Latest Updates on

Just to update on the latest blog posts at I am trying to bring up the page rank for my Blogspot site, hence blogging there for the time being.

This book Why Before How: Singapore Math Computation Strategies, Grades 1-6 is surprisingly very popular. As an Amazon Affiliate, one of the most popular book I promote on my site is actually this book. It is a Singapore Math book that focuses on the “Why” before the “How”, which is very important as nowadays questions are designed to be solved using thinking, not just mechanical procedures.



Building a strong career in Internet Marketing

Hope this post is useful for students considering studying marketing in the future!

Building a strong career in Internet Marketing

If you want to break into the internet marketing field, there’s no time like the present. According to research, the amounts dedicated to digital marketing in enterprises of all sizes will steadily increase over the course of the next few years.

The internet marketing field is rather wide, and you’ll have to choose one or two areas you’re most comfortable with, but for all of these fields, the requirements for you in order to build a strong career and hence prove your worth to prospective clients and employers will mostly be the same.

The following is a list of five things you can do to distinguish yourself as an Internet marketing consultant, given by key players in the industry:

  • Marketing experience

A diploma or degree in a marketing related field will only go so far in honing your skill as a marketer; the more valuable education is the more experience you’ll gain working different cases out in the field. Most clients and employers look for candidates who have noteworthy marketing experience, so start building your expertise as soon as possible.

While in college, take up jobs and internships that will allow you to apply your classroom education and be involved hands-on in any marketing campaigns that come around you, no matter how small. Search for internships to occupy your holiday times while you are in school, so that you create for yourself an advantage over other recent graduates once you’re churned out into the job market.

  • Understand the field

Read everything you can in the field of Internet marketing that interests you: trends and statistics, new technologies, news, terminologies, metrics etc. You should also have a good working knowledge of all the metrics and analytical tools that are applied to the measurement of the efficacy of your campaign.

There are many methods of measuring effectiveness, so you should know as many as you can, and where each can be applied in order to add value to your client’s projects and campaigns.

  • Have an online presence

Create for yourself a vibrant online presence because all your clients will look into that before taking you on. Employers are also likely to choose the candidate with the stronger online presence when they have matching qualifications. Build your personal online brand as this may also be effective if you want to launch out and begin your own Internet marketing gig.

  • Jack of all trades, master in one

It’s good to know a little something about every field of internet marketing, but it’s better to have one or two fields that you know inside out. Distinguish yourself in areas of greatest interest, but know where and how you can find assistance in any other field if the need for it arises in the course of handling your employer’s or client’s businesses.

Begin by dipping your foot into the practical and basic aspects of everything, and then narrow down to the one you’re performing the best at.

  • Peer reviews and networks

Take advantage of all opportunities to build your knowledge and networks. Engage with peers in career fairs, conferences and other meet-up forums, and exchange ideas and experience. Also take advantage of such gathering to evaluate your work and gain tips on how they can be improved. Jealously nurture your offline relationships as you do the online relationships.

Author Bio

John Lewis has 5 years’ experience in internet marketing. For more information and guidance on internet marketing and to view and receive top web reviews for design work, contact us below



Tips to becoming an Oracle DBA

Here are some tips on becoming an Oracle database administrator. It will be useful for students interested in computer science and IT. 🙂

Tips to becoming an Oracle DBA

The Oracle database is the most sophisticated and complex database today. Knowing enough to become a database administrator is not an easy task. Oracle dataset administration is only recommended for information technology, information systems and computer science professionals who have undergone the relevant Oracle training.

The Oracle DBA’s position and salary attracts many young graduates, but few know exactly what it takes before they can earn this hallowed title in any company. An Oracle DBA is typically a senior-level manager in the smaller companies, mid-level in much bigger corporations, and their annual salaries can go as high as $ 100,000-250,000.

But the money does come with its load of responsibility – data management for the whole company, with the risk of grounding all operations with just a slight glitch. The first thing any aspiring DBA will have to remember is that database administration is just like any other profession; there’s no shortcut leading to the top.

Preparation, preparation and more preparation!

You can’t wake up one morning and decide to enroll for a DBA course, more so an Oracle DBA course. Majority of the successful DBAs in Oracle began to learn after obtaining their Bachelor’s and even Master’s degree in an IT related field. This is a career move that will require thought and plenty of preparation beforehand, and a lot of dedication after.

Oracle DBA requires 24/7 unfailing commitment, with long hours (since most of your work begins after everyone has checked out for the day) and on-call duty during holidays and other important occasions. That’s not all, as a DBA, you must keep yourself updated with every new change that comes in the Oracle and computer systems technology or you risk obsolescence.

You can now see that the Oracle DBA does earn every one of the dollars he’s paid, right?

Below is a list of qualities you should have in order to succeed in the pursuit of a career in Oracle Database Administration:

  • Communication skills

An Oracle DBA will constantly be in communication with end-users and managers to determine their data needs and act accordingly. College-level communication skills will be a must, with outstanding abilities to communicate through any medium and interpret information provided.

  • Business degree

It helps a lot if you have a college degree in business administration from a proper graduate training institution. This equips you with the foundational understanding of business systems and processes, which is required in order to best perform your job as an Oracle Applications DBA.

  • Foundational DBA skills

Prior to becoming an Oracle DBA, which is more demanding and complex, it’s recommended that you practice database administration at lower levels. Oracle has designed levels of learning for beginners, and practicing as you pursue OCA and OCM certification will be very helpful. This is because an Oracle DBA should understand other related database technologies as well e.g. Oracle Application Server and Java – J2EE, JDeveloper, Apache.

  • College classes

In preparation for a career in DBA, Operations Research is a class you want to take in your CS or IT course. This involves the development of complex decision rules and their application to real-life datasets. The back-end data store is usually Oracle, and it provides a great platform to prepare for the job setting.

Author Bio

Tom Foster is an expert in database administration. For more information on WordPress, SQL, Oracle and other database management and administration, contact the database professionals by visiting their website.



How to join 9 Dots using 4 Lines? (Advanced Version)

This is a humorous math comic based on the popular brainteaser: How do we join 9 dots using 4 lines?

