Desperate Times Calls For Desperate Measures There is only one choice. At an emergency sitting of The Temple Parliament convened by The High Priestess today in the face of the current flying teapots crisis, a motion was passed with a 100% (1-0) majority to amend Article (1 + x)n of The Temple Constitution, requiring all passing through the Temple Gates to make a compulsory Jφss Sticks offering at the voting altar (see photo above). Students who fail to comply shall be deemed guilty of an offence punishable by an exponential increase in the amount of homework not exceeding x100 times the existing amount. Remember … Voting Is Compulsory. Your Vote Is Secret. So have you made your Jφss Sticks offering today? P.S. Before any of you start accusing this as a blatant plagiarism of another finalist’s idea, let it be known that Miss Loi never thought of this as copying, but that she’s simply localising an inspirational idea. P.P.S. Anyone has the Tamil fonts for “Please Vote“? Miss Loi’s Omy.sg Interview These days, being a blog awards finalist comes with great responsibility and … umm … extra tasks. Just when Miss Loi was coming to terms with the great timing of Omy.sg’s request for “two pictures of your hand, doing anything you think is symbolic of blogging” (which arrived right after she removed her nail art), in came another request for a short email interview: Click to enlarge. Even though she’s been pretty busy these couple of weeks (hence the lower frequency of blog posts - hopefully this will change soon), being the archetypical goody-two-shoe award nominee that she is, Miss Loi shall nonetheless strive to fulfill this obligation in the best manner that she can … 1. How long have you been blogging and why did you start blogging? Looking through the archives (i.e. the Ten-Year Series portion on the bottom-left of this blog), you’ll find that the total number of posts add up to 191 (including this post). Actually “blogging” can be further split in two x-y components i.e. x: thinking of what to write {x: 1 hour ≤ x ≤ 3 hours each across 3 days, x ∈ R} y: the actual writing/copy-and-pasting/images creation process {y: 1 hour ≤ x ≤ 5 hours, y ∈ R} So taking the average values of x and y to be approximately 4.5 hrs and 2.5 hrs respectively, and multiplying by the number of posts, you’ll get: ∴ How long has Miss Loi been blogging = (4.5+2.5) hrs × 191 = 1337 hrs (55.7 days) As since this blog started 560 days ago (at the time of writing), blogging has taken up roughly 47.75/561 = 9.93% (correct to 3 significant figures) of her life (which is about right in terms of work-life balance ) As for why she started blogging, let’s just say that a Darth Vader-ish voice echoed suddenly in her head on one fateful day … Note: Blogging time excludes the time spent on replying comments. 2. How do you feel to be in the running as one of the finalists in the first Singapore Blog Awards? What do you think is your chance of winning? Ans to Part 1: Since being selected as a finalist, the shape of Miss Loi’s lips can be expressed by the function: f(x) = ax2, where a > 0 It’s now up to voters and the judges to increase the value of that coefficient a to as high as possible, but not too high as her mouth would then start to look a bit weird. But please, please she begs you not to let a fall to below zero! Ans to Part 2: According to the judging criteria, it’s 70% to the judges and 30% to the voters. Since the judges are supposed to be impartial and not be influenced by the results of the voting, we shall assume that winning the votes (V) and being picked by the judges (J) are two mutually exclusive events. Now to calculate the chances of Jφss Sticks winning, we need to consider all the possibilities: Jφss Sticks wins the votes AND being picked by the judges i.e. P(V)P(J) Jφss Sticks loses the votes but got picked by the judges with judging margin (mj) > vote margin (mv) i.e. [1-P(V)](P(mj > mv|J) Jφss Sticks NOT picked by the judges but wins the votes with vote margin > the judging margin i.e. P(mv > mj|V)[1-P(J)] So to obtain the grand probability of Jφss Sticks winning P(W), we need to add up all the possibilities above i.e. P(W) = P(V)P(J) + [1-P(V)](P(mj > mv|J) + P(mv > mj|V)[1-P(J)] Which is non-trivial as without mind-reading abilities to extract more data from the judges’/voters’ minds, we won’t be able to calculate P(V) and P(J), let alone the *conditional probabilities in the cases mentioned above. ARE YOU SURE THIS QUESTION IS IN THE SYLLABUS?! *Not in syllabus - O-Level students are advised not to be alarmed. 3. Who do you think are the strongest bloggers in the category you are nominated for and why? Miss Loi’s Temple has been heavily bombarded by flying teapots all week! You say leh?! But having said that, Miss Loi likes the designs in Dandy Angel’s collection very much 4. Name some of the bloggers whom you look up to and why (need not be in the running for the Singapore Blog Awards, and can mention overseas bloggers too)? *STERN MOOD ON* At this point, Miss Loi would like to pay a special tribute to a teacher blogger known as Stressed Teacher, whose blog was unceremoniously taken down without warning earlier this year under mysterious circumstances. His frank writings had provided an enlightening insight into the daily working lives of teachers in Singapore, beyond the veil of glossy brochures depicting smiling noble teachers teaching in surreal classes of well-behaved students. In a nutshell, his blog should have been compulsory reading to all aspiring teachers and to all who wonder why Singapore is a Tuition Nation. *STERN MOOD OFF* Your prediction for the winners in each of the 7 categories: Best Youth Blog ? Best Design Blog ? Best Blog Shop ? Most Entertaining Blog ? Most Insightful Blog ? Best Individual Blog ? Best Photo Blog ? Oh heavens you want Miss Loi to go through all that probability calculations again?! Here ends Miss Loi’s ’short’ OMY email interview. *Rushes off to save The Temple from the massive attack of flying teapots by getting as many people as possible to vote daily for Jφss Sticks* *dodges a flying teapot* 救命啊！！！ *dodges another flying teapot* “A Celebration of Youth” Today is Youth Day (actually it’s yesterday). Billed as a day for the “celebration of youth” (whatever that means), this doesn’t mean much to the average Singaporean students as most tend to treat it more as a “celebration of no need to go to school!“. Grim reminders … but that anime card is sooo cute hor Coming hot on the heels of someone’s birthday, today also serves as a grim reminder of how far those innocent days of her youth have slipped into distant memory, especially with evil SMSes such as this: Happy Birthday! Your birthday cake is getting more crowded now haha. *Exact message differs as Miss Loi couldn’t remember the original sms which was promptly deleted. Hmmph! Even though today no need to go to school!, many, however, ended up mocking ‘celebrating’ with Miss Loi at The Temple - which goes some ways in making her feel like a kawaii teeny (this phrase sounds familiar) youth again, since she was surrounded by youthful people from dawn to dusk. In any case, regardless of whether you’ve been doing stuffs that … umm … youths tend to do, be it shopping, slacking, going to the movies, playing computer games, gossiping, comparing boyfriends/girlfriends, forming cliques, following the ‘in’-crowd, throwing tantrums, being overly-sensitive, getting emo, dun friend you, dun want to talk to you … (wait … don’t adults do these too???) … Miss Loi hopes it’s not too late to wish everyone a Happy Youth Day! On a brighter note, the race for the BEST BLOG SHOP is heating up with Jφss Sticks going neck and neck with a formidable teeny spree shop and a fast-spinning CD Shop! So please, please remember to vote daily to give Miss Loi the required energy and nourishment to keep up with the youths. Seems like July is being hit by blog awards fever, as Jφss Sticks has just been nominated (along with several other big guns) for Ping.sg’s Most Entertaining Blog & Most Interactive Blog Awards! And this time, there’s no kawaii teeny