How to choose a toilet using Mathematics

We have seen how to cut a cake using the mathematical way, but did you know Mathematics can also be used when choosing toilets?

Here’s how:


Featured book:

Common Core Math 4 Today, Grade 4: Daily Skill Practice (Common Core 4 Today)

Build a foundation and focus on what matters most for math readiness with Common Core Math 4 Today: Daily Skill Practice for fourth grade. This 96-page comprehensive supplement contains standards-aligned reproducible activities designed to focus on critical math skills and concepts that meet the Common Core State Standards. Each page includes 16 problems to be completed during a four-day period. The exercises are arranged in a continuous spiral so that concepts are repeated weekly. An assessment for the fifth day is provided for evaluating students’ understanding of the math concepts practiced throughout the week. Also included are a Common Core State Standards alignment matrix and an answer key.

Recommended Maths Tuition Singapore

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

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

O Level 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

Cost of education in Singapore

Source: http://www.epigami.sg/blog/cost-of-education-in-singapore/

How much does it cost to educate a child in Singapore?

Answer: $80,940 or approximately 3 Round-the-World Trips!

Read more at: http://www.epigami.sg/blog/cost-of-education-in-singapore/

Release of O Level Results 2014

Sincerely wishing every student all the best for their O Level Results!

Meanwhile, all Secondary 3 to 4 students should start studying hard for their O Levels. 🙂

It has been many years since the release of my O Level Results. Sincerely wish my students to do well and even surpass me in their O Level Results.

maths-tutor-o-level-cert
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.

O Level Maths Group Tuition at Bishan

Start Maths Revision Early for the Best Results!

O Level Group Tuition @ Bishan starting in 2014!

Maths is a subject that requires students to start revision / practice early!

It needs consistent practice and last minute studying is not going to work well!

Many students have the wrong concept that they can start practising questions one or two months before the O Levels. The problem is, without constant practice, the questions from the Ten Year Series would be too difficult for students to even begin attempting the questions! This is especially true for Additional Mathematics. This leads to panic and is not the desired study strategy. This is the main reason why it is possible to score very low (less than 20 marks out of 100) in Maths, if the student does not have solid foundation or has lack of practice. To avoid this scenario, start practicing and revising Maths now! Many students already start studying / learning in advance during the December holidays. January is still a good time to start! As the Chinese proverb states: “一年之计在于春一日之计在于晨”, the best time to begin planning for a task is in Spring.

Also, the current O Level Maths is not like the O Level of the past! Due to higher education standards nowadays, and competition from foreigners (especially China students whose pet subjects are Maths and Chinese), the bell curve for E Maths has shifted very very high. Rumours have it that 90 marks is necessary for a guaranteed A1 in E Maths.

On the bright side, it is very possible to improve in Maths with practice. Look at the Mathematics questions in O Levels, one long question is around 10 marks. Answering that one question correctly will already boost your score by 10 marks. (2 grades). Answering two long questions correctly will boost score by a whopping 20 marks!

Hesitate no longer! Start revising for your Maths now!

O Level Group Tuition @ Bishan starting in 2014!

Bishan-Ang Mo Kio area to get new JC in 2017

Source: http://news.asiaone.com/news/edvantage/bishan-ang-mo-kio-area-get-new-jc-2017

Bishan-Ang Mo Kio area to get new JC in 2017

The site for the new JC at the junction of Sin Ming Avenue and Marymount Road.
Lee Jian Xuan

Saturday, Jan 04, 2014

SINGAPORE – A new junior college that will open in 2017 for students from three Integrated Programme (IP) schools will likely be built on the site of the Asian Golf Academy near Bishan.

A statement on the Ministry of Education (MOE) website says the new campus will be at the junction of Sin Ming Avenue and Marymount Road, where the driving range is located.

The area is also zoned for an educational institution, according to the Urban Redevelopment Authority’s Draft Master Plan 2013.

Singapore’s 20th school to offer a JC programme will take in IP students from Catholic High School, CHIJ St Nicholas Girls’ School and the Singapore Chinese Girls’ School. It will also admit more than 100 students from other secondary schools who have completed their O levels.

It will be the newest JC since Innova JC in Woodlands was completed in 2005.

Read more at: http://news.asiaone.com/news/edvantage/bishan-ang-mo-kio-area-get-new-jc-2017

Maths Group Tuition starting in 2014!

https://mathtuition88.com/

Maths Group Tuition starting in 2014!

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

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

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

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

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).
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.)