(Hint: Think out of the box. See the solution here: Answer)

However, Spiked Math has added a new twist to the riddle. Enjoy the comic!



Featured book:

Comic-Strip Math: Problem Solving: 80 Reproducible Cartoons With Dozens and Dozens of Story Problems That Motivate Students and Build Essential Math Skills

Math + Comics = Learning That’s Fun! Help students build essential math skills and meet math standards with 80 laugh-out-loud comic strips and companion mini-story problems. Each reproducible comic and problem set reinforces a key math skill: multiplication, division, fractions, decimals, measurement, geometry, and more. Great to use for small-group or independent class work and for homework! For use with Grades 3-6.

The Math of Ebola


In the past week, world leaders have started using a mathematical term when they talk about the Ebola epidemic in West Africa.

“It’s spreading and growing exponentially,” President Obama said Tuesday. “This is a disease outbreak that is advancing in an exponential fashion,” said Dr. David Nabarro, who is heading the U.N.’s effort against Ebola.

Students who have learnt how the exponential graph looks like will know that the exponential function grows extremely quickly. exponential graph

In fact, for large enough x, the exponential function e^x will be larger than any polynomial function, say x^{100}. For example, when x=700, e^{700}=1.01\times 10^{304}, while 700^{100}=3.23 \times 10^{284}.

Fortunately, there is some good news:

Before we all start panicking (which I have been working hard not to do, myself), the world did get some welcome news this week. On Tuesday, President Obama announced plans for the U.S. military to provide 1,700 hospital beds in West Africa. It will also help set up training facilities for health care workers.

Featured book:

An Introduction to Bioinformatics Algorithms (Computational Molecular Biology)

This introductory text offers a clear exposition of the algorithmic principles driving advances in bioinformatics. Accessible to students in both biology and computer science, it strikes a unique balance between rigorous mathematics and practical techniques, emphasizing the ideas underlying algorithms rather than offering a collection of apparently unrelated problems.The book introduces biological and algorithmic ideas together, linking issues in computer science to biology and thus capturing the interest of students in both subjects. It demonstrates that relatively few design techniques can be used to solve a large number of practical problems in biology, and presents this material intuitively.An Introduction to Bioinformatics Algorithms is one of the first books on bioinformatics that can be used by students at an undergraduate level. It includes a dual table of contents, organized by algorithmic idea and biological idea; discussions of biologically relevant problems, including a detailed problem formulation and one or more solutions for each; and brief biographical sketches of leading figures in the field. These interesting vignettes offer students a glimpse of the inspirations and motivations for real work in bioinformatics, making the concepts presented in the text more concrete and the techniques more approachable.PowerPoint presentations, practical bioinformatics problems, sample code, diagrams, demonstrations, and other materials can be found at the Author’s website.

The important thing is to keep thinking

This is a really inspirational story to me. “The important thing is to keep thinking.”

keep thinking


Now, I want you to imagine for a moment that you live in the United States, to be exact: New Hampshire. You’re a recruiter at the University of New Hampshireand your job is to hire the best people to become professors and lecturers.

Now suppose one day you get an application from this guy, Zhang Yitang, a 50-something mathematician. Since getting his PhD from Purdue, he’s struggled to find an academic job, working as a motel clerk and a Subway sandwich maker. I wouldn’t blame you if you passed over him.

It turns out if you had skipped Zhang Yitang, you’d have been making a big mistake, because a few weeks ago this 57-year old Chinese mathematician made headlines around the world when he proved a result in number theory which has been challenging mathematicians for years.

Featured book:

How Not to Be Wrong: The Power of Mathematical Thinking

The Freakonomics of matha math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do–the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman–minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Secondary 4 O Level E Maths and A Maths Group Tuition, Bishan

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)


The ideal Singapore JC subject combination for applying to Medicine

Why Additional Maths (A Maths) is important for entering Medicine:

Pathway: A Maths (O Level) –> H2 Maths (A Level) –> NUS Medicine


Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.

Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :

H2 Chemistry, H2 Biology, H2 Mathematics


Quote: pre-requisites for nus medicine will be H2 Chem and H2 bio or physics.

as for what’s best,
H2 math is almost a must since without it you’ll be ruling out a lot of ‘back-up courses’

Maths tutoring adds up for students: OECD study (Singapore PISA tuition effect)


Many of the world’s most mathematically gifted teenagers come from countries with the most lucrative tutoring industries.

Figures released this week show tutoring in Asia’s powerhouses is widespread, with participation rates more than double those  in Australia, though the extent to which their success is a result of a punishing study schedule is unclear.

In test results released by the OECD, 15-year-olds from Shanghai  topped the mathematics rankings, performing at a level equivalent to three years ahead of students in Australia.
Read more:

Study Tips from MIT


Tooling and Studying: Effective Breaks

Even as an MIT student, you can’t study all the time. In fact, we learn better by switching gears frequently. Here are some tips for breaking up your study time effectively.

  • Approach the same material in several different ways. This increases learning by using different brain pathways. Read a textbook section, aloud if possible, then review your lecture notes on the same concept. Write a one-sentence summary of a chapter or a set of questions to test your understanding. Then move on to the next textbook section.
  • Study in blocks of time. Generally, studying in one-hour blocks is most effective (50 minutes of study with a ten-minute break). Shorter periods can be fine for studying notes and memorizing materials, but longer periods are needed for problem-solving tasks, psets, and writing papers.
  • Break down large projects (papers, psets, research) into smaller tasks. The Assignment Timeline can help with this. Check off each task on your to-do list as you finish it, then take a well-earned break.
  • Plan regular breaks. When building a schedule for the term, srategically add several regular breaks between classes and in the evenings. Take 20-30 minutes; never work through these scheduled breaks. Our minds need an occasional rest in order to stay alert and productive, and you can look forward to a reward as you study. If your living group has a 10 pm study break, or you have a circle of friends that likes to go out for ice cream together at 7 on Wednesdays, put that on your schedule. These small, brief gatherings will become more welcome as the term intensifies.
  • Get up and move. Research shows that sitting for more than three hours a day can shorten your life by up to two years. At least every hour, stand up, stretch, do some yoga or jumping jacks, or take a walk, and breathe deeply.
  • Schedule meals to relax and unwind with friends; don’t just inhale food while tooling.
  • Turn off your phone while studying and on when you take a break. You may think you are multitasking when you text someone while reading or doing problems, but often the reverse is true. An assignment done while texting or following tweets will likely take two or three times longer and not turn out as well.
  • If you tend to lose track of time while using your phone or computer, schedule fixed times for Facebook and other fun things, and set an alarm to remind you of the end of that period.

