## How to develop students’ interest in mathematics

For interest in Math, it is totally understandable that many students may find math boring. One way to overcome it is to try to think of each Math question like a puzzle or game (like a Sudoku or Crossword Puzzle). Solving a Math question correctly should bring joy and a sense of achievement just like completing a stage of a game or a puzzle. And the more questions one solves, the better one gets at it.
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”
― Bertrand Russell
In the Singapore context, basically, Math is quite compulsory in SG education system (up till JC, even arts subject combinations requires math), but once JC is over one can skip Math entirely in university. So a secondary student just have to work hard for math for the upcoming few years, and “get it over with”, if he/she really does not like math. Similarly for Chinese, students need to work hard up till Secondary 4, score well and be exempted in JC. Math can be considered the “easiest” subject to get A, as long as one gets the answer correct he/she will get the full marks, many students complain that getting A for English or other humanities subjects like Literature is much harder due to strict or subjective marking.
The important thing is not to give up. Currently, in the Singapore education system it is quite common for students to “fail” exams (fail as in score below 50), especially in secondary school and JC internal exams. It is very possible to improve upon working hard after the failure.
“Trust me, its normal, I never passed a single A math test/exam during my sec 3/4 school years, got A2 for O levels in the end. (Mugged really hard after prelims) What matters is understanding the content I feel.”
– This student never passed a single A math test/exam up till prelims but eventually got A2 for O levels after “mugging” really hard after prelims.
Source: Reddit
trust me youre not alone. from mid sec 3 to prelims in sec 4 i got F9 all the way. but then in the end i got an A2 in olevels. one thing u need to know is to NEVER stop believing in yourself. keep on pushing urself all the way till the finishing point. aft seeing my score for prelims, i alm gave up but i told myself to atleast PASS amaths and i’d be satisfied with it. i started spamming my TYS, practice as much as i could. never give up and whenever in doubt just ask ur cher. it rly helps! atb and ik u can do it:))
Source: Reddit
dude chill. i got 8% for mye in sec 3 for A Math. form teacher told me drop the subject, but i didnt. ended up o level got A2. just do work given and practice more.
– This guy even more “power”, he got just 8/100 for Mid-year exams, but improved to A2 in O Levels.
Source: Reddit

## How to be good in Additional Mathematics

Recently, I saw that many people searched the following terms on Google and landed on my website:

2. ## How to be good in additional mathematics.

Let me try to answer the above questions:

## Why is the mid-year exams difficult and many people fail it?

Usually teachers will set the mid-year exams and the prelims at a (much) higher level than the actual O Levels. This is the current trend, which may result in many people failing the mid-year exam. The idea may be to motivate students to study harder and avoid being complacent with their results. Do not be demoralized by failing the exam! On the contrary, do reevaluate your study strategies, and strive to improve your knowledge and technique in mathematics.

## How to be good in additional mathematics.

The way to be good at additional mathematics is the same as the way to be good at piano, chess, and virtually any human endeavour. The key to improving is practice! Practice with understanding is the key. Would you imagine to be possible to improve in playing the piano without practicing the song? Improve in badminton without training? Definitely not! Similarly, improving in additional mathematics is not possible without practice. This is why the Ten Year Series is such a popular book: it is indeed the most useful book you can buy for studying Additional Mathematics.

Practicing with understanding helps with Application of Concepts, Increase Speed, Accuracy, which all helps in being good at additional mathematics.

In addition, during the practice sessions, try to practice checking for careless mistakes. It will help tremendously in improving your grades. Practicing with understanding means that we need to understand the method used, to the extent that if the teacher sets a slightly different question we are still able to do it. This is the secret to being good at additional maths. 🙂

From a well-known actress, math genius and popular contestant on “Dancing With The Stars”—a groundbreaking guide to mathematics for middle school girls, their parents, and educators

## 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!

## The Aims of Additional Maths (New Syllabus)

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

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

## Ten Year Series: How many questions or papers to practice for Maths O Levels / A Levels?

This is a question to ponder about, how many questions or papers to practice for Maths O Levels / A Levels for the Ten Year Series?

If you searched Google, you will find that there is no definitive answer of how many questions to practice for Maths O Levels/ A Levels anywhere on the web.

For O Level / A Level, practicing the Ten Year Series is really helpful, as it helps students to gain confidence in solving exam-type questions.

Here are some tips about how to practice the Ten Year Series (TYS):

1) Do a variety of questions from each topic. This will help you to gain familiarity with all the topics tested, and also revise the older topics.

2) Fully understand each question. If necessary, practice the same question again until you get it right. There is a sense of satisfaction when you finally master a tough question.

3) Quality is more important than quantity. It is better to do and understand 1 question completely than do many questions but not understanding them.

Back to the original query of how many questions or papers to practice for Maths O Levels / A Levels for the Ten Year Series, I will attempt to give a rough estimate here, based on personal experience.

5 Questions done (full questions worth more than 5 marks) will result in an improvement of roughly 1 mark in the final exam.

(The 5 Questions must be fully understood. )

So, if a student wants to improve from 40 marks to 70 marks, he/she should try to do 30×5=150 questions (around 7 years worth of past year papers). Repeated questions are counted too, so doing 75 questions (around 3 years worth of past year papers) twice will also count as doing 150 questions. In fact, that is better for students with weak foundation, as the repetition reinforces their understanding of the techniques used to solve the question.

If the student starts revision early, this may work out to just 1 question per day for 5 months. Of course, the 150 questions must be varied, and from different subject topics.

 Marks improved by Long Questions to be done Approx. Number of years of TYS OR (even better) 10 50 2 1 year TYS practice twice 20 100 4 2 year TYS practice twice 30 150 6 3 year TYS practice twice 40 200 8 4 year TYS practice twice 50 250 10 5 year TYS practice twice

This estimate only works up to a certain limit (obviously we can’t exceed 100 marks). To get the highest grade (A1 or A), mastery of the subject is needed, and the ability to solve creative questions and think out of the box.

