Sec 4 Maths Tuition @ Bishan

Maths Group Tuition starting in 2014!

https://mathtuition88.com/group-tuition/

Secondary Four O Level Maths Tuition (E Maths & A Maths Tuition) at Bishan starting in 2014!

Location: Block 230 Bishan Street 23 #B1-35 S(570230)

Schedule: Monday 7pm-9pm

Thursday 7pm-9pm

(Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.)

Google Maps: http://goo.gl/maps/chjWB

Email: mathtuition88@gmail.com

Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.

Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.

Directions to Bishan Tuition Centre:

A) Via BISHAN MRT (NS17/CC15)

(10 minutes by foot OR 2 bus stops from Junction 8. From J8, please take bus numbers, 52, 54 or 410 from interchange. The centre is just after Catholic High School, just beside Clover By-The-Park condominium.

Other landmarks are: the bus stop which students alight is in front of Blk 283, where Cheers minimart and Prime supermarket are.)

It’s one street away from Raffles Institution Junior College (RIJC), previously known as Raffles Junior College (RJC). It’s also very convenient for students of Catholic Junior College (CJC), Anderson Junior College (AJC), Yishun Junior College (YJC) and Innova Junior College (IJC).

Other secondary schools located near Bishan are Catholic High School, Kuo Chuan Presbyterian Secondary School, and Raffles Institution (Secondary).

Secondary 4 Maths Tuition @ Bishan starting in 2014.

https://mathtuition88.com/group-tuition/

https://mathtuition88.com/

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)

Email: mathtuition88@gmail.com

Book Review: Topology, James R. Munkres

Topology (2nd Edition)

This book is the best introductory book on Topology, an upper undergraduate/graduate course taken in university. I have written a short book review on it.

Excerpt:

Book Review: Topology
Book’s Author: James R. Munkres
Title: Topology
Prentice Hall, Second Edition, 2000

It is often said that one must not judge a book by its cover. The book with a plain cover, simply titled “Topology”, is truly a rare gem and in a class of its own among Topology books.

One striking aspect of the book is that it is almost entirely self-contained. As stated in the preface, there are no formal subject matter prerequisites for studying most of the book. The author begins with a chapter on Set Theory and Logic which covers necessary concepts like DeMorgan’s laws, Countable and Uncountable Sets, and the Axiom of Choice.

The first part of the book is on General Topology. The second part of the book is on Algebraic Topology. The book covers Topological Spaces and Continuous Functions, Connectedness and Compactness, and Separation Axioms. Some other material in the book include the Tychonoff Theorem, Metrization Theorems and Paracompactness, Complete Metric Spaces and Function Spaces, and Baire Spaces and Dimension Theory.

The book defines connectedness as follows: The space $X$ is said to be connected if there does not exist a separation of $X$ . (A separation of $X$ is defined to be a pair $U$ , $V$ of disjoint nonempty open subsets of $X$ whose union is $X$ .) Other sources may define connectedness by, $X$ is connected if $\nexists$ continuous $f:X\twoheadrightarrow \mathbf{2}$ .

Also, the proof of Urysohn’s Lemma in the book was presented slightly differently from other books as they did not use dyadic rationals to index the family of open sets. Rather, the book lets $P$ be the set of all rational numbers in the interval $[0,1]$ , and since $P$ is countable, one can use induction to define the open sets $U_p$ . In hindsight, the dyadic rationals approach in other sources may be more explicit and clearer.

An interesting new concept mentioned in the book is that of locally connectedness (not to be confused with locally path connectedness). A space $X$ is said to be locally connected at $x$ if for every neighborhood $U$ of $x$ , there is a connected neighborhood $V$ of $x$ contained in $U$ . If $X$ is locally connected at each of its points, it is said simply to be locally connected. For example, the subspace $[-1,0)\cup (0,1]$ of $\mathbb{R}$ is not connected, but it is locally connected. The topologists’ sine curve is connected but not locally connected.

In general, the content of the book is comprehensive. The other book, “Essential Topology”, did not cover some topics like the Urysohn Lemma, regular spaces and normal spaces.

Approach
The author’s approach is generally to give a short motivation of the concept, followed by definitions and then theorems and proofs. Examples are interspersed in between the text. The motivation tends to be a little bit too short though. For instance, in other books there is some motivation of how balls can determine the metric in a metric space, leading to the concepts of “candidate balls” $\mathcal{C}=\{C_\epsilon (x)\}_{\epsilon >0, x\in X}$ . This useful concept is not found in the book Topology, nor the other book Essential Topology.

One interesting explanation of the terminology “finer” and “coarser” is found in the book. The idea is that a topological space is like “a truckload full of gravel”‘ — the pebbles and all unions of collections of pebbles being the open sets. If now we smash the pebbles into smaller ones, the collection of open sets has been enlarged, and the topology, like the gravel, is said to have been made finer by the operation.

