## Learning with Passion and Enthusiasm (Motivational Video)

The best way to learn is to learn with passion and enthusiasm. See the excellent motivational video below!

Without passion, learning becomes a chore like doing housework, and it becomes boring and tiring. Needless to say, such learning is not only burdensome but also ineffective and inefficient.

Sometimes kids who are smart don’t do well in school, because they don’t have the motivation or enthusiasm to learn. Check out our blog post on: Motivational Books for the Student (Educational).

## Michael De La De Maza Chess Book

This book is quite famous, or some may say “infamous”, in the circle of Chess books. The author is an adult player who managed to gain roughly 400 rating points in 400 days. To be precise, he gained 400 USCF rating points in the first year, and almost 300 USCF rating points in the second year, finally ending up with a rating of 2041. His original rating was 1321.

This is quite a meteoric rise for an adult. It is well documented that for many reasons, adults tend to improve slower than children when learning chess. Similarly, for music, languages, etc. Firstly, children’s brains are more “plastic” and flexible, and they have more time and less outside commitments to study chess.

The basic principles in his book seems to be to study tactics, which are “combo moves” in chess that can change the course of the game. Making a tactical mistake can spell the end of the game for either player.

The opposite of tactics is strategy. Strategic masters are Anatoly Karpov, Tigran Petrosian, and the current World Champion Magnus Carlsen. They play in a calm and controlled manner and accumulate a small advantage. Strategic mistakes tend not to lose immediately, but may lead to a slow and steady deterioration of the position.

The best author on strategic chess (for beginning to intermediate players) is probably Jeremy Silman. His book “The Amateur’s Mind” is a classic book:

## Christmas Present for Gifted Kids

This microscope set will be ideal for gifted children who are interested in biology, or science in general. Learning about the microscope is the first step towards the study of life sciences/medicine/biological sciences.

This set is made and endorsed by National Geographic, a popular science magazine in the US.

## H2 Math Bell Curve

As mentioned in H2 Maths Distinction Rate (Percentage of As), the national distinction rate for H2 Math is usually around 50%. That is, 50% of all students will get ‘A’ grade for H2 Math. (Note that this statistic is heavily skewed by the top tier JCs where close to 80%-90% of all students get ‘A’ for H2 Math.)

According to numerous online sources, such as Reddit, this year’s (2018) H2 Math paper was significantly harder than previous years. It featured many “out-of-the-box” questions that are not found in the Ten-Year-Series. The “bug” question featuring a “bug” walking in a zig-zag fashion and falling into a “blackhole” stumped many students. Certain topics, such as PnC (Permutations and Combinations) are totally left out, prompting students to say that it is a case of “PnC —> “high investment Low returns “ More like “high investment NO returns”. (Update: The “bug” question is a disguised PnC question.)

Despite all these, there are still many students who honestly think that the paper was doable, or even easy. Probably these are the students who have practiced Prelim papers of top schools like Hwa Chong or Raffles, and hence are used to such tough questions.

The usual consensus is that a high 70s mark (>75) is sufficient to get A for H2 Math. Low 70s (70-74) is quite risky and may either be ‘B’ or ‘A’ grade depending on the difficulty of the paper.

Someone actually created a poll (https://strawpoll.com/zh7r7xh7) for the H2 Math 2018 scores. It is quite possible to predict your own score accurately since the answers will be circulating online soon after the exam. Based on the poll, ignoring the typo error that is “75-89” is meant to be “75-79”, we can see that the cut-off for ‘A’ grade for 2018 should be in the range 70-74. This is based on the hypothesis that the 50% distinction rate holds.

The bellcurve for A levels is apparently set by SEAB (Singapore Examinations and Assessment Board), while Cambridge does the marking. According to an “old examiner report“, Cambridge likened grading to swimming a lap. They said that a candidate who could ‘compete a lap’ would be given due credit regardless of the number of people who also completed the lap. After Cambridge finishes marking and gives the numerical score, the bell curving will be processed by SEAB to determine the final grade, that is, ‘A’, ‘B’, ‘C,’ and so on. This is probably necessary to ensure a “consistent” grade distribution so that university admissions can go smoothly, and that grades from different years are roughly comparable.

