## Thursday, 10 December 2015

## Tuesday, 24 March 2015

### Calculate UAS Points

# Calculate UAS Points / JC Ranking Points

# How to Calculate JC Ranking Points?

Check out this JC Ranking Points site to double check your calculations and to learn how the JC Ranking Points for University admission is calculated!Site: http://mathtuition88.com/2014/03/10/calculate-ranking-points-jc/

# Math Notes bundled with Free Exam Papers

Also check out our Highly Condensed Math Notes bundled with Free Exam Papers for practice! E Maths / A Maths / H2 Maths Notes available.Site: http://mathtuition88.com/math-notes-worksheets-sale/

## Sunday, 15 February 2015

### How to get First Class Honours or Summa Cum Laude

Recently I graduated with First Class Honours (Mathematics) and I would like to share some tips on how to achieve it!

Disclaimer: This post is not to boast about my achievements, but rather to teach other university undergraduates some strategies to achieve their goal. Getting First Class Honours (or Summa Cum Laude) is merely a humble and small achievement to be honest, but for many students it would be a very helpful thing to have for their future career or further studies. Hence, I sincerely hope this post will give some idea how to achieve the goal of getting First Class Honors. Students aiming for the very respectable grade classification of Second Upper Honours (or magna cum laude) would also definitely find this post useful.

Students who wish to read more about how to find your ideal college or university may want to read this excellent book The College Solution: A Guide for Everyone Looking for the Right School at the Right Price (2nd Edition). Also useful is 1001 Things Every College Student Needs to Know: (Like Buying Your Books Before Exams Start).

There is a joke that most university students only have time to choose two out of the following: Good Grades, Social Life, and Enough Sleep.

There is a time management life hack that I personally use and find it very useful. It is called the Pomodoro Technique. This technique can allow the busy college students to achieve some studying in bursts of 30 minutes, which is proven to be the optimal attention span of an average human! The Pomodoro Method is basically about studying / working for 25 minutes, and then taking a short break of around 5 minutes. Every four cycles, take a longer break (e.g. 15-30 minutes). This allows students to break a huge task into smaller and more manageable chunks of 30 minutes. Pomodoro Technique Illustrated (Pragmatic Life) has more details on this amazing time management technique.

Another important time management technique is what to do during long commutes on the train or bus. I live in one of the smallest countries in the world (Singapore), but my daily commute to the university could be as long as 2 hours (to and fro). Reading some notes or books during the traveling time could be really productive over the long term. If you prefer reading ebooks, you could consider the Amazon Kindle Paperwhite with Special Offers, Wi-Fi, Black which is one of the best ebook readers out there.

Another tip for those suffering from sinus or nose problems is to try nasal irrigation or sinus rinse. It took me almost 10 years to discover this. I was suffering badly from sneezing and sinus problems almost monthly. After using this NeilMed Sinus Rinse - 2 Bottles - 250 Premixed Packets I am 95% free from my previous sinus issues which were quite bad. I have been recommending this to almost everyone that I know who has sinus issues.

If your university has an option for an overseas exchange, do check it out. Sometimes modules taken on an overseas exchange are do not count for your GPA, and hence has an effect of preserving your grades. For example, if your GPA is currently enough to get a summa cum laude provided you maintain your score, going on an overseas exchange programme would freeze your GPA or CAP. Also, overseas exchange modules are notoriously easy to pass. Hence, if you pass all your exchange programme modules, you have effectively maintained your summa cum laude or First Class Honours grade at zero risk.

Another strategy is to go for easier modules to increase your GPA or CAP, effectively pulling them up. By now you would know that not all courses are graded equally, and some courses require much less effort but hand out As more liberally. However, please take note that this should not be the main objective of your studies at college, since taking courses like the proverbial "underwater basket weaving" courses do not improve your knowledge in any way! Hence, this technique should be used only sparingly.

Disclaimer: This post is not to boast about my achievements, but rather to teach other university undergraduates some strategies to achieve their goal. Getting First Class Honours (or Summa Cum Laude) is merely a humble and small achievement to be honest, but for many students it would be a very helpful thing to have for their future career or further studies. Hence, I sincerely hope this post will give some idea how to achieve the goal of getting First Class Honors. Students aiming for the very respectable grade classification of Second Upper Honours (or magna cum laude) would also definitely find this post useful.

Students who wish to read more about how to find your ideal college or university may want to read this excellent book The College Solution: A Guide for Everyone Looking for the Right School at the Right Price (2nd Edition). Also useful is 1001 Things Every College Student Needs to Know: (Like Buying Your Books Before Exams Start).

### What is First Class Honours?

Majority of students at the undergraduate level would have heard of the term 1st Class Honours, but some may be unsure of what it means. First Class Honours is a terminology traditionally used in British universities or universities based on the UK system. It represents one of the highest achievements attainable in terms of academics for undergraduates. Usually students would have to achieve a certain GPA (Grade Point Average) and also satisfy certain additional requirements such as getting a certain grade for the final honours thesis. The term Summa Cum Laude (latin for "with highest honors") is usually used in American universities instead, but it is basically the same thing. For the university I graduated from, the National University of Singapore (NUS), students need to get a CAP (Cumulative Average Point) of at least 4.5/5, in addition to at least an A- for the final year project (this requirement has since been scrapped).### Is it Difficult to get Summa Cum Laude

Most schools will try to prevent grade inflation by controlling the number of students who get First Class Honours. This may be done through bell curving grades for individual modules. Hence, the percentage of students who get Summa Cum Laude may be kept low, though this percentage can vary from university to university. Hence, getting First Class Honours takes planning and strategy as it may be challenging to attain.### How to get Summa Cum Laude/Magna Cum Laude

Congratulations for finding this website, as I will endeavor to share with you all the tips for getting the First Class Honours or Summa Cum Laude. Ideally, the earlier you start planning and making your strategy, the better. Since Summa Cum Laude depends on your GPA (Grade Point Average), every year matters. Many students start planning too late, and even though their grade improves their earlier GPA drags their overall grades down, making getting the Summa Cum Laude difficult or even impossible.### Study Consistently and Revise Constantly

This first tip may seem like a cliche or no-brainer, but essentially it is the key to achieving your Summa Cum Laude. Never leave your revision to the last minute. Do tutorials on time even though you may not be required to hand in them. Clarify doubts as soon as possible to prevent them from piling up. Check out this book Study Strategies Made Easy: A Practical Plan for School Success for some study strategies that are both practical and concrete.### Time Management

For most people, time is really tight in college. 24 hours a day is barely enough to all the things that a college major is supposed to do.There is a joke that most university students only have time to choose two out of the following: Good Grades, Social Life, and Enough Sleep.