Shifts must be made in education system to prepare young for future: Heng Swee Keat


SINGAPORE: Education Minister Heng Swee Keat has said that two important shifts must be made in the education system in order to prepare the young for the future.

In a Facebook post on Friday evening, Mr Heng said firstly, the education system must help the young acquire deep skills and integrate theory with practice through applied learning.

Secondly, the system should make it easier for students to continue learning in their areas of strength and interest, and encourage lifelong learning.

Mr Heng said the education system needs to better link the interest and strengths of students to jobs of the future.

He explained that when students develop a deep interest, when their imagination is captured, they can go on to do wonderful things.

Formula to guess Month of Birthday from Singapore NRIC

Latest Update: We have created a JavaScript App to Guess Birthday Month from NRIC


Here is a Math Formula trick to have fun with your friends, to guess their Month of Birthday given their NRIC, within two tries.

(only works for Singapore citizens born after 1970)

The formula is: take the 3rd and 4th digit of the NRIC, put them together, divide by 10, and multiply by 3.

For an example, if a person’s NRIC is S8804xxxx, we take 04, divide by 10 to get 0.4

Then, 0.4 multiplied by 3 gives 1.2

Then, guess that the person is either born in January (round down 1.2 to 1) or February (round up 1.2 to 2). There is a high chance that you are right! Usually, round up for the first six months (Jan to Jun), and round down for the last six months (Jul to Dec).

This formula was developed and tested by me. There are some exceptions to the rule, but generally it works fine especially for people born from 1980 to 2000.

Hope you have fun with maths, and impress your friends!


O Level Maths Tutor — Practice Makes Perfect Article


Complexity and the Ten-Thousand-Hour Rule


Forty years ago, in a paper in American Scientist, Herbert Simon and William Chase drew one of the most famous conclusions in the study of expertise:

There are no instant experts in chess—certainly no instant masters or grandmasters. There appears not to be on record any case (including Bobby Fischer) where a person reached grandmaster level with less than about a decade’s intense preoccupation with the game. We would estimate, very roughly, that a master has spent perhaps 10,000 to 50,000 hours staring at chess positions…

In the years that followed, an entire field within psychology grew up devoted to elaborating on Simon and Chase’s observation—and researchers, time and again, reached the same conclusion: it takes a lot of practice to be good at complex tasks. After Simon and Chase’s paper, for example, the psychologist John Hayes looked at seventy-six famous classical composers and found that, in almost every case, those composers did not create their greatest work until they had been composing for at least ten years. (The sole exceptions: Shostakovich and Paganini, who took nine years, and Erik Satie, who took eight.)

This is the scholarly tradition I was referring to in my book “Outliers,” when I wrote about the “ten-thousand-hour rule.” No one succeeds at a high level without innate talent, I wrote: “achievement is talent plus preparation.” But the ten-thousand-hour research reminds us that “the closer psychologists look at the careers of the gifted, the smaller the role innate talent seems to play and the bigger the role preparation seems to play.” In cognitively demanding fields, there are no naturals. Nobody walks into an operating room, straight out of a surgical rotation, and does world-class neurosurgery. And second—and more crucially for the theme of Outliersthe amount of practice necessary for exceptional performance is so extensive that people who end up on top need help. They invariably have access to lucky breaks or privileges or conditions that make all those years of practice possible. As examples, I focussed on the countless hours the Beatles spent playing strip clubs in Hamburg and the privileged, early access Bill Gates and Bill Joy got to computers in the nineteen-seventies. “He has talent by the truckload,” I wrote of Joy. “But that’s not the only consideration. It never is.”

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数学补习 (碧山)


教O Level E Maths 和 A Maths.



Additional Maths — from Fail to Top in Class

Really glad to hear good news from one of my students.

From failing Additional Maths all the way, he is now the top in his entire class.

Really huge improvement, and I am really happy for him. 🙂

To other students who may be reading this, remember not to give up! As long as you persevere, it is always possible to improve.

NUS Maths Alumnus Dr Yeo Sze Ling mentioned in National Day Rally 2013

Ad: Maths Group Tuition available in 2014

Dr Yeo Sze Ling is sincerely a good example of perseverance for all Maths students, including myself!

(Go to 01h18m50s)



But perhaps the most memorable moment of all was when Lee became visibly emotional after sharing the heartwarming success story of visually handicapped A-star researcher Dr Yeo Sze Ling.

“Sze Ling proves that you can do well if you try hard, no matter what your circumstances, and that is also how we can contribute back to society, to keep the system fair for all,” said Lee, who then visibly teared and choked up,  but quickly composed himself.

PM Lee was emphasising the importance of meritocracy in Singapore’s education system, which he acknowledged needed more changes — for example, it can be more holistic and less competitive.


5 awarded prestigious President’s Scholarship at Istana ceremony

Maths Group Tuition starting in 2014


SINGAPORE – Five government scholarship recipients, including a missionaries’ child who grew up in Papua New Guinea and a Youth Olympic Games triathlete, have been awarded the prestigious President’s Scholarships this year, at a ceremony at the Istana on Friday evening.

Get the full story from The Straits Times.

Here is the full speech by President Tony Tan:

Deputy Prime Minister Teo Chee Hean and Mrs Teo

Minister for Education Heng Swee Keat


Chairman and Members of the Public Service Commission

Ladies and Gentlemen

Good evening.

Each year, the Public Service Commission awards scholarships to outstanding young men and women who want to serve Singapore and Singaporeans through a career in the Public Service. The most prestigious undergraduate scholarship awarded by the Commission is the President’s Scholarship.

