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• ## Math Forum

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## Preschool Math Tuition Books and Toys

There seems to be an increasing demand for kindergarten Maths tuition for children of ages 2-6. (I have received many such requests lately.) Many parents are worried that their child may lose at the “starting line” which is Primary 1, hence are preparing beforehand during the ages of 2-6.

Possibly, at this age the best way to learn is through play, that is why Math Toys are very useful.

Skoolzy Rainbow Counting Bears Toy is suitable for age 2, 3, 4, 5 or 6 year old preschoolers to learn to add, count, sort & stack.

Goodnight, Numbers is an award-winning bestselling bedtime story for kids, that help them familiarize with numbers.

The Pattern Blocks and Boards toy is useful for developing pattern recognition and visualization skills; all very useful skills when it comes to the GEP Logic Section at age 9. PSLE has some very tough visualization questions on nets of cubes, only children with strong visualization skills will be able to solve them. It is notoriously hard to train for such questions (though there are some tips and techniques), it is almost like either you see it or you don’t.

Strong Visualization is needed to solve this type of questions, which appear in both GEP and PSLE. Source: How2become.com

Times Tables would be the most challenging Math for children of the age group 3-6. Hence, early mastery of this subject will give your child a headstart to learn other more advanced math.

This 4-in-1 book bundle enables your child to learn about the alphabet, shapes, colors, math, as well as animals.

This LEGO (Duplo) set teaches numbers, basic math skills, and includes fun activity cards. Very educational and fun toy.

## Cheap Digital Piano Singapore

Do you know that there is a decent digital piano selling for just $599 on Qoo10? Qoo10 Link here (with other piano recommendations): https://www.qoo10.sg/gmkt.inc/Special/Special.aspx?sid=7452#subtheme_53572 It is the Casio CDP-135 Digital Piano, with 88 Weighted Keys. It is an excellent choice for parents with children who are starting on piano. The child may show some initial interest in learning piano, but who knows, children may just give up after a few weeks. Buying a upright piano will cost at least S$3000, and if the child gives up it ends up as a “white elephant” collecting dust.

$599 is certainly affordable for most Singaporeans, and it will serve as a first piano for young children. If they have a sustained interest, after a few years an upgraded piano can be bought. An additional benefit is that digital pianos never go out of tune. With Singapore’s humid weather and young children hitting the keys, actual pianos may go out of tune frequently. Video of the Casio CDP-130, which is an older version of Casio CDP-135. (That means the CDP-135 is even better than what is shown in the video below.) The pianist plays Fantaisie-Impromptu, which is a difficult classical piece (above Grade 8 level). Hence, playing grade 1-5 classical pieces is no problem on the Casio CDP-135. If you are willing to fork out a little bit more cash, the Yamaha P-125 is a good catch (around$950). (Also found on my Qoo10 piano recommendations page.)

Basically, the Yamaha P-125 is the top tier of the P range, P for portable. For Yamaha, the ranking goes like this P<YDP<CLP (Clavinova). For beginners, P-125 will be more than enough. YDP is for intermediate players, and Clavinova is for musicians and for actual performance.