spree blogs. *Sweats* It’s Miss Loi Vs The Kawaii Teeny Spree Blogs In SG Blog Awards! Friends, comrades and countrymen! The time has come for the hundreds and thousands of you readers (yes YOU - don’t act blur!) of this blog to step forth from the shadows of your LCD monitor and take action! For the lines have been drawn, and Jφss Sticks has survived Nomination Day and is now a finalist of the Singapore Blog Awards! Contesting in the … umm … relatively obscure category of BEST BLOG SHOP (afterall one can purchase kawaii exam papers here), Miss Loi nonetheless faces a fierce ten-corner fight against the likes of a CD shop, a kawaii teeny jewelry shop, a kawaii teeny spree shop, a kawaii teeny spree shop, a kawaii teeny spree shop, a kawaii teeny spree shop, a kawaii teeny spree shop, a kawaii teeny spree shop (that entices voters with a special kind of ‘nude bra’!), and … hold your breath … a kawaii teeny spree shop. As such, Miss Loi implores you to stop your MSN chat, stop your computer game, stop ogling at Japanese models close all your windows (i.e. those in your computer screen) and head over to this link and click the “Vote Now” button: Next, SCROLL DOWN to enter your e-mail, choose a password on the spot and click the “Start Voting!” button (and fill in the rest of your particulars honestly when asked - please avoid using names like “Cristiano Ronaldo” that might immediately invalidate your vote): Once you’ve done that, a very nervous kan cheong woman (surrounded by nine other menacing icons) should magically appearing before your very eyes! It’s now the time to save this damsel in distress by clicking on her kan cheong picture! And since voting is a DAILY AFFAIR, it’s IMPERATIVE that it gets into your subconsciousness to save this kan cheong woman each day before you start your daily MSN chat, computer game, and … umm … Japanese collections viewing routine. And who knows, you might even win a *travel package to Bangkok, Vietnam or a luxurious resort package in Phuket! The road ahead is long and grueling (30 June to 31 July to be precise), and Miss Loi is handicapped from the start as she does not have enough aunties, uncles, cousins, friends, friends’ friends … friendsn, programmers to vote her on a daily basis, especially when the rest have already mobilized their kawaii teeny shopping clone armies. So please help send Miss Loi into the eternal Blogging Hall of Fame! And in return she’ll promise you an UPGRADE of your visiting experience, and MORE GOOD YEARS of challenging math questions & exam papers and … umm … post more kawaii photos of herself! nevermind. Vote wisely. Vote Jφss Sticks! And while you’re at it, do support Miss Loi’s friends and her fellow Pingsters in the blogosphere too (luckily none of them are competing in Miss Loi’s category *phew*): Best Youth Blog Crazy Hamster Jaymes007 Most Insightful Blog Simply Jean Ieatishootipost DK Most Entertaining Blog Eastcoastlife Marina Sheylara Best Individual Blog Chillycraps *Applicable only if you’re human and not some vote cheating program A Critical Birthday Wish Folk heroes are often born underumm … dramatic circumstances Ken (not his real name) was a cute, bubbly inquisitive kid (with a pair of chubby cheeks that everyone likes to pinch and twist) who used to do well in his studies. No one knows how and why and when he began to believe that he could pass exams by revising from scratch minutes before they start, but nevertheless he stuck to his belief, over and over again, and his grades plummeted tragically as a result. Understandably worried, his parents enlisted the help of a famous temple medium (who came highly recommended by vegetable seller’s wife from the neighbourhood market) in a bid to snap Ken out of his mysterious trance. After some dramatic rituals which involved a temporary solar eclipse followed by multi-coloured flags shooting out from somewhere behind the medium’s body, the medium has this to say (after receiving a BIG FAT ang bao): Translated from Hokkien: Your son has been possessed by a very evil Last-Minute Buddha Foot Hugging Spirit. It is beyond my powers to save him. *Takes another BIG FAT ang bao* Your immense sincerity has suddenly unlocked my mind … Let it be known that your son can only be saved by a Great Tutor who is born on a date given by the solution to this matrix equation: where the top and bottom element of the resultant column matrix is the month and day of birth respectively. Once you’ve obtained the date, remember that you MUST go and wish this tutor “HAPPY BIRTHDAY!” on the big day itself in order for your child to stand any chance of being saved! Since this should be really straightforward to anyone with the most basic knowledge of matrices, Ken’s parents (who have no knowledge of O-Level maths) will gladly let you pinch (and twist) his chubby cheeks for eternity if you can help them find the tutor’s birthdate! Extending The Temple - Rekindling A Love-Hate Relationship Talk about friends in need. As it’s becoming imperative that The Temple expands asap, Miss Loi shamelessly turns to Billy, Vika, Kludd (grrr …) and other friends again for help, even though their last meeting ended in rather acrimonious circumstances. Let’s hope that she doesn’t foul it up this time P.S. This short update notwithstanding, Miss Loi really hopes to be back blogging soon P.P.S. Miss Loi’s latest schedule is up, for those who’re waiting for it. Miss Loi Is Sunday Times’ Cover Girl! Miss Loi’s poor little Nokia phone and email inbox are experiencing very high volumes of enquiries at the moment. As there’s only one Miss Loi attending to all your queries, she seeks your kind patience and understanding if she’s a little slow in getting back to you. Also, thank you all so much for the emails and smses of well wishes and encouragement. Miss Loi feels very bad that she is unable to attend to all non-urgent messages at present, but she hopes to be able to reply everyone when the dust has settled. To all parents/students making enquiries: please do NOT turn up at The Temple unannounced and risk a wasted trip as Miss Loi may be out giving private tuition at the time! In any case, the preferred method of communication at the moment is to contact Miss Loi via phone or email (please leave your contact number) and she’ll get back to you once she’s done with her classes. Lastly do note that: Miss Loi does NOT teach PSLE/Primary-level mathematics. Miss Loi’s private home tuition slots are FULL for now. Miss Loi’s Secondary One/Two classes are FULL for now. If you haven’t yet done so, please register as a member to be instantly informed of announcements of new schedules and classes. Thank you for your cooperation and kind understanding. Chances are that you would’ve bumped into Miss Loi today. Be it during your morning cup of kopi siew dai … Drink too much kopi not good okay … Or when you’re ogling at magazine cover girls at the news stand … Stop staring at Jade Seah! Look south … Or when you were in the midst of your … umm … unspeakable business … Oh heavens you’ve ran out of toilet paper!DOOOON’T!!!!!!! Even as her stern face continues to scare the living LMBFH Syndrome out of every school-going kid in Singapore, Miss Loi would like to extend a warm welcome to all Straits Times readers to Jφss Sticks! And despite their scheming roles in cajoling a thousand kitties out of Miss Loi’s LV bag and being guilty of a GLARING, GLARING error, she’s eternally grateful to journalist Mavis and photographer Ashleigh for putting this little maths tutor on the hallowed pedestal of 五大超级补习天王天后 (lit. The Five Heavenly Super Tutors) - alright Miss Loi invented this mahjong-combo-sounding name herself haha This one cannot … that one cannot … this one eyes too small … that one face bloated … As the Temple Gates now creak and groan from the sudden massive, massive influx of Mathematical refugees, Miss Loi seeks your kind patience and understanding if she’s a little slow in getting back to you, as she still has her classes today. Time to return all the calls. Looks like it’s gonna be a long, long night. P.S. As Miss Loi has just been unmasked