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

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

Maths Challenge

Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty):

maths challenge

Source: Anderson E Maths Prelim 2011

If you have solved the problem, please email your solution to mathtuition88@gmail.com .

(Include your name and school if you wish to be listed in the hall of fame below.)

Students who answer correctly (with workings) will be listed in the hall of fame. 🙂

Hall of Fame (Correct Solutions):

1) Ex Moe Sec Sch Maths teacher Mr Paul Siew

2) Queenstown Secondary School, Maths teacher Mr Desmond Tay

3) Tay Yong Qiang (Waiting to enter University)

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

Source: http://sgforums.com/forums/2297/topics/439605

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

Source: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=40&t=12228

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’

Math is at the heart of physics. (O Level Maths and Physics Tips)

Source: http://www.academictips.org/acad/physic/physics_study_skills.html

Studying and practising Mathematics is one of the most useful things an O level student can do.

Not only are the two Maths (E Maths and A Maths) highly intertwined, studying Maths can actually help the students’ Physics too. There are some topics like Vectors and Kinematics in Physics that are also present in Mathematics.

Math is at the heart of physics. So the better your math, the better you’ll do in physics.

A good working knowledge of algebra and trigonometry is needed for Physics.

Mnemosyne with a mathematical formula.
Mnemosyne with a mathematical formula. (Photo credit: Wikipedia)

Mathematics is not a spectator sport (How to study Maths for Humanities students)

Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.

I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.

One of the top mathematical physicists, Edward Witten, majored in history and minored in linguistics! (http://en.wikipedia.org/wiki/Edward_Witten)

Mathematics is not a spectator sport

Source: http://www.math.umn.edu/~rogness/math1001/syllabus/node20.html

Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics.  Sometimes this means doing even more than the assigned problems.  (See “time committment” above.)  This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.

I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself.  But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.

Small Group Maths Tuition at Bishan (O Level E Maths and A Maths)

Maths Tuition @ Bishan by Patient Tutor, NUS 1st Class Honours,

Ex-RI (GEP)


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

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

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

*Small Group Maths Tuition available in 2014 —

Registration/enquiries open now*

Website: https://mathtuition88.com/

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

Subjects for tuition:
•O level (Secondary): E Maths, A Maths

Tutor is patient, experienced and qualified. (from Raffles

Institution (GEP), NUS Mathematics Dean’s List)

Please email us at mathtuition88@gmail.com for more details.

Website: https://mathtuition88.com/

About Tutor: https://mathtuition88.com/singapore-math-tutor/
Fees & Schedule: https://mathtuition88.com/singapore-math-tuition-fees-schedule/
Contact Us: https://mathtuition88.com/singapore-math-tuition-contact-us/
https://mathtuition88.com/2013/05/21/free-exam-papers/
https://mathtuition88.com/2013/07/19/maths-tuition-centre/
https://mathtuition88.com/category/maths-tuition/
https://mathtuition88.com/tag/maths-tuition/
http://mathtuition88.blogspot.sg/

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

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

Why are China students so good at Math & Sciences?

Source: http://sgforums.com/forums/8/topics/475066

Quote:

I’m sure many secondary school/Junior College students have know some China scholars in your schools scoring results that are seemingly impossible to reach (90+ for H2 Maths etc.) But when asked what’s their secret to scoring so well, they said they just study & memorize the same way any other student would do before exams. 

I heard from my seniors that China scholars usually study till 2 am every night, but I don’t buy into that. I think they’re just exaggerated rumors to explain their excellent grades. Some of my friends say that China’s education gave them really solid foundation, such that they can grasp concepts much faster than the rest.  

Anybody know their secret to doing so well?

Read more at http://sgforums.com/forums/8/topics/475066

It seems like the secret of the China scholars is “practice makes perfect”!

http://ideas.time.com/2013/08/20/dont-just-practice-over-practice/

The Time magazine even recommends Over-Practicing (http://ideas.time.com/2013/08/20/dont-just-practice-over-practice/)

Over-Practicing Makes Perfect

The brain can get by on less energy when you overlearn a task
Read more: Over-Practicing Makes Perfect | TIME.com http://ideas.time.com/2013/08/20/dont-just-practice-over-practice/#ixzz2mQyatOKF