Basically, it is not sustainable for Apple to keep increasing the price significantly for every new model. Otherwise, the iPhone 20 will cost like S$3000? A corollary to Moore’s Law is that electronic devices are supposed to get better (but cheaper) as time passes. One of the first Apple Macintosh cost US$2495 in 1984, which is around US$5694 when adjusted for inflation. When will iPhone XR start price reduction in Singapore? This case will be good for protecting your iPhone XR if you get it after the price reduction: Spigen Tough Armor Designed for Apple iPhone XR Case (2018) – Black Posted in maths tuition | Tagged , , | Leave a comment ## 2019 Calendar (Singapore) Printable Singapore Calendar 2019 Quite a nice calendar template that I frequently use. From Calendar Labs. For those looking for a more awesome and colorful calendar, do check out this “Hubble Space 2019 Calendar”. Possibly one of the most impressive calendars you can buy on the internet. Posted in maths tuition | Tagged , | Leave a comment ## What are the Most Scoring Topics of Mathematics in JEE Main? With a few days left for the JEE Main Exam 2019, the stress of the candidates is at its peak. One of the cohesive and most scoring subject out of the three subjects in JEE Main is Mathematics. To prepare well for this section, you need to know the most scoring and important chapters of the subject to score good marks. The subject which is based on calculations and formula and has the vast syllabus need lots of practice and smart strategies to score good marks. Having 16 chapters in the syllabus and everything is dependent on each other, the JEE Main Mathematics can be mastered yourself only by more practice. So, here we are discussing some of the important chapters of the subject Mathematics that you need to have at your fingertips to crack JEE Main 2019. How to Score More Marks in JEE Main Mathematics? After completing with your JEE Main syllabus 2019, you need to focus on the scoring topics in every section which demands little extra effort and time. Your revision days must include the clear idea of important and most scoring topics in JEE Main Mathematics subject. We have listed the scoring topics in Mathematics below for you: The complete syllabus of Mathematics is divided into 4 sections which are: • Trigonometry • Calculus • Algebra • Coordinate Geometry Now, before moving ahead with the important chapters, let’s study the complete syllabus of the maths. We believe that the subject Mathematics takes lesser time as compared to other subjects of JEE Main Physics and Chemistry. You can easily cover the major portion of the subject during the preparation of your boards. Check out the complete syllabus for the JEE Main 2019 for Maths Section:  Topics Units of Topics Algebra Complex Numbers and Quadratic Equations Matrix and Determinants Permutations and Combinations Mathematical Reasoning and Induction Binomial Theorem Sequences and Series Statistics and Probability Calculus Sets, Relations and Functions Limit, Continuity and Differentiability Applications of Derivations Integral Calculus Differential Equations Coordinate Geometry Straight Lines Circles and Conic Sections Three-Dimensional Geometry Vector Algebra Trigonometry Trigonometric Identities and Equations After the complete syllabus, we are providing here the important chapters which you need to put more focus on. The important topics which we have mentioned are based on the analysis of previous year question papers. The topics which we have started with are based on the weightage in the JEE Main Examination. JEE Main Mathematics Topics  High Weightage Topics Low Weightage Topics 1. 3-Dimensional Geometry 2. Vectors 3. Straight Line, Circle 4. Probability Distribution 5. Determinant and Matrices 6. Limits, Continuity and Differentiability 7. Complex Numbers 8. Quadratic Equation 9. Binomial Theorem 10. Conic Sections 1. Trigonometric Equations 2. Statistics 3. Mathematical Logic 4. Set and Relation 5. Height and Distance 6. Properties of Triangle 7. Permutations and Combinations 8. Indefinite Integral 9. Trigonometric Ratio and Functions Now, it’s the right time to peep into the scoring topics by checking out the number of questions asked from these topics in last years and the maximum marks these topics cover. Here is the tabulated form of the scoring topics of Mathematics in JEE Main 2019. Also Checkout here – Top 5 jee main preparation apps  Topics Number of Questions Maximum Marks Differential Calculus 7 28 Integral Calculus 4 16 Coordinate Geometry 3 12 Coordinate Geometry (3-D) 2 8 Matrix and Determinants 2 8 Probability 2 8 Trigonometry 2 8 Some Points to Remember for Mathematics in JEE Main 2019 • Topics like Matrix and Determinants, Application of Derivations, Complex Numbers are simple and on the same hand scoring topics. • We recommend you focus on topics like Vectors and 3D, rather than Probability or Definite and Indefinite Integration. The reason being there is the marginal score for the examiner in these topics in the context of the questions. • Devote your time to Algebra as this chapter is scoring and easy on the same hand. • Pure Trigonometry questions are rarely asked in the JEE Main. This topic involves many formulas, once you mastered that you can score well. • The Circles chapter is the easiest chapter under the category of Analytical Geometry. If you have a good understanding of the concepts, you will be able to score well in this topic. As this chapter has no formula to mug up, only concept to clear, take no chance to skip this topic. • The chapter of Differential Calculus involves only one formula, so it is easy to master this topic with the sheer amount of practice. • If you ready to play brain game, go for the chapter Integral Calculus. Under this only one topic Definite Integrals has the minimal set of formulas, once mastered you can score excellently. • The chapter Vectors is the extension of the chapter Coordinate Geometry and so is easy and most scoring of all the topics. Chapters on Planes is easy and quick to solve. Spend your time considerably in the reading theory of all the chapters and then move ahead with the practice. If you cover all the scoring topics which we have provided, we are sure you can score good marks in Mathematics in JEE Main 2019. Keep these points in your mind and start with your revision confidently. Don’t forget to download JEE Main preparation app. It provides free study notes, quizzes, mock test, previous year papers, and all the updates related IIT JEE exams. Posted in maths tuition | Leave a comment ## Math Facebook Page Do like and follow our Facebook page at: https://www.facebook.com/mathtuition88/. It includes additional material not found on this website, including educational news and others. On the PC version of mathtuition88.com, it is also accessible as a Facebook widget on the bottom right side of the webpage. Posted in maths tuition | Tagged | Leave a comment ## Buy Enfagrow Milk (Official Store) at Discount Everyone knows milk powder is very expensive in Singapore. 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[$175.00](▼42%)2018 Stainless Steel Rubbish Chute Hopper Installation 1 year warranty. WWW.QOO10.SG Posted in maths tuition | Tagged , | Leave a comment ## My First Try On Nasi Lemak Nasi Lemak is a Malay dish. When I first came to Singapore, I tried it. But didn’t have any deep impressions on it. The specialty of it lies in rice, which is cooked with coconut milk. But when I had it before, rice was cold, so I couldn’t taste the fragrance of coconut milk. The other day, I tried cooking rice with coconut milk, the rice turned out very nice. So I bought pandan leaves, lemon grass, sambal chili sauce and decided to cook my first nasi lemak. Rice part: 1 cup rice ( I used the ones with some brown rice mixed in) 70 ml coconut milk 1 1/2 cup water 1 stalk pandan leave (make into a knot) 1 stalk lemon grass (pat lightly with knife) 1/2 tsp salt Put all the ingredients above into rice cooker and press the cooking bottom. Trust me your kitchen will smell… View original post 307 more words Posted in maths tuition | Leave a comment ## Checkmate Black King on 1st rank (Sicilian Defense, O’Kelly Variation) I try to play Sicilian in the “Delayed Alapin” style with c3 followed by d4. The black player, though lower rated, is quite an experienced player with over 11,000 rapid games played on Lichess. The turning point was 14. d5! I did not fully calculate all the lines, but I thought it was worth giving up the isolated d-pawn for a very active position, with my rook lined up against the black queen. The tactics worked out well in the end, in fact it turns out that white can always regain the pawn. Lichess seems to have rating deflation: Many players (including myself) who were once rated over 2000 for rapid, are now dropping back to 1900 rating range. It seems due to an influx of good players into Lichess. Also see: Lichess to FIDE Elo Rating Conversion. Final Position: Posted in maths tuition | Tagged , | Leave a comment ## Ohm Electricity Review Do check out our Ohm Electricity Review at: Ohm$20 Promo Code: OHMREF25CC5A.