today, she would like to apologise if she has rudely shattered your maths tutor fantasies in any way. The Phantom Car of PIE No one knows how the legend of the Phantom Car of PIE began. It is said that lousier drivers on the PIE every morning can sometimes hear the eerie squealing of tyres and the roar of an engine, accompanied by thumping techno music, that heralded the momentary appearance of a mysterious black car in their mirrors. Eye witness accounts tell of a sexy slim lady with pale flawless complexion behind its wheel, with nary a spill from the paper cup of kopi peng perched on the cup-holder as she overtook from the left in one mesmerizing move, casting a bone-chilling glance of irritation as she passed. During these moments, sleeping students being ferried to school in SUVs have been known to suddenly sit up and recite aloud trigonometry formulae, and taxi drivers have been reported to suddenly stop scolding the government and instead expound the applications of integration to their (disinterested) passengers. All these, however, remain as an urban legend to a particular lorry driver cruising at a leisurely speed along the PIE’s right-most lane this morning, much to the annoyance of the long train of cars behind. But it all changed when a vicious 100+ BPM techno track sounded from nowhere to drown out Teresa Teng’s crooning voice in his stereo. The needles in his instrument panel started to swing wildly, and all the denials in the world couldn’t prepare him from the blinding aura emanating from that innocuous-looking black car in his mirror … Assuming the black car appeared right next to the lorry at t = 0, the diagram shows the speed-time graph of the lorry and the black car during a period of 60 seconds. Find the acceleration of the car in the first 10 seconds; the distance travelled by the car during the 60 seconds; the distance travelled by the lorry during the 60 seconds; the time when the car overtakes the lorry (if it does), and the time when the lorry overtakes the car (if it does). NOTE: When you see a speed-time graph in an E-Maths Kinematics question, it’s almost inevitable that you’ll have to recall that: Distance covered = area under the graph DON’T be confused with your average speed = total distance/total time formula you learnt in PSLE! P.S. While many of Miss Loi’s Sec 3 students were smirking at her for insulting their intelligence when doing Parts 1-3, for some reason quite a number of them weren’t smirking anymore when they reached Part 4. Cristiano Ronaldo Signs For Jφss Sticks According to Miss Loi’s students, some major football tournament is kicking-off tonight (which will likely result in some sleepy students and late handing up of homework for this month. Tsk tsk.). Incidentally, during a routine scan of the list of members who’ve signed up, an eagle-eyed Miss Loi spotted a certain “Cristiano Ronaldo” on the list. Portions masked to protect Cristiano Ronaldo from being spammed by the paparazzi Since his name rings a bell even to Miss Loi’s football-illiterate ears, she reckoned that he must be a very famous player (and quite handsome too she was told). As to why Cristiano Ronaldo was checking out Miss Loi’s maths exam papers so close to a major football tournament, it’ll probably remain a mystery for a long time to come. Perhaps he needs more practice on quadratic curves in order to Bend It Like Beckham? UPDATE: Miss Loi has just received word that David Beckham has signed for Jφss Sticks today! Apparently, maths is now an integral part of a footballer’s curriculum. Miss Loi vs The Big Bad Dog No, this is not the dogthat traumatized Miss Loi’s childhood Ever since a harrowing experience of being pursued by a big bad dog when she was a very cute child, it’s safe to say that there isn’t much love lost between Miss Loi and the canine population. Unfortunately, being a private tutor means that she often has to live with the occupational hazard of facing big bad dogs at her students’ house. They range from fierce growling beasts with salivating tongues (which she always gives a wide berth of ≥ 5m) to the cute but irritatingly … umm … hum sup kind who never fail to … umm … climb all over her in an attempt to lick away the top layer of her Shu Uemura makeup, create a saliva trail up and down her legs, and often leaving a helpless Miss Loi thinking … 你虽然得到了我的身体，但你永远得不到我的心！ … as a solitary tear drop flows down her face. And on this topic, Miss Loi found herself face-to-face with a particularly nasty-looking dog one day, as she waited at the porch for the maid to open the door to her student’s house. As she stared into its pair of big dark eyes, notice was served of its enormous strength when she found that it was held back by not one but FOUR leashes tied to various points around the porch. But the maid was taking ages, and a bored Miss Loi decided it was time to exact some measure of revenge for her traumatized childhood. Yoohoo Doggie … how does it feel to be all tied up huh? *Sticks out tongue and makes monkey face* Grrrrr … Came the friendly reply as it reared its huge white furry head. Not happy? Come and get me lor. Oops but you can’t! Hur hur hur! GRRRRRRRRRRR!!! And so in a severe lesson on complacency, the angry dog managed to break one of the leashes in a mighty show of strength, just as her (petrified) student appeared at the door! Miss Loi! Three leashes won’t hold him for long! I have a rope I can throw to pull him back by the neck - but I dunno how long I should throw?! Given that the lengths of the three remaining leashes are 6m, 2m and 7m, and that they are tied to three corners of a rectangular area, with Miss Loi’s student standing at the fourth corner. Find x, the length of the rope, that the student must throw. Miss Loi how?! You know I’m only Sec Two! I haven’t learn Trigonometry yet!!! Now isn’t the time for excuses! Sec Two students should be able to solve this - I’ve just taught you Pythagoras Theorem last week! Can you please help Miss Loi before she becomes dog food?! Miss Celine Loi Messes Up Her SG Blog Awards Nomination The nomination stage of the inaugural S’pore Blog Awards has reached fever pitch. Since its inception a month ago, it has attracted a steady stream of nominations for blogs ranging from the critically-acclaimed to the critically lame. And as a testament to the immense success of this campaign, their nomination list now resembles a weekend Toto queue at your neighbourhood booth, choked full of all of the 阿鸡阿狗阿猫 (lit. the chicks, the dogs and the cats) of Singapore’s blogosphere taking their solitary potshots at eternal online fame. HUAT AH!!![source] But like others before her, this particular 小猫 too fell victim to the beckoning lure of the bright lights of internet fame and hence, in true LMBFH fashion, decided to join the Toto queue register Jφss Sticks on the eve of nomination deadline. After performing a series of complex probability and statistical calculations, taking into account factors like: The standard deviation of other bloggers’ levels of cuteness and sexiness The mean and median number of cute and sexy photos in other blogs The likelihood of scandals (as they tend to happen in the aftermath of all contests) , she concluded that the path of least resistance lies in the Best Design Blog Category (with just 46 nominees at the time of writing), which offers the best chance of striking Toto being selected compared to, say, the Best Individual Blog Category (267 nominees at time of writing and rising fast), where bloggers currently live in Third World overcrowded conditions: Length of Toto queue as of 1 June (Sunday) And so like a nervous Ah Lian joining her first pageant, Miss Loi proceeded to fill up the online registration form. It didn’t help that the first field demanded her NRIC number. After deliberating for a year, Miss Loi finally decided to (grudgingly) disclose her age to them in the spirit of competition. *Hmmph!