Another point to note is that the book does not use Category Theory. Personally, I would prefer the Category approach, since it can make proofs neater, and it provides additional insight to the nature of the theorem. We also note that the other book “Essential Topology”, also does not explicitly use Category Theory. But upon closer examination, the book has expressed commutative diagrams in words, which is not as clear as in diagram form.

Organization
The organization of the book is similar to most other books, except that it covers Connectedness and Compactness before the Separation Axioms. The concept of Hausdorff spaces, however, is covered way earlier, immediately after the discussion of closure and interior of a set. This enables theorems like “Every compact subspace of a Hausdorff space is closed” to be proved in the Compactness chapter.

Style
The author’s style is to combine rigor in proofs and definitions, with intuitive ideas in the examples and commentary. This makes it both a good textbook to learn from, and a good reference for proofs too.

This informal style in the commentary makes for a especially good read. For instance, a mathematical riddle is mentioned: “How is a set different from a door?” (For interested readers, the answer can be found on page 93.)

Also, there are many figures in the book, 84 sets of figures to be precise. This is rather good for a math book, and I would recommend the book to visual learners.

However, to learn Topology from this book alone may be difficult. Even though there are exercises to practice, there are no solutions and very few hints. Also, the book uses the terminology “limit point”, which can be confusing.

The book has surprisingly few typographical errors. While reading through the book, I only spotted a trivial one on page 107, where a function written as “ $F$ ” should be “ $f$ ” instead. Upon consulting an errata list, there was only one page of errors.

Conclusion
In conclusion, despite some shortcomings of the book, Topology is a great book, and if there was one Topology book that I could bring to a desert island, it would be this one.

Chapter Headings

Part I: General Topology

Set Theory and Logic
Topological Spaces and Continuous Functions
Connectedness and Compactness
Countability and Separation Axioms
The Tychonoff Theorem
Metrization Theorems and Paracompactness
Complete Metric Spaces and Function Spaces
Baire Spaces and Dimension Theory

Part II: Algebraic Topology

The Fundamental Group
Separation Theorems in the Plane
The Seifert-van Kampen Theorem
Classification of Surfaces
Classification of Covering Spaces
Applications to Group Theory

For more undergraduate Math book recommendations, check out Undergraduate Level Math Book Recommendations.

Performing well in math is generally a result of hard work, not innate skill

Source: http://www.huffingtonpost.com/jordan-lloyd-bookey/getting-a-d-in-mathand-th_b_4220609.html

Recently, I read this article in The Atlantic about the myth of being innately “bad at math,” and how performing well in math is generally a result of hard work, not innate skill. By all accounts, I should have known this, but it only took that one semester to break down years of confidence in my aptitude. In the article, the author notes several patterns we see that reinforce this myth. The one that resonated most with me was as follows:

“The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are ‘math people,’ and work hard in the future, cementing their advantage.”

And the B students (or in my case D student), well, they assume it’s about skill level and from that point forward it’s a self-fulfilling prophecy.

My mentor convinced me to apply to business school, and when he asked why I wouldn’t apply to Wharton, I said, “too quantitative.” I was scared. But he convinced me to apply, and after a crash course in Calculus, I learned that if I worked hard enough, indeed I could have success… even when my classmates were so-called quant jocks.

For me, it worked out, but for millions of kids in our education system, the ending isn’t so happy. Instead, parents determine at a very young age that a child has or does not have math skills. And, I would argue, they — we — do the same with reading. We decide that it’s one or the other, left or right brain. Instead, we can acknowledge our kids’ struggles with a particular subject, while continuing to encourage and remind them that a consistent effort can make a tremendous difference, but it takes perseverance.

What do I wish my teacher had done? I wish he had told me that I could do everything my classmates were doing, but I lacked the preparation before I ever stepped foot in his classroom. If only he had instilled that confidence in me, that simple knowing that I could do better, who knows what else I might have tackled coming out of high school.

Study Tips for Mathematics

Here are some useful study tips for Mathematics. The key to acing Maths is to understand that practice is key for Mathematics!

Sincerely hope these tips help.

Please do not study Maths like studying History, Literature or Geography, the study method for Maths is totally different and opposite from studying Humanities. Reading a Maths textbook without practicing is not very helpful at all.

Once a student understands the basic theory of a certain topic (usually just one or two pages of information), he or she can move on to practicing actual questions immediately. While practicing, the student will then learn more and more knowledge and question-answering strategies for that Maths topic.

Even if you already know how to do a question, it is useful to practice it to improve on speed and accuracy.

The study strategy for Maths and Physics are kind of similar, hence usually you will find that students who are good in Maths will also be good in Physics, and vice versa.

Students from China usually do very well in Maths exams because they understand the strategy for studying Maths (which works very well up till JC level), namely a lot of practice with understanding. The strategy is called “题海战术” in Chinese, which means “immersing oneself in a sea of questions”.