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*Use my Ohm Referral Code to get 20 off: OHMREF25CC5A ## Ohm Website “Flickering” or Refreshing? Official Solution: Hi, the cause is most likely due to a cache and time-out issue. You could clear the cookies and cache, close off all the browsers and open that up again. Alternatively, you can also use a private “incognito browser” if you are using Chrome as your browser. Let us know if you still face issues and we will be happy to assist. Thank you, Team Ohm. ## Ohm Energy: Free second electricity bill Dear customer, Thank you for choosing Ohm and successfully signing up with us from 1 November 2018. To show our appreciation, your second electricity bill for the premises you registered with us is free. You will also find more information on the Terms and Conditions of this Promotion (OhmNow and Save) on our website. If you have any questions or concerns, please contact our friendly Customer Care at 1800-835-6463 or customer-care@ohm.sg for further assistance. Sincerely, Team Ohm Posted in maths tuition | Tagged , | Leave a comment ## Meat Ball With Running Egg When I made wantons in the morning, some filling was left. And I didn’t have any plan to make more wantons, so I used those left minced chicken filling to cook this dish. I know there is a Scotch Egg. But I kind of cook it in a different way, especially the meat part. So I just called it “Meat Ball With Running Egg”. 🙂 Original wanton filling is : 200g minced chicken, 5 chopped Shiitake mushroom, 4 chopped water chestnuts, 1 tablespoon light soy sauce, 2 tsp oyster sauce, 1 tsp salt, 1 tsp black pepper, 1/2 tsp minced ginger. There was about 1/4 left. To add more flavor to the meat part, I also add in 2 tablespoon shredded mozzarella cheese, and 1 tablespoon chopped spring onion. For the running egg. Boil some water ( doesn’t need to cover eggs, because eggs can be steamed too). When water… View original post 210 more words Posted in maths tuition | 2 Comments ## What to do if fail O level Singapore Recently, there is positive news that polytechnic students no longer need to “depend” on their O level results to enter university. Most students will aim for JC (Junior College) or Poly (Polytechnic) admission after their O levels. Outright failure (F9) is quite rare for O levels, but students need to be careful as too many borderline passes like D7/C6 can lead to a score that is technically a pass, but not enough to enter JC or Poly. (See: Academic grading in Singapore: How many marks to get A in Maths for PSLE, O Levels, A Levels) ## What to do if do badly for O level Singapore for key subjects ## Method 1: Write Appeal Letters Certain subjects (especially Mathematics) are more important to pass than others. According to this post on Quora, failing Mathematics can mean “auto rejection from all poly courses”. Failing English is also quite serious as Poly seems to require D7 and above for English. This may be a problem for foreign students. There are indeed students who ace all subjects except English, they qualify for JC but not polytechnic! (See this post on Kiasuparents.) The solution is: write appeal letters. Polytechnics do have some room for discretionary admission for borderline cases. So do try this option and do not give up. “So off I went to most of the polytechnics to talk to their lecturers and submit my appeal. SP I did not go because I felt they were too good for me. Ngee Ann Poly I did not submit my appeal out of silly pride because the lecturer I talked to mocked & laughed at me. But for the rest, the lecturers I talked to were pretty kind even though they honestly tell me my chances are low. So I wrote my appeal letters talking about myself, my journey, what I did wrong, what I could have done & why I am suitable for the course I am applying. RP was the first to accept me for their IT course and made me go through some programme first. Temasek come later wanting to interview me but I declined as I accepted RP offer already. NYP rejected me without an interview.” Source: https://www.quora.com/Whats-your-story-after-failing-O-levels-in-Singapore ## Method 2: Alternative Route of ITE -> Poly -> Degree This alternative route is also possible. The journey is not easy though, as this Quora post mentions: “So I took my Higher Nitec in Information Technology in 2004. The only reason why I took Information Technology was because I was good with computers. I did HTML coding in secondary school and I was good at Photoshop. That was a great advantage. For me, Higher Nitec was much easier than O Levels. I easily scored a high GPA in 2006 and managed to get a place in Nanyang Polytechnic where I continued studying Information Technology. To be honest, polytechnic was far more challenging but I was determined to prove my parents wrong. I continued my full-time studies while working part-time as a barista so that I can pay my school fees and daily expenses. It wasn’t easy and some days I did skip classes because I was burnt out from work and school. I did fairly