There is a time management life hack that I personally use and find it very useful. It is called the Pomodoro Technique. This technique can allow the busy college students to achieve some studying in bursts of 30 minutes, which is proven to be the optimal attention span of an average human! The Pomodoro Method is basically about studying / working for 25 minutes, and then taking a short break of around 5 minutes. Every four cycles, take a longer break (e.g. 15-30 minutes). This allows students to break a huge task into smaller and more manageable chunks of 30 minutes. Pomodoro Technique Illustrated (Pragmatic Life) has more details on this amazing time management technique.

Another important time management technique is what to do during long commutes on the train or bus. I live in one of the smallest countries in the world (Singapore), but my daily commute to the university could be as long as 2 hours (to and fro). Reading some notes or books during the traveling time could be really productive over the long term. If you prefer reading ebooks, you could consider the Amazon Kindle Paperwhite with Special Offers, Wi-Fi, Black which is one of the best ebook readers out there.

### Get Enough Sleep

Getting enough sleep is essential if you are aiming for a First Class Honours or Summa Cum Laude. Trying to cut down on sleep may lead to sleep deprivation which is not good. Sleep deprivation may lead to depression, weight gain, or even worse things like heart diseases. Most people need around 7 to 8 hours of sleep to function optimally. There are some people out there with special genes that make them need less sleep. Margaret Thatcher was one of the famous people who only needed 4 hours of sleep a night! Unfortunately, this gene is rare and most people don't have it. Personally, I am a long sleeper who needs 8 to 9 hours of sleep to function optimally. This is a major disadvantage, to be honest, when comparing with those people who can survive on 6 hours of sleep (or less!) However, I still managed to get Summa Cum Laude, and you can do it too! Remember, it is not worth it to sacrifice your health to get Summa Cum Laude or First Class Honours... One trick is to take power naps. Power naps as short as 5-8 minutes have been proven to be effective to raise alertness! I took power naps in the school library (the most comfortable place in school to sleep). It was a bit embarrassing at first, but many other people were also doing the same. :) I read this book Take a Nap! Change Your Life. and it gave me plenty of ideas of how to fit in power naps to get enough sleep, and also some interesting info on polyphasic sleeping and sleep cycles.### Health Issues

Health issues is incredibly important if you are aiming to get Summa Cum Laude or First Class Honours. First, mental health is very important to the student. Signs of depression and insomnia must be taken seriously and help be sought as soon as possible. Nutrition is also important, the brain consumes a massive amount of energy and we need to supply the brain cells with enough nutrition and vitamins. Personally, I drink this BRAND'S Essence of Chicken (6 x 2.3 fl oz.) which is a good alternative to caffeine. For me, coffee is only useful as a last resort, since I experience a caffeine slump after the effects of caffeine wear off.Another tip for those suffering from sinus or nose problems is to try nasal irrigation or sinus rinse. It took me almost 10 years to discover this. I was suffering badly from sneezing and sinus problems almost monthly. After using this NeilMed Sinus Rinse - 2 Bottles - 250 Premixed Packets I am 95% free from my previous sinus issues which were quite bad. I have been recommending this to almost everyone that I know who has sinus issues.

### Subject Specific Advice

Personally, I majored in Mathematics, and here I would like to give some advice to undergraduates majoring in math. The transition from high school math to undergraduate math is a big one. The most important difference being the idea of proofs. Undergraduate math is mostly about proving, and that is usually the hardest part. Also, finding a good Math textbook is incredibly important. I have listed a few of the very best Math textbooks at my website here.Also, while reading those Math books, be sure to try out some of the exercises as Math is all about practice rather than rote learning.### Seek help from Friends and Seniors

This is also a good tip that can be really helpful. Borrowing notes or previous test exams from friends and seniors who took the course a few semesters earlier can literally improve your grade by a huge amount. I had a good friend who lent me some notes and previous quizzes which he took the previous semester. Working through the test papers last semester was a major advantage for me, as I realized during the exam that the lecturer recycled some questions from the previous semester! The question, though slightly modified and different, were similar in style and format. Most students will agree that this is a huge and significant advantage, and may be the key to achieving your summa cum laude or first class honours. This technique really works because most of the time, professors are really busy people who don't really have time to set novel and new questions each semester. They will most often modify existing questions from the previous semester to generate new questions for the current semester.### Gaming the GPA System (Legally)

This section is about how to game the university or college system to achieve your GPA. Of course, this needs to be done legally, and depends on each university or college.If your university has an option for an overseas exchange, do check it out. Sometimes modules taken on an overseas exchange are do not count for your GPA, and hence has an effect of preserving your grades. For example, if your GPA is currently enough to get a summa cum laude provided you maintain your score, going on an overseas exchange programme would freeze your GPA or CAP. Also, overseas exchange modules are notoriously easy to pass. Hence, if you pass all your exchange programme modules, you have effectively maintained your summa cum laude or First Class Honours grade at zero risk.

Another strategy is to go for easier modules to increase your GPA or CAP, effectively pulling them up. By now you would know that not all courses are graded equally, and some courses require much less effort but hand out As more liberally. However, please take note that this should not be the main objective of your studies at college, since taking courses like the proverbial "underwater basket weaving" courses do not improve your knowledge in any way! Hence, this technique should be used only sparingly.

### The End

That's about all I have to share, hope it was helpful! Do post any comments below, especially if you have any other tips to share. Thanks and good luck!### The Math of Valentine's Day and Love

Valentine's Day is just over. Maths is really useful, watch this humorous video to learn how Math can help you find your true love!

## Sunday, 8 February 2015

### How to Flip a Coin to Land Heads Up

One good book by Professor Persi Diaconis is: Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks. A professional mathematician and also a magician, Persi Diaconis reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician.

## Saturday, 7 February 2015

### A Math comic that only Math majors will understand

This is really a comic that Math Majors will empathize with...

It is probably due to lazy textbook authors who leave almost everything as an exercise, and every other theorem is "trivial". Such a textbook is of very little pedagogical value.

On the other hand, an example of a good Math Textbook is Abstract Algebra, 3rd Edition by Dummit and Foote. It is one of the most widely acclaimed textbooks for Abstract Algebra, one of the most arcane and esoteric fields of Math. I have also written a book review on Topology by James R. Munkres, another excellent Math book.

## Thursday, 5 February 2015

### RI/RJC Free Prelim Math Full Solution

Let's go through how to solve this RI/RJC Prelim Vectors Question.

(i)

First, we can note that we can let $\mu=0$ and $\lambda=1$ for convenience since the vector equation holds for all values of $\lambda , \mu$. Then we have $\textbf{r}=\left( \begin{array}{c}6\\t\\2\end{array}\right)$. Putting this into the given equation in (i), we have $12+3t+2=5$, hence $t=-3$.

(ii) Let M be the midpoint of AB. Note that M will lie on the plane $\pi_1$! By the Midpoint Theorem,

$\vec{OM}=\frac{1}{2}[\vec{OA}+\vec{OB}]=\left( \begin{array}{c}4\\-6\\7+\frac{1}{2}s\end{array}\right)$.

Since M lies on the plane, $\vec{OM}\cdot \left(\begin{array}{c}2\\3\\1\end{array}\right)=5$. Expanding the dot product, we get $s=16$.