The Simpsons and Their Mathematical Secrets

Science Book a Day

the-simpsons-and-their-mathematical-secrets
By Simon Singh

Synopsis: Some have seen philosophy embedded in episodes of The Simpsons; others have detected elements of psychology and religion. Simon Singh, bestselling author of Fermat’s Last Theorem, The Code Book and The Big Bang, instead makes the compelling case that what The Simpsons’ writers are most passionate about is mathematics. He reveals how the writers have drip-fed morsels of number theory into the series over the last twenty-five years; indeed, there are so many mathematical references in The Simpsons, and in its sister program, Futurama, that they could form the basis of an entire university course. Using specific episodes as jumping off points – from ‘Bart the Genius’ to ‘Treehouse of Horror VI’ – Simon Singh brings to life the most intriguing and meaningful mathematical concepts, ranging from pi and the paradox of infinity to the origins of numbers and the most profound outstanding problems that haunt…

View original post 126 more words

Mr Heng, however, noted that how well a child does in school depends on how motivated he is.

Source: http://www.channelnewsasia.com/news/singapore/parents-urged-to-consider/898332.html

Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.

          Minister for Education Heng Swee Keat (Photo: MOE)

SINGAPORE: Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.

Writing on his Facebook page, Mr Heng said it would be good for parents to have an open talk with their children to know what type of secondary school they are interested in.

Mr Heng, however, noted that how well a child does in school depends on how motivated he is.

So he encourages parents to carefully consider the kind of environment that will best motivate their children, and enable them to develop themselves fully in the next four to five years.

Some children, he said, are late developers and the right environment helps them thrive.

Mr Heng urged parents to think of how best they can help their children develop confidence and enjoy the space to discover his talents and passions.

Continue reading at http://www.channelnewsasia.com/news/singapore/parents-urged-to-consider/898332.html

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

https://mathtuition88.com/

Maths Group Tuition starting in 2014!

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

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

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

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

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). 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.)

Recommended Maths Olympiad Books for Self Learning / Domain Test

Math Olympiad Books are useful for GEP/DSA preparation. It is also useful for the latest type of test called Domain Tests, which is basically a subject test (Math included) for entry into top secondary schools like the Raffles / Hwa Chong family. There are different subject domains (depending on the school), ranging from General domain / Academic domain / CCA domain.

A First Step to Mathematical Olympiad Problems (Mathematical Olympiad Series)

The Art of Problem Solving, Vol. 1: The Basics

The first book is written by Professor Derek Holton. Prof Holton writes a nice column for a Math magazine, which gives out books as prizes to correct solutions.

GEP Math Olympiad Books

If you are searching for GEP Math Olympiad Books to prepare for the GEP Selection Test, you may search for Math Olympiad Books for Elementary School. Note that Math Olympiad Books for IMO (International Mathematics Olympiad) are too difficult even for a gifted 9 year old kid!

A suitable book would be The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions.

Other Suitable Math Olympiad Books for GEP

These are some books that are very popular and highly rated on Amazon.


Challenging Problems in Algebra (Dover Books on Mathematics)

Challenging Problems in Geometry (Dover Books on Mathematics)
Math Circles for Elementary School Students: Berkeley 2009 and Manhattan 2011 (MSRI Mathematical Circles Library)

My Best Mathematical and Logic Puzzles (Dover Recreational Math)
The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics)

The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics)

Secondary 4 O Level E Maths and A Maths @ Bishan

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

 

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

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).

Asia-Pacific higher education is becoming a global force: Confucian Zone of Education

Source: http://www.timeshighereducation.co.uk/411726.article

Asia-Pacific higher education is becoming a global force, but only some nations in the region have achieved or approached parity with Western Europe and North America.

The truly spectacular success story is from the Confucian zone in East Asia. Japan achieved high participation rates and research-intensive universities in the 1970s: now Hong Kong, Singapore, South Korea, Taiwan and China are following suit. Student numbers and research are growing by leaps and bounds.

East Asia embodies a new Confucian model of higher education. The key is the willingness of families to invest in schooling, tertiary education and extra tuition. Households are driving the growth in participation. Private investment is secured less by neoliberal ideology than an older Confucian respect for self-formation via education, within a social hierarchy “harmonised” by fierce competition for university entry.

China and Singapore maintain higher public funding. But the jury is still out on the extent to which these systems can foster a spirit of openness, criticism and free-wheeling creativity.