good, scored a 2.6 GPA in 2009 and went on to serve my 2-year mandatory national service in the military. In 2011, after finishing my national service, I was employed in an institution as an IT support. In 2012, I had plans to take up part-time degree. So I moved on in 2013, got a better paying job, took my part-time BSc in Cyber Forensics and Information Security Management and graduated. Working full-time and taking a part-time degree has got to be the most taxing feeling I have ever had. I had to juggle work with studies. There were school projects and essays. It was challenging but I made it.” Source: https://www.quora.com/Whats-your-story-after-failing-O-levels-in-Singapore ## Method 3: O Level Private Candidate Another possible route is retaking O levels as a private candidate. This route is also not easy as it involves discipline in studying by oneself. Possibly a better option is to enroll in private schools, or hire private tutors for those weaker subjects. ## Method 4: Go Overseas This method is unfortunately only for those who are well off (a.k.a. rich). The Singaporean O Level is the hardest version of the O Levels (compared to the UK or the Hongkong papers). Hence, chances are high that even a relatively academically weak Singaporean student can do quite well in overseas education systems like Australia, UK, US, etc. ## Motivational Do read our blog on: Inspirational story: From EM3 and Normal (Technical) to PhD. Also very motivational is: From PSLE 124 to PhD A*Star Researcher. Nowadays, having a failure in the early section of education is not the end. There are different pathways to success, though some are longer than others. As Robert Frost wrote, “Two roads diverged in a wood, and I— I took the one less traveled by, And that has made all the difference.” Also, read our highly popular posts on: Posted in maths tuition | Tagged , | Leave a comment ## Good news for Poly students: O Level “not counted” for Uni admissions Should be good news for most Poly students. It is good to aim for a decent grade for key subjects like E maths and A maths though, as they may still be required for certain subjects in university. For example, a polytechnic student who wishes to apply to a computer science course at NUS would need at least a B3 in O-Level Additional Mathematics. Source: Channel News Asia SINGAPORE: Polytechnic graduates applying to the National University of Singapore (NUS) and the Nanyang Technological University (NTU) from 2020 will no longer have their O-Level grades be considered for admission, except for certain courses. This comes with the Ministry of Education (MOE) removing an existing requirement for an applicant’s O-Level results to comprise 20 per cent of his University Admissions Score (UAS). The UAS is a framework adopted by the six autonomous universities to benchmark and rank applicants’ academic abilities for admission to university. Posted in a math tuition, nus cut off points | Tagged , , | 1 Comment ## Sweden: From Safest to Most Dangerous Country in Europe From young, through news and media my impression of Sweden is that it is a truly 1st world country on par with Switzerland, Norway, Denmark, etc. Also, my impression is that it used to be very safe, possibly one of the safest countries in the world. But recently, Sweden seems to have risen to the rank of one of the most dangerous country in Europe, and some say the world! It is truly saddening and unbelievable. (I started to research on Sweden as I was searching for some jobs that had overseas travel requirements.) From the way the online news media are portraying it, Sweden is very dangerous, almost on the level of Iraq/Iran/Afghanistan. I will definitely not dare to visit, let alone work there in the future. ## Sources: “Mass immigration, mass raping mass crimes evil place to live was great now it’s a hell hole” “STOCKHOLM — Sweden may be known for its popular music, IKEA and a generous welfare state. It is also increasingly associated with a rising number of Islamic State recruits, bombings and hand grenade attacks.” The claim: Many young male migrants arrived in Sweden over the past few years, when the country accepted unprecedented numbers of refugees, and there has been a huge rise in sexual crime in Sweden especially in the southern port city of Malmo.” “The number of explosions caused by hand grenades has increased in Sweden in recent years. There were fewer than five in 2014 but at least 20 in 2017, and a further 39 grenades were seized by police.” YouTube video: Some people have started wearing bulletproof vests in Sweden. Posted in Sweden | Tagged , | Leave a comment ## Motivational: Bear cub climbs ice mountain to reunite with mama bear One of the most motivational nature videos of the year! If you liked this video, you should also like this Iguana vs Snakes video: Posted in maths tuition | Tagged , | Leave a comment ## Useful Things to Know About Science Centre Singapore Before Visiting Singapore has a reputation for not only being one of the most toured countries in