* Next came the Blog Details section, which seemed straightforward enough to complete. Last came the “Short description about yourself/your blog” section - that crucial area of the form which presents the opportunity for bloggers to execute their Level 99 hard-selling pitching skills imploring the judges to take a second look. Following the tuition industry’s emphasis on personal testimonies, Miss Loi decided to string together a collection of some of the more … umm … encouraging comments from her dear readers. So instead of a typical: Hi I’m Miss Loi. I’m a sexy maths tutor and this is my blog. I blog about maths, tuition, and anything under the sun. But in reality, I’m just a simple girl. You might experience the unnerving feeling of seeing your own comment from your past life here: With a satisfied smile on her face, she clicked the ‘Submit’ button and to her horror this is what’s currently showing on the nomination list: Instead of Jφss Sticks, the title of this blog is now affectionately known by the utterly, utterly un-glam name of MISS LOI. And a certain Celine Loi has suddenly taken over as the author of this blog! Checking back, she realized that in her haste she’d mistakenly took the form’s Blog Nickname field for Blogger’s Nickname. But why on earth would a blog have a nickname?! To the best of her knowledge, Miss Loi hasn’t come across any blog that comes with an ‘official’ name and an accompanying nickname. Maybe she should start to call Jφss Sticks Jossy from now on *shudders* So there you have it. Please support Celine Loi of MISS LOI’s fame in this year’s S’pore Blog Awards! Ewwwwwwww. NEWFLASH: This new blogger Celine Loi now finds herself within the list of “heavier-weight” bloggers (nothing to do with her real weight okay!) on omy.sg’s official blogs (here & here). She was feeling really flattered to be featured alongside the likes of Blinkymummy and Eastcoastlife (albeit being way way way way way way way way down the list), but when she saw the blog positioned two places above hers … PING.SG Depicted As A ‘Sin’ In Popular Bookstore Ad Most compulsive serial assessment books collectors (i.e. those whose life’s calling is to attempt EVERY assessment book known to mankind) among us in Singapore invariably end up as The A-Grade Cookies Of 1º 22′ N 103º 48′ E Miss Loi onboard her flying craftbound for 1º22′N 103º48′E A million pins and needles pierced Miss Loi’s tender-smooth skin as soon as she stepped out of her flying craft onto a strange world located at Sector 1º 22′ N 103º 48′ E. The mild breeze of spring was a distant memory as the harsh sauna-like atmosphere of 1º 22′ N 103º 48′ E’s climate mercilessly ruined her make-up in an instant. Desperately seeking shelter from the heat, she was reminded on how much slower some things can be here, compared to the previous world centered around Sector 35° 45′ N 139° 22′ E, especially with regards to mass transportation. Traveling through the surreal high-rise landscape of 1º 22′ N 103º 48′ E, she suddenly felt hungry and so she headed to the nearest bakery to buy some cookies in which this place is famous for. While at the bakery she was intrigued by a ‘QC machine’ where rows of cookies were constantly being carried via a conveyor belt into it for inspection, while another belt at the opposite end dropped those which passed the inspection out from the machine onto waiting trays. Those are our premium A-grade cookies. A staff at the counter pointed out proudly. Only about half of them came out. What happened to the rest? Quizzed an ever-observant Miss Loi. The rejects? To the dustbin via an opening beneath the machine. You wouldn’t want to show customers your rejects would you? Huh? What a waste! No choice lah! Boss wants to raise standards, competition is tough with other bakeries these days. Why don’t you try improving your baking process to prepare better cookies so that more will pass QC? EH CHAR BOH! YOU THINK I SO FREE LIKE YOU ISIT? EVERYDAY HAVE TO OPEN SHOP AT 7AM! HAVE TO HANDLE UP TO 40 COOKIES AT A TIME! HAVE TO ATTEND TO CUSTOMERS! HAVE TO ATTEND STUPID STAFF MEETINGS! HAVE TO WRITE REPORT! HAVE TO SUBMIT BAKING PLAN FOR NEXT WEEK! SOMETIMES HAVE TO ATTEND BAKING WORKSHOPS! SOMETIMES EVEN KENNA ARROWED TO ORGANIZE COMPANY GATHERING! MANY TIMES THE COOKIES NO TIME TO BAKE PROPERLY I HAVE TO SEND THEM IN - OF COURSE REJECT LAH! I JOINED THIS SHOP COZ I LOVE TO BAKE COOKIES BUT HR NEVER TELL ME GOT SO MANY OTHER CCA! He paused to catch his breath. AFTER JUNE WILL BE WORSE. BOSS EXPECTS ME TO FINISH BAKING ALL THE COOKIES IN THREE MONTHS FOR THE SA2 INSPECTION! THINK IF REALLY CAN’T COPE I’LL HAVE TO SECRETLY OUTSOURCE THE COOKIE BAKING PROCESS LIKE WHAT AH SENG DID AT THE OTHER BAKERY - EVERYONE SAYS HIS COOKIES VERY TASTY BUT NOT HE BAKE ONE! I’M VERY TIRED ALREADY - I HAVEN’T HAD A PROPER REST IN A YEAR! I’M NOT LIKE THAT COOKIE MACHINE YOU KNOW?! YOU KNOW?! EH YOU GOT LISTEN TO ME OR NOT?!!! Seeing the violence brewing in his eyes (plus that kitchen knife lying within 10 cm of his hand), Miss Loi wisely paid for her bag of premium A-Grade cookies and quickly left the shop. Moments later, she finally arrived at the familiar surroundings of her own little outsourcing factory - just in time to process a fresh shipment of raw cookies from that lazy Ah Seng. As she proceeded to prepare the cookies meticulously (up to six at a time), she already knew that each of them came with different ingredients, and so different baking techniques and amount of time are required to bring out the best taste from every single one of them. It’s great to be home again. P.S. Please check your Google Earth if you’re still unsure where 1º 22′ N 103º 48′ E is. One Small Step In Her Charles & Keith Shoes, A Giant Leap For Her Palpitating Heart Since the beginning of time, mankind has always sought to outdo ourselves. Whether it’s about climbing the highest mountain, Scaling the tallest height, Blazing the fastest speed, Or simply being the most sadistic. And so a timid Miss Loi stood, with wobbly legs, before three of the meanest modern devices mankind has ever built with wicked intent this side of the world. Her life and her students’ mid-year exam results flashed before her eyes, as she looked up in awe at the flowing entrails of these mighty beasts, and pondered if it was indeed her destiny that brought her to this spot. But pondering should be the last thing on her mind, for she would loathe to waste her ¥1200 entry ticket has always told her students to face up to their challenges … … and now the time has come for her to live up to her own words. And so it came to pass that on this day, a visibly-trembling Miss Loi held her breath, stole one last glance at the monstrous machina towering before her, and took that fateful step forward … . . . … to take a few more photos before heading off to more comfortable environs. Sorry folks, after a brief calculation on the tracks’ geometric properties and the kinematics involved, Miss Loi concluded that the resultant angular velocities were a little too much for her poor little palpitating heart. Besides, the 50-60% discounts at Gotemba Premium Outlets were difficult to resist okay! *** Before you start calling Miss Loi a chicken, here’re some vids on the action that Miss Loi missed out (which till now she still didn’t regret after viewing them!): 1) FUJIYAMA (4th longest & 6th tallest in the world) 2) DODONPA (Highest acceleration and 3rd fastest in the world) 3) EEJANAIKA (7th tallest & most inversions i.e. sadistic in the world) Daddy Daddy Boy … As the examples below show, music is deeply ingrained in the consciousness of Tokyo’s urbanites. Strolling along the endless stretches of malls and boutiques in downtown Tokyo, Miss Loi was constantly reminded of the lameness and shallowness of her genre of ah lian dance music, as mere mortals like her couldn’t even begin to fathom how these siao char bors and siao da bors managed to redefine musical sophistication to a new level. Music courses through the veins of this siao char bor indeed - all the way through her … umm … legs (NSFW?) The pure musical emotions emanating from this siao da bor was so overwhleming that people around him started hugging each other - even though he didn’t quite seem to know where his audience was Pure energy