Source for diagram below: Email from JobsCentral BrightMinds

The ‘I’m bad at math’ myth

Source: http://www.dallasnews.com/opinion/sunday-commentary/20131108-the-im-bad-at-math-myth.ece?nclick_check=1

For high school math, inborn talent is much less important than hard work, preparation and self-confidence.

How do we know this? First of all, both of us have taught math for many years — as professors, teaching assistants and private tutors. Again and again, we have seen the following pattern repeat itself:

Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.

On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it — maybe 80 or 85 percent, a solid B.

The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes and fall further behind.

The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.

Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.

…

So why do we focus on math? For one thing, math skills are increasingly important for getting good jobs these days — so believing you can’t learn math is especially self-destructive. But we also believe that math is the area where America’s “fallacy of inborn ability” is the most entrenched. Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough.

Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth- and eighth-graders score quite well in international math comparisons — beating countries like Germany, the U.K. and Sweden — our high-schoolers underperform those countries by a wide margin. This suggests that Americans’ native ability is just as good as anyone’s, but that we fail to capitalize on that ability through hard work.

In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math — for example, Andrew Hacker has called for algebra to no longer be a requirement. The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x.

We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hardworking foreigners. But even more important, it may contribute to inequality. A great deal of research has shown that technical skills in areas like software are increasingly making the difference between America’s upper middle class and its working class. While we don’t think education is a cure-all for inequality, we definitely believe that in an increasingly automated workplace, Americans who give up on math are selling themselves short.

Too many Americans go through life terrified of equations and mathematical symbols. What many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.” And so they exclude themselves from quite a few lucrative career opportunities. This has to stop.

The Boy Who Loved Math: The Improbable Life of Paul Erdos (Hardcover)

The secret to being good at Maths (or any other subject) is to like it and enjoy it. This would make working hard and practicing Maths easier and more efficient. 2 hours can easily fly past while doing Maths if one is interested in it.

This is a storybook (suitable for young kids) about “The Boy Who Loved Math”, a true story about the Mathematician Paul Erdos.

The Boy Who Loved Math: The Improbable Life of Paul Erdos

Most people think of mathematicians as solitary, working away in isolation. And, it’s true, many of them do. But Paul Erdos never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn’t learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made “Uncle Paul” a great man.

A-level Marks/Grade required to enter NUS

NUS Cut Off Points (COP)

Source: http://www.nus.edu.sg/oam/gradeprofile/sprogramme-igp.html

Table 1: Grade Profiles of the 10^th and 90^th percentiles of A-Level Applicants offered places for courses at NUS in Academic Year 2012-2013²

NUS Courses	Representative Grade Profile 3H2/1H1
NUS Courses	10th percentile	90th percentile
Faculty of Law
Law*	AAA/A	AAA/A
School of Medicine
Medicine*	AAA/A	AAA/A
Nursing*	BCC/C	AAA/C
Faculty of Dentistry
Dentistry*	AAA/A	AAA/A
School of Design & Environment
Architecture*	ABB/B	AAA/A
Industrial Design*	BBB/B	AAA/A
Project & Facilities Management	BBC/C	ABB/C
Real Estate	BBC/B	AAB/B
Faculty of Engineering
Engineering	ABB/C	AAA/A
Bioengineering	ABB/C	AAA/A
Chemical Engineering	AAA/B	AAA/A
Civil Engineering	BBC/B	AAA/B
Electrical Engineering	BCC/B	AAA/B
Environment Engineering	BBB/C	AAA/B
Engineering Science	BBB/C	AAA/A
Industrial & Systems Engineering	AAB/B	AAA/A
Materials Science & Engineering	AAB/B	AAA/A
Mechanical Engineering	ABB/C	AAA/A
School of Computing
Computing (Computer Science)	BBC/C	AAA/A
Computing (Information Systems)	BBB/C	AAA/B
Faculty of Engineering & School of Computing
Computer Engineering	BCC/B	AAA/B
Faculty of Science
Pharmacy	AAA/A	AAA/A
Science	BBC/B	AAA/A
School of Business
Business Admin	AAA/B	AAA/A
Business Admin (Accountancy)	AAA/A	AAA/A
Faculty of Arts & Social Sciences
Arts & Social Sciences	BBB/B	AAA/A
Arts & Social Sciences (MT related)	BBC/C	BBB/B
Environmental Studies
Environmental Studies	AAB/B	AAA/A

* Courses that require interview &/or test.

²Double degrees are excluded from the table.

In China, all parents know that maths is the number one subject in schools

Source: http://www.telegraph.co.uk/education/maths-reform/9338540/Numeracy-Campaign-What-we-can-learn-from-China.html

‘Above all, it is a cultural thing.” Professor Lianghuo Fan is reflecting on the differences he has noticed between maths education in China and Singapore, where he lived and taught for 40 years, and in Britain, where he is now based. “In China, all parents know that maths is the number one subject in schools, and they expect that in a modern society everyone must be comfortable with maths, even if that means they have to work hard at it.“That attitude is passed on to their children. But here in Britain, you can feel students’ attitude about mathematics is different. They feel all right if they say they don’t like mathematics.”