Asia, but also for being a perfect place to incorporate a business. This is strongly attributed to its excellent tourist spots and also regulations that can allow even a foreigner to set up a business in Singapore. If you are a foreigner, you just need a Visa Express entrepass to start a new business or to relocate an existing one to Singapore. If you want to take a vacation in the next few months, then Singapore is the perfect place for you to go. If you are traveling with your children, you can rest assured that the kids will have an unforgettable experience from all the fun they will have. One of the places you can visit is Science Centre Singapore, situated at Jurong East, which is a museum full of exhibitions and learning opportunities for children. If you want to visit this place, here are some useful things you need to know. 1. Free entry for Singaporeans and permanent residents on specific days When is the right time for you to visit Science Centre Singapore? If you are a Singaporean or a permanent resident, it is recommended that you visit during the off-peak days when you are not required to pay any entry fee. The off-peak days are usually normal weekdays during school time, excluding all public holidays. School holidays, public holidays, and weekends are usually the peak days, and visiting at these times means you will have to pay an entry fee. However, if you are a Singaporean or a permanent resident, you will still get a discounted entry fee during the peak days. 2. Extra admission charges There are special exhibitions in Science Centre Singapore located at the Annex, which require extra fees if you want to view them. Science Centre Singapore also has areas like the Butterflies Up-Close Exhibition, which likewise demands additional entry fees. 3. Closed dates Science Centre Singapore is open almost year-round, but it is closed on certain dates each month of the year. While most of these closure dates usually fall on Mondays (but not every Monday), it is recommended that you visit Science Centre Singapore’s website in order to get a full schedule outlining the closure dates. This is to make sure that you avoid making a trip there when it is closed. 4. Science shows For the entire day, Science Centre Singapore conducts engaging science shows for its visitors. These shows include the dramatic and electrifying Tesla Oil Demonstration, as well as the Fire Tornado Demonstration. Just like with the closure dates, you can check out their website to find out the times for the shows. 5. Where to eat You may be planning to spend a full day at Science Centre Singapore, and it is thus convenient to know where you can have your meals. The most convenient joints are the Coffee Bee, located at the Annex, or McDonald’s, situated at the main entrance. For additional dining options, you can go to the Omni Theatre Building, where you will find the Lijiang Restaurant and a kids’ cafe. Posted in maths tuition | Leave a comment ## How to Change UOB Card PIN Number ## How to change UOB ATM PIN It is recommended to change your UOB PIN number/password immediately upon receipt of the mailer. However, it is not very clear how exactly to change your UOB Debit Card PIN number. The answer is that it is not possible to change the UOB PIN number online. (I called the UOB customer service at 1800 222 2121 to find this out.) Changing the UOB PIN Number is only possible at a UOB ATM machine. ## How to change UOB Phone Banking PIN Same as above, UOB Phone Banking PIN cannot be changed online. It can be changed at any UOB ATM machine. The Phone Banking “Username”, or “Access Code” as it is called, is your NRIC number (numerical digits only, without “S” or the final letter). Posted in maths tuition | Tagged | Leave a comment ## Factorize 2^n-1 (when n is composite) ## How to Factorize 2^n-1 If $n$ is composite, we may write $n=ab$ where $a,b>1$. Then, \begin{aligned} 2^n-1&=2^{ab}-1\\ &=(2^a-1)(1+2^a+2^{2a}+2^{3a}+\dots+2^{(b-1)a}). \end{aligned} The key point is that both factors are greater than 1. ## Example If $a=2, b=5$, we can see that $2^{10}-1=1023=(2^2-1)(1+2^2+2^4+2^6+2^8)$. ## How to Remember this Result The hard part is remembering this identity: $\boxed{2^{ab}-1=(2^a-1)(1+2^a+2^{2a}+2^{3a}+\dots+2^{(b-1)a})}$. It is essentially a “telescoping sum”, and you can prove it by expanding the right hand side and cancelling all like terms. We can also view it as a Geometric Series as follows: $\dfrac{1((2^a)^b-1)}{2^a-1}$ is the sum of a Geometric Progression with first term 1, and common ratio $2^a$, for a total of $b$ terms. That is, $\dfrac{1((2^a)^b-1)}{2^a-1}=1+2^a+2^{2a}+\dots+2^{(b-1)a}$. Multiplying both sides by $2^a-1$ gives the boxed result. ## Applications Primes of the form $2^n-1$ are known as Mersenne Primes. Using the result above, we can show that if $2^n-1$ is a prime, then $n$ is a prime. (We prove the contrapositive: If $n$ is composite, then we show that $2^n-1$ is also composite.) Posted in maths tuition | Tagged | Leave a comment ## Ohm20 Promo Code: OHMREF25CC5A