It is awarded to young Singaporeans who have the integrity and commitment to work for Singapore’s continued success. To be awarded a President’s Scholarship, one must demonstrate more than just excellence in academic and non-academic pursuits. One must also show a strong ethos for public service, impeccable character, remarkable leadership and dedication towards improving the lives of Singaporeans.

2013 President’s Scholars This evening, the President’s Scholarship is awarded to five exceptional young individuals who have distinguished themselves based on their leadership capabilities and calibre, and their passion to bring the nation forward.

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Studying at NUS Mathematics Department

Maths Group Tuition to start in 2014!


The history  of the Department of Mathematics at NUS traces back to 1929, when science  education began in Singapore with the opening of Raffles College with less than  five students enrolled in mathematics. Today it is one of the largest  departments in NUS, with about 70 faculty members and       teaching staff supported  by 13 administrative and IT staff.  The Department offers a wide selection  of courses (called modules) covering wide areas of mathematical sciences with  about 6,000 students enrolling in each semester. Apart from offering B.Sc.  programmes in Mathematics, Applied Mathematics and Quantitative Finance, the  Department also participates actively in major interdisciplinary programs,  including the double degree programme in Mathematics/Applied Mathematics and  Computer Science, the double major       programmes in Mathematics and Economics as  well as with other subjects, and the Computational Biology programme. Another  example of the Department’s student centric educational philosophy is the   Special Programme in Mathematics (SPM), which is specially designed for a  select group of students who have a strong passion and aptitude for  mathematics. The aim is to enable these students to build a solid foundation  for a future career in mathematical research or state-of-the-art applications  of mathematics in industry.

The  Department is ranked among the best in Asia in mathematical  research.   It offers a diverse and vibrant program in graduate  studies, in fundamental as well as applied mathematics. It promotes  interdisciplinary applications of mathematics in science, engineering and  commerce. Faculty members’ research covers all major areas of contemporary  mathematics. For more information, please see research overview, selected publications, and research     awards.

Academic grading in Singapore: How many marks to get A in Maths for PSLE, O Levels, A Levels

Maths Group Tuition


Singapore‘s grading system in schools is differentiated by the existence of many types of institutions with different education foci and systems. The grading systems that are used at Primary, Secondary, and Junior College levels are the most fundamental to the local system used.

Overcoming Math Anxiety

Featured book:

“If you’ve ever said ‘I’m no good at numbers,’ this book can change your life.” (Gloria Steinem)

Primary 5 to 6 standard stream

  • A*: 91% and above
  • A: 75% to 90%
  • B: 60% to 74%
  • C: 50% to 59%
  • D: 35% to 49%
  • E: 20% to 34%
  • U: Below 20%

Overall grade (Secondary schools)

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

The GPA table for Raffles Girls’ School and Raffles Institution (Secondary) is as below:

Grade Percentage Grade point
A+ 80-100 4.0
A 70-79 3.6
B+ 65-69 3.2
B 60-64 2.8
C+ 55-59 2.4
C 50-54 2.0
D 45-49 1.6
E 40-44 1.2
F <40 0.8

The GPA table differs from school to school, with schools like Dunman High School excluding the grades “C+” and “B+”(meaning grades 50-59 is counted a C, vice-versa) However, in other secondary schools like Hwa Chong Institution and Victoria School, there is also a system called MSG (mean subject grade) which is similar to GPA that is used.

Grade Percentage Grade point
A1 75-100 1
A2 70-74 2
B3 65-69 3
B4 60-64 4
C5 55-59 5
C6 50-54 6
D7 45-49 7
E8 40-44 8
F9 <40 9

The mean subject grade is calculated by adding the points together, then divided by the number of subjects. For example, if a student got A1 for math and B3 for English, his MSG would be (1+3)/2 = 2.

O levels grades

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

The results also depends on the bell curve.

Junior college level (GCE A and AO levels)

  • A: 70% and above
  • B: 60% to 69%
  • C: 55% to 59%
  • D: 50% to 54%
  • E: 45% to 49% (passing grade)
  • S: 40% to 44% (denotes standard is at AO level only), grade N in the British A Levels.
  • U: Below 39%

H2 Maths 2012 A Level Solution Paper 2 Q6; H2 Maths Group Tuition


H_0: \mu=14.0 cm

H_1: \mu\neq 14.0 cm


\bar{x}\sim N(14,\frac{3.8^2}{20})

For the null hypothesis not to be rejected,


-1.95996<\frac{\bar{x}-14}{3.8/\sqrt{20}}<1.95996 (use GC invNorm function!)

12.3<\bar{x}<15.7 (3 s.f.)

(iii) Since \bar{x}=15.8 is out of the set 12.3<\bar{x}<15.7, the null hypothesis would be rejected. There is sufficient evidence that the squirrels on the island do not have the same mean tail length as the species known to her.

(technique: put in words what H_1 says!)

Singapore matematika kuliah

Kami penuh waktu Matematika guru, Mr Wu (Citizen Singapura), memiliki pengalaman yang luas (lebih dari 7 tahun) di les matematika. Mr Wu telah mengajar matematika sejak tahun 2006.

Mr Wu adalah pasien dengan siswa, dan akan menjelaskan konsep jelas kepada mereka. Dia mendorong untuk siswa lemah, sedangkan siswa yang lebih kuat tidak akan merasa bosan karena Mr Wu akan memberikan latihan yang cukup menantang bagi mereka untuk belajar lebih banyak. Singkatnya, setiap siswa harus mengalami perbaikan setelah kuliah.

Mr Wu lulus dengan B.Sc. (First Class Honours) dengan Mayor di Matematika (National University of Singapore).

Kami sangat percaya bahwa kepribadian dan karakter guru adalah sama pentingnya dengan kualifikasi akademik. Untuk Matematika Tutor, kesabaran ketika menjelaskan kepada siswa mutlak diperlukan.