When a student practices TYS questions, it is essential that he/she fully understands the question. This is where a tutor is helpful, to go through the doubts that the student has. Doing a question without understanding it is essentially of little use, as it does not help the student to solve similar questions should they come out in the exam.

## 积少成多: How can doing at least one Maths question per day help you improve! (Maths Tuition Revision Strategy)

We all know the saying “an apple a day keeps the doctor away“. Many essential activities, like eating, exercising, sleeping, needs to be done on a daily basis.

Mathematics is no different!

Here is a surprising fact of how much students can achieve if they do at least one Maths question per day. (the question must be substantial and worth at least 5 marks)

This study plan is based on the concept of 积少成多, or “Many little things add up“. Also, this method prevents students from getting rusty in older topics, or totally forgetting the earlier topics. Also, this method makes use of the fact that the human brain learns during sleep, so if you do mathematics everyday, you are letting your brain learn during sleep everyday.

Let’s take the example of Additional Mathematics.

Exam is on 24/25 October 2013.

Let’s say the student starts the “One Question per day” Strategy on 20 May 2013

Days till exam: 157 days  (22 weeks or 5 months, 4 days)

So, 157 days = 157 questions (or more!)

Each paper in Ten Year Series has around 25 questions (Paper 1 & Paper 2), so 157 questions translates to more than 6 years worth of practice papers! And all that is achieved by just doing at least one Maths question per day!

A sample daily revision plan can look like this. (I create a customized revision plan for each of my students, based on their weaknesses).

 Topic Monday Algebra Tuesday Geometry and Trigonometry Wednesday Calculus Thursday Algebra Friday Geometry and Trigonometry Saturday Calculus Sunday Geometry and Trigonometry

(Calculus means anything that involves differentiation, integration)

(Geometry and Trigonometry means anything that involves diagrams, sin, cos, tan, etc. )

(Algebra is everything else, eg. Polynomials, Indices, Partial Fractions)

By following this method, using a TYS, the student can cover all topics, up to 6 years worth of papers!

Usually, students may accumulate a lot of questions if they are stuck. This is where a tutor comes in. The tutor can go through all the questions during the tuition time. This method makes full use of the tuition time, and is highly efficient.

Personally, I used this method of studying and found it very effective. This method is suitable for disciplined students who are aiming to improve, whether from fail to pass or from B/C to A. The earlier you start the better, for this strategy. For students really aiming for A, you can modify this strategy to do at least 2 to 3 Maths questions per day. From experience, my best students practice Maths everyday. Practicing Ten Year Series (TYS) is the best, as everyone knows that school prelims/exams often copy TYS questions exactly, or just modify them a bit.

The role of the parent is to remind the child to practice maths everyday. From experience, my best students usually have proactive parents who pay close attention to their child’s revision, and play an active role in their child’s education.

This study strategy is very flexible, you can modify it based on your own situation. But the most important thing is, practice Maths everyday! (For Maths, practicing is twice as important as studying notes.) And fully understand each question you practice, not just memorizing the answer. Also, doing a TYS question twice (or more) is perfectly acceptable, it helps to reinforce your technique for answering that question.

If you truly follow this strategy, and practice Maths everyday, you will definitely improve!

Hardwork $\times$ 100% = Success! (^_^)

There is no substitute for hard work.” – Thomas Edison

## A Maths Tuition: Trigonometry Formulas

Many students find Trigonometry in A Maths challenging.

This is a list of Trigonometry Formulas that I compiled for A Maths. Students in my A Maths tuition class will get a copy of this, neatly formatted into one A4 size page for easy viewing.

A Maths: Trigonometry Formulas

$\mathit{cosec}x=\frac{1}{\sin x}$$\mathit{sec}x=\frac{1}{\cos x}$

$\cot x=\frac{1}{\tan x}$$\tan x=\frac{\sin x}{\cos x}$

(All Science Teachers Crazy)

$y=\sin x$

$y=\cos x$

$y=\tan x$

$\frac{d}{\mathit{dx}}(\sin x)=\cos x$

$\frac{d}{\mathit{dx}}(\cos x)=-\sin x$

$\frac{d}{\mathit{dx}}(\tan x)=\mathit{sec}^{2}x$

$\int {\sin x\mathit{dx}}=-\cos x+c$

$\int \cos x\mathit{dx}=\sin x+c$

$\int \mathit{sec}^{2}x\mathit{dx}=\tan x+c$

Special Angles:

$\cos 45^\circ=\frac{1}{\sqrt{2}}$

$\cos 60^\circ=\frac{1}{2}$

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\sin 45^\circ=\frac{1}{\sqrt{2}}$

$\sin 60^\circ=\frac{\sqrt{3}}{2}$

$\sin 30^\circ=\frac{1}{2}$

$\tan 45^\circ=1$

$\tan 60^\circ=\sqrt{3}$

$\tan 30^\circ=\frac{1}{\sqrt{3}}$

$y=a\sin (\mathit{bx})+c$ Amplitude: $a$; Period: $\frac{2\pi }{b}$

$y=a\cos (\mathit{bx})+c$ Amplitude: $a$; Period: $\frac{2\pi }{b}$

$y=a\tan (\mathit{bx})+c$ Period: $\frac{\pi }{b}$

$\pi \mathit{rad}=180^\circ$

Area of  $\triangle \mathit{ABC}=\frac{1}{2}\mathit{ab}\sin C$

Sine Rule:  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Cosine Rule:  $c^{2}=a^{2}+b^{2}-2\mathit{ab}\cos C$