tag:blogger.com,1999:blog-284874042024-02-07T21:20:25.384-08:00MathematicsALL CONTENTS ARE COPYRIGHTEDKhor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.comBlogger40125tag:blogger.com,1999:blog-28487404.post-19825275197930517282015-10-01T08:38:00.000-07:002015-10-01T08:38:19.667-07:00Mersenne Numbers<div dir="ltr" style="text-align: left;" trbidi="on">
<u><a href="https://drive.google.com/open?id=0B3NUi_7xrhYgLUJJMWFXbHowa0E">MERSENNE NUMBERS</a></u></div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-43190197595300020762015-09-22T07:14:00.002-07:002015-09-22T07:14:44.237-07:00STRONG INDUCTION (Postage Stamp Problem)<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://drive.google.com/open?id=0B3NUi_7xrhYgMnpIYkFkWW0ya2M">STRONG INDUCTION (Postage Stamp Problem)</a><br />
<br />
<br />
<br />
IB Class 2014-2015-2016 this is dedicated to you all</div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-9547755150018114272015-08-30T20:30:00.000-07:002015-09-08T04:09:06.748-07:00MATH FROM THE HEART<div dir="ltr" style="text-align: left;" trbidi="on">
To get a copy of my new book, Math From The Heart, please click on the link below:<br />
<br />
<a href="http://beanhwak.wix.com/mathfromtheheart">MATH FROM THE HEART</a><br />
<br />
The covers below have brief descriptions and a summary of what to expect in the book.<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGqDLYysS7YeL7ASeOffBpmYcA1DYUgpidM820ZM2WasBXocJNlYrveH6ut8Kr7X4YvfBceeELMXNrwKMih47bDuxkfwr0RrkzoaB0ifssqnshH4S-UQyLHk-EwtRVIZoY4fxN/s1600/MathFromTheHeart+-+Front+Cover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGqDLYysS7YeL7ASeOffBpmYcA1DYUgpidM820ZM2WasBXocJNlYrveH6ut8Kr7X4YvfBceeELMXNrwKMih47bDuxkfwr0RrkzoaB0ifssqnshH4S-UQyLHk-EwtRVIZoY4fxN/s640/MathFromTheHeart+-+Front+Cover.jpg" width="451" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgytHW1XA-Vq6TvGyMOWSbtQc_YMjAYL_uC790NXZtZ6C6CBr0XjUKLwj4nE4xB9ia-y-emSelckMssk2msBNyDv76be8mcxNhro_yUtRXaJVXyUVSOvgZV0UBXLFDi-KIF2NHF/s1600/BackCover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgytHW1XA-Vq6TvGyMOWSbtQc_YMjAYL_uC790NXZtZ6C6CBr0XjUKLwj4nE4xB9ia-y-emSelckMssk2msBNyDv76be8mcxNhro_yUtRXaJVXyUVSOvgZV0UBXLFDi-KIF2NHF/s640/BackCover.jpg" width="452" /></a></div>
<br />
<br />
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.<br />
<div>
<br /></div>
</div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com1tag:blogger.com,1999:blog-28487404.post-10916710895789792902015-08-22T06:29:00.000-07:002015-09-08T04:03:57.554-07:00STRONG MATHEMATICAL INDUCTION<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://drive.google.com/open?id=0B3NUi_7xrhYgdzV6aTJXeGRfcWM"><span id="goog_1786245588"></span><span id="goog_1786245589"></span>https://drive.google.com/open?id=0B3NUi_7xrhYgdzV6aTJXeGRfcWM</a><br />
<br />
I dedicate this page to all my <b>IB students in TAYLOR'S COLLEGE SRI HARTAMAS.</b><br />
<br />
You are my inspiration.</div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-62909501056412747112015-05-24T09:26:00.001-07:002015-05-24T09:26:43.373-07:00ALBERT BERNARD AND CHERYL'S BIRTHDAY PROBLEM<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://drive.google.com/open?id=0B3NUi_7xrhYgSFM1Q05PYk9UelU&authuser=0" target="_blank">https://drive.google.com/open?id=0B3NUi_7xrhYgSFM1Q05PYk9UelU&authuser=0</a></div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-24193343022834884262014-12-23T21:59:00.003-08:002014-12-23T21:59:52.402-08:00DIRAC'S THEOREM - PROOF BY MATHEMATICAL INDUCTION<div dir="ltr" style="text-align: left;" trbidi="on">
A proof by mathematical induction. Dedicated to my IB students of TCSH <b><br /></b>
<b>Thanks to my <i><span style="color: red;">IB</span></i> students at <u><i><span style="color: red;">TCSH</span></i></u>, </b><br />
<b><br /></b>
<b>This proof is dedicated to all of you, an inspiration that comes from our math lessons together. </b><br />
<b>I have looked into some books and internet sources and so far the proof uses the approach of a supposition of a longest path.</b><br />
<b><br /></b>
<b>I welcome you all to study the proof by mathematical induction given here and tell me if I overlooked something. </b><br />
<b><br /></b>
<b>This is one way how you can do a math exploration.</b><br />
<br />
<b>Please click <a href="https://drive.google.com/file/d/0B3NUi_7xrhYgdFNQX2JsMFVsd00/view?usp=sharing" target="_blank">here</a> for the proof. </b></div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-32944507803339513642014-09-27T17:41:00.000-07:002014-09-27T18:02:18.270-07:00SMK SEAFIELD MATH TALK 2014<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://www.dropbox.com/s/k2rbirh2vflom76/MATH%20TALK%20SMK%20USJ%202014.pdf?dl=0">MATHEMATICS - SELECTED STPM QUESTIONS FOR REVISION </a><br />
<br />