Tutor Kualifikasi:

NUS: B.Sc. (First Class Honours) dengan Mayor di Matematika, Daftar Dean (Top 5% dari seluruh Fakultas Ilmu)

A Level: Matematika (A), Fisika (A), Kimia (A), Biologi (A), General Paper (A1)

O Tingkat: (Raffles Institution)

Bahasa Inggris (A1), Gabungan Humaniora (A1), Geografi (A1), Matematika (A1), Matematika Tambahan (A1), Fisika (A1), Kimia (A1), Biologi (A1), Bahasa Cina lebih tinggi (A2)

PSLE: (Nanyang Primer) 281, Lee Hsien Loong Excellence Award

Bahasa Inggris (A *), Bahasa Cina (A *), Matematika (A *), Sains (A *), Bahasa Cina Tinggi (Distinction), Ilmu Sosial (Distinction)

Apakah dalam Program PMP dari Pratama ke tingkat sekunder.

Terdaftar dengan MOE sebagai Guru Bantuan

(Orang tua yang ingin melihat sertifikat Mr Wu silahkan email kami. Orang tua juga dapat melihat profil StarTutor Mr Wu pada, dengan sertifikat diverifikasi.)

Meskipun kualifikasi akademik Mr Wu, ia tetap seorang guru yang rendah hati dan sabar. Juga, orang tua dapat yakin bahwa Mr Wu mengajar pada tingkat yang siswa dapat sepenuhnya mengerti. Untuk A Level, kami akan mencoba untuk mengajarkannya dengan cara yang jelas dan sederhana sehingga bahkan Sec 3/4 siswa dapat mengerti. Untuk O Levels, kita akan mengajarkannya sedemikian rupa sehingga bahkan Sec 1/2 siswa dapat memahami, dan sebagainya.

Mr Wu hanyalah orang biasa yang telah menguasai keterampilan dan teknik yang diperlukan untuk unggul dalam matematika di Singapura. Dia ingin mengajarkan teknik ini untuk siswa, maka memilih untuk menjadi Matematika penuh waktu guru. Mr Wu telah mengembangkan metode sendiri untuk memeriksa jawaban, mengingat rumus (dengan pemahaman), yang telah membantu banyak siswa. Banyak pertanyaan Math dapat diperiksa dengan mudah, menyebabkan siswa menjadi 100% yakin nya atau jawabannya bahkan sebelum guru menandai jawabannya, dan mengurangi tingkat kesalahan ceroboh.

Mr Wu juga kakak dari dua mahasiswa kedokteran. Adiknya sedang belajar Kedokteran di Universitas Monash, dan adiknya sedang belajar Kedokteran di Yong Loo Lin School of Medicine, NUS.

Tujuan Pengajaran:

Tujuan pengajaran adalah untuk memungkinkan siswa untuk memahami konsep-konsep dalam silabus, meningkatkan minat pada pelajaran, dan untuk menjelaskan dengan jelas metode untuk memecahkan masalah matematika. Matematika adalah subjek yang sangat kumulatif, dasar yang kuat diperlukan untuk maju ke tingkat berikutnya. Kami sangat berharap dapat membantu lebih banyak siswa membangun fondasi yang kuat di Matematika.

Untuk Matematika, kami percaya bahwa cara terbaik untuk maju adalah melalui praktek dan pemahaman. Teknik untuk memeriksa jawaban dan metode singkat untuk menjawab pertanyaan lebih cepat berguna. Ketekunan sangat penting dalam Matematika, yang penting adalah untuk tidak menyerah, dan terus mencoba!

Untuk individu Matematika kuliah, tutor dapat melakukan perjalanan ke rumah siswa.

“Didiklah anak di jalan yang patut baginya: dan ketika dia sudah tua, dia tidak akan menyimpang dari itu.”

– Amsal 22:6

H2 Maths 2012 A Level Paper 2 Q4 Solution; H2 Maths Tuition


1 Jan 2001 –> $100

1 Feb 2001 —> $110

1 Mar 2001 –> $120

Notice that this is an AP with a=100d=10

\displaystyle\begin{array}{rcl}S_n&=&\frac{n}{2}(2a+(n-1)d)\\    &=&\frac{n}{2}(200+10(n-1))>5000    \end{array}


From GC, n>23.5

n=24 (months)

This is inclusive of 1 Jan 2001!!!

Thus, 1 Jan 2001 + 23 months —> 1 Dec 2002


1 Jan 2001 –> 100

end of Jan 2001 –> 1.005(100)

1 Feb 2001 –> 1.005(100)+100

end of Feb 2001 –> 1.005[1.005(100)+100]=1.005^2 (100)+1.005(100)

From the pattern, we can see that

\displaystyle\begin{array}{rcl}S_n&=&1.005^n(100)+1.005^{n-1}(100)+\cdots+1.005(100)\\    &=&\frac{a(r^n-1)}{r-1}\\    &=&\frac{1.005(100)[1.005^n-1]}{1.005-1}\\    &=&\frac{100.5(1.005^n-1)}{0.005}\\    &=&20100(1.005^n-1)    \end{array}




From GC, n>43.7

So n=44 months (inclusive of Jan 2001 !!!)

1 Jan 2001+36 months —> 1 Jan 2004

1 Jan 2004+7 months —> 1 Aug 2004

Then on 1 Sep 2004, Mr B will deposit another $100, making the amount greater than $5000.

Hence, answer is 1 Sep 2004.


Let the interest rate be x %.

Note that from Jan 2001 to Nov 2003 is 35 months. (Jan 2001 to Dec 2001 is 12 months, Jan 2002 to Dec 2002 is 12 months, Jan 2003 to Nov 2003 is 11 months :))


Modifying our formula in part ii, we get

\displaystyle S_n=\frac{(1+x/100)(100)[(1+x/100)^n-1]}{(1+x/100)-1}=4900

Setting n=35 and using GC, we get


Hence, the interest rate is 1.80%.