## Alexa Ranking: Reaching 1 million

Thanks to all readers, mathtuition88.com is reaching 1 million in global Alexa Rank. (Currently 1,093,528 global rank). Our next target will be to reach and maintain below 1 million global Alexa Rank! All our traffic is organic traffic, from search engines.

Alexa Traffic Rank is a measure of popularity of a website. The most popular website, in this case Google.com, will have a Alexa rank of 1. The second most popular, Youtube.com, will have a rank of 2, and so on.

Chrome users should install the free Alexa Chrome Extension, it is very good to check the traffic rank of your website. Also, when you visit your own website, it will be counted by Alexa, and your Alexa ranking will be improved. From my experience, it is quite fast, it does not slow down your internet browser at all.

## Boric Acid Singapore

In Singapore, cockroaches are impossible to completely eradicate due to the tropical climate which is ideal for cockroaches. In many other countries, a common method to kill cockroaches is using Boric Acid. Boric acid is considered a natural substance, and is effective at killing cockroaches. It works as a “stomach poison affecting the insects’ metabolism, and the dry powder is abrasive to the insects’ exoskeletons”. As such, it is impossible to develop a “resistance” to boric acid, unlike for insecticides where numerous cockroaches are now immune to insecticides.

Boric acid is also considered non-toxic, it is similar to table salt in its toxicity level. Boric acid has a “secondary kill” effect: cockroaches who die will be eaten by other cockroaches, leading to a chain reaction of cockroach deaths. Hence, it is more effective than sprays or traps which only kill the cockroach that is targeted.

However, when one starts to look for boric acid in Singapore, it is quite hard to find it in the pure powder form. Whether it is banned, or is simply not popular, it seems that no one on the internet knows.

I found a cockroach bait containing Boric Acid in Qoo10 below. It is a Malaysian brand. It is written on the packaging that boric acid is the active ingredient, and I also double confirmed with their Facebook customer service. Here it is:

WWW.QOO10.SG

## 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

## 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:

## Ohm Electricity Review

Do check out our Ohm Electricity Review at: Ohm $20 Promo Code: OHMREF25CC5A. It includes 5 strong reasons to choose Ohm as your electricity provider! *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

## 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

## 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)

## 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:

## 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.

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.

## 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).

## 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.)

## 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.

## 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.

## 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:

## 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.

## 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.

The most famous application of Blockchain is “Bitcoin”. Whoever bought just $1000 worth of Bitcoin around year 2010 would be a millionaire now. However, other than “Bitcoin” and cryptocurrencies, blockchain technology do have other uses. So is blockchain useful or not? Only time will tell. See also our previous posts: Source: Channel News Asia Blockchain has been heralded as a potential panacea for everything from poverty and famine to cancer. In fact, it is the most overhyped – and least useful – technology in human history. In practice, blockchain is nothing more than a glorified spreadsheet. But it has also become the byword for a libertarian ideology that treats all governments, central banks, traditional financial institutions, and real-world currencies as evil concentrations of power that must be destroyed. ## Integration by parts, DI method This DI method is American way, better than the UK Cambridge O level technique. (Traditional Method learnt at O-Level) Integration by Parts: NEW Technique taught by this UC-Berkley Chinese Mathematician: “DI” Method First Stop: “D column at… 2nd Stop: 3rd Stop:$latex displaystyle int {e^{x}}sin {x} dx$View original post 1 more word ## Analysis by Timothy Gowers Why easy analysis problems are easy by Timothy Gowers (UK, Fields Medal 1998) Timothy Gowers is teaching in Cambridge, he wrote the thick volume of “Princeton Math Encyclopedia.” He is a very good mathematician, who likes to explain simple fundamental Math questions (like why 2+2=4, multiplication is commutative,…), in the process making abstract math simple to understand. If you have recently met epsilons and deltas for the first time, then you may find the problems you are asked to solve on examples sheets very hard. On the other hand, you will notice that your lecturers, supervisors etc. do not find them hard at all. Why is this? ” Read on … https://www.dpmms.cam.ac.uk/~wtg10/autoanalysis.html Below is my attempt to rewrite the Example 1 with Latex epsilon-delta notation for easy reading. Example 1. I wish to prove that the sequence (1,0,1,0,1,0,…) does not converge.$latex text{Let me set the sequence }