Professor Fan is not alone in highlighting this national phobia of ours about maths. The government has this week shown itself determined to tackle the problem head on with the unveiling of a new “back-to-basics” primary school maths curriculum, with a renewed emphasis on times-tables, mental arithmetic, fractions and rote learning.

Most people over 40 will see the proposals as a return to the classroom practice of their childhood – but in its introductory remarks the Department for Education claimed inspiration from Asian model that Professor Fan knows so well: “I never heard a child in China or Singapore say that they don’t like maths’,” he stresses, “without a sense of embarrassment.”

We are sitting in a café near Southampton University – where 50-year-old Professor Fan has been head of the Mathematics and Science Education Research Centre since 2010 – as we try to decide if anything lies behind the popular stereotype that Asian children are “naturally” better at maths than those in the West. It is, for example, in the core storyline of Safe, the recent Hollywood blockbuster, starring Jason Statham. An 11-year-old girl, Mei (played by Chinese-born actress Catherine Chan), is a maths prodigy who can decode number sequences at a glance – and therefore has to be protected from the baddies.

Chinese Math Students vs English Math Students

Source: http://toshuo.com/2007/chinese-math-students-vs-english-math-students/

This is a recent test used in England:

$a diagnostic math test for first year university students in England$

Here’s a Chinese math test:

$a math question from a Chinese college entrance test$

Now we know why students from China are so good at Maths!

The Aims of Additional Maths (New Syllabus)

Additional Mathematics is kind of important, if your child is intending to pursue any studies related to Mathematics in university. Business, Accounting, Economics, and of course Engineering and Physics are examples of courses requiring some Mathematics.

Source: http://www.seab.gov.sg/oLevel/2013Syllabus/4038_2013.pdf

AIMS
The syllabus is intended to prepare students adequately for A Level H2 Mathematics and
H3 Mathematics, where a strong foundation in algebraic manipulation skills and
mathematical reasoning skills are required.
The O Level Additional Mathematics syllabus assumes knowledge of O Level Mathematics.
The general aims of the mathematics syllabuses are to enable students to:
• acquire the necessary mathematical concepts and skills for continuous learning in
mathematics and related disciplines, and for applications to the real world
• develop the necessary process skills for the acquisition and application of mathematical
concepts and skills
• develop the mathematical thinking and problem solving skills and apply these skills to
formulate and solve problems
• recognise and use connections among mathematical ideas, and between mathematics
and other disciplines
• develop positive attitudes towards mathematics
• make effective use of a variety of mathematical tools (including information and
communication technology tools) in the learning and application of mathematics
• produce imaginative and creative work arising from mathematical ideas
• develop the abilities to reason logically, to communicate mathematically, and to learn
cooperatively and independently

Arthur Benjamin: The magic of Fibonacci numbers

Source: http://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html?utm_source=newsletter_weekly_2013-11-09&utm_campaign=newsletter_weekly&utm_medium=email&utm_content=talk_of_the_week_button

Math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)

Watch the video at http://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html?utm_source=newsletter_weekly_2013-11-09&utm_campaign=newsletter_weekly&utm_medium=email&utm_content=talk_of_the_week_button

Good night’s sleep adds up to better exam results – especially in maths

To all students taking Maths exams, do have a good night’s sleep before the exam!

Source: http://www.telegraph.co.uk/health/healthnews/5486844/Good-nights-sleep-adds-up-to-better-exam-results-especially-in-maths.html

Researchers found that higher scores were related to greater sleep quality, especially less awakenings rather than the actual length of time asleep.

The team of researchers, led by Dr Jennifer Cousins at the University of Pittsburgh, studied 56 adolescents and compared their sleep patterns with their exam grades.

They found those that enjoyed deeper, less disturbed, sleep were the most successful, especially in maths but also in English and history.

Those who fell asleep and awoke easily – especially at weekends – were found to have better exam results.

Higher maths scores were related to less night awakenings, less time spent in bed, higher sleep efficiency and great sleep quality.

Formula to guess Month of Birthday from Singapore NRIC

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

Website: http://mathtuition88.blogspot.sg/2014/12/javascript-app-to-calculate-birthdate.html

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!

Shakuntala Devi’s 84th birthday: Google doodles a calculator for the human computer

Source: http://ibnlive.in.com/news/shakuntala-devis-84th-birthday-google-doodles-a-calculator-for-the-human-computer/432095-11.html

$Shakuntala Devi\'s 84th birthday: Google doodles a calculator for the human computer$

New Delhi: Google is celebrating the 84th birth anniversary of mathematical genius Shakuntala Devi, nicknamed “human computer” for her ability to make complex mental calculations, with a doodle on its India home page.

The doodle salutes Shakuntala Devi’s amazing calculating abilities with a doodle that resembles a calculator.

