Thursday, October 01, 2015
Tuesday, September 22, 2015
Sunday, August 30, 2015
MATH FROM THE HEART
To get a copy of my new book, Math From The Heart, please click on the link below:
MATH FROM THE HEART
The covers below have brief descriptions and a summary of what to expect in the book.
The title of the book MATH FROM THE HEART is inspired by the words on the farewell card given by the Upper Six (2010) students of Penang Free School. Thanks my dear students.
MATH FROM THE HEART
The covers below have brief descriptions and a summary of what to expect in the book.
The title of the book MATH FROM THE HEART is inspired by the words on the farewell card given by the Upper Six (2010) students of Penang Free School. Thanks my dear students.
Saturday, August 22, 2015
STRONG MATHEMATICAL INDUCTION
https://drive.google.com/open?id=0B3NUi_7xrhYgdzV6aTJXeGRfcWM
I dedicate this page to all my IB students in TAYLOR'S COLLEGE SRI HARTAMAS.
You are my inspiration.
I dedicate this page to all my IB students in TAYLOR'S COLLEGE SRI HARTAMAS.
You are my inspiration.
Sunday, May 24, 2015
Tuesday, December 23, 2014
DIRAC'S THEOREM - PROOF BY MATHEMATICAL INDUCTION
A proof by mathematical induction. Dedicated to my IB students of TCSH
Thanks to my IB students at TCSH,
This proof is dedicated to all of you, an inspiration that comes from our math lessons together.
I have looked into some books and internet sources and so far the proof uses the approach of a supposition of a longest path.
I welcome you all to study the proof by mathematical induction given here and tell me if I overlooked something.
This is one way how you can do a math exploration.
Please click here for the proof.
Thanks to my IB students at TCSH,
This proof is dedicated to all of you, an inspiration that comes from our math lessons together.
I have looked into some books and internet sources and so far the proof uses the approach of a supposition of a longest path.
I welcome you all to study the proof by mathematical induction given here and tell me if I overlooked something.
This is one way how you can do a math exploration.
Please click here for the proof.
Saturday, September 27, 2014
SMK SEAFIELD MATH TALK 2014
MATHEMATICS - SELECTED STPM QUESTIONS FOR REVISION
SOLUTIONS
BE LUCKY
I express sincere thanks for the opportunity, Students! Your attention, cooperation, willingness to learn and good attendance gave a very good impression. Salute to your school! I wish you all great success in your exam. Special thanks also to Pn. Baizura and Pn. Chin for the support, both your presence throughout gave me added inspiration and showed how much you care for your students to do well. Congratulations SMK SEAFIELD.
SOLUTIONS
BE LUCKY
I express sincere thanks for the opportunity, Students! Your attention, cooperation, willingness to learn and good attendance gave a very good impression. Salute to your school! I wish you all great success in your exam. Special thanks also to Pn. Baizura and Pn. Chin for the support, both your presence throughout gave me added inspiration and showed how much you care for your students to do well. Congratulations SMK SEAFIELD.
Wednesday, April 02, 2014
https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing
STPM FURTHER MATHEMATICS PAPER 2 - QUESTIONS & SOLUTIONS
My best wishes go to all taking this paper in May 2014.
This question paper is obtained from the specimen given together with the 2012 syllabus and exam format published by Majlis Peperiksaan Malaysia
https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing
My best wishes go to all taking this paper in May 2014.
This question paper is obtained from the specimen given together with the 2012 syllabus and exam format published by Majlis Peperiksaan Malaysia
https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing
Monday, January 20, 2014
CEVA'S & MENELAUS THEOREMS
Ceva's & Menelaus Theorem
https://drive.google.com/file/d/0B3NUi_7xrhYgdFFGTkpuVGFOYkE/edit?usp=sharing
A proof of CEVA'S & MENELAUS'S theorems without using triangles.
Both proofs use one property where fractions are equal as given below.