View original post 174 more words

## 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

## 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).

## 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.

## 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.

## 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)

$latex 1 : 1 implies sum = 2 = 2^1 equiv 2 mod 1$

$latex 1: 2 :1implies sum = 4 = 2^2 equiv 2 mod 2 ;(equiv 0 mod 2)$

$latex 1 :3 :3 :1 implies sum = 8= 2^3 equiv 2 mod 3$

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

View original post

## Backpack/School Bag Review: Targus Pandora

This bag (Targus brand) is very affordable at $19.90 (limited time only). It is suitable for students and even working adults, who would like a backpack that can store securely a laptop. It even has a raincoat (!!!) to protect your bag against the heavy rain that is so common in Singapore. Students in Junior College, Polytechnic, and University will likely find it very good and useful since they have to bring their computer laptop to school. It can store a lot of books/laptop equipment such as wires, chargers, etc. Do grab it fast if you like it, it is available on Qoo10 for a limited time only. From my experience, there is no where else online/or in retail where you can get such a good deal in terms of laptop bags. [$19.90](▼67%)[Samsonite]Authentic Samsonite n Targus Backpack / Laptop Backpack / Laptop Bag / Unisex / School backpack

WWW.QOO10.SG

## How do students in Singapore from the Express, Normal Academic and Normal Technical streams perceive each other?

Recently, this CNA (Channel News Asia) video is very popular on YouTube. Do check it out. Basically, due to the segregated nature of the education system, GEP, IP (Integrated Programme), Express, Normal Academic and Technical students rarely mix with each other, if at all. Hence, there may be some prejudices and biased views from each side towards the other.

A more in depth official commentary can be found here: https://www.channelnewsasia.com/news/cnainsider/regardless-class-race-religion-survey-singapore-income-divide-10774682

In light of this, the story of From PSLE 124 to PhD A*Star Researcher is very remarkable, on how a student overcame prejudices from society to reach his full potential. Do read it if you haven’t.

## Poll: Opinion on Fewer exams for Primary and Lower Secondary Students?

I have added a poll to see what readers think of this new proposal?

Actually mid-year exams and assessments may have a role as a “buffer” to reduce the weightage of the final exam. Removing mid-year exams actually has the effect of transferring more weightage to the final exam, making it more stressful? It boils down to whether people prefer a grading based on 100% weightage for final year exam, or something like 30% mid-year, 20% assessments and 50% final exams. Based on personal experience, many students (including myself) do prefer having a mid-year exam so that their results of the year is not entirely based on the final exams.

Also, for people who are natural procrastinators, who tend to do things at the last minute (possibly around 90% of the human population?), cancelling exams at the Primary 1 and Primary 2 level may end up causing a false sense of security, leading to a frantic panic attack at Primary 3? As a tutor, I receive numerous tutoring requests as late as September/October (for the final year exam), hence I know that numerous students/parents tend to panic at the last minute due to procrastination.

Possibly a worst case scenario that can end up is that the child does not learn well the fundamentals during P1 and P2, and this is undetected by his/her parents due to the absence of exams. Suddenly at P3, the reality is unveiled and it comes as a sudden shock. The P3 student has to catch up with the two years of fundamentals (P1 & P2) quickly before it is too late, as many subjects are cumulative in the sense that P3 topics relies on previous knowledge of P1 and P2 material.

Nonetheless, it is a new policy and it is good to see some changes coming that is intended to reduce the stress of young students. The time “saved” from doing exams can potentially be channeled into learning something new that is not found in the traditional syllabus. Scrapping the class/level position is good, there is no need to be obsessed with being “first” in class at such a young age. Possibly a percentile grade is still necessary for parents to gauge how their child is doing. Keeping PSLE is also good, despite PSLE being stressful it is actually a meritocratic system that theoretically allows a talented student from a poor family to rise to the top.

Source: Channel News Asia

The changes will be implemented in stages, beginning with the removal of all weighted assessments and exams for Primary 1 and 2 students from next year. Weighted assessments, said MOE, can take various modes such as class tests, presentations or group projects.