(iii) We need to show that the normals of the two planes are perpendicular.

$\mathbf{n_1}=\left( \begin{array}{c}2\\3\\1\end{array}\right)$ First we note that B also lies on $\pi_2$. We can obtain a normal of $\pi_2$ by taking the cross product $\mathbf{n_2}=\vec{AB}\times\left( \begin{array}{c}3\\-2\\0\end{array}\right)=\left( \begin{array}{c}4\\6\\-26\end{array}\right)$

We then calculate that $\mathbf{n_1}\cdot\mathbf{n_2}=0$. (shown)

If we draw a diagram, we can see that the shortest distance from A to the line of intersection is actually $|\vec{AM}|$, where M is the midpoint found earlier. $\vec{AM}=\vec{OM}-\vec{OA}=\left(\begin{array}{c}2\\3\\1\end{array}\right)$. Thus $|\vec{AM}|=\sqrt{2^2+3^2+1^2}=\sqrt{14}$.

(i)

First, we can note that we can let $\mu=0$ and $\lambda=1$ for convenience since the vector equation holds for all values of $\lambda , \mu$. Then we have $\textbf{r}=\left( \begin{array}{c}6\\t\\2\end{array}\right)$. Putting this into the given equation in (i), we have $12+3t+2=5$, hence $t=-3$.

(ii) Let M be the midpoint of AB. Note that M will lie on the plane $\pi_1$! By the Midpoint Theorem,

$\vec{OM}=\frac{1}{2}[\vec{OA}+\vec{OB}]=\left( \begin{array}{c}4\\-6\\7+\frac{1}{2}s\end{array}\right)$.

Since M lies on the plane, $\vec{OM}\cdot \left(\begin{array}{c}2\\3\\1\end{array}\right)=5$. Expanding the dot product, we get $s=16$.

(iii) We need to show that the normals of the two planes are perpendicular.

$\mathbf{n_1}=\left( \begin{array}{c}2\\3\\1\end{array}\right)$ First we note that B also lies on $\pi_2$. We can obtain a normal of $\pi_2$ by taking the cross product $\mathbf{n_2}=\vec{AB}\times\left( \begin{array}{c}3\\-2\\0\end{array}\right)=\left( \begin{array}{c}4\\6\\-26\end{array}\right)$

We then calculate that $\mathbf{n_1}\cdot\mathbf{n_2}=0$. (shown)

If we draw a diagram, we can see that the shortest distance from A to the line of intersection is actually $|\vec{AM}|$, where M is the midpoint found earlier. $\vec{AM}=\vec{OM}-\vec{OA}=\left(\begin{array}{c}2\\3\\1\end{array}\right)$. Thus $|\vec{AM}|=\sqrt{2^2+3^2+1^2}=\sqrt{14}$.

## Wednesday, 4 February 2015

### Graph Theory Olympiad Question!

January's Math Olympiad Question was on Graph Theory.

There are 2015 points in the space, no three of them are lying on the same line and no

four of them are lying on the same plane. Any pair of points is connected by a segment.

The k-coloring of these $2015 \choose 2$ segments is a coloring of each segment into one of the k

colors so that each color is used at least once. Find the minimal possible value of k for

which any k-coloring contains a triangle with differently colored edges.

Sounds interesting? Check out the Question and Solution at: http://www.fen.bilkent.edu.tr/~cvmath/Problem/problem.htm

How to learn more about Graph Theory? Graph Theory is usually taught in university Math / Applied Math courses. Computer Science courses will most probably learn some graph theory too. It is a highly interesting topic that is "elementary" in a sense that it does not use deep theorems, but some counting and combinatoric principles. However, the simplicity is deceptive and Graph Theory has some highly challenging problems. Do check out this book The Fascinating World of Graph Theory by some highly regarded authors like Gary Chartrand (expert in Graph Theory). The author Arthur Benjamin is known for being a very interesting author who also specializes in Mathematical Magic Tricks.

There are 2015 points in the space, no three of them are lying on the same line and no

four of them are lying on the same plane. Any pair of points is connected by a segment.

The k-coloring of these $2015 \choose 2$ segments is a coloring of each segment into one of the k

colors so that each color is used at least once. Find the minimal possible value of k for

which any k-coloring contains a triangle with differently colored edges.

Sounds interesting? Check out the Question and Solution at: http://www.fen.bilkent.edu.tr/~cvmath/Problem/problem.htm

How to learn more about Graph Theory? Graph Theory is usually taught in university Math / Applied Math courses. Computer Science courses will most probably learn some graph theory too. It is a highly interesting topic that is "elementary" in a sense that it does not use deep theorems, but some counting and combinatoric principles. However, the simplicity is deceptive and Graph Theory has some highly challenging problems. Do check out this book The Fascinating World of Graph Theory by some highly regarded authors like Gary Chartrand (expert in Graph Theory). The author Arthur Benjamin is known for being a very interesting author who also specializes in Mathematical Magic Tricks.

## Monday, 2 February 2015

### The Math of Rock, Paper, Scissors!

Who knew the simple game Rock, Paper, Scissors had mathematical implications, and could be found in nature!

Hannah Fry discusses the Math behind the ecological balance of lizards, which turns out to be a natural example of Rock, Paper, Scissors!

There is also a psychological and logical "strategy" of playing Rock, Paper, Scissors shown in the video below.

Hannah Fry discusses the Math behind the ecological balance of lizards, which turns out to be a natural example of Rock, Paper, Scissors!

There is also a psychological and logical "strategy" of playing Rock, Paper, Scissors shown in the video below.

Finally, who would have thought that there is actually a Rock, Paper, Scissors championship! The world champion is a guy called Bob "The Rock"!

Do check out this book Growing Patterns: Fibonacci Numbers in Nature based on another ubiquitous pattern in nature, the Fibonacci Numbers.

## Wednesday, 28 January 2015

### How to Install Mario Games on TI-84 Plus Graphic Calculator?

The TI-84 is a really powerful calculator, capable of graphing and complex calculations. Wait... There is more! It can even install games like Mario!

First, you will need a cable to connect your TI-84 (Plus Pocket SE is what most JC students use in Singapore) to the computer.

Now, to enter the game, click on Apps and select MirageOS. If everything goes well, you should enter MirageOS. Click Enter to search for Mario and you should enter the Mario Game for TI-84+. Press "2nd", which is equivalent to the "A" button on Gameboy, and you should be ready to start. Have fun!

To quit, press "clear" to reach MirageOS, then press "mode".

Note, the Mario game can be found under "prgm", but accessing it there does not work. It will give either "ERR: ARCHIVED" or "ERR: SYNTAX".

To delete Mario from your calculator, go to 2nd->mem->Mem Mgmt/Del. You may remove Mario from the calculator once you reach there.