from this siao cha bor was so infectious that the police had to intervene to save the guy in the green T-Shirt from succumbing to her subliminal effect As of this moment, “Daddy Daddy Boy … Daddy Daddy Boy …” is still replaying inside Miss Loi’s head. Oh dear think Miss Loi can’t escape her subliminal effect too! Daddy Daddy Boy … Daddy Daddy Boy … Daddy Daddy Boy … Daddy Daddy Boy … *starts putting on green T-shirt and rolls up mid-rift* Akihabara (秋葉原) also known as Electric Town or AKIBA in short. It’s best-known as one of the largest shopping areas on Earth for electronic, computer, anime, and otaku goods. Sprawled in every direction off the main street Chūō-dōri (中央通り) are more smaller streets with even more electronics stores. On Sunday afternoons, the main street is blocked to vehicle traffic and the area becomes a bit of a flea market - you can walk freely along the main avenue and many small vendors set up tables on the side streets. You can’t miss the street performers; everything from maid-fetish karaoke to incan music can be heard on a good Sunday. [source] P.S. siao cha bor and siao da bor are local slangs for crazy woman and crazy man respectively. Miss Loi’s Cute Little Stay In A Cute Little Village After descending from Japan’s second-highest mountain, Miss Loi found herself in a cute little village. With cute little houses scattered everywhere. Each of which were built with a not-so-cute amount of labour. Miss Loi ended up staying in one particular cute little house. That served up a cute little dinner. All these made Miss Loi feel really keen to return on another time when things are supposedly even cuter. Even though it’ll burn another cute little hole in her cute little wallet Thanks for reading this cute little update from a cute little Miss Loi just before she tucks into her cute little bed. Shirakawa-gō (白川郷) is a historic village in Gifu. It was registered as a UNESCO World Heritage Site on December 9, 1995. The village is famous for its farmhouses, which are built in a unique architectural style known as gasshō (合掌). The name means “hands together” as in prayer, referring to the steep roofs that keep the snow off in the winter. Underneath the roofs, the large attic area was used to house silkworms. Another feature which has brought fame to the village is that the recent Japanese anime series ‘Higurashi No Naku Koro Ni’. Although the village residents are not too altogether thrilled that an anime series depicting large levels of violence has based itself on their village, it has brought the tourists nonetheless. [source] Guess Where I Am? :) An exhausted Miss Loi realizing too late that snow and suitcases don’t get along too well At 3,015m, Tateyama is one of Japan’s tallest mountains, and is considered one of both Japan’s Three Famous Mountains and Japan’s Three Holy Mountains. It’s here that one will find the highest onsen in Japan. The Tateyama Kurobe Alpine Route (立山黒部アルペンルート) is a famous mountain sightseeing route between Tateyama, Toyama and Ōmachi, Nagano, Japan. The route is just 37km in length, but the vertical interval is as large as 1,975m. It takes 7 different public transports with 5 different modes, namely funicular, bus, trolleybus, aerial tramway, and walking. Of the triple-peaked Tateyama range, the most popular climb is the peak named Oyama, from which, on a clear day, it is possible to see Mt Fuji. [source] One Night In Bangkok But No Trace Of Pingsters *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. When Rabbits Munch On Fresh Green Grass, They Cannot See The Storm Coming From The Horizon Platinum Fashion Mall - One of the stops onMiss Loi’s pilgrimage trail. Like starving rabbits freed from the shackles of their little Sergeant Loi’s Mid-Year Boot Camp 2008 - Finding Your Roots With Remainder & Factor Theorems This heavy thing is causing permanent damageto her previously-rebonded hair 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 … Remainder & Factor Theorems A. REMAINDER THEOREM If f(x) is divided by (x - a) ⇒ the remainder is f(a) 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 = f(2) = 4(2)3-5(2)+1 = 23 f(-3) = 4(-3)3-5(-3)+1 = -92 → note it’s divided by x (+) 3 so you’re have to sub in (-)3 instead f(½) = 4(½)3-5(½)+1 = -1 → note when divided by (2x-1) → you’ll have to convert it to the form (x-½) first and then sub in the ½ DON’T waste time doing long division in remainder theorem questions!!! B. FACTOR THEOREM If f(x) is divided by (x - a) and the remainder is 0 ⇔ f(a)=0 ⇒ (x - a) is a factor of f(x) ⇒ f(x) is exactly divisible by (x - a) From your Sec Two Expansion & Factorisation chapter: Expansion → remove brackets Factorisation → put back brackets ⇒ final answer must always be in brackets! 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! C. SOLUTION OF EQUATIONS When you spot the keywords Solve and/or = 0 in your exam question, it means you’ll normally have to: Find the factors of an equation f(x) (usually cubic) Find the roots of f(x)=0 (i.e. final answer must be in the form: x = a, b … where a, b, … are the roots) e.g. Solve 3x3 - 10x2 + 9x - 2 = 0 Ans: Let f(x) = 3x3 - 10x2 + 9x - 2. Find the first factor via trial and error Try x=1: f(1) = 3(1)3 - 10(1)2 + 9(1) - 2 = 0 (YAY!) ⇒ (x-1) is a factor Find the remainder expression by either COMPARING COEFFICIENTS: 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). Factorize the remaining quadratic expression 3x2-7x+2 (via quick Trial and Error method described in B above): 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. SAMPLE PRACTICE 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 the value of k, the remainder when f(x) is divided by x+3 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) Since remainder is 8 when divided by (x-3), f(3) = (-1)(3-1)(3-2)(3-k) = 8 (using Remainder Theorem from A above) ⇒ k = 7 Now using k = 7 above, f(x) = (-1)(x-1)(x-2)(x-7) 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!). Good Luck For Your Mids! P.S. To the reader who longs and yearns to see Miss Loi’s divine face again, a very heartbroken and upset Sergeant Loi was last seen charging out of camp with her Katana sword, vowing to hunt this reader down, and slice him into many pieces and use the Remainder Theorem to turn whatever that remains of him into 人肉叉烧包 (human buns)! Sergeant Loi’s Mid-Year Boot Camp 2008 - Rationalising The Rationale Of Surds Don’t worry.These aliens are often friendlier than they look. *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* The Rationale of Surds A. WHAT IS A SURD? 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. √2 is a surd (=1.4142135623 … when you press your calculator) √9 is NOT a surd (= 3 when you press your calculator - WOW NO DECIMALS!) *Actually can also be cube-root, nth-root etc. but let’s not go there … B. THE OPERATIONS OF SURDS *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: √18 = √(9 × 2) = √9 × √2 = 3√2 → Using B(2) and a tiny bit of trial and error to get the (9 × 2) 3√2 + 5√2 = (3 + 5)√2 = 8√2 → Using B(4) (√5 - √2)2 = (√5 - √2)(√5 - √2) = √5√5 - √5√2 - √2√5 + √2√2 = 5 - √10 - √10 + 2 → Using B(1) + B(2) = 7 - 2√10 → Using B(4) DON’T ever do this: √(a+b) ≠ √a + √b → WRONG! √(a-b) ≠ √a - √b → WRONG! e.g. √64 ≠ √32 + √32! √25 ≠ √12 + √13! C. CONJUGATE SURDS (h√a + k√b)(h√a - k√b) = h2a - k2b (Note the MINUS sign on the RHS) 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! D. RATIONALISING THE DENOMINATORS OF SURDS 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 a single term → multiply top & bottom by denominator term e.g. If denominator consists of 2 terms → multiply top & bottom by conjugate of denominator e.g. SAMPLE PRACTICE QUESTIONS Simplify . Ans: → multiply top & bottom with conjugate surds (C) Given that , 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* Of Matrices & Miss Loi’s Day Of Labour This year’s Great Labour Day Racing Circuitcertainly looks tame compared to last year’s *Takes off helmet* *Shows kindly & benign face* On a day when Singapore’s working class was left to reflect on their social standing in the current status quo, May 1st (by