Continue reading at http://www.timeshighereducation.co.uk/411726.article

O Level Maths Tuition Flyer

O Level Group Tuition Flyer
O Level E Maths & A Maths
Tuition at Bishan
碧山数学补习
Location: Block 230 Bishan Street 23 #B1-35 S(570230)
Schedule:
• Monday 7pm-9pm (E Maths)
• Thursday 7pm-9pm (A Maths)
Website: https://mathtuition88.com/group-tuition/
Tutor: Mr Wu
(from RI GEP, NUS Maths 1st Class Honours, Dean’s List)
Class size is limited to 8 students only! (Small Group Tuition)

Study Tips from MIT

Source: http://web.mit.edu/uaap/learning/study/breaks.html

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.

O Level E Maths and A Maths Tuition @ Bishan by Patient Tutor, NUS 1st Class Honours, Ex-RI (GEP)

Maths Tuition @ Bishan by Patient Tutor, NUS 1st Class Honours, Ex-RI (GEP)
——————————————————————————–
https://mathtuition88.com/group-tuition/

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

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

*Small Group Maths Tuition available in 2014 — Registration/enquiries open now*

Website: https://mathtuition88.com/

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

Subjects for tuition:
•O level (Secondary): E Maths, A Maths

Tutor is patient, experienced and qualified. (from Raffles Institution (GEP), NUS Mathematics Dean’s List)

Please email us at mathtuition88@gmail.com for more details.

Website: https://mathtuition88.com/

About Tutor: https://mathtuition88.com/singapore-math-tutor/
Fees & Schedule: https://mathtuition88.com/singapore-math-tuition-fees-schedule/
Contact Us: https://mathtuition88.com/singapore-math-tuition-contact-us/
https://mathtuition88.com/2013/05/21/free-exam-papers/
https://mathtuition88.com/2013/07/19/maths-tuition-centre/
https://mathtuition88.com/category/maths-tuition/
https://mathtuition88.com/tag/maths-tuition/

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.

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

Dansk: Dedikeret til matematik

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.

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 10th and 90th percentiles of A-Level Applicants offered places for courses at NUS in Academic Year 2012-20132

NUS Courses

Representative Grade Profile 3H2/1H1

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.

2 Double degrees are excluded from the table.

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.

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

Puzzles to Puzzle You

Maths Skills to be a Doctor

Doctor and Lawyer are the top two favourite careers in Singapore. Do doctors need to use Maths? Read the below to find out.

Even if Maths is not directly needed, the logical thinking skills learnt in Mathematics will definitely be of great use. 🙂

I am not a medical doctor, but my two younger siblings are medical students, and the Mathematical knowledge and thinking skills have definitely helped them in their medical studies.

Source: http://www.rossu.edu/medical-school/students/Mathematics-in-Medicine-.cfm

Functional numeracy is as essential to an aspiring medical professional as functional literacy. As a physician, perhaps the most important mathematical skills you will need are:

1. Basic mathematical knowledge sufficient to calculate drug doses, concentrations, etc.

2. An understanding of the core statistical concepts most commonly represented in the medical literature.

3. Knowledge of algebra to understand calculations of acid–base status, etc.

4. Ability to appreciate whether or not results are mathematically plausible.    (Nusbaum, 2006)

The careful logical reasoning that is necessary for the study of mathematics is an essential element of clinical reasoning. Although you do not need higher mathematics to get through medical school, you will need the ability to manipulate numbers, including fractions, ratios, powers of 10 and logarithms. You will also need a basic understanding of probability, graphs and simple algebra. You will need to rearrange equations and convert between units of measure.

 

Source: http://everydaylife.globalpost.com/kind-math-work-doctor-know-26082.html

It’s often unclear from your interactions with a doctor how much math she is using in order to treat you. While not all doctors have to use math as directly and frequently as engineers do, all of them must understand the complex mathematical equations that inform different medical treatments in order to administer treatments correctly.

Dosages and Half-Life

One of the most common ways in which doctors use mathematics is in the determination of medicine prescriptions and dosages. Doctors not only have to use basic arithmetic to calculate what dosage of a particular drug will be effective for your height and body type over a specific period of time, they will also have to be aware of the medicine’s cycle through the body and how the dosage of one drug compares with the dosage of a similar type of drug. Sometimes doctors have to use calculus to figure out the right dosage of a drug. Calculus is the study of how changing variables affect a system. In the human body, the kidney processes medicine. However, people’s kidneys are at varying levels of health. Doctors can designate the kidney as a changing function in a calculus equation known as the Cockroft-Gault equation. This equation uses the level of creatine in a patient’s blood to find the level of the kidney’s functioning, which allows the doctor to determine the appropriate dose.