Want to be a true master at the TI-84 Calculator? Check out this book Ti-84 Plus Graphing Calculator For Dummies! Get up-to-speed on the functionality of your TI-84 Plus calculator Completely revised to cover the latest updates to the TI-84 Plus calculators, this bestselling guide will help you become the most savvy TI-84 Plus user in the classroom!

First, you will need a cable to connect your TI-84 (Plus Pocket SE is what most JC students use in Singapore) to the computer.

### Steps to Install Mario on TI GC

- Go to http://tiwizard.com/downloads/mirage-os-1-2/ and install MirageOS. Once you download it, right-click send to TI Device. You may send it to Archive.
- Next, go to http://tiwizard.com/downloads/mario-2-0/ and install Mario 2.0, the engine for the Texas Instrument Mario Game. Similarly, once you download it, right-click and send to TI Device, under Archive.
- Finally, go to http://tiwizard.com/downloads/mario-2-0/ and install Super Mario Land Level Pack. There are eight levels in total.

Now, to enter the game, click on Apps and select MirageOS. If everything goes well, you should enter MirageOS. Click Enter to search for Mario and you should enter the Mario Game for TI-84+. Press "2nd", which is equivalent to the "A" button on Gameboy, and you should be ready to start. Have fun!

To quit, press "clear" to reach MirageOS, then press "mode".

Note, the Mario game can be found under "prgm", but accessing it there does not work. It will give either "ERR: ARCHIVED" or "ERR: SYNTAX".

To delete Mario from your calculator, go to 2nd->mem->Mem Mgmt/Del. You may remove Mario from the calculator once you reach there.

Want to be a true master at the TI-84 Calculator? Check out this book Ti-84 Plus Graphing Calculator For Dummies! Get up-to-speed on the functionality of your TI-84 Plus calculator Completely revised to cover the latest updates to the TI-84 Plus calculators, this bestselling guide will help you become the most savvy TI-84 Plus user in the classroom!

## Monday, 26 January 2015

### NUS Math Talk: Mathemusical Conversations: Mathematics and Computation in Music Performance and Composition (13 - 15 February 2015)

For those interested in the union of the two diverse subjects Mathematics and Music, do check out this symposium by NUS:

**Mathemusical Conversations**Organizing Committee |

*Original Protagonists*- Louis Chen (National University of Singapore)
- Bernard Lanskey (National University of Singapore)
- Bernard Tan (National University of Singapore)

*Program Chairs*- GÃ©rard Assayag (Institut de Recherche et Coordination Acoustique/Musique)
- Elaine Chew (Queen Mary University of London)

*Local Organizing Committee*- Jenny Ang (National University of Singapore)
- I-Shyan Tang (National University of Singapore)
- Rachel Tang (National University of Singapore)
- Craig de Wilde (National University of Singapore)

Overview |

Mathemusical Conversations is an international workshop bringing together world experts and emerging scholars in and across mathematics and music, with a special focus on mathematical and computational research in music performance and composition that serve as the foundation for understanding and enabling human creativity and for future music technologies.

Read more at: http://www2.ims.nus.edu.sg/Programs/015wmusic/index.php

This symposium reminds me of the book Science and Music (Dover Books on Music) by Sir James H. Jeans, the quintessential book on the intersection of Science and Music. Read more about this wonderful and amazing book here.

## Saturday, 24 January 2015

### Hilarious Math Video

What is 25 divided by 5?

Watch this humorous video on what can go wrong when dividing!

Do also check out this very interesting book titled "Introductory Calculus For Infants". It is a humorous math book about the storybook adventure of two friends as they explore the wonders of calculus.

## Friday, 23 January 2015

### Singapore Math Books

If you are interested to read more about Singapore Math, check out this site on Singapore Math Books!

### The Mystery of the Sine of Nines: sin 999=sin 9999 ?

Today while playing with my calculator, I discovered a curious fact:

sin(999)=-0.987688

sin(9999)=-0.987688

sin(99999)= -0.987688

Note:

In fact, the sine of any number of nines (more than 3), always led to the same number!

This may not work with other digits, for example "8":

sin(888)= 0.20791

sin(8888)=-0.92718

sin(88888)=-0.52992

As a math tutor, definitely I was curious about the mathematics behind this phenomenon. If you want to try to unravel the mystery, do give it a try before reading the answer!

###

The mystery is pretty straightforward once we notice the following:

$\sin (9999^\circ)=\sin (999^\circ+ 25(360^\circ))$

As we know, adding 360 degrees to an angle doesn't affect the result of its sine, since $\sin (x+360^\circ)=\sin (x)$. sin(9999) is actually sine of 25 times of 360 added to 999, hence they are essentially the same value!

Thus, sin(9999)=sin(999).

We can then proceed to show sin(99999)=sin(9999) in a similar way. This will keep on working since 9000=25x360 is already a multiple of 360, hence 9000...000 (more than 3 zeroes) will also be a multiple of 360!

This concludes the mysterious case of the Sine of Nines (it rhymes!).

Trigonometry is a really fun subject. But could it be taught better? Trigonometry often leads to nasty irrational numbers, for example sin(60) is already an irrational number ($\sqrt{3}/2$). Professor Wildberger, author of Divine Proportions: Rational Trigonometry to Universal Geometry argues that there is a better way to present Trigonometry, via the very novel (most people haven't heard of it, let alone seen it) Rational Trigonometry. I have followed his videos on YouTube, and personally it is an interesting idea. With Rational Trigonometry, irrational numbers (which are highly problematic if one thinks about them deeply) are banished, and we can only work with rational numbers.

Check out the book here:

sin(999)=-0.987688

sin(9999)=-0.987688

sin(99999)= -0.987688

Note:

**All angles in degrees.**In fact, the sine of any number of nines (more than 3), always led to the same number!

This may not work with other digits, for example "8":

sin(888)= 0.20791

sin(8888)=-0.92718

sin(88888)=-0.52992

As a math tutor, definitely I was curious about the mathematics behind this phenomenon. If you want to try to unravel the mystery, do give it a try before reading the answer!

###
__The Mystery of the Sine of Nines__

The mystery is pretty straightforward once we notice the following:$\sin (9999^\circ)=\sin (999^\circ+ 25(360^\circ))$

As we know, adding 360 degrees to an angle doesn't affect the result of its sine, since $\sin (x+360^\circ)=\sin (x)$. sin(9999) is actually sine of 25 times of 360 added to 999, hence they are essentially the same value!

Thus, sin(9999)=sin(999).

We can then proceed to show sin(99999)=sin(9999) in a similar way. This will keep on working since 9000=25x360 is already a multiple of 360, hence 9000...000 (more than 3 zeroes) will also be a multiple of 360!

This concludes the mysterious case of the Sine of Nines (it rhymes!).

Trigonometry is a really fun subject. But could it be taught better? Trigonometry often leads to nasty irrational numbers, for example sin(60) is already an irrational number ($\sqrt{3}/2$). Professor Wildberger, author of Divine Proportions: Rational Trigonometry to Universal Geometry argues that there is a better way to present Trigonometry, via the very novel (most people haven't heard of it, let alone seen it) Rational Trigonometry. I have followed his videos on YouTube, and personally it is an interesting idea. With Rational Trigonometry, irrational numbers (which are highly problematic if one thinks about them deeply) are banished, and we can only work with rational numbers.

