = (x-1)(3x-1)(x-2) = 0
⇒ x = 1, 2, ⅓
When you see the keywords Solve and/or = 0, final answer must be in the form x = a, b … i.e. don’t stop at factorising → minus marks!
Sometimes the quadratic equation in Step 3 cannot be easily factorised → you’ll have to use the Quadratic Formula to find the two solutions. You’ll normally get the hint when you see terms like ±√ within the question.
The cubic polynomial f(x) is such that the coefficient of x3 is -1 and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x) has a remainder of 8 when divided by x-3, find
Ans:
Since 1, 2 and k are roots, a(x-1)(x-2)(x-k) = 0
→ straightaway write down in factorized form once roots are known
→ always remember to include the coefficient a for x3 for it may not always be 1!
And since coefficient of x3 = -1
⇒ a = -1
⇒ (-1)(x-1)(x-2)(x-k) = 0
Let f(x) = (-1)(x-1)(x-2)(x-k)
Remainder when divided by x+3:
→ f(-3) = (-1)((-3)-1)((-3)-2)((-3)-7) = 200
*For some reason, students have a habit of expanding the entire expression after they’ve written down everything in factorized form = what a waste of time. Tsk.
As always, get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample question! Check out further questions on factor theorem!
Print this out if necessary and remember the above procedures by heart … and do let Miss Loi know which topics and stuffs you would like to see in her next set of Maths Notes 
Till then, understand that the ultimate root of your own equation is to prepare youself in mind and in soul for the Great War at year’s end. So don’t be afraid to make all the mistakes you need to make now (as long as you know what mistakes you’re making!).
*Puts on helmet*
*SHOWS STERN & MEAN FACE*
*Sounds bugle* EVERYBODY WAKE UP!
Sergeant Loi is back from her May Day leave - only to find The Temple in a state of 兵慌马乱 as the mid-year exams loom.
To whip everyone back to shape, Sergeant Loi shall complete the trinity (which began with indices, and followed by logarithms) with the concluding drill on surds today!
Despite the scary-looking longish workings, surds are the most straightforward part of the trinity. For most parts, the TWO main things you’ll ever need to know are how to simplify (with a dose of trial-and-error common sense) and rationalise surd expressions.
That’s it! Now let’s go eat some surds for breakfast!
*Cracks whip*
High-class definition:
An irrational root of a real number. *sweats*
Simple O Level definition:
A *square-root of a number that results in endless decimal places when you press your calculator e.g.
*Actually can also be cube-root, nth-root etc. but let’s not go there …
*Compare operations B(2) & B(3) to the Rules of Indices (Part C) and you’ll realize they’re like long-lost twins!
e.g. Simplifying surd expressions:
DON’T ever do this:
√(a+b) ≠ √a + √b → WRONG!
√(a-b) ≠ √a - √b → WRONG!
e.g.
√64 ≠ √32 + √32!
√25 ≠ √12 + √13!
e.g. (√3 + √2)(√3 - √2) = 3 - 2 = 1
DON’T ever do these:
(√a - √b)2 ≠ (√a2 - √b2) → WRONG!
(√a + √b)(√a - √b) ≠ (√a)2 + (√b)2 → WRONG!
Having a surd in the denominator is IMPROPER, UNGLAM, SINFUL & IMMORAL!!!
So we need to rationalise the denominators by multiplying the top and bottom by the same number with respect to the denominator i.e.
If denominator consists of 2 terms → multiply top & bottom by conjugate of denominator e.g.
.
Ans:
→ multiply top & bottom with conjugate surds (C)
, find the value of k.
Ans:
→ Rationalize all the sinful terms with surds in denominator!
→ Now simplify the surds using B(2) above and a tiny bit of trial and error
→ split √6 into √2√3 since we’re going to compare with the √3 term on RHS
via comparing coefficient of √3
As always, get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample questions! Check out more surds in action!
Print this out if necessary and remember the above procedures by heart, for if you fail in rationalizing surds in your exams, you’ll need to write a 1000000-word essay to Sergeant Loi explaining the rationale for not punishing you!
*Cracks whip*
iyah sadded