Youngest NUS graduates for 2012 – 08Jul2012


Published on Jul  9, 2012

SINGAPORE – Douglas Tan was only seven years old when he discovered a knack for solving mathematical problems, tackling sums meant for the upper primary and secondary levels.
He went on to join the Gifted Programme in Rosyth Primary School and, in 2006, enrolled in the National University of Singapore High School of Math and Science (NUSHS). At 15, he was offered a place at the National University of Singapore (NUS) Faculty of Science to study mathematics.
Tomorrow, the 19-year-old will be this year’s youngest graduate at NUS, receiving his Mathematics degree with a First Class Honours. This puts him almost six years ahead of those his age.
Douglas, who is currently serving his National Service (NS), said the thought of going to prestigious universities overseas never occurred to him. “I was just happy doing what I was doing – solving math problems,” he said.
In every class he took, Douglas was the youngest but it was neither “awkward nor tough to fit in”, he said. In fact, his age was a good conversation starter and his classmates, who were typically three to five years older, would take care of him.
Seeing that he could complete his degree before he entered NS, Douglas took on three modules a semester and completed the four-year course in just two and a half years.
The longest he had ever spent on a math problem was 10 hours over a few days. “I’m a perfectionist. When I do a problem, I try to do it with 100 per cent,” he noted.
Douglas aspires to be a mathematician and is looking into a Masters degree but he has yet to decide if he wants to do it here or overseas.
Another young outstanding graduate this year is 20-year-old Carmen Cheh, who received her degree in Computer Science last Friday with a First Class Honours and was on the dean’s list every academic year of the four-year course.
Offered a place at the NUS School of Computing after three and a half years in NUSHS, Carmen was then the youngest undergraduate of the programme at 16.
She was introduced to computer science and concept programming at 11 by her father, a doctor who also challenged her to solve puzzles he created. Her inability to solve them spurred her interest in the subject.
Carmen, who is from Perak in Malaysia, said she decided to study for her degree in Singapore as she wanted to study in a country she felt “comfortable” in. At the same time, she was awarded an ASEAN scholarship to study in the Republic.
Next month, Carmen will begin her doctoral programme in Computer Science with a research assistantship at the University of Illinois at Urbana-Champaign.
The youngest ever to enrol into the NUS undergraduate programme is Abigail Sin, who entered the Yong Siew Toh Conservatory of Music at 14. She graduated in 2010 at age 18 with First Class Honours. She also received the Lee Kuan Yew gold medal.
This week, NUS celebrates the graduation of 9,913 students, its largest cohort in six years.­0000039/Theyre-ahead-of-the-class

Information about Mathematics Department Courses (Nanyang JC)


H1 Mathematics

H1 Mathematics provides a foundation in mathematics for students who intend to enrol in university courses such as business, economics and social sciences. The syllabus aims to develop mathematical thinking and problem solving skills in students. A major focus of the syllabus will be the understanding and application of basic concepts and techniques of statistics. This will equip students with the skills to analyse and interpret data, and to make informed decisions. The use of graphic calculator is expected.

H2 Mathematics

H2 Mathematics prepares students adequately for university courses including mathematics, physics and engineering, where more mathematics content is required. The syllabus aims to develop mathematical thinking and problem solving skills in students. Students will learn to analyse, formulate and solve different types of problems. They will also learn to work with data and perform statistical analyses. The use of graphic calculator is expected.

This subject assumes the knowledge of O-Level Additional Mathematics.

Continue reading at

There’s more to mathematics than grades and exams and methods


When you have mastered numbers, you will in fact no longer be reading numbers, any more than you read words when reading books. You will be reading meanings. (W. E. B. Du Bois)

When learning mathematics as an undergraduate student, there is often a heavy emphasis on grade averages, and on exams which often emphasize memorisation of techniques and theory than on actual conceptual understanding, or on either intellectual or intuitive thought. There are good reasons for this; there is a certain amount of theory and technique that must be practiced before one can really get anywhere in mathematics (much as there is a certain amount of drill required before one can play a musical instrument well). It doesn’t matter how much innate mathematical talent and intuition you have; if you are unable to, say, compute a multidimensional integral, manipulate matrix equations, understand abstract definitions, or correctly set up a proof by induction, then it is unlikely that you will be able to work effectively with higher mathematics.

However, as you transition to graduate school you will see that there is a higher level of learning (and more importantly, doing) mathematics, which requires more of your intellectual faculties than merely the ability to memorise and study, or to copy an existing argument or worked example. This often necessitates that one discards (or at least revises) many undergraduate study habits; there is a much greater need for self-motivated study and experimentation to advance your own understanding, than to simply focus on artificial benchmarks such as examinations.

Continue reading at

EDUC115N: How to Learn Math (Stanford Online Maths Education Course )

I will be attending this exciting online course by Stanford on Math Education. Do feel free to join it too, it is suitable for teachers and other helpers of math learners, such as parents.


EDUC115N: How to Learn Math 


About This Course

In July 2013 a new course will be available on Stanford’s free on-line platform. The course is a short intervention designed to change students’ relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning.


1. Knocking down the myths about math.        Math is not about speed, memorization or learning lots of rules. There is no such  thing as “math people” and non-math people. Girls are equally capable of the highest achievement. This session will include interviews with students.

2. Math and Mindset.         Participants will be encouraged to develop a growth mindset, they will see evidence of  how mindset changes students’ learning trajectories, and learn how it can be  developed.

3. Mistakes, Challenges & Persistence.        What is math persistence? Why are mistakes so important? How is math linked to creativity? This session will focus on the importance of mistakes, struggles and persistence.

4. Teaching Math for a Growth Mindset.      This session will give strategies to teachers and parents for helping students develop a growth mindset and will include an interview with Carol Dweck.

5. Conceptual Learning. Part I. Number Sense.        Math is a conceptual subject– we will see evidence of the importance of conceptual thinking and participants will be given number problems that can be solved in many ways and represented visually.

6. Conceptual Learning. Part II. Connections, Representations, Questions.        In this session we will look at and solve math problems at many different  grade levels and see the difference in approaching them procedurally and conceptually. Interviews with successful users of math in different, interesting jobs (film maker, inventor of self-driving cars etc) will show the importance of conceptual math.

7. Appreciating Algebra.        Participants will learn some key research findings in the teaching and learning of algebra and learn about a case of algebra teaching.