Check out the book here:

## Wednesday, 21 January 2015

### When does JC 1 School Start?

For JC 1 students, they have a month of holidays!

According to MOE Website, school for JC 1 students starts on Mon, 2 Feb 2015. And soon after that, it will be Chinese New Year. :)

Meanwhile, JC 1 students are advised to start reading up on their own! This is so that they can be ahead of the syllabus which is very hectic in JC. Being one step ahead is a huge advantage.

Also, JC students can read some motivational books such as Outliers: The Story of Success to improve their lives through actions! Remember that Aristotle said that "Excellence is a habit"!

According to MOE Website, school for JC 1 students starts on Mon, 2 Feb 2015. And soon after that, it will be Chinese New Year. :)

Meanwhile, JC 1 students are advised to start reading up on their own! This is so that they can be ahead of the syllabus which is very hectic in JC. Being one step ahead is a huge advantage.

Also, JC students can read some motivational books such as Outliers: The Story of Success to improve their lives through actions! Remember that Aristotle said that "Excellence is a habit"!

## Sunday, 18 January 2015

### JC or Poly? Some tips on choosing between JC or Poly

According to this Straits Times article, JCs offer "broader options" and a quicker route to a university degree.

Our view is that "all roads lead to Rome", no matter which path you take, if you work hard and persevere, you will reach the destination eventually. A downside of the current JC system is that "triple science" i.e. Physics, Chemistry, Biology combination is no longer allowed. Nor is Further Maths in the syllabus anymore (heard that it may be making a comeback though). This is bad news for those passionately interested in science, since they may have to drop one science subject that they love.

Do also check out our post on Which JC is good?

Another article here showcases different students who chose different paths. For those who are interested in early childhood education, a polytechnic route may be more direct, as mentioned by student Mark Lim.

Some good points about the JC route is that the maths syllabus there is more rigorous, especially if you take the H2 maths syllabus. It would provide a solid foundation for university maths, like multivariable calculus. As a tutor for university students, I have realised that students without H2 Maths background would struggle for the university maths modules, since it is hard to learn calculus over a short time in university. Check out what is H1, H2, H3 maths in this article.

Students who wish to know more about the psychology of learning math can check out the below book by Barbara Oakley. This century has been said to be the most important century since the beginning for mankind for Math. Nowadays everything we use in daily lives, from smart phones, computers, has something to do with Math!

Our view is that "all roads lead to Rome", no matter which path you take, if you work hard and persevere, you will reach the destination eventually. A downside of the current JC system is that "triple science" i.e. Physics, Chemistry, Biology combination is no longer allowed. Nor is Further Maths in the syllabus anymore (heard that it may be making a comeback though). This is bad news for those passionately interested in science, since they may have to drop one science subject that they love.

Do also check out our post on Which JC is good?

Another article here showcases different students who chose different paths. For those who are interested in early childhood education, a polytechnic route may be more direct, as mentioned by student Mark Lim.

Some good points about the JC route is that the maths syllabus there is more rigorous, especially if you take the H2 maths syllabus. It would provide a solid foundation for university maths, like multivariable calculus. As a tutor for university students, I have realised that students without H2 Maths background would struggle for the university maths modules, since it is hard to learn calculus over a short time in university. Check out what is H1, H2, H3 maths in this article.

Students who wish to know more about the psychology of learning math can check out the below book by Barbara Oakley. This century has been said to be the most important century since the beginning for mankind for Math. Nowadays everything we use in daily lives, from smart phones, computers, has something to do with Math!

### Using Computer to Teach Maths: Good or Bad? (Discussion)

The topic of using computer to teach mathematics is a controversial one. Yes, there are many benefits of using computers for calculation, but also some drawbacks.

Conrad Wolfram (in the above video) presents an excellent case of using computer to teach mathematics. This is really a good idea, to be honest. (The caveat is that Conrad is linked to the company Wolfram founded by his brother Stephen Wolfram. Wolfram is a computational math software company.)

Personally, I feel that once a student has mastered a skill to a certain degree, for example solving quadratic equations, there is no point making him/her solve quadratic equations ad infinitum over and over again. Using a computer/calculator that can solve quadratic equations is perfectly acceptable.

On a higher level, once a student knows how to compute eigenvalues/eigenvectors of a matrix, there is really little point in calculating eigenvalues by hand, which can be really tedious.

However, on the other hand, manual/mental calculation is an essential skill that is at the foundation of mathematics. Many mathematical theorems, no matter how abstract, have roots in calculation. To come up with a theorem, many mathematicians do extensive calculations to come up numerical evidence that a theorem is probably true, then try to prove it. Riemann came up with his famous Riemann Hypothesis after some calculation that the real part of the non-trivial zeroes of the Riemann Zeta function is always half. If you are interested in learning more about the Riemann Hypothesis, this book Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics is an excellent introduction to the subject for laymen.

Finally, manual calculation, despite being tedious and cumbersome, is also a skill. As a maths tutor over the years, I have seen some subtle changes in the average mental calculation skills of students after the calculator was permitted in Grade 5 (11 years old) in Singapore. Students who have memorized their time tables and used to mental calculation would have no problem telling what is 8x7, and what is 50-36.20, mentally. However, there are some students who are too used to calculators who may not be able (or willing) to calculate the above sums mentally. However, we must note that there are many great mathematicians who are poor at mental calculation. Grothendieck, one of the top mathematicians in the 1900s, once claimed that "57 is a prime number". As a result, 57 is known as a "Grothendieck prime".

What do you think about using computer to teach maths? Please write your comments below!

Also, check out this controversial book by Stephen Wolfram:

Although criticized by many for "pretending that he is the inventor of standard ideas and facts in computer science", there are some merits to this book. Galileo proclaimed that nature is written in the language of mathematics, but Wolfram would argue that it is written in the language of programs and, remarkably, simple ones at that. Sounds interesting...

## Saturday, 17 January 2015

### AES: Advanced Encryption Standard

This is a very nice, relatively short and sweet video about AES: Advanced Encryption Standard.

It is currently one of the most secure ways of encrypting data, and is used by the US government.

Also, check out this book on Cryptography, Understanding Cryptography: A Textbook for Students and Practitioners, rated rather highly by many people on Amazon.

It is currently one of the most secure ways of encrypting data, and is used by the US government.

*AES has swept away old faithful DES, and is now the workhorse of business and government cryptography. Our entire civil order relies on its integrity. Here we explain how it works, and discover how a string of simple crypto primitives combine to such a robust cipher for which no mathematical compromise was ever published.*Also, check out this book on Cryptography, Understanding Cryptography: A Textbook for Students and Practitioners, rated rather highly by many people on Amazon.