virtue of its proximity to the Mids) has traditionally been Miss Loi’s Day of Labour. But with the advent of The Temple, the distance travelled is much less this year, with a corresponding drop in the number of stunts overtaking manoevuers needed in order to get to her students’ place on time. Which also means that Miss Loi actually has time to help that butchy Sergeant Loi (who is on leave today and thereby sparing the serene Temple Grounds from her KPKB for the first time this week) post her Matrices notes: Ever since the bulk of the Matrices chapter has been migrated over to the New EMaths Syllabus, according to Section 1.4 of the AMaths Syllabus, about the only time you’ll ever see matrices appearing in your AMaths papers would be when you’re asked to solve a pair of simultaneous equations using the inverse matrix method. The following, then, is really all you need to know Solving Simultaneous Equations Via Inverse Matrix A. HOW TO MULTIPLY MATRICES B. DETERMINANT OF A 2X2 MATRIX Determinant of matrix M = is given by: |M| = = ad - bc If |M| = 0 ⇒ M is singular. If |M| ≠ 0 ⇒ M is non-singular. C. INVERSE OF A 2X2 MATRIX For a non-singular matrix M = , D. THE INVERSE MATRIX METHOD AX = B ⇒ X = A-1B *Note: AX = B ⇏ X = BA-1! SAMPLE PRACTICE QUESTION Use the inverse matrix method to solve the simultaneous equations: 5x + y = -8 -x + 2y = 17 Ans: *See the words inverse matrix method in question - SIANZ!* Can you see that the pair of simultaneous equations are actually part of matrix multiplications shown in A above? So you can convert to matrix form: You can then move the 4 x4 matrix to the RHS of the equation as highlighted in D above: Now to find the inverse matrix : As described in B above: Determinant → = (5)(2)-(1)(-1) = 11 ≠ 0 ⇒ non-singular ⇒ inverse exists! As described in C above: So Sub the inverse into the equation in step i: Do your multiplication! As described in A above: ⇒ x = -3, y = -7 Note: most of the time, you should end up with a 2 x 1 matrix after multiplying. Know with true faith the methods above. Be cautious with the pointers and common mistakes in red. Understand with thy heart the representative sample question at hand. Print this out if necessary and commit to memory the above procedures, and be comforted that no matter what happens, Miss Loi shall always be here to support you, in spirit and in soul. HAPPY LABOUR DAY! *Drifts away like 倩女幽魂* Sergeant Loi’s Mid-Year Boot Camp 2008 - Defeat Partial Fractions In Three Devastating Moves Within its pages lies the secretto defeating Partial Fractions *Puts on helmet* *SHOWS STERN & MEAN FACE* *Sounds bugle* EVERYBODY FALL IN! Today you’ll learn to deal with a new enemy originally from the A-Level campaign. Something never been seen by your previous O-Level comrades, nor has it appeared in the pages of the old Ten-Year Series 武林秘籍 (ala Secret Manual). But fret not! Though it looks formidable at first, its size also makes it unwieldy and predictable, so master the rules of engagement (see A. and B. below) and follow the standard 三大招式 (Three Devastating Moves) detailed in each of the Sample Questions below, and you’ll be on your way to defeating these Partial Fractions! NOW ALL TURN TO PAGE 1 OF YOUR 武林秘籍 (2008 revised edition)!!! *Cracks whip* Frag The Partial Fractions! A. COMPULSORY PRE-CHECK The degree of a polynomial is the highest power of x. e.g. p(x) = 4x3 - 12x2 - x - 4 ⇒ degree = 3 q(x) = (x - 1)(x + 2) ⇒ degree = 2 ( ∵ when expanded q(x)=x2+x-2) For : if degree [ p(x) x) ] ⇒ PROPER ⇒ proceed with main Partial Fraction calculations (YAY!) if degree [ p(x) ≥ q(x) ] ⇒ IMPROPER ⇒ Long Division Time! (see Qn 2 below) (SIANZ!) (note it’s greater OR EQUAL) B. THE RULES OF PARTIAL FRACTIONS ENGAGEMENT For : (*Have you ‘propered’ this first? See above.) Rule If q(x) contains Partial Fraction must contain 1 linear factor(ax+b) for each linear factor 2 repeated linear factor(ax+b)2 for each repeated linear factor 3 quadratic factorx2+c2 for each quadratic factor (x2 - b2) can be factorized further into (x + b)(x - b) → two linear factors! (≠ quadratic/repeated linear factor!) SAMPLE PRACTICE QUESTIONS (Note the standard 三大招式 steps). Express in partial fractions. Ans: 第一式 (绝招) Check: degree of (7x+4) = 1 x+1)(x-2)2 = 3 ⇒ PROPER (YAY!) 第二式 So → 1 x linear factor (2x+1) and → 1 x repeated linear factor (x-2)2 Using Rules 1 & 2 from the table above, we have: *Note there’re two components for the repeated linear factor (x-2)2! 第三式 (绝招) Multiply both sides by (2x+1)(x-2)2, 7x+4 = A(x-2)2 + B(2x+1)(x-2) + C(2x+1) To find A, B and C, sub in suitable values for x that makes certain components disappear: Sub x = 2, Sub x = , Sub x = 0, A = , C = , Hence, Express in partial fractions. Ans: 第一式 Check: degree of (x4+9) = 4 > degree of (x3+3x) = 3 ⇒ IMPROPER ⇒ LONG DIVISION TIME!!! (SIANZ! ) 第二式 Now can be factorized further to → 1 x linear factor (x) and → 1 x quadratic factor (x2+3) Using Rules 1 & 3 from the table above, we have: *Note: all we need is the quotient (x) from the long division in i. 第三式 Multiply both sides by x(x2+3), x4+9 = x2(x2+3) + A(x2+3) + (Bx+C)x To find A, B and C, sub in suitable values for x that makes certain components disappear or your life easier: Sub x = 0, ⇒ 9 = (0)(3) + A(3) + (C)(0) ⇒ A = 3 Oh we can’t reduce other components to 0 with another substitution → need simultaneous equations here: Sub x = 1 (to make your life easier), A = 3, ⇒ 1+9 = (1)(4) + (3)(4) + B + C ⇒ B + C = -6 —– (1) Sub x = -1 (to make your life easier), A = 3, ⇒ 1+9 = (1)(4) + (3)(4) + (-B + C)(-1) ⇒ B - C = -6 —– (2) Solving (1) & (2), B = -6, C = 0 Hence, As always, get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample questions! Print this out if necessary and remember the above procedures by heart, for if you don’t Sergeant Loi will unleash her own version of the 三大招式 upon you! *Cracks whip!* Sergeant Loi’s Mid-Year Boot Camp 2008 - Fall In For Logarithm Training! Drop that log and Sergeant Loi will tie youto a log (and tickle your bare feet)! *Puts on helmet* *SHOWS STERN & MEAN FACE* *Sounds bugle* EVERYBODY FALL IN! Today’s drill is going to be a little longer (and tougher) than the previous one, since so many of you were tragically killed in action at logarithmic minefields over the years. So to prevent yourself from adding to the end-of-year body count, get ready for Log PT! PICK UP YOUR LOGS NOW! EXERCIIIIIIISE BEGIN! *Cracks whip* The Laws of Logarithms A. IF YOU DON’T KNOW THESE, CAN CLOSE SHOP & FORGET ABOUT THE REST! → This is what the log key does on your calculator! → This is what the ln key does on your calculator! From (1) above, you can deduce that: and From (2) above, you can deduce that: and → many forget this! B. THE OFT-MISUNDERSTOOD LAWS OF LOGARITHMS PRODUCT LAW: DON’T ever do these: → WRONG! → WRONG! QUOTIENT LAW: DON’T ever do these: → WRONG! → WRONG! → WRONG! POWER LAW: DON’T ever do this: → WRONG! (note the brackets) CHANGE-OF-BASE LAW: DON’T ever do this: → WRONG! e.g. ≠ ! Instead it should be SAMPLE PRACTICE QUESTIONS Solve . Ans: → using Change-of-Base Law from B(4) above (remember that c can be any arbitrary value) → using Power Law from B(1) and from A(2) the denominator . . → using Power Law from B(1) again. → CAN cancel both sides since both logs are of the same base. … the rest you should be able to solve on your own! The mass, m of a radioactive substance, at time t days after being first observed, is given by the formula . Find the value of t when the mass is half of its value at t = 0. Ans: When t = 0, → somehow many fail to realize this When m is half of m when t = 0, → ln both sides when you’re typically looking for a x in ex → Using Quotient Law from B(2) for L.H.S. and Power Law from B(3) for R.H.S. → since ln 1 = 0 from A(3) and ln e = 1 from A(6) above As usual, get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample questions! Check out this question for further practice! Print this out if necessary and stay on the right side of the laws above - for if you don’t Sergeant Loi will literally tie you to a log and unleash unspeakable terrors (e.g. tickling your bare feet) upon you! *Cracks whip!