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4. Ohm absorbs the transmission loss. (Basically electrical energy is lost as heat while travelling through the cable, Ohm absorbs this and charges consumer based on metered usage. This is worth approximately 3.4% savings.)
5. 3-month trial period. If within 3 months you decide to change plans, there is no penalty. Hence, you are not locked in to a fixed price which may turn out to be undesirable.

Use my Ohm Referral Code to get $20 off: OHMREF25CC5A ## Fixed Rate vs Discount off Tariff Currently (1st November 2018), Ohm fixed rate is 18.14 cents/kWh (incl. GST) while the Discount off Tariff (22%) is effectively 20.14 cents/kWh (incl. GST). However, it is not impossible for the SP Tariff to drop (see graph below). If the SP Tariff drops, say to 20.20 (excl. GST) which is the Jan 2017 price, then 22% Discount off Tariff would be effectively 16.86 cents/kWh (incl. GST) which beats the fixed rate! (Working: 20.20 x 1.07 x 0.78=16.86) Nobody knows for sure whether the SP Tariff will drop as it depends on a lot of complex factors including oil price, etc. However, currently with 12 electricity providers in a small country like Singapore, there is a great deal of competition, and SP is likely to lower its price to remain competitive. Historical SP Tariff (excluding GST). Source: SP Group ## Conclusion: Choose Ohm Everyone should change a supplier in the open electricity market for savings. There are no drawbacks of doing so. In particular, there is no such worry of “blackouts” or “unreliable electricity supply” as SP group is still operating the national power grid. Posted in maths tuition | Tagged , , | 1 Comment ## Scientists Use Math To Discover Why BTS Jin Is The Most Handsome Recently, the hottest topic in Singapore is “BTS concert”. BTS is a Korean band that is extremely popular among the young students in Singapore. The BTS tickets in Singapore are completely sold out in less than 4 hours. (Possibly there are many people “scalping” tickets for resale, also known as “Yellow Cow Tickets” 黄牛票.) Fans of BTS are known as “The Army”. According to this website, Korean scientists have “mathematically” proven why Jin, a member of BTS, is the most handsome of all. His nickname is “worldwide handsome”. Essentially, the idea is using the Golden Ratio, a special number that appears frequently in nature. See also our previous posts: Source: Koreaboo A plastic surgeon has reported that he studied 269 Asian male faces and concluded that BTS’s Jin is scientifically the most proportional and handsome Asian face. The doctor mentioned 1:1.618 as the “golden ratio” for having a perfectly proportional face. Most often, when applied to facial symmetry, this ratio uses the measures of the width from one ear to the other (1) and for the hairline to the chin (1.618)… And Jin’s face exactly measures up. Many of BTS videos have hundreds of millions of views. This is one of them: Posted in maths tuition | Tagged , | Leave a comment ## The Hardest H3 Math Question (Combinatorics) I think this may be one of the hardest H3 Math Questions in history. It is taken from RI H3 Prelim 2018. It seems that even in top schools like RI, there are less than 50 people taking H3 Maths in any given year. Part (d) is extremely hard to get the formula for general r. In fact during the exam it is probably wise to skip such questions or give partial answers (e.g. the formula for r=3) as it is not worth the time for 3 marks. See also our related blog posts: Posted in maths tuition | Tagged , | 2 Comments ## Test your Circuit Breaker today; Circuit breaker can save you from electrocution Do forward this to your family and friends. Especially for older homes, the circuit breaker could have broken down silently without anyone noticing. Pressing a button at home regularly could save your life. This is the “test” button, typically denoted by a “T” on the circuit breaker, a safety device found in all households and buildings. If you press that button and all electricity cuts off, that means it is functioning. A working circuit breaker will cut off electricity in the event of a current leakage, like when someone touches a live wire, minimising the chances of fatal electrocution. Posted in maths tuition | Tagged , , | Leave a comment ## New York Professor: Blockchain is a lie, and the least useful technology The most famous application of Blockchain is “Bitcoin”. Whoever bought just$1000 worth of Bitcoin around year 2010 would be a millionaire now. However, other than “Bitcoin” and cryptocurrencies, blockchain technology do have other uses. So is blockchain useful or not? Only time will tell.