## Friday, 16 January 2015

### Parents go for Maths Tuition

Source: http://mypaper.sg/top-stories/parents-go-tuition-help-their-kids-20150108

Kudos to these highly commendable parents, who have taken the initiative to learn Primary School Maths to teach their children!

Despite sounding slightly ridiculous at first, tuition for parents is actually a good idea, especially if one of the parents (e.g. the mother) is a stay-at-home parent. This is because no matter how often a child goes for tuition, the tuition teacher can't accompany the child 24 hours, whereas the parent can.

Also, if the parent can do maths, it inspires the child and builds confidence. Imagine how demoralised a child may feel if the Maths problem is so difficult that even his beloved father and mother whom he/she looks up to can't solve it!

As a former Primary School Maths Tutor (I have since moved on to tutoring at secondary level onwards), I have to admit that some of the PSLE questions can be real tough. Even as a math graduate from NUS with years of experience, and an A* for PSLE Maths, I have to crack my brains and put on my thinking cap just to solve a PSLE question using elementary methods like model drawing. No wonder children will find it tough!

Also, some of the questions are designed to be tough for students using the traditional recommended method of model drawing. Examples of these kind of questions is when the model is 3 units, but the question requires dividing the 3 units into two. This leads to "half a unit" which is problematic, unless the student knows what to do (subdivide each unit into two smaller parts). Hence, students equipped with just the standard skill set of "draw model" naturally will find it very difficult to solve the problem.

A student who has mastered algebra at primary 6 level actually has a huge advantage over his peers. Most PSLE questions can be reduced to pair of linear simultaneous equations with two variables. This is amazingly easy to solve for those who have mastered solving such equations. However, this is a highly controversial method in pedagogy, since there are many who insist that algebra should not be taught so early.

If parents do not have the time or budget to go for tuition (also tuition teachers who teach parents are still currently rare), the next best thing is to read a maths book. Books like Step by Step Model Drawing: Solving Word Problems the Singapore Way, written by Singapore Math expert Dr Yeap Ban Har, will enlighten parents on the divine art of drawing models. Model drawing will be able to solve 80%-90% of all PSLE Math questions, other than those questions specially designed to be anti-model, or model-unfriendly.

For the remaining 10% of problems (usually the last few problem sums) that are anti-model, trying to use the model method will lead to epic frustration. An algebra-model hybid approach using "u" for units, and "p" for parts would most likely be the ideal solution. A book like Practical Algebra: A Self-Teaching Guide, Second Edition, would be what parents need to refresh their memory on Algebra.

Another fantastic book suitable for parents:

Finally, do check out a list of GEP Books for parents who are interested in preparing their child for GEP: http://mathtuition88.com/2013/11/11/recommended-books-for-gep-selection-test/

*AS HE copied the solution to the maths problem sum onto his worksheet, he realised that he was lost.**Primary school mathematics is tough.**But this was not a primary school pupil struggling with the question. He was a father of two in a course on primary school maths.**He was one of several parents going for "tuition" so they can better understand what their children have to deal with in school.**On Dec 6, Mohd Yusof Maruwi, who is in his early 60s, and his wife, Sanisah Ismail, 45, attended an eight-hour session on solving primary school maths problems. It was held at a multi-purpose room at Muhajirin Mosque.**- from**http://mypaper.sg/top-stories/parents-go-tuition-help-their-kids-20150108*Kudos to these highly commendable parents, who have taken the initiative to learn Primary School Maths to teach their children!

Despite sounding slightly ridiculous at first, tuition for parents is actually a good idea, especially if one of the parents (e.g. the mother) is a stay-at-home parent. This is because no matter how often a child goes for tuition, the tuition teacher can't accompany the child 24 hours, whereas the parent can.

Also, if the parent can do maths, it inspires the child and builds confidence. Imagine how demoralised a child may feel if the Maths problem is so difficult that even his beloved father and mother whom he/she looks up to can't solve it!

As a former Primary School Maths Tutor (I have since moved on to tutoring at secondary level onwards), I have to admit that some of the PSLE questions can be real tough. Even as a math graduate from NUS with years of experience, and an A* for PSLE Maths, I have to crack my brains and put on my thinking cap just to solve a PSLE question using elementary methods like model drawing. No wonder children will find it tough!

Also, some of the questions are designed to be tough for students using the traditional recommended method of model drawing. Examples of these kind of questions is when the model is 3 units, but the question requires dividing the 3 units into two. This leads to "half a unit" which is problematic, unless the student knows what to do (subdivide each unit into two smaller parts). Hence, students equipped with just the standard skill set of "draw model" naturally will find it very difficult to solve the problem.

A student who has mastered algebra at primary 6 level actually has a huge advantage over his peers. Most PSLE questions can be reduced to pair of linear simultaneous equations with two variables. This is amazingly easy to solve for those who have mastered solving such equations. However, this is a highly controversial method in pedagogy, since there are many who insist that algebra should not be taught so early.

If parents do not have the time or budget to go for tuition (also tuition teachers who teach parents are still currently rare), the next best thing is to read a maths book. Books like Step by Step Model Drawing: Solving Word Problems the Singapore Way, written by Singapore Math expert Dr Yeap Ban Har, will enlighten parents on the divine art of drawing models. Model drawing will be able to solve 80%-90% of all PSLE Math questions, other than those questions specially designed to be anti-model, or model-unfriendly.

For the remaining 10% of problems (usually the last few problem sums) that are anti-model, trying to use the model method will lead to epic frustration. An algebra-model hybid approach using "u" for units, and "p" for parts would most likely be the ideal solution. A book like Practical Algebra: A Self-Teaching Guide, Second Edition, would be what parents need to refresh their memory on Algebra.

Another fantastic book suitable for parents:

Finally, do check out a list of GEP Books for parents who are interested in preparing their child for GEP: http://mathtuition88.com/2013/11/11/recommended-books-for-gep-selection-test/

## Monday, 12 January 2015

### Winnie The Pooh Maths Olympiad Question!

Check out this interesting Math Olympiad question on Winnie the Pooh and sweets!

Competition Math for Middle School

Written for the gifted math student, the new math coach, the teacher in search of problems and materials to challenge exceptional students, or anyone else interested in advanced mathematical problems. Competition Math contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks. "I wish I had a book like this when I started my competition career." Four-Time National Champion MATHCOUNTS coach Jeff Boyd "This book is full of juicy questions and ideas that will enable the reader to excel in MATHCOUNTS and AMC competitions. I recommend it to any students who aspire to be great problem solvers." Former AHSME Committee Chairman Harold Reiter

**Question: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1411q.pdf****Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1412a.pdf****Featured Book on Maths Olympiad:**Competition Math for Middle School

Written for the gifted math student, the new math coach, the teacher in search of problems and materials to challenge exceptional students, or anyone else interested in advanced mathematical problems. Competition Math contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks. "I wish I had a book like this when I started my competition career." Four-Time National Champion MATHCOUNTS coach Jeff Boyd "This book is full of juicy questions and ideas that will enable the reader to excel in MATHCOUNTS and AMC competitions. I recommend it to any students who aspire to be great problem solvers." Former AHSME Committee Chairman Harold Reiter

### O Level Top Scorer 2015

Although MOE has ceased publishing the names of O Level Top Scorers, there is still some general statistics about O Level Top Scorers.