Currently, Primary 1 students do not have exams, but weighted assessments are conducted throughout the year. Primary 2 students now have weighted assessments throughout the year, as well as a year-end exam.

Secondary 1 students will also no longer have a mid-year examination from next year. From 2020 and 2021, this will also be removed for Primary 3, Primary 5 and Secondary 3 students.

## Chope.co Review

Chope.co is a restaurant reserving website that provides diners with benefits and rewards for reserving their seats at restaurants! “Chope” is a Singlish slang for “reserving a seat”. Reserving a seat is often important since the majority of  Singaporeans eat out on weekends/weekday dinner/and special occasions. This means that the restaurant is crowded during those popular times, and failing to reserve a seat may mean long waiting times or even worse, not finding a seat.

Join me on Chope and earn a SGD$10 restaurant voucher! Fulfill your first Chope reservation and earn a SGD$10 restaurant voucher after dining. Simply book through Chope using this link https://cho.pe/hna9y and you’re all set.

## Cool Fact: Cockroaches are becoming Endangered/Extinct in Russia (and other post-Soviet states)

Quite amazing that the cockroach, which is one of the most hardy animals, is actually becoming endangered/extinct in Russia? Possibly the cold weather has something to do with it, in addition to modern technology. Any Russian readers would like to confirm that this is true?

A side note that in tropical Singapore, cockroaches are far from endangered despite frequent fuming and spraying of insecticides, usually at the rubbish chutes. In fact, in most HDB apartments, spraying insecticides at the rubbish chutes actually may increase the number of cockroaches in the house due to those escaping/flying from the rubbish chute where they ordinarily live.

Quote: A mass depopulation of cockroaches has been observed since the beginning of the 21st century in Russia and other countries of the former USSR. Observers have noted a quick disappearance of various types of cockroaches from cities and towns in Russia, AzerbaijanKazakhstanUkraineMoldova, and Belarus.

Quote: House cockroaches began to disappear in Moscow during the beginning of the 2000s. Many Russians were even making jokes about it saying that it was one of advantages of Putin’s regime.

## From PSLE 124 to PhD A*Star Researcher

Source: A-star Official Website

For those familiar with the Singapore education system, you would know that PSLE 124 is not a good score by any standard. Yet Dr Vincent Lim, through his hard work and perseverance, managed to push on and graduate from university with first class honours, eventually earn a PhD and land a job at the prestigious A*STAR’s Institute of Medical Biology.

I believe the chances of this happening is truly rare in Singapore, possibly even rarer than striking 1st prize in TOTO. Singapore’s education system is known to be not too forgiving, once you make a “slip”, it is hard to get back onto the fast track. It must have taken tremendous courage, perseverance and hard work to overcome the odds to achieve this.

Truly amazing! Do share this to encourage those with children not doing too well in primary school. Certainly, late developers do exist and if given the right environment and nurturing support, they can blossom to reach their fullest potential.

Inspirational quote:

My advice for people who didn’t do well in school is this: it’s never the end. Society may sometimes seem to say: ‘This is your one job, you need to do well in school!’ But that’s not true. There’s never just one job; that’s not the reason you were born for.

Grades are not the most important thing. It is merely a stepping stone; if you’ve got no stone to step on, then run, jump, and climb. What is important is to never give up on yourself and to always keep your options open.”

-Dr Vincent Lim

## Get Official Ivy League (U Penn) degree online

Source: The Inquirer

Note that this is the first time an Ivy League university is offering a full degree online. Previously, some universities do offer some module credit or unofficial courses online, but this time University of Pennsylvania is offering its new bachelor of applied arts and sciences degree online.

Do check out their official course page here: Penn LPS Online.

So far I don’t see any restriction on nationality, that means possibly Singaporeans can apply too.

Some pointers that you may want to take note:

• If post-secondary credentials are from an institution outside the US, transcripts must be evaluated on a course-by-course basis by World Education Services, Inc. (WES).
• BAAS students are only required to come to campus for two extended weekends as they complete the program.

## Varignon’s Theorem (Surprising Geometry Theorem)

I first learnt it from Quora:

“Take any quadrilateral. It doesn’t have to be any special kind of a quadrilateral. Then connect the midpoints of its sides.