Shakuntala Devi found a slot in the Guinness Book of World Record for her outstanding ability and wrote numerous books like ‘Fun with Numbers’, ‘Astrology for You’, ‘Puzzles to Puzzle You’, and ‘Mathablit’. She had the ability to tell the day of the week of any given date in the last century in a jiffy. Coming from a humble family, Shakuntala Devi’s father was a circus performer who did trapeze, tightrope and cannonball shows.

Recommended Calculus Book for Undergraduates

Thomas’ Calculus (12th Edition)

Thomas’ Calculus is the recommended textbook to learn Undergraduate Calculus (necessary for Engineering, Physics and many science majors). It is used by NUS and can be bought at the Coop.

Full of pictures, and many exercises, this book would be a good book to read for anyone looking to learn Calculus in advance.

What is the Difference between H1 Mathematics, H2 Mathematics and H3 Mathematics?

Source: http://www.temasekjc.moe.edu.sg/what-we-do/academic/mathematics-department

Note: Additional Mathematics is very helpful to take H2 Mathematics in JC!

Curriculum

There are three mathematics syllabi, namely H1 Mathematics, H2 Mathematics and H3 Mathematics.

Students who offered Additional Mathematics and passed the subject at the GCE ‘O’ level examination may take up H2 Mathematics. Students posted to the Arts stream and did not offer Additional Mathematics at the GCE ‘O’ level examination are not allowed to take H2 Mathematics but may consider taking up H1 Mathematics. However, students who are posted to the Science stream but did not offer Additional Mathematics at the GCE ‘O’ level examination are advised to offer H2 Mathematics if they intend to pursue Science or Engineering courses at a university. Students who wish to offer H3 Mathematics must offer H2 Mathematics as well.

The use of a Graphing Calculator (GC) without a computer algebra system is expected for these Mathematics syllabi. The examination papers will be set with the assumption that candidates will have access to GCs.

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 topics covered include Graphs, Calculus and Statistics. A major focus of the syllabus would be the understanding and application of basic concepts and techniques of statistics. This would equip students with the skills to analyse and interpret data, and to make informed decisions.

H2 Mathematics

H2 Mathematics prepares students adequately for university courses including mathematics, physics and engineering, where more mathematics content is required. The topics covered are Functions and Graphs, Sequences and Series, Vectors, Complex Numbers, Calculus, Permutations and Combinations, Probability, Probability Distributions, Sampling, Hypothesis Testing, and Correlation and Regression. Students would learn to analyse, formulate and solve different kinds of problems. They would also learn to work with data and perform statistical analysis.

H3 Mathematics

H3 Mathematics offers students who have a strong aptitude for and are passionate about mathematics a chance to further develop their mathematical modeling and reasoning skills. Opportunities abound for students to explore various theorems, and to read and write mathematical proofs. Students would learn the process of mathematical modeling for real-world problems, which involves making informed assumptions, validation and prediction. Students may choose from the three H3 Mathematics modules, namely the MOE-UCLES module, the NTU Numbers and Matrices module and the NUS Linear Algebra module.

The MOE-UCLES module is conducted by tutors from our Mathematics Department. The three main topics to be investigated are Graph Theory, Combinatorics and Differential Equations. This module would be mounted only if there’s demand.

The NTU Numbers and Matrices module is conducted by lecturers from the Nanyang Technological University (NTU). Students would have to travel to Hwa Chong Institution to attend this module.

The NUS Linear Algebra module is conducted by lecturers at the National University of Singapore (NUS). Students who offer this module would have to attend lessons together with the undergraduates at the university.

JC Cut Off Points

JC Cut Off Points (COP)

To sign up for JC Tuition (subjects other than Math, e.g. GP Tuition): Check out this recommended tuition agency: StarTutor!

Aggregate Scores of Junior Colleges (JC)

Outliers: The Story of Success This is a very inspirational book on why do some people succeed, and what makes high-achievers different? Famous author Malcolm Gladwell reveals the secret and how it is possible for average ordinary people to achieve the same results. (Best Seller on Amazon.com)

Check out our post on Recommended Graphical Calculator for JC.

Also check out our post on: Which JC is Good?

RJC Cut Off Points: Arts 3, Science 3
HCI Cut Off Points: Arts 3, Science 3
VJC Cut Off Points: Arts 5, Science 4
NJC Cut Off Points: Arts 5, Science 5
ACS(I) Cut Off Points: Science 5
ACJC Cut Off Points: Arts 7, Science 6
TJC Cut Off Points: Arts 7, Science 6
AJC Cut Off Points: Arts 10, Science 8
MJC Cut Off Points: Arts 9, Science 9
NYJC Cut Off Points: Arts 9, Science 9
SAJC Cut Off Points: Arts 9, Science 9
CJC Cut Off Points: Arts 10, Science 10
SRJC Cut Off Points: Arts 13, Science 13
TPJC Cut Off Points: Arts 13, Science 14
JJC Cut Off Points: Arts 13, Science 16
PJC Cut Off Points: Arts 16, Science 16
YJC Cut Off Points: Arts 20, Science 20
IJC Cut Off Points: Arts 20, Science 20

L1R5 aggregate scores/ Cut Off Points (with bonus points) of students admitted to JCs in the 2012 Joint Admissions Exercise (JAE).