* Sergeant Loi’s Mid-Year Boot Camp 2008 - Fall In For Logarithm Training! Drop that log and Sergeant Loi will tie youto a log (and tickle your bare feet)! *Puts on helmet* *SHOWS STERN & MEAN FACE* *Sounds bugle* EVERYBODY FALL IN! Today’s drill is going to be a little longer (and tougher) than the previous one, since so many of you were tragically killed in action at logarithmic minefields over the years. So to prevent yourself from adding to the end-of-year body count, get ready for Log PT! PICK UP YOUR LOGS NOW! EXERCIIIIIIISE BEGIN! *Cracks whip* The Laws of Logarithms A. IF YOU DON’T KNOW THESE, CAN CLOSE SHOP & FORGET ABOUT THE REST! → This is what the log key does on your calculator! → This is what the ln key does on your calculator! From (1) above, you can deduce that: and From (2) above, you can deduce that: and → many forget this! B. THE OFT-MISUNDERSTOOD LAWS OF LOGARITHMS PRODUCT LAW: DON’T ever do these: → WRONG! → WRONG! QUOTIENT LAW: DON’T ever do these: → WRONG! → WRONG! → WRONG! POWER LAW: DON’T ever do this: → WRONG! (note the brackets) CHANGE-OF-BASE LAW: DON’T ever do this: → WRONG! e.g. ≠ ! Instead it should be SAMPLE PRACTICE QUESTIONS Solve . Ans: → using Change-of-Base Law from B(4) above (remember that c can be any arbitrary value) → using Power Law from B(1) and from A(2) the denominator . . → using Power Law from B(1) again. → CAN cancel both sides since both logs are of the same base. … the rest you should be able to solve on your own! The mass, m of a radioactive substance, at time t days after being first observed, is given by the formula . Find the value of t when the mass is half of its value at t = 0. Ans: When t = 0, → somehow many fail to realize this When m is half of m when t = 0, → ln both sides when you’re typically looking for a x in ex → Using Quotient Law from B(2) for L.H.S. and Power Law from B(3) for R.H.S. → since ln 1 = 0 from A(3) and ln e = 1 from A(6) above As usual, get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample questions! Check out this question for further practice! Print this out if necessary and stay on the right side of the laws above - for if you don’t Sergeant Loi will literally tie you to a log and unleash unspeakable terrors (e.g. tickling your bare feet) upon you! *Cracks whip!* Sergeant Loi’s Mid-Year Boot Camp 2008 - Obey The Rules of Indices! No one messes around with Sergeant Loi! The Mids are just around the corner. A time when students are put through grueling tests to realize how little they’ve actually learnt in a semester dominated by fun and laughter, peace and joy. Unfortunately in this critical time, no word has yet been heard from Miss Loi - who is presumed to be still trapped in that fitting room since a few days ago. And so to fill this void … *Puts on helmet* *SHOWS STERN & MEAN FACE* Ok boys and girls, this is Sergeant Loi sent by The Temple to maintain discipline in Miss Loi’s absence! In the coming days, you shall be subjected to a series of no-nonsense DRILLS and exercises on several ‘Hot Topics’ that you MUST complete in order to survive your Mids! Rest assure that, with the menacing taskmaster Sergeant Loi around, there shall be no silly stories, lame content and fooling around on this blog, for she is not as cheong hei as the Sexy Maths Tutor there is no time to lose if you want to pass your Mids! *Sounds bugle* EVERYBODY FALL IN! Sergeant Loi’s first drill with you shall be on Indices! *Cracks whip* The Rules of Indices A. SIMPLIFY THOSE WITH INDICES 1 OR 0 i.e. duuuuh! B. FOR THE SAME BASE (a) WITH DIFFERENT INDICES (m,n): MULTIPLY IS TO PLUS, DIVIDE IS TO MINUS, POWER IS TO MULTIPLY ONLY for the same base (i.e. a)! DON’T ever do this: → WRONG! C. THOSE WITH COMMON INDICES CAN BE MARRIED ONLY for those with same indices (i.e. n)! Couples with different indices cannot get along! D. INDICES GET INVERTED WHEN TRANSFERRED TO THE OPPOSITE SIDE e.g. (The negative (-) sign follows across to the other side!) (The index gets inverted on the other side!) SAMPLE PRACTICE QUESTION If , find the value of . Ans: → using B(1)+B(2) above → using C(1) above → using B(2) above Get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample question! Check out this question for further practice! Print this out if necessary and obey the above rules strictly - for if you don’t and end up fumbling in your exams Sergeant Loi will throw you to the deepest dungeons beneath The Temple where unspeakable miseries shall be heaped upon you! *Cracks whip!* N.B. On the other hand, if you have any valuable input to add to the notes above, you might even get a medal from Sergeant Loi for your contributions! Miss Loi’s Unfortunate Confluence of Factors 如有雷同纯属巧合 Fine contemporary design On a day when Singaporeans were admiring the modern contemporary design and user-friendliness of a certain toilet, Miss Loi was shopping for her new collection of clothes at a boutique in Orchard Road - something she had planned to do all along over a period of time. As fate has it, a confluence of factors made it possible for Miss Loi to shop this day, namely: 1) The new collection has just arrived, 2) There’s a store-wide sale going on, and 3) her tuition session has just been postponed. A sexy set of yellow top and a pair of green bottoms caught her fancy, and she proceeded to try them out in the smallish fitting room, after being accompanied there by the store’s Ah Lian sales assistant. After locking the fitting room door and flipping her set of clothes over it, Miss Loi suddenly detected a faint burning smell coming from beyond the room. Sensing danger, she desperately tried to unlock the door but as fate would have it again, another confluence of factors contrived to land her in trouble, namely: 1) A fire had started in the boutique, 2) the door lock was stuck, and 3) she neither had the space nor strength to kick the door open. To make matters worse, she got the following reply when she shouted to the Ah Lian sales assistant for help: Sorry I need to call my boss first to see if she allows me to kick open the door! Wait the door damaged and she cut my pay how?! Just when all hope seemed lost, she looked up and spotted a stylish un-grilled window on the wall! Using her powers of mathematical geometric projection … PQRS is a rectangle. The window ABCD is a square. M is the mid-point of PS. Prove that ΔPBS ≡ QDR and state the case of congruency. Calculate the length of BM and hence, calculate AC. Find the area of the square ABCD. Given that a vain Miss Loi has always known herself intimately (mathematically speaking) and that the largest cross-sectional area of her *ahem* lithe figure is only 30 cm2, should she attempt to escape through this window, or wait for the Ah Lian to get permission from her boss? A quick decision is needed, for there are only 11 more minutes before the fire overcomes the boutique! IMPORTANT: To add to the congested confluence of factors, in a fit of panic, Miss Loi has suddenly forgotten all her trigonometry formulae! But fortunately this can be done by simple calculation using Similarities & Congruencies concepts learnt in Secondary Two, where students are typically not taught the likes of Trigonometry and Pythagoras’ Theorem yet. So in a desperate bid to solve this, Miss Loi has to recall these hieroglyphs: *Please, please remember that for all cases involving two sides, the angle has to be adjacent (i.e. in-between the two sides concerned)! Lastly, note the word hence appearing in the question, and recognize that, unlike some toilets, not all diagrams are user-friendly enough to include all information from the question (e.g. the whereabouts of point M) → write down all unrepresented info in the diagram as soon as you see them in the question to prevent yourself from getting confused later (especially in your upcoming Mids). Irrefutable Evidence of Students Not Focussing On The Right Traits of Tutors CASE STUDY 1 Scene of Crime: Student’s house Student’s Mom: Miss Loi, do you have any H2 Chemistry tutor to recommend to my Ah Boy? Miss Loi: Sorry I don’t. Coz a GOOD JC Chemistry tutor is quite