This year (2015), 83.3% of students scored 5 or more passes, which is the best performance in the past 20 years. Congratulations to all who did well!

According to this article in 2012, Lim Min from Crescent Girls’ School and Zhong Yingyi and Chai Yung Ci from CHIJ St Nicholas Girls’ School scored 10 A1s in the exams (11 A1s inclusive of mother tongue language). This is a very commendable effort by these O Level top students.

Another source from Kiasuparents shows that Cedar Girls' Secondary School is a consistent producer of O Level Top Scorers, with some having a total of 11 A1s in a single sitting. Seems like currently many of the O Level Top Students come from girls' schools. This may be due to the fact that girls are less playful and more likely to do their revision consistently, a huge advantage in terms of acing exams.

The Top Student in O Levels from Chung Cheng High School (2011) is Zeng Ding who has scored a very commendable 8 A1s (EL, HCL, CL, EMath, AMath, Chem, Bio, Comb Humanities) and 1 A2 (Phy).

Congratulations to all these O Level Top Students, especially those receiving their results in 2015! For those who are not top students, but tried their best, they too deserve a round of applause for their hard work and dedication.

The Secrets of Top Students: Tips, Tools, and Techniques for Acing High School and College

Unlock your academic potential with tips, tools, and techniques from some of the best students in the country.

This year (2015), 83.3% of students scored 5 or more passes, which is the best performance in the past 20 years. Congratulations to all who did well!

According to this article in 2012, Lim Min from Crescent Girls’ School and Zhong Yingyi and Chai Yung Ci from CHIJ St Nicholas Girls’ School scored 10 A1s in the exams (11 A1s inclusive of mother tongue language). This is a very commendable effort by these O Level top students.

Another source from Kiasuparents shows that Cedar Girls' Secondary School is a consistent producer of O Level Top Scorers, with some having a total of 11 A1s in a single sitting. Seems like currently many of the O Level Top Students come from girls' schools. This may be due to the fact that girls are less playful and more likely to do their revision consistently, a huge advantage in terms of acing exams.

The Top Student in O Levels from Chung Cheng High School (2011) is Zeng Ding who has scored a very commendable 8 A1s (EL, HCL, CL, EMath, AMath, Chem, Bio, Comb Humanities) and 1 A2 (Phy).

Congratulations to all these O Level Top Students, especially those receiving their results in 2015! For those who are not top students, but tried their best, they too deserve a round of applause for their hard work and dedication.

**Featured Book:**The Secrets of Top Students: Tips, Tools, and Techniques for Acing High School and College

Unlock your academic potential with tips, tools, and techniques from some of the best students in the country.

Author Stefanie Weisman was a top student all her life, graduating first in her class from Stuyvesant High School and Columbia University and getting degrees in both history and computer science. But it wasn't because she was a "natural" or smarter than everyone else -- it was because she had developed powerful and time-saving techniques for studying, taking notes, writing papers, taking tests, and much, much more, which anyone can put into practice!

## Sunday, 11 January 2015

### The Math of Noah's Ark

Source: Creation Ministries

Was Noah's Ark round? A scholar Dr Irving Finkel claims that the Noah's Ark was actually round, based on a translation of a small Babylonian tablet, named the Ark Tablet.

However, there is a rebuttal by Creation.com, which involves some mathematical arguments.

The Ark Tablet has the following verse: "Draw out the boat you will make on a circular plan; let her length and breadth be equal, let her floor area be one field, let her sides be one nindan high.". The phrase "length and breadth" be equal clearly suggests a square base rather than a round base. More calculations involving the surface area of bitumen needed to coat the Ark suggests that a square based ark is more consistent with the calculations, rather than a circular base.

Read more about it at: http://creation.com/real-noahs-ark?utm_media=email&utm_source=infobytes&utm_content=sg&utm_campaign=emails

Was Noah's Ark round? A scholar Dr Irving Finkel claims that the Noah's Ark was actually round, based on a translation of a small Babylonian tablet, named the Ark Tablet.

*A replica of "Noah's Ark" according to Dr Finkel.**A ship modeled after the biblical description of Noah's Ark, "Johan's Ark", in the Netherlands*However, there is a rebuttal by Creation.com, which involves some mathematical arguments.

The Ark Tablet has the following verse: "Draw out the boat you will make on a circular plan; let her length and breadth be equal, let her floor area be one field, let her sides be one nindan high.". The phrase "length and breadth" be equal clearly suggests a square base rather than a round base. More calculations involving the surface area of bitumen needed to coat the Ark suggests that a square based ark is more consistent with the calculations, rather than a circular base.

Read more about it at: http://creation.com/real-noahs-ark?utm_media=email&utm_source=infobytes&utm_content=sg&utm_campaign=emails

### Singapore IB Top Student

Source: http://www.straitstimes.com/news/singapore/education/story/singapore-among-top-asia-pacific-region-ib-exams-20150105

Out of over 2000 students who sat for the IB exams, Singapore produced 66 perfect scorers! (45 points) One of them is Seah Jun Jie, 18, who switched from the Express stream to the Integrated Programme (IP) in Secondary 3.

Australia is a distant second with 31 perfect scorers.

On average, Singaporean IB students scored 36.43 points.

Read more about the IB HL Math: http://mathtuition88.blogspot.sg/2014/12/ib-hl-math.html

Also, here is a Hitler parody on YouTube about "Hitler takes the IB HL Math Test". It is pretty funny, but gives an insight on the type of questions that can appear in the IB HL Math Test, for instance, a question on f(x+y)=f(x)+f(y), which has no numbers! This is related to something called Cauchy's functional equation!

Please note that this video is not created by me, and only watch it if you have a sense of humour!

IB Mathematics Higher Level Course Book: Oxford IB Diploma Program

Out of over 2000 students who sat for the IB exams, Singapore produced 66 perfect scorers! (45 points) One of them is Seah Jun Jie, 18, who switched from the Express stream to the Integrated Programme (IP) in Secondary 3.

Australia is a distant second with 31 perfect scorers.

On average, Singaporean IB students scored 36.43 points.

Read more about the IB HL Math: http://mathtuition88.blogspot.sg/2014/12/ib-hl-math.html

Also, here is a Hitler parody on YouTube about "Hitler takes the IB HL Math Test". It is pretty funny, but gives an insight on the type of questions that can appear in the IB HL Math Test, for instance, a question on f(x+y)=f(x)+f(y), which has no numbers! This is related to something called Cauchy's functional equation!

Please note that this video is not created by me, and only watch it if you have a sense of humour!