Surprisingly, you will always get a parallelogram!”

Quite a nice result. Some googling revealed that the name of this theorem is called Varignon’s Theorem.

An illustration is found here:

## RI vs HCI vs NUSH

Many excellent P6 students will be spoilt for choice at this stage, as they have been accepted by multiple schools under the DSA. Here are some views on RI versus HCI versus NUS High, which are the top 3 choices for boys strong in math/science:

RI emphasize “all-rounder” and “leadership” in their culture. My personal experience is that it can get a bit competitive since many people there are literally good in all forms of studies (all subjects in humanities/sciences/languages maybe except Chinese), sports, and music, etc. The culture is similar in RGS. I find that there are some cultural and personality differences between the typical RI/RGS student and the typical HCI/NYGH student.

The good points are that RI does have a lot of activities and opportunities like overseas school trips, top coaches for most CCAs, etc, that many schools don’t have. Also, many RI students are successful in securing government scholarships for top universities since their portfolio will be built up in a balanced way during their studies; there are many Community Involvement Programmes and other activities to boost the student’s portfolio.

Certainly NUSH and HCI are very good schools too. Possibly advantages of NUSH is greater focus on science/math and advantage of HCI is greater emphasis on Chinese culture and tradition, which is useful as China is becoming a world power.

Maybe you can check out this thread on RI vs HCI: https://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=48&t=25209&start=370.

## Sir Michael Atiyah to reveal his awesome proof of the Riemann Hypothesis

According to the official twitter account of the Heidelberg Laureate Forum, Sir Michael Atiyah will prove the Riemann Hypothesis during the talk on Monday Sept. 25.

According to him, it is a “simple” proof, based on previous work by von Neumann, Hirzebruch and Dirac. It is likely to have some relation to theoretical physics, since Dirac is a theoretical physicist. It has been rumored for quite some time that the Riemann Hypothesis is related to theoretical physics.

The Riemann Hypothesis is the most famous and most difficult problem in mathematics. Sir Michael Atiyah is a 89 year old gentleman currently. It will be really groundbreaking if the Riemann Hypothesis is found to be successfully proved.

Do check out our previous posts on the Riemann Hypothesis:

## Amazon Founder Jeff Bezos Originally Wanted to be a Theoretical Physicist

The world’s richest man is currently Jeff Bezos, founder of Amazon.

Few people know that he was an undergraduate at Princeton with the goal of becoming a theoretical physicist! What made him change his mind? Watch the video below.

Summary: Jeff Bezos was stuck on a Partial Differential Equation (PDE) question for 3 hours. Even while collaborating with his room mate, he could not find the answer. Upon consulting his Sri Lankan genius classmate, “Yosantha”, Yosantha solved the problem almost instantaneously in his mind!

Also check out our previous posts on Partial Differential Equations:

## NTUC Income Insurance Review

NTUC is a widely recognized name in Singapore, with most people having bought something from their flagship grocery store NTUC Fairprice.

NTUC is also very reliable and has various insurance policies that are beneficial to those who buy it. Most Singaporeans like to go overseas during the school vacations, a good travel insurance is essential to safeguard your health and wellbeing. NTUC Income is one of the few travel insurances that provides coverage for pre-existing medical conditions.

Check out NTUC Insurance today! (Please click on the link to enter the official NTUC Insurance website.)

Key Product Highlights:

Travel Insurance:
• Income’s Enhanced PreX plans provide the widest coverage for pre-existing medical conditions
• Coverage for families with unlimited number of children insured under the Family cover
• Coverage for travel delay, trip cancellation, medical expenses and loss of money and personal baggage while overseas
• Check out our great deals here.