Source: Channel News Asia

Blockchain has been heralded as a potential panacea for everything from poverty and famine to cancer. In fact, it is the most overhyped – and least useful – technology in human history.

In practice, blockchain is nothing more than a glorified spreadsheet. But it has also become the byword for a libertarian ideology that treats all governments, central banks, traditional financial institutions, and real-world currencies as evil concentrations of power that must be destroyed.

## Integration by parts, DI method

This DI method is American way, better than the UK Cambridge O level technique.

(Traditional Method learnt at O-Level) Integration by Parts:

NEW Technique taught by this UC-Berkley Chinese Mathematician: “DI” Method

First Stop: “D column at…

2nd Stop:

3rd Stop:

$latex displaystyle int {e^{x}}sin {x} dx$

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## Analysis by Timothy Gowers

Why easy analysis problems are easy
by Timothy Gowers (UK, Fields Medal 1998)

Timothy Gowers is teaching in Cambridge, he wrote the thick volume of “Princeton Math Encyclopedia.”

He is a very good mathematician, who likes to explain simple fundamental Math questions (like why 2+2=4, multiplication is commutative,…), in the process making abstract math simple to understand.

If you have recently met epsilons and deltas for the first time, then you may find the problems you are asked to solve on examples sheets very hard. On the other hand, you will notice that your lecturers, supervisors etc. do not find them hard at all. Why is this? ” Read on …

https://www.dpmms.cam.ac.uk/~wtg10/autoanalysis.html

Below is my attempt to rewrite the Example 1 with Latex epsilon-delta notation for easy reading.

Example 1.

I wish to prove that the sequence (1,0,1,0,1,0,…) does not converge.