Junior College	Arts	Science/IB
Anderson JC	10	8
Anglo-Chinese JC	7	6
Anglo-Chinese School (Independent)	–	5
Catholic JC	10	10
Hwa Chong Institution	3	3
Innova JC	20	20
Jurong JC	13	16
Meridian JC	9	9
Nanyang JC	9	9
National JC	5	5
Pioneer JC	16	16
Raffles Institution	3	3
Serangoon JC	13	13
St. Andrew’s JC	9	9
St. Joseph Institution	–	–
Tampines JC	13	14
Temasek JC	7	6
Victoria JC	5	4
Yishun JC	20	20

Source: http://www.moe.gov.sg/education/admissions/jae/files/jae-info.pdf

http://www.dunearn.edu.sg/students/junior-college-admission-cut-off-points-2013

JC Cut Off Points (Bonus Points)

For students seeking admission to JC/Poly/ITE and with the following CCA grades:a. Grades of A1 – A2 (2 points)b. Grades of B3 – C6 (1 point)

For students seeking admission to JC/MI courses and with grades of A1 to C6 in both their first languages (i.e. English and a Higher Mother Tongue). This is provided that these choices come before any Poly/ITE choices.(2 points)

For students seeking admission to JC/MI courses and with grades of A1 to C6 in Malay/Chinese (Special Programme) (MSP/CSP) or Bahasa Indonesia (BI) as their third language. This is provided that these choices come before any Poly/ITE choices.(2 points)

For students from feeder schools if they choose their affiliated Junior College course(s) as their:a. 1st choice, or b. 1st and 2nd choices. (2 points)

The bonus points can be deducted from their total points, and will be helpful to enter the JC (depending on the JC’s Cut Off Points). Theoretical Minimum Score is 0 points (if under CLEP or MLEP programme), otherwise minimum score is 2 points.

New Additional Maths Syllabus (Syllabus 4047) TO BE IMPLEMENTED FROM YEAR OF EXAMINATION 2014

http://www.seab.gov.sg/oLevel/2014Syllabus/4047_2014.pdf

There are some minor changes to the A Maths Syllabus in 2014. Wishing everyone taking the new syllabus all the best!

Main Differences

Topics Added:

– knowledge of $a^3+b^3=(a+b)(a^2-ab+b^2)$ and $a^3-b^3=(a-b)(a^2+ab+b^2)$ is needed

Topics Removed:

– Intersecting chords theorem and tangent-secant theorem for circles removed

– exclude solving simultaneous equations using inverse matrix method

Sec 4 O Level Maths Tuition

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

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)

Email: mathtuition88@gmail.com

Studying at NUS Mathematics Department

Maths Group Tuition to start in 2014!