Car & Motorcycle Insurance:
• Income is Singapore’s No. 1 Motor Insurer in terms of market share.
• Up to 69% off car insurance premiums with your existing NCD
• Unparalleled value added services at no extra cost:
– One-stop post-accident solution for your vehicle claims & repairs
– Mobile app that lets you complete & submit an accident report anywhere within minutes

Enhanced Home Insurance:
• 15% premium discount with purchase of a 3-year plan
• Comprehensive coverage for home contents, renovations and personal belongings

Foreign Maid Insurance:
• Personal accident, hospital & surgical expenses coverage for helpers
• Wages compensation if your helper is hospitalized
• Buy maid insurance online within minutes

PA Assurance:
• 40% discount on premiums for children if at least 1 parent is insured under same policy
• Coverage for 21 infectious diseases (e.g Zika, Dengue Fever, HFMD) with optional infectious disease cover
• Coverage for permanent disability and medical expenses for injury due to an accident

## 20% of Singapore’s workforce will be “displaced” by 2028 due to AI

According to the article by Today newspaper, around 20.6% of Singapore’s workforce will be “displaced” by 2028 due to technology and AI. This is quite scary news by the reliable newspaper Today. Although “displaced” is a tricky word and need not mean jobless or retrenched, nevertheless students should be mindful of this when they choose their major in polytechnics and university. Many esteemed jobs like accountancy, may or may not still be viable in 2028, as robots AI may likely have progressed to such a stage that they can easily take over human jobs. Non-degree jobs such as insurance agent and property agent may also be at risk. The bottom line is that if AI has progressed to the stage of being cheap and good, the big bosses will adopt it readily to lower their cost and maximize their profit.

Concerned parents and students should certainly read the below book, especially those who are about to choose their major in polytechnic or university. It is a “New York Times-bestselling guide to how automation is changing the economy, undermining work, and reshaping our lives”. As the saying goes, 男（女）怕入错行, the greatest fear of men (and women) is to enter the wrong profession. Checking out the future prediction of experts like Martin Ford is certainly a good idea. Imagine studying 4 years for a job that suddenly becomes extinct in 2028.

It is not an accident that Computer Science (and related subjects) is now one of the top and most popular majors in Singapore and many countries.

Source: Today

Workers in Singapore will be hit hard by technological disruptions with the Republic’s labour market set to face the largest degree of job displacement regionally in the next decade, based on a study on the impact of artificial intelligence (AI) on workers in six South-east Asian economies.

The new study by technology company Cisco and economic forecasting agency Oxford Economics also found that Singapore will have to confront the biggest mismatch between skills and jobs created among the countries in the region.

The findings were released on Wednesday (Sept 12) on the sidelines of the World Economic Forum on Asean (Association of South-east Asian Nations), a high-level gathering on innovation and entrepreneurship in Hanoi.

Data showed that about one-fifth of Singapore’s full-time equivalent workforce (20.6 per cent) will have their jobs displaced by 2028. This is higher than the figures for Vietnam (13.8 per cent), Thailand (11.9 per cent), the Philippines (10.1 per cent), Indonesia (8.1 per cent) and Malaysia (7.4 per cent).

Do check out this new website (http://lifebeyondgrades.sg/), which as its name implies is about emphasizing that school life is not all about grades, even in Singapore. It is kind of an official website, being funded by National Youth Council (see their FAQ.)

It is good that nowadays parents, teachers and the education sector has started to realize that grades is not everything in life. The FAQ section is very interesting and actually kind of reveals the future direction that Singapore education is heading towards. A few key points:

• “Why can’t we do away with the PSLE” –> Implication: PSLE is never going to be scrapped, at least not in the near future.
• “Why can’t we do away with CL2” —> Mother Tongue is here to stay for the time being.

Their article section is quite new, but also contains good articles. Do check out the “What is LQ” talk featuring Jack Ma.

Related: Check out Jamie Yeo’s PSLE score here. Hint: It is enough to enter most if not all secondary schools.

## The most addictive theorem in Applied mathematics

What is your favorite theorem ?

I have 2 theorems which trigger my love of Math :

1. Chinese Remainder Theorem:韩信点兵, named after a 200 BCE Han dynasty genius general Han Xin （韩信） who applied this modern “Modular Arithmetic” in battle fields.
2. Fermat’s Last Theorem：The Math “prank” initiated by the 17CE amateur Mathematician Pierre de Fermat kept the world busy for 380 years until 1974 proved by Andrew Wiles.

Note 1: Lycée Pierre de Fermat (Classe Préparatoire) happens to be my alma mater named after this great Mathematician born in the same southern France “Airbus City” Toulouse.

Note 2: His another Fermat’s Little Theorem is used in modern computer cryptography.