**Featured Book:**

IB Mathematics Higher Level Course Book: Oxford IB Diploma Program

## Saturday, 10 January 2015

### H2 Maths Syllabus and Formula Sheet

## H2 Maths Syllabus and Help Sheet (MF15)

This is the latest updated H2 Maths Syllabus and Formula Sheet, for the year 2015.

H2 Maths Syllabus: https://mathtuition88.files.wordpress.com/2015/01/9740_2015.pdf

H2 Maths Formula Sheet (Printable): https://mathtuition88.files.wordpress.com/2015/01/listmf15.pdf

Hope it helps!

Official Source: https://www.seab.gov.sg/pages/nationalExaminations/GAL/School_Candidates/2015_GCE_A.asp

Understanding Analysis (Undergraduate Texts in Mathematics)

Review (on Amazon.com):

Once in a while, a book comes along that is so wonderfully written, the reader reflexively searches for other books by its author. Understanding Analysis is a prime example of this rare breed (Unfortunately, this is Abbott's only book as far as I know: write more!).

Undergraduates often begin analysis courses with dread and finish in a state of utter confusion,knowing the definitions of key phrases, and sometimes even being able to supply proofs for some elementary results, but having no intution as to why the main theorems are pertinent.

**Featured Book:**Understanding Analysis (Undergraduate Texts in Mathematics)

Review (on Amazon.com):

Once in a while, a book comes along that is so wonderfully written, the reader reflexively searches for other books by its author. Understanding Analysis is a prime example of this rare breed (Unfortunately, this is Abbott's only book as far as I know: write more!).

Undergraduates often begin analysis courses with dread and finish in a state of utter confusion,knowing the definitions of key phrases, and sometimes even being able to supply proofs for some elementary results, but having no intution as to why the main theorems are pertinent.

## Thursday, 8 January 2015

### Topics taught in JC 1 / JC 2 H2 Maths

What are the topics taught in JC1 H2 Maths?

What are the topics taught in JC2 H2 Maths?

Source: http://jcmath.wiki.hci.edu.sg/JC1+%26+JC2+Topics

Ans:

It differs from school to school, HCI teaches the topics in the following order below. The order may be different for different schools, though. Some topics definitely have to be taught first, for instance Differentiation is taught first before Integration almost all the time. After these two are taught, then students can move on to learn Maclaurin Series and Differential Equations.

What are the topics taught in JC2 H2 Maths?

Source: http://jcmath.wiki.hci.edu.sg/JC1+%26+JC2+Topics

Ans:

It differs from school to school, HCI teaches the topics in the following order below. The order may be different for different schools, though. Some topics definitely have to be taught first, for instance Differentiation is taught first before Integration almost all the time. After these two are taught, then students can move on to learn Maclaurin Series and Differential Equations.

## JC 1 H2 Mathematics Topics

- Sequences and Series
- Graphing Techniques
- Inequalities and System of Equations
- Functions
- Differentiation and its Applications
- Integration and its Applications
- Vectors
- Binomial Expansion
- Maclaurin Series

## JC 2 H2 Mathematics Topics

- Differential Equations
- Complex Numbers
- Permutation and Combination
- Probability
- Binomial and Poisson Distributions
- Normal Distribution
- Sampling
- Hypothesis Testing
- Linear Correlation and Regression

### Dragon Curve and Jurassic Park!

Here are two fantastic videos about the Dragon Curve from Numberphile!

The Dragon Curve is a little known fractal that is very beautiful and mysterious. It can be obtained by simply folding a piece of paper!

This video very aptly and clearly describes the Dragon Curve, which can be found in the book of Jurassic Park. (Many people have watched Jurassic Park, but few have read the book, hence the Dragon Curve is unknown to many.)

Legendary Computer Scientist Don Knuth introduces his beautiful "Dragon Curve" sculpture in his home. And also a moral to be learnt: It's ok to make mistakes, just learn from them! "Err and err and err again, but less and less and less." — Piet Hein. How is this quote of wisdom related to the Dragon Curve? Watch the video to find out!

The Dragon Curve is a little known fractal that is very beautiful and mysterious. It can be obtained by simply folding a piece of paper!

Lastly, just a sneak peek of the upcoming Jurassic World Official Trailer! Jurassic World will be released in 3D by Universal Pictures on June 12, 2015. Excited?

### SMU Calculus MATH 001 Tuition

## SMU Calculus MATH 001 Tuition

Mr Wu can teach tuition for the SMU Calculus Math 001 module.

Here is a testimonial from one of his previous students (with zero H2 Maths background!):

The previous module mentioned refers to the SMU Calculus Math 001 module. He is now taking the SMU Stat 101 module from SMU.

By the way, the SMU Calculus Math 001 is pretty challenging. It includes multivariable calculus which is something new and not in H2 Mathematics syllabus!

The previous module mentioned refers to the SMU Calculus Math 001 module. He is now taking the SMU Stat 101 module from SMU.

By the way, the SMU Calculus Math 001 is pretty challenging. It includes multivariable calculus which is something new and not in H2 Mathematics syllabus!

## Tuesday, 6 January 2015

### JavaScript XOR Hexadecimal App!

This is a simple JavaScript application that can

Hope it helps!

XOR: Exclusive disjunction or exclusive or is a logical operation that outputs true whenever both inputs differ (one is true, the other is false). It is symbolized by infix operator XOR. (Read more at: Wikipedia: XOR)

Hexadecimal: Base 16 numbers, using symbols 0–9 to represent values zero to nine, and A,B,C,D,E,F (or alternatively a–f) to represent values ten to fifteen. (Wikipedia: Hexadecimal)

A Smarter Way to Learn JavaScript: The new approach that uses technology to cut your effort in half

**XOR Hexadecimals (Hex)**,**2 characters at a time**. The output is in**2 digits**, meaning that**"0" is written as "00"**.Hope it helps!

XOR: Exclusive disjunction or exclusive or is a logical operation that outputs true whenever both inputs differ (one is true, the other is false). It is symbolized by infix operator XOR. (Read more at: Wikipedia: XOR)

Hexadecimal: Base 16 numbers, using symbols 0–9 to represent values zero to nine, and A,B,C,D,E,F (or alternatively a–f) to represent values ten to fifteen. (Wikipedia: Hexadecimal)

**Featured Book:**A Smarter Way to Learn JavaScript: The new approach that uses technology to cut your effort in half

## Monday, 5 January 2015

### Javascript Application to Split Text Every Few Characters

This is a simple JavaScript application that can

For instance,

Hope it helps!

JavaScript: The Definitive Guide: Activate Your Web Pages (Definitive Guides)

**split text every "n" characters, and add a separator of your choice in between. (E.g. separated by comma, space, semicolon, etc.)**For instance,

**given the input:"abcde12345", separating using the default settings will output:"ab,cd,e1,23,45".**Hope it helps!

**References:**JavaScript: The Definitive Guide: Activate Your Web Pages (Definitive Guides)

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