Source: http://ww1.math.nus.edu.sg/

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

Source: http://en.wikipedia.org/wiki/Academic_grading_in_Singapore

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%

List of Secondary Schools in Singapore; A Maths Tuition

Source: http://en.wikipedia.org/wiki/List_of_secondary_schools_in_Singapore

Mainstream schools

Name	Type	School code	Area^[2]	Notes	Website
Admiralty Secondary School	Government	3072	Woodlands		[1]
Ahmad Ibrahim Secondary School	Government	3021	Yishun		[2]
Anderson Secondary School	Government, Autonomous	3001	Ang Mo Kio		[3]
Anglican High School	Government-aided, Autonomous, SAP		Bedok
Anglo-Chinese School (Barker Road)	Government-aided		Novena
Anglo-Chinese School (Independent)	Independent, IP		Dover	Offers the IB certificate
Ang Mo Kio Secondary School	Government	3026	Ang Mo Kio
Assumption English School	Government-aided		Bukit Panjang
Balestier Hill Secondary School	Government		Novena
Bartley Secondary School	Government	3002	Toa Payoh
Beatty Secondary School	Government	3003	Toa Payoh
Bedok Green Secondary School	Government		Bedok
Bedok North Secondary School	Government		Bedok
Bedok South Secondary School	Government		Bedok
Bedok Town Secondary School	Government		Bedok
Bedok View Secondary School	Government		Bedok
Bendemeer Secondary School	Government		Kallang
Bishan Park Secondary School	Government		Bishan
Boon Lay Secondary School	Government		Jurong West
Bowen Secondary School	Government		Hougang
Broadrick Secondary School	Government		Geylang
Bukit Batok Secondary School	Government		Bukit Batok
Bukit Merah Secondary School	Government		Bukit Merah
Bukit Panjang Govt. High School	Government, Autonomous		Chua Chu Kang
Bukit View Secondary School	Government		Bukit Batok
Catholic High School	Government-aided, Autonomous, SAP, IP		Bishan
Canberra Secondary School	Government		Sembawang
Cedar Girls’ Secondary School	Government, Autonomous	3004	Toa Payoh
Changkat Changi Secondary School	Government		Tampines
Chestnut Drive Secondary School	Government		Bukit Panjang
CHIJ Katong Convent	Government-aided, Autonomous		Marine Parade
CHIJ Secondary (Toa Payoh)	Government-aided, Autonomous	7004	Toa Payoh
CHIJ St. Joseph’s Convent	Government-aided		Sengkang
CHIJ St. Nicholas Girls’ School	Government-aided, Autonomous, SAP		Ang Mo Kio
CHIJ St. Theresa’s Convent	Government-aided		Bukit Merah
Chong Boon Secondary School	Government		Ang Mo Kio
Chua Chu Kang Secondary School	Government		Chua Chu Kang
Church Secondary School	Government-aided
Chung Cheng High School (Main)	Government-aided, Autonomous, SAP		Marine Parade
Chung Cheng High School (Yishun)	Government-aided		Yishun
Clementi Town Secondary School	Government		Clementi
Clementi Woods Secondary School	Government		Clementi
Commonwealth Secondary School	Government, Autonomous		Jurong East
Compassvale Secondary School	Government		Sengkang
Coral Secondary School	Government		Pasir Ris
Crescent Girls’ School	Government, Autonomous		Bukit Merah
Damai Secondary School	Government		Bedok
Deyi Secondary School	Government		Ang Mo Kio
Dunearn Secondary School	Government		Bukit Batok
Dunman High School	Government, Autonomous, IP, SAP		Kallang
Dunman Secondary School	Government, Autonomous		Tampines
East Spring Secondary School	Government		Tampines
East View Secondary School	Government		Tampines
Edgefield Secondary School	Government		Punggol
Evergreen Secondary School	Government		Woodlands
Fairfield Methodist Secondary School	Government-aided, Autonomous		Queenstown
Fajar Secondary School	Government		Bukit Panjang
First Toa Payoh Secondary School	Government	3208	Toa Payoh
Fuchun Secondary School	Government		Woodlands
Fuhua Secondary School	Government		Jurong West
Gan Eng Seng School	Government		Bukit Merah
Geylang Methodist School (Secondary)	Government-aided		Geylang
Greendale Secondary School	Government		Punggol
Greenridge Secondary School	Government		Bukit Panjang
Greenview Secondary School	Government		Pasir Ris
Guangyang Secondary School	Government		Bishan
Hai Sing Catholic School	Government-aided		Pasir Ris
Henderson Secondary School	Government		Bukit Merah
Hillgrove Secondary School	Government		Bukit Batok
Holy Innocents’ High School	Government-aided		Hougang
Hong Kah Secondary School	Government		Jurong West
Hougang Secondary School	Government		Hougang
Hua Yi Secondary School	Government		Jurong West
Hwa Chong Institution	Independent, IP, SAP		Bukit Timah
Junyuan Secondary School	Government		Tampines
Jurong Secondary School	Government		Jurong West
Jurong West Secondary School	Government		Jurong West
Jurongville Secondary School	Government		Jurong East
Juying Secondary School	Government		Jurong West
Kent Ridge Secondary School	Government		Clementi
Kranji Secondary School	Government		Chua Chu Kang
Kuo Chuan Presbyterian Secondary School	Government-aided		Bishan
Loyang Secondary School	Government		Pasir Ris
MacPherson Secondary School	Government		Geylang
Manjusri Secondary School	Government-aided		Geylang
Maris Stella High School	Government-aided, Autonomous, SAP	7111	Toa Payoh
Marsiling Secondary School	Government		Woodlands
Mayflower Secondary School	Government		Ang Mo Kio
Methodist Girls’ School (Secondary)	Independent		Bukit Timah