8. Going From This Course to a New Mathematical Future.        This session will review the ideas of the course and think about the way towards a new mathematical future.

Make Britain Count: ‘Stop telling children maths isn’t for them’


“The title comes from the central argument of the book,” says Birmingham-raised
Boaler, “namely the idea that maths is a gift that some have and some don’t.
That’s the elephant in the classroom. And I want to banish it. I believe
passionately that everybody can be good at maths. But you don’t have to take my word for it. Studies of the brain show that all kids can do well at maths,
unless they have some specific learning difficulty.”

But what about those booming Asian economies, with their ready flow of mathematically able graduates? “There are a lot of misconceptions about the methods that are used in China, Japan and Korea,” replies Boaler. “Their way of teaching maths is much more conceptual than it is in England. If you look at the textbooks they use, they are tiny.”

Professor Boaler’s tips on how parents can help Make Britain Count.

1 Encourage children to play maths puzzles and games at home. Anything with a dice will help them enjoy maths and develop numeracy and logic skills.

2 Never tell children they are wrong when they are working on maths problems. There is always some logic to what they are doing. So if your child multiplies three by four and gets seven, try: “Oh I see what you are thinking, you are using what you know about addition to add three and four. When we multiply we have four groups of three…”

3 Maths is not about speed. In younger years, forcing kids to work fast on maths is the best way to start maths anxiety, especially among girls.

4 Don’t tell your children you were bad at maths at school. Or that you disliked it. This is especially important if you are a mother.

5 Encourage number sense. What separates high and low achievers in primary school is number sense.

6 Encourage a “growth mindset” – the idea that ability changes as you work more and learn more.

Tangent Secant Theorem (A Maths Tuition)

Nice Proof of Tangent Secant Theorem:

Note: The term “Square of Sum less Square” means a^2-b^2=(a+b)(a-b)

The proof of the Tangent Secant Theorem, though not tested, is very interesting. In particular, the proof of the first case (DA passes through center) should be accessible to stronger students.

The illustration for theorem about tangent and...
The illustration for theorem about tangent and secant (Photo credit: Wikipedia)

Finding equation of circle (A Maths) 8 mark Question!


Find the equation of the circle which passes through A(8,1) and B(7,0) and has, for its tangent at B, the line 3x-4y-21=0.


Recall that the equation of a circle is (x-a)^2+(y-b)^2=r^2, where (a,b) is the centre of the circle, and r is the radius of the circle.

Substituting A(8,1) into the equation, we get:

\boxed{(8-a)^2+(1-b)^2=r^2} — Eqn (1)

Substituting B(7,0), we get:

\boxed{(7-a)^2+(0-b)^2=r^2} — Eqn (2)

Equating Eqn (1) and Eqn (2), we get

64-16a+a^2+1-2b+b^2=49-14a+a^2+b^2 which reduces to

\boxed{b=8-a} — Eqn (3)

after simplification.

Now, we rewrite the equation of the tangent as \displaystyle y=\frac{3}{4}x-\frac{21}{4} (make y the subject)

Hence, the gradient of the normal is \displaystyle\frac{-1}{\frac{3}{4}}=-\frac{4}{3}

Let the equation of the normal be \displaystyle y=-\frac{4}{3}x+c

Substitute in  B(7,0) we get \displaystyle 0=-\frac{4}{3}(7)+c

Hence \displaystyle c=\frac{28}{3}

Thus equation of normal is \displaystyle \boxed{y=-\frac{4}{3}x+\frac{28}{3}}

Since the normal will pass through the centre (a,b) we have

\boxed{b=-\frac{4}{3}a+\frac{28}{3}} — Eqn (4)

Finally, we equate Eqn (3) and Eqn (4),

\displaystyle 8-a=-\frac{4}{3}a+\frac{28}{3}

\displaystyle \frac{1}{3}a=\frac{4}{3}



Substituting back into Eqn (1), we get r=5

Hence the equation of the circle is:


Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question)

A bag A contains 9 black balls, 6 white balls and 3 red balls. A bag B contains 6 black balls, 2 white balls and 4 green balls. Ali takes out 1 ball from each bag randomly. When Ali takes out 1 ball from one bag, he will put it into the other bag and then takes out one ball from that bag. Find the probability that

(a) the ball is black from bag A, followed by white from bag B,
(b) both the balls are white in colour,
(c) the ball is black or white from bag B, followed by red from bag A,
(d) both the balls are of different colours,
(e) both the balls are not black or white in colours.

probability maths tuition


(a) \displaystyle\frac{9}{18}\times\frac{2}{13}=\frac{1}{13}

(b) Probability of white ball from bag A, followed by white ball from bag B=\displaystyle=\frac{1}{2}\times\frac{6}{18}\times\frac{3}{13}=\frac{1}{26}

Probability of white from B, followed by white from A=\displaystyle=\frac{1}{2}\times\frac{2}{12}\times\frac{7}{19}=\frac{7}{228}

Total prob=\displaystyle\frac{205}{2964}

(c) Prob. of ball is black or white from bag B=\displaystyle\frac{6}{12}+\frac{2}{12}=\frac{8}{12}


(d) Prob of both red = P(red from A, followed by red from B)=\displaystyle\frac{1}{2}\times\frac{3}{18}\times\frac{1}{13}=\frac{1}{156}

P(both green)=P(green from B, followed by green from A)=\displaystyle\frac{1}{2}\times\frac{4}{12}\times\frac{1}{19}=\frac{1}{114}

P(both black)=P(black from A, followed by black from B)+P(black from B, followed by black from A)=\displaystyle\frac{1}{2}\times\frac{9}{18}\times\frac{7}{13}+\frac{1}{2}\times\frac{6}{12}\times\frac{10}{19}=\frac{263}{988}

P(both white)=\displaystyle\frac{205}{2964} (from part b)

\displaystyle 1-\frac{1}{156}-\frac{1}{114}-\frac{263}{988}-\frac{205}{2964}=\frac{1925}{2964}


P(neither black nor white from A, followed by neither black nor white from B)=\displaystyle\frac{1}{2}\times\frac{3}{18}\times\frac{5}{13}=\frac{5}{156}

P(neither black nor white from B, followed by neither black nor white from A)=\displaystyle\frac{1}{2}\times\frac{4}{12}\times\frac{4}{19}=\frac{2}{57}


3D Trigonometry Maths Tuition



(a) Draw a line to form a small right-angled triangle next to the angle 18^\circ

Then, you will see that

\angle ACD=90^\circ-18^\circ=72^\circ (vert opp. angles)

\angle BAC=180^\circ-72^\circ=108^\circ (supplementary angles in trapezium)

By sine rule,

\displaystyle \frac{\sin\angle ABC}{30}=\frac{\sin 108^\circ}{40.9}

\sin\angle ABC=0.697596

\angle ABC=44.23^\circ

\angle ACB=180^\circ-44.23^\circ-108^\circ=27.77^\circ=27.8^\circ (1 d.p.)