difficult to find. Mom *turns to student*: Eh Ah Boy, I thought that time you were having tuition with the other girl Chemistry tutor? Student *looks down and whispers* Errr … she very ugly … Miss Loi: Oooi! How can you say that?! Student: Oh it happens that she can’t teach well too. Miss Loi: Anyhow say one right? Student: … CASE STUDY 2: Scene of Crime: Student’s House Student: Eh Miss Loi, you want to know more about my new science tutor? Miss Loi: What? Student: From the top (of my house) look down, she looks like an Ah Sam (阿婶). Miss Loi: You’re so bad! Student: But when she comes up, she looks more ‘proportional’ as her face is now more ‘proportional’ to her body. Miss Loi: … -_- CASE STUDY 3: Scene of Crime: Miss Loi’s Temple Miss Loi: Heard that your mom has found you a new history tutor. Student: Yeah, she’s an 18-year-old girl - just finished A-Levels with 5 distinctions. Miss Loi: Wow. So is she good? Pretty? Student *face starts to contort* umm … ok lah … at least can entertain me. Miss Loi: *shakes head* Miss Loi now shudders to think what her student might be saying to the 阿婶 tutor about Miss Loi behind her back. *Note: Actual conversations altered slightly in order to ‘get the point across’ to readers. Tsk. A Maths Tutor’s Offer To Another Maths Tutor On Tax Filing Day 如有雷同纯属巧合 Miss Paimia (not her real name - name altered to protect her identity) is a math tutor working at Tekan Tuition Centre (TTC) (not their real name - name altered to protect their identity) in Novena. Born in an impoverished village in Southeast Asia, she was approached and persuaded by an ‘agent’ when she was twelve to come to Singapore, where she was promised a life of luxury, living in houses that dwarf her attap farmhouse, with a cost of living lower than her village, and with local students so stupid that she’ll be guaranteed top place in the education system year after year. Her dreams vanished instantly when, upon arriving in Singapore after a thousand-kilometer sampan journey, she was whisked away to TTC, given a smallish HDB flat to live in (though the entire building did dwarf her farmhouse), discovered that a cup of kopi peng in Novena costs > SGD$1, and read about this year’s O Level results. Worse was to follow when her new employees brutally made her memorize the 2008 GCE O Level EMaths and AMaths Syllabus in double-quick time, and forced her to service up to 40 disorderly/havoc/lame/naughty/whatever students at a time in class. IRAS’ Revenue House in Novenawhere tax evaders disappear andare never seen again But in her darkest hours, a silver lining appeared in the form of another tuition centre (name withheld to protect its identity) nearby. Each day from her decrepit classroom, Miss Paimia would peer through the narrow gaps of her grilled window - to admire cosy classes of angelic, orderly students (yeah right.) being taught by the soothing maths tutor (name withheld to protect her identity) there - scenes that she longed to be a part of. So imagine her joy when she bumped into the math tutor today on the way to file her income tax at IRAS in Novena (sadly, TTC doesn’t even have internet for her to do eFiling). Embracing the tutor in a tight bear hug, she implored her to take her in and help end her misery. As the first thing in the poor tutor’s mind now was how to extricate herself from that suffocating bear hug, she glanced at Miss Paimia’s tax information and found that: Given that Miss Paimia works 365 days a year (12 hours/day), she effectively earned $30/hour in 2007, after deducting her income taxes (assuming as a ‘Foreign Talent’ she’s not eligible for any tax relief). It was also revealed that her pre-tax hourly rate was increased by 50% plus an extra $3.05 per hour at the beginning of 2007. If the tutor offers to increase her 2006 pre-tax hourly rate by 75%, and she only needs to work an average of 340 days a year (12 hours/day), should Miss Paimia take up her offer? Please use IRAS’ 2007 tax rates for your calculations: Chargeable Income Rate (%) Gross Tax Payable ($) First $20,000Next $10,000 03.50 0350 First $30,000Next $10,000 -5.50 350550 First $40,000Next $40,000 -8.50 9003400 First $80,000Next $80,000 -14 430011200 First $160,000Next $160,000 -17 1550027200 First $320,000Next $320,000 -20 42700  NOTE: While such percentages questions from the Arithmetic chapter may look longish and tricky and intimidating, they are usually pretty straightforward and ’sure-scores’ in any E-Maths papers. The following statements should be common sense to you: When y increases by x% ⇒ new value of y is When y decreases by x% ⇒ new value of y is Lastly, do spare a thought for your parents and adults as, while these questions are easy for you to score, be rest assured that none of us look forward to solving this every year Now to all adults who have managed to bear with Miss Loi until this point, Have You Filed Your Taxes? International Friendship Day [source] Today, many schools across Singapore celebrate International Friendship Day leading to the cancellation of some of Miss Loi’s sessions. Tsk. Which is a little strange as the actual international International Friendship Day appears to be traditionally celebrated on the first Sunday of August - a little too close for comfort to another Big Day perhaps? For those new to this, it’s a day when schools are suddenly transformed into mini United Nations of sorts, when flags of foreign countries are flown, where foreign cyborgs are reprogrammed to stop mugging for a day of cultural performances, and where Miss Loi’s student is seriously wondering whether to turn up in school naked after being ‘arrowed’ to cosplay as Africans. All these, in the noble name of increasing students’ understanding of Singapore’s relations with neighbouring countries and beyond … as well as nurture the spirit of friendship and collaboration among different people. While it’s a bit optimistic to expect a few cosplay sessions and performances to have any effect on students’ awareness of Singapore’s diplomatic positions on worldly affairs, Miss Loi nonetheless hopes that students can take this day to reflect on their situation compared to what’s happening to their peers around the world, namely: Be glad that you have the chance to attend school. 3 million of your peers in Southeast Asia don’t (especially if you’re a girl). Be grateful for your uneventful journey to school (save for the usual traffic jam at the school gate), for sometimes it can be a little challenging for your peers in other countries just to get to school. Today got school? Please pay attention and don’t always fall asleep in your comfy air-conditioned classroom. Spare a thought for your peers in other countries: If they can pay attention, so can you. [source] Don’t always say that you can’t understand your ‘Cher, and don’t always depend on someone to help you understand the topics. In some countries, the ‘chers don’t even turn up. “Senior student” leading class in Indonesia Don’t always complain that you have no time for revision/homework (amidst all your phone chats/SMSes/MSN etc.). Some of your peers really have no time. Similarly, don’t waste your time and your parents’ hard-earned money by fooling around in tuition classes. To some of your peers with zero access to such educational luxuries, self-directed learning offers the only hope to a better life. Be thankful that everyone is given (more or less) a fair chance of success in our education system. In a certain country, you may end up hitting yourself against a brick wall no matter how good your grades are. On the other hand, do be aware that there are students elsewhere who are studying much, much, much, much more harder than you, with their own joss sticks sessions extending till midnights. Miss Loi should start picking up Korean soon So let this be Miss Loi’s message for today: As you enjoy today’s cosplay sessions, remember not to take for granted what you’re blessed with, but at the same time recognize that in an increasingly-connected age, you may not necessarily be as good as you think you are and there will always be room for improvement.