Montfort Secondary School	Government-aided		Hougang
Nan Chiau High School	Government-aided, SAP		Sengkang
Nan Hua High School	Government, Autonomous, SAP		Clementi
Nanyang Girls’ High School	Independent, IP, SAP		Bukit Timah	Affiliated to Hwa Chong Institution
National Junior College	Government, IP		Bukit Timah
Naval Base Secondary School	Government		Yishun
New Town Secondary School	Government		Queenstown
Ngee Ann Secondary School	Government-aided, Autonomous		Tampines
Northlight School	Independent
North View Secondary School	Government		Yishun
North Vista Secondary School	Government		Sengkang
Northbrooks Secondary School	Government		Yishun
Northland Secondary School	Government		Yishun
NUS High School of Mathematics and Science	Independent, IP, Specialised			Offers the NUS High School Diploma
Orchid Park Secondary School	Government		Yishun
Outram Secondary School	Government		Central
Pasir Ris Crest Secondary School	Government		Pasir Ris
Pasir Ris Secondary School	Government
Paya Lebar Methodist Girls’ School (Secondary)	Government-aided, Autonomous		Hougang
Pei Hwa Secondary School	Government		Sengkang
Peicai Secondary School	Government		Serangoon
Peirce Secondary School	Government		Bishan
Ping Yi Secondary School	Government		Bedok
Pioneer Secondary School	Government	3062	Jurong West
Presbyterian High School	Government-aided		Ang Mo Kio
Punggol Secondary School	Government		Punggol
Queenstown Secondary School	Government		Queenstown
Queensway Secondary School	Government		Queenstown
Raffles Girls’ School (Secondary)	Independent, IP		Central	Affiliated to Raffles Institution
Raffles Institution	Independent, IP		Bishan
Regent Secondary School	Government		Chua Chu Kang
Riverside Secondary School	Government		Woodlands
River Valley High School	Government, Autonomous, IP, SAP		Jurong West
St. Andrew’s Secondary School	Government-aided	7015	Toa Payoh
St. Patrick’s School	Government-aided		Bedok
School of Science and Technology, Singapore	Independent, Specialised		Clementi
School of the Arts, Singapore	Independent, Specialised			Offers the IB certificate
Sembawang Secondary School	Government		Sembawang
Seng Kang Secondary School	Government		Sengkang
Serangoon Garden Secondary School	Government		Serangoon
Serangoon Secondary School	Government		Hougang
Shuqun Secondary School	Government		Jurong East
Si Ling Secondary School	Government		Woodlands
Siglap Secondary School	Government		Pasir Ris
Singapore Chinese Girls’ School	Independent		Novena
Singapore Sports School	Independent, Specialised
Springfield Secondary School	Government		Tampines
St. Anthony’s Canossian Secondary School	Government-aided, Autonomous		Bedok
St. Gabriel’s Secondary School	Government-aided		Serangoon
St. Hilda’s Secondary School	Government-aided, Autonomous		Tampines
St. Margaret’s Secondary School	Government-aided, Autonomous		Bukit Timah
St. Joseph’s Institution	Independent		Novena
Swiss Cottage Secondary School	Government		Bukit Batok
Tampines Secondary School	Government		Tampines
Tanglin Secondary School	Government		Clementi
Tanjong Katong Girls’ School	Government, Autonomous		Marine Parade
Tanjong Katong Secondary School	Government, Autonomous		Marine Parade
Teck Whye Secondary School	Government		Chua Chu Kang
Temasek Academy	Government, IP			Affiliated to Temasek Junior College
Temasek Secondary School	Government, Autonomous		Bedok
Unity Secondary School	Government		Chua Chu Kang
Victoria Junior College	Government, IP
Victoria School	Government, Autonomous
West Spring Secondary School	Government		Bukit Panjang
Westwood Secondary School	Government		Jurong West
Whitley Secondary School	Government		Bishan
Woodgrove Secondary School	Government		Woodlands
Woodlands Ring Secondary School	Government		Woodlands
Woodlands Secondary School	Government		Woodlands
Xinmin Secondary School	Government, Autonomous		Hougang
Yio Chu Kang Secondary School	Government		Ang Mo Kio
Yishun Secondary School	Government		Yishun
Yishun Town Secondary School	Government, Autonomous		Yishun
Yuan Ching Secondary School	Government		Jurong West
Yuhua Secondary School	Government		Jurong West
Yusof Ishak Secondary School	Government		Bukit Batok
Yuying Secondary School	Government-aided		Hougang
Zhenghua Secondary School	Government		Bukit Panjang
Zhonghua Secondary School	Government, Autonomous		Serangoon

St Gabriel’s Secondary School Mathematics Syllabus

Source: https://sites.google.com/a/moe.edu.sg/st-gabriel-s-secondary-school-maths-dept/syllabuses

For more information on the various Mathematics syllabuses, please click on the links provided at

https://sites.google.com/a/moe.edu.sg/st-gabriel-s-secondary-school-maths-dept/syllabuses

Bukit Panjang 2010 P1 Q3a Logarithm Question Solution (A Maths Tuition)

Question:
Solve the following equation:

(a) $5^{2x}-7^x-35(5^{2x})+36(7^x)=0$

Solution:

$-34(5^{2x})+35(7^x)=0$

$35(7^x)=34(5^{2x})$

Ln both sides, we get

$\ln 35 + x\ln 7=\ln 34+2x\ln 5$

$\ln 35-\ln 34=x(2\ln 5-\ln 7)$

$\displaystyle \boxed{x=\frac{\ln 35-\ln 34}{2\ln 5-\ln 7}=0.0228}$

Tangent Secant Theorem (A Maths Tuition)

Nice Proof of Tangent Secant Theorem:

http://www.proofwiki.org/wiki/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)