(b) By Sine Rule,

\displaystyle\frac{AB}{\sin\angle ACB}=\frac{30}{\sin 44.23^\circ}

AB=\frac{30}{\sin 44.23^\circ}\times\sin 27.77^\circ=20.04=20.0 m (shown)


\angle BCD=\angle ACD-\angle ACB=72^\circ-27.77^\circ=44.23^\circ

By Cosine Rule,

BD^2=40.9^2+50^2-2(40.9)(50)\cos 44.23^\circ=1242.139

BD=35.24=35.2 m


\displaystyle\frac{\sin\angle BDC}{40.9}=\frac{\sin 44.23^\circ}{35.24}

\sin\angle BDC=0.80957

\angle BDC=54.05^\circ

angle of depression = 90^\circ-54.05^\circ=35.95^\circ=36.0^\circ (1 d.p.)


Let X be the point where the man is at the shortest distance from D. Draw a right-angle triangle XDC.

\displaystyle\cos 72^\circ=\frac{XC}{50}

XC=50\cos 72^\circ=15.5 m

Tips on attempting Geometrical Proof questions (E Maths Tuition)

Tips on attempting Geometrical Proof questions (O Levels E Maths/A Maths)

1) Draw extended lines and additional lines. (using pencil)

Drawing extended lines, especially parallel lines, will enable you to see alternate angles much easier (look for the “Z” shape). Also, some of the more challenging questions can only be solved if you draw an extra line.

2) Use pencil to draw lines, not pen

Many students draw lines with pen on the diagram. If there is any error, it will be hard to remove it.

3) Rotate the page.

Sometimes, rotating the page around will give you a fresh impression of the question. This may help you “see” the way to answer the question.

4) Do not assume angles are right angles, or lines are straight, or lines are parallel unless the question says so, or you have proved it.

For a rigorous proof, we are not allowed to assume anything unless the question explicitly says so. Often, exam setters may set a trap regarding this, making the angle look like a right angle when it is not.

5) Look at the marks of the question

If it is a 1 mark question, look for a short way to solve the problem. If the method is too long, you may be on the wrong track.

6) Be familiar with the basic theorems

The basic theorems are your tools to solve the question! Being familiar with them will help you a lot in solving the problems.

Hope it helps! And all the best for your journey in learning Geometry! Hope you have fun.

“There is no royal road to Geometry.” – Euclid

Animation of a geometrical proof of Phytagoras...
Animation of a geometrical proof of Pythagoras theorem (Photo credit: Wikipedia)

Reason for Maths Tuition

My take is that Maths tuition should not be forced. The child must be willing to go for Maths tuition in the first place, in order for Maths tuition to have any benefit. Also, the tuition must not add any additional stress to the student, as school is stressful enough. Rather Maths tuition should reduce the student’s stress by clearing his/her doubts and improving his/her confidence and interest in the subject. There is a quote “One important key to success is self-confidence. An important key to self-confidence is preparation.“. Tuition is one way to help the child with preparation.

Parallelogram Maths Tuition: Solution



(a) We have \angle APQ=\angle ARQ (opp. angles of parallelogram)

AP=RQ (opp. sides of parallelogram)

AR=PQ (opp. sides of parallelogram)

Thus, \triangle APQ\equiv\triangle QRA (SAS)

Similarly, \triangle ABC\equiv\triangle CDA (SAS)

\triangle CHQ\equiv\triangle QKC (SAS)

Thus, \begin{array}{rcl}\text{area of BPHC}&=&\triangle APQ-\triangle ABC-\triangle CHQ\\    &=&\triangle QRA-\triangle CDA-\triangle QKC\\    &=& \text{area of DCKR}    \end{array}



\angle ACD=\angle HCQ (vert. opp. angles)

\angle ADC=\angle CHQ (alt. angles)

\angle DAC=\angle CQH (alt. angles)

Thus, \triangle ADC is similar to \triangle QHC (AAA)

Hence, \displaystyle\frac{AC}{DC}=\frac{QC}{HC}

Thus, AC\cdot HC=DC\cdot QC


Tuition That We May Have To Believe In

This insightful article makes a really good read.

Quotes from the article:

To be honest, the amount to be learnt at each level of education is constantly increasing, and tuition could just help you get that edge over others. After all, it was meant to be supplementary in nature.

The toughest part at the end of the day however, is probably this: getting the right tutor.

guanyinmiao's musings (Archived: July 2009 to July 2019)

This commentary, “Tuition That We May Have To Believe In”, is a reply to a previous article on tuition by Howard Chiu (Mr.), “Tuition We Don’t Have To Believe In” (Read).

I must say Howard’s article had me on his side for a moment. He appealed to me emotively. Nothing like a mental picture of some kid attending hours and hours of tuition immediately after school when he could well be enjoying himself thoroughly with… an iPhone or iPad (I highly doubt kids these days still indulge their time at playgrounds). But the second time I read his article, I silenced the part of my brain which still prays the best for children, so do pardon me if I sound a tad too pragmatic at times.

The overarching assertion that Howard projects his points from is that there is “huge over consumption of this good”. Firstly, private tutoring…

View original post 1,472 more words

Maths Tuition Free Exam Papers (Primary, Secondary, O Levels, A Levels) Links

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