(a/p) = (b/q) = (c/r) = ... = (a + b + c+ ...)/(p + q + r + ...)
https://drive.google.com/file/d/0B3NUi_7xrhYgdFFGTkpuVGFOYkE/edit?usp=sharing
A proof of CEVA'S & MENELAUS'S theorems without using triangles.
Both proofs use one property where fractions are equal as given below.
(a/p) = (b/q) = (c/r) = ... = (a + b + c+ ...)/(p + q + r + ...)
Thursday, October 31, 2013
STPM Further Mathematics Model Exam Paper 1
STPM Further Mathematics Model Paper 1
STPM Further Mathematics Model Paper 1 - Solutions
I have selected questions to cover almost all of the syllabus. Happy solving!
STPM Further Mathematics Model Paper 1 - Solutions
I have selected questions to cover almost all of the syllabus. Happy solving!
Monday, October 07, 2013
STPM Trial Exam Paper 2013
STPM Further Math Trial Exam Paper 1 - 2013
STPM Further Math Trial Exam Paper 1 - 2013 - Solution
I feel it is not practical to have students travel to Penang to take the trial exam for Further Math. Two main reasons are:
1. It will take too much time to travel. for those who are too far from Penang.
2. The cost in travelling and accommodation should not be just to take the test.
I promise to set a trial paper for students taking STPM Further Math 2013 - Paper 1. Please help inform that the trial exam paper is posted here. I hope students find this paper beneficial and provide a good guide for them to study. I think include almost everything in the syllabus.
If anyone can find a hotel to sponsor a seminar room and accommodation then we can have a seminar to discuss the solutions and make preparation for the coming STPM Further Math Paper
Best regards from me.
Thursday, April 12, 2012
Monday, January 30, 2012
Sunday, January 29, 2012
Thursday, January 26, 2012
Saturday, January 07, 2012
Teaching Mathematics
Teaching Mathematics In the Higher Forms
Teaching geometric progression offers opportunities to talk about the "wonders" compound interest, how money doubles at 10% every 7 years. Details on saving regularly every month for 10 years and the stop completely can result in more money being saved for a life-time if the same amount is saved every month but starting 10 years late.
Teaching definitions using one word helps many students understand definitions such as
logarithm, weight, center of gravity, standard deviation, half-life, light years etc. Of course some definitions can be taught in this manner. eg What is force? What is calculus?
Examination questions on mathematics make teacher spent much time teaching skills in calculation and concepts and methods. If questions in mathematics more space for matters related to say health issues, environment, borrowing money etc, I believe teachers will also devote time on these areas.
Teaching geometric progression offers opportunities to talk about the "wonders" compound interest, how money doubles at 10% every 7 years. Details on saving regularly every month for 10 years and the stop completely can result in more money being saved for a life-time if the same amount is saved every month but starting 10 years late.
Teaching definitions using one word helps many students understand definitions such as
logarithm, weight, center of gravity, standard deviation, half-life, light years etc. Of course some definitions can be taught in this manner. eg What is force? What is calculus?
Examination questions on mathematics make teacher spent much time teaching skills in calculation and concepts and methods. If questions in mathematics more space for matters related to say health issues, environment, borrowing money etc, I believe teachers will also devote time on these areas.
Monday, February 07, 2011
Greater Appreciation of Math for Pre-U Students
Greater Appreciation in Mathematics For Pre-U Students
The power point slides were used in the colloquium presented by me for form six teachers organized by the Penang Education Department hosted by Methodist Boys' School last year.
The power point slides were used in the colloquium presented by me for form six teachers organized by the Penang Education Department hosted by Methodist Boys' School last year.
Wednesday, January 26, 2011
Olympiad Training Question On Algebra
An Exercise on Algebra
The question rephrase can be rephrase as follows.
If (x, y) are points on the curve x^3 + y^3 = x -y then (x, y) is always in the interior of the ellipse x^2 + 4y^2 = 1.
The question rephrase can be rephrase as follows.
If (x, y) are points on the curve x^3 + y^3 = x -y then (x, y) is always in the interior of the ellipse x^2 + 4y^2 = 1.
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