Cancer Treatment

When a doctor administers radiation therapy to a cancer patient, the radiation beams have to cross each other at specific angles, so that they harm the cancerous tumor without harming the surrounding healthy tissue. The precise numbers for these angles must be calculated mathematically. Cancer tends to respond to any drug by mutating so that its DNA is no longer affected by that drug. Oncologists and medical scientists have decided to target cancerous tumors with many different kinds of drugs at once so that the cancer is unable to respond adequately. They use complex mathematical models that plot the speed and timing of the cancer’s different mutations to figure out what combinations and dosages of different drugs should be used.

Medical Images and Tests

Doctors in medical imaging use two-dimensional images of a patient’s body taken from thousands of angles to create a three-dimensional image for analysis. Determining what angles should be used and how they will fit together requires mathematics. Medical researchers who study disease will analyze the mathematical dimensions of these images. Neurologists who run EEGs on patients to measure their brain waves must add and subtract different voltages and use Fourier transforms to filter out signal static. Fourier transforms are used to alter functions in calculus.

Treatment Research

Medical scientists working with cardiologists use differential equations to describe blood flow dynamics. They also build sophisticated computer models to find the ideal size of an artificial aorta and where to place it in an infant pending a heart transplant. Doctors have to read medical journals to keep up on the latest scientific findings for the benefit of their patients. In addition to describing the calculus used to model health conditions, medical journal studies also make heavy use of statistics and probability to describe the health conditions of whole populations and the likelihood that different treatments will be effective.

Maths Skills to be a Good Lawyer

Doctor and Lawyer are the top two favourite careers in Singapore. On the surface, Lawyers seem not to need much maths, but recent research shows that Mathematics skills and thinking may be crucial to becoming a better Lawyer.

Source: http://news.illinois.edu/news/13/0403numeracy_ArdenRowell.html

There is a “highly significant relationship” between law students’ math skills and the substance of their legal analysis, according to research from Arden Rowell, a professor of law and the Richard W. and Marie L. Corman Scholar at Illinois.

CHAMPAIGN, Ill. — The stereotype of lawyers being bad with numbers may persist, but new research by two University of Illinois legal scholars suggests that law students are surprisingly good at math, although those with low levels of numeracy analyze some legal questions differently.

According to research from Arden Rowell and Jessica Bregant, there is a   “highly significant relationship” between law students’ math skills and the substance of their legal analysis, suggesting that legal analysis – and by extension, legal advice – may vary with a lawyer’s native math skills.

What the research shows is that math matters to lawyers more – and for different reasons – than people have realized,” said Rowell, a professor of law and the Richard W. and Marie L. Corman Scholar at Illinois. “People are only now starting to pay attention to the fact that lawyers and judges who are bad at math can make mistakes that ruin people’s lives. That implicates numeracy as a neglected but potentially critical aspect of legal education, because it’s not something that law schools have traditionally focused on when selecting students.”

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

O Level Maths Group Tuition

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

https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

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

Mathematics homework

E Maths Group Tuition Centre; Clementi Town Secondary School Prelim 2012 Solution

Travel-boat-malta
Travel-boat-malta (Photo credit: Wikipedia)

Q5) The speed of a boat in still water is 60 km/h.

On a particular day, the speed of the current is x km/h.

(a) Find an expression for the speed of the boat

(I) against the current, [1]

Against the current, the boat would travel slower! This is related to the Chinese proverb, 逆水行舟,不进则退, which means “Like a boat sailing against the current, we must forge ahead or be swept downstream.”

Hence, the speed of the boat is 60-x km/h.

(ii) with the current. [1]

60+x km/h

(b) Find an expression for the time required to travel a distance of 80km

(I) against the current,  [1]

Recall that \displaystyle \text{Time}=\frac{\text{Distance}}{\text{Speed}}

Hence, the time required is \displaystyle \frac{80}{60-x} h

(ii) with the current. [1]

\displaystyle \frac{80}{60+x} h

(c) If the boat takes 20 minutes longer to travel against the current than it takes to travel with the current, write down an equation in x and show that it can be expressed as x^2+480x-3600=0   [2]

Note: We must change 20 minutes into 1/3 hours!

\frac{80}{60-x}=\frac{1}{3}+\frac{80}{60+x}

There are many ways to proceed from here, one way is to change the Right Hand Side into common denominator, and then cross-multiply.