$latex text{Let me set the sequence } View original post 174 more words Posted in maths tuition | Leave a comment ## Book of Wisdom 1 Wis 7:7-11 (Book of Wisdom or “Wisdom of Solomon”) I prayed, and prudence was given me; I pleaded, and the spirit of wisdom came to me. I preferred her to scepter and throne, and deemed riches nothing in comparison with her, nor did I liken any priceless gem to her; because all gold, in view of her, is a little sand, and before her, silver is to be accounted mire. mire – deep mud Posted in maths tuition | Tagged , , | Leave a comment ## No Exams Singapore The latest policy update is that there will be reduced or no exams for certain levels such as lower primary and lower secondary. Do check out our Poll writeup for more details: Poll: Opinion on Fewer exams for Primary and Lower Secondary Students? It seems that it is quite a dilemma; parents find exams stressful, yet exams are viewed as necessary by most parents to measure how their child is learning. According to Today Online, tuition centres have great success offering their own “in-house exams” to fill in the gap. At the end of the day, the “big exams” like PSLE, O-Levels, A-Levels are still present, and that is the major feature in the education landscape. It is quite like “lump sum payment” (single exam at end of the year) versus “payment by installments” (multiple exams throughout the year). In the end, the full sum still has to be paid (students still have to study the material to pass the final exam). Posted in maths tuition | Tagged , | Leave a comment ## Inequalities : RMS, AM, GM, HM Posted in maths tuition | Leave a comment ## Integral of x^x from 0 to 1$latex boxed {displaystyleint_{0}^{1}{x^{x}dx }= frac {1}{1^1} – frac {1}{2^2} +frac {1}{3^3} – frac {1}{4^4} + frac {1}{5^5} +…}latex boxed {displaystyleint_{0}^{1}{x^{-x}dx }= frac {1}{1^1} +frac {1}{2^2} +frac {1}{3^3} + frac {1}{4^4} + frac {1}{5^5} + …}$View original post Posted in maths tuition | Leave a comment ## H3 Mathematics Resource Page H3 Mathematics is the pinnacle of the Junior College Mathematics syllabus in Singapore. It contains a glimpse of actual Math that Mathematicians do, and it requires true mathematical understanding and technique to do well. (H1/H2 math requires a lot of practice, but not true understanding. It is quite common for students to “apply the method” and get the correct answer without having any idea of what they are actually doing.) Topics in H3 Mathematics include Functions, Sequence and Series, Combinatorics, and even Number Theory. Certain schools also include topics like Linear Algebra and Differential Equations. Certainly, the H3 Math questions have a Math Olympiad style to them. Here are some practice questions for H3 Math (more will be added in the future), with some hints. Questions are adapted from actual H3 prelim papers. ## Functions Q1) The function $f$ is such that $f(x+2)=af(x+1)-f(x)$, for all real $x$ and some constant $a$. (i) In the case that $f$ is a linear function, find all possibilities for $f$ and $a$. (ii) In the case that $f(0)=0$ and $|f(1)|=1$, use mathematical induction to prove that $f(n-1)f(n+1)+1=[f(n)]^2$ for all positive integers $n$. (iii) In the case that $a=2$, sketch one possibility for $f$ which is not linear. Hint: (i) Write $f(x)=mx+c$ and substitute it into the question. You should reach two cases, $a=2$ or $m=0$. For the case $a=2$, there is no other restriction. For the case $m=0$, either $a=2$ or $c=0$. (iii) Try a step function. ## Sequence and Series ## Combinatorics Q1) Mr H uses a software to generate distinct codes of the form $\overline{x_1x_2x_3x_4x_5}$, where $x_i\in\{0,1,2,3,4,5\}$. What is the least number of codes Mr H should generate such that there are at least two distinct codes that satisfy: $\boxed{x_1+x_3=x_2+x_4}$. [3 marks] Hint: No, the answer is not 12. Draw a possibility diagram for $x_1+x_3$, essentially a table with 6×6=36 entries detailing what combinations are there for $x_1+x_3$. Then list cases (a popular technique for combinatorics), based on each value of $x_1+x_3$. For example, the case $x_1+x_3=0$ only has 1 option namely $x_1=x_3=0$. Then $x_2+x_4$ can have 35 other options such that $x_2+x_4$ is different from $x_1+x_3$. The last digit $x_5$ has no restrictions so there are 6 options. Hence the total number of ways for this case is 1x35x6=210. Finally, after adding up all the cases, use pigeonhole principle (add one) to conclude the answer, which is 6901. ## Number Theory Q1) Let m, n, M and N be positive integers. Given that gcd(M,N)=1 and $mN^2=nM^2$, use Mathematical Induction to show that $M^2\mid m$ and $N^2\mid n$. [5 marks] Hint: First prove for the trivial case M=1 or N=1. Then write $M=p_1p_2\dots p_k$ and $N=q_1q_2\dots q_l$, where $p_i$, $q_j$ are primes. Use Euclid’s Lemma twice to prove that $p_1^2\mid m$. By induction, show that $M^2\mid m$. I think the key point is that Generalized Euclid’s Lemma is probably not allowed otherwise it is very easy. Posted in maths tuition | Tagged , | 2 Comments ## My favorite Fermat Little Theorem with Pascal Triangle Fermat Little Theorem: For any prime integer p, any integer m$latex boxed {m^{p} equiv m mod p} &s=3$When m = 2,$latex boxed{2^{p} equiv 2 mod p}&fg=aa0000$Note: 九章算数 Fermat Little Theorem (m=2) Pascal Triangle (1653 AD France ）= (杨辉三角 1238 AD – 1298 AD)$latex 1 : 1 implies sum = 2 = 2^1 equiv 2 mod 1latex 1: 2 :1implies sum = 4 = 2^2 equiv 2 mod 2 ;(equiv 0 mod 2)latex 1 :3 :3 :1 implies sum = 8= 2^3 equiv 2 mod 3$1 4 6 4 1 => sum = 16= 2^4 (4 is non-prime)$latex 1 :5 :10: 10: 5: 1 implies sum = 32= 2^5 equiv 2 mod 5\$

[PODCAST]

https://kpknudson.com/my-favorite-theorem/2017/9/13/episode-4-jordan-ellenberg

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