\displaystyle \frac{80}{60-x}=\frac{60+x}{3(60+x)}+\frac{240}{3(60+x)}=\frac{300+x}{3(60+x)}

Cross-multiply,

240(60+x)=(300+x)(60-x)

14400+240x=18000-300x+60x-x^2

x^2+480x-3600=0 (shown)

(d) Solve this equation, giving your answers correct to 2 decimal places. [2]

Using the quadratic formula,

\displaystyle x=\frac{-480\pm\sqrt{480^2-4(1)(-3600)}}{2}=7.386 \text{ or } -487.386

Answer to 2 d.p. is x=7.39 \text{ or } -487.39

(e) Hence, find the time taken, in hours, by the boat to complete a journey of 500 km against the current. [2]

Now we know that the speed of the current is 7.386 km/h.

Hence, the time taken is \frac{500}{60-7.386}=9.50 h

Maths Group Tuition at Bishan 2014

Maths Group Tuition starting in 2014!

Secondary to JC Classes for Maths Group Tuition starting in 2014!

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

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

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).

Mobius Strip

Ad: Maths Group Tuition 2014

Source: http://www.youtube.com/watch?v=BVsIAa2XNKc

Source: http://en.wikipedia.org/wiki/M%C3%B6bius_strip

The Mobius Strip is a really interesting mathematical surface with just one side. It is easy to make, and cutting it produces many surprising effects! 🙂

The Möbius strip or Möbius band (UK /ˈmɜrbiəs/ or US /ˈmbiəs/; German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.[1][2][3]

A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. In Euclidean space there are two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. That is to say, it is a chiral object with “handedness” (right-handed or left-handed).

The Möbius band (equally known as the Möbius strip) is not a surface of only one geometry (i.e., of only one exact size and shape), such as the half-twisted paper strip depicted in the illustration to the right. Rather, mathematicians refer to the (closed) Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any closed rectangle with length L and width W can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in 3-dimensional space, and others cannot (see section Fattest rectangular Möbius strip in 3-space below). Yet another example is the complete open Möbius band (see section Open Möbius band below). Topologically, this is slightly different from the more usual — closed — Möbius band, in that any open Möbius band has no boundary.

It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.[4]

The Euler characteristic of the Möbius strip is zero.

Understanding the Birthday Paradox

Source: http://betterexplained.com/articles/understanding-the-birthday-paradox/

23 people. In a room of just 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching.

Put down the calculator and pitchfork, I don’t speak heresy. The birthday paradox is strange, counter-intuitive, and completely true. It’s only a “paradox” because our brains can’t handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenarios we’re involved in (both faulty assumptions, by the way).

Let’s see why the paradox happens and how it works.

Continue reading at http://betterexplained.com/articles/understanding-the-birthday-paradox/

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%

Prime Minister Lee Hsien Loong Truly Outstanding Mathematics Student

Just to share an inspirational story about studying Mathematics, and our very own Prime Minister Lee Hsien Loong. 🙂

Source: http://www2.ims.nus.edu.sg/imprints/interviews/BelaBollobas.pdf

(page 8/8)

Interview of Professor Béla Bollobás, Professor and teacher of our Prime Minister Lee Hsien Loong

I: Interviewer Y.K. Leong

B: Professor Béla Bollobás

I: I understand that you have taught our present Prime
Minister Lee Hsien Loong.

B: I certainly taught him more than anybody else in
Cambridge. I can truthfully say that he was an exceptionally
good student. I’m not sure that this is really known in
Singapore. “Because he’s now the Prime Minister,” people
may say, “oh, you would say he was good.” No, he was truly
outstanding: he was head and shoulders above the rest of
the students. He was not only the first, but the gap between
him and the man who came second was huge.

I: I believe he did double honors in mathematics and computer science.

B: I think that he did computer science (after mathematics) mostly because his father didn’t want him to stay in pure mathematics. Loong was not only hardworking, conscientious and professional, but he was also very inventive. All the signs indicated that he would have been a world-class research mathematician. I’m sure his father never realized how exceptional Loong was. He thought Loong was very good. No, Loong was much better than that. When I tried to tell Lee Kuan Yew, “Look, your son is phenomenally good: you should encourage him to do mathematics,” then he implied that that was impossible, since as a top-flight professional mathematician Loong would leave Singapore for Princeton, Harvard or Cambridge, and that would send the wrong signal to the people in Singapore. And I have to agree that this was a very good point indeed. Now I am even more impressed by Lee Hsien Loong than I was all those years ago, and I am very proud that I taught him; he seems to be doing very well. I have come round to thinking that it was indeed good for him to go into politics; he can certainly make an awful lot of difference.

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