<a href="https://www.dropbox.com/s/w8yuy5160x304tx/Solution%20Math%20Talk.pdf?dl=0">SOLUTIONS</a><br />
<br />
<a href="https://www.dropbox.com/s/54gswizw7c2dmkh/Gmail%20-%20Be%20Lucky%20-%20How%20_.pdf?dl=0">BE LUCKY</a><br />
<br />
<br />
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. <br />
<br /></div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com2tag:blogger.com,1999:blog-28487404.post-48558568367529063582014-04-02T19:14:00.000-07:002014-04-02T19:14:04.594-07:00https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing">STPM FURTHER MATHEMATICS PAPER 2 - QUESTIONS & SOLUTIONS</a><br />
<br />
My best wishes go to all taking this paper in May 2014.<br />
<br />
This question paper is obtained from the specimen given together with the 2012 syllabus and exam format published by Majlis Peperiksaan Malaysia<br />
<br />
<a href="https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing" rel="nofollow">https://drive.google.com/file/d/0B3NUi_7xrhYgY2M0Qmw4VURJY2c/edit?usp=sharing</a></div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com3tag:blogger.com,1999:blog-28487404.post-19631642430406424732014-01-20T23:31:00.000-08:002014-01-20T23:31:29.968-08:00CEVA'S & MENELAUS THEOREMS<div dir="ltr" style="text-align: left;" trbidi="on">
<u>Ceva's & Menelaus Theorem</u> <br />
<a href="https://drive.google.com/file/d/0B3NUi_7xrhYgdFFGTkpuVGFOYkE/edit?usp=sharing">https://drive.google.com/file/d/0B3NUi_7xrhYgdFFGTkpuVGFOYkE/edit?usp=sharing</a><br />
<br />
A proof of CEVA'S & MENELAUS'S theorems without using triangles.<br />
Both proofs use one property where fractions are equal as given below. <br />
(a/p) = (b/q) = (c/r) = ... = (a + b + c+ ...)/(p + q + r + ...) </div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-24617728968689164062013-10-31T23:44:00.001-07:002013-10-31T23:44:29.017-07:00STPM Further Mathematics Model Exam Paper 1<div dir="ltr" style="text-align: left;" trbidi="on">
<a href="https://drive.google.com/file/d/0B3NUi_7xrhYgdEx6R3EyTEV5MEU/edit?usp=sharing">STPM Further Mathematics Model Paper 1</a><br />
<br />
<a href="https://drive.google.com/file/d/0B3NUi_7xrhYgaW01M09vc1hWRkk/edit?usp=sharing">STPM Further Mathematics Model Paper 1 - Solutions</a><br />
<br />
I have selected questions to cover almost all of the syllabus. Happy solving!</div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com4tag:blogger.com,1999:blog-28487404.post-80630949057064966542013-10-07T23:55:00.000-07:002013-10-07T23:55:32.077-07:00STPM Trial Exam Paper 2013<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<a href="https://docs.google.com/file/d/0B3NUi_7xrhYgSFJBNDhoR2lzSHM/edit?usp=sharing">STPM Further Math Trial Exam Paper 1 - 2013</a><br />
<br />
<a href="https://docs.google.com/file/d/0B3NUi_7xrhYgSkROaVVlcUdkV1E/edit?usp=sharing">STPM Further Math Trial Exam Paper 1 - 2013 - Solution</a><br />
<br />
I feel it is not practical to have students travel to Penang to take the trial exam for Further Math. Two main reasons are:<br />
1. It will take too much time to travel. for those who are too far from Penang.<br />
2. The cost in travelling and accommodation should not be just to take the test.<br />
<br />
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.<br />
<br />
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 <br />
<br />
Best regards from me.</div>
Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com1tag:blogger.com,1999:blog-28487404.post-10501046699910294812012-04-12T19:54:00.000-07:002012-04-12T19:54:30.785-07:00Probability<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<a href="http://probability/">Probability</a><br />
<br />
Examples and Questions base on the required contents in the new STPM Math Syllabus.</div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com3tag:blogger.com,1999:blog-28487404.post-91240270866743137432012-01-30T18:09:00.000-08:002012-01-30T18:09:29.718-08:00An Infinite Product<div dir="ltr" style="text-align: left;" trbidi="on">
I am thankful to have the chance to enjoy solving this problem.<br />
Click <a href="https://docs.google.com/open?id=0B3NUi_7xrhYgMTdlYWEwNDEtOGU4My00OGNkLTgyOTgtMzUyOWZhZWVjNDli">here</a> for the solution. <br />
<br /></div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-63289226049388918942012-01-29T06:58:00.000-08:002012-01-29T06:58:12.128-08:00Further Math STPM 2010 Answers<div dir="ltr" style="text-align: left;" trbidi="on">
Click <a href="https://docs.google.com/open?id=0B3NUi_7xrhYgZjY5MWU0NjctZjhlMS00ZTVhLTlmOTUtYjNjYzk4MmVlOTYw">here</a> for Further Mathematics STPM 2010 Answers.</div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-78759058383533698032012-01-26T06:47:00.001-08:002012-01-26T06:47:48.413-08:00Further Math 2003 Answers<div dir="ltr" style="text-align: left;" trbidi="on">
Click <a href="https://docs.google.com/open?id=0B3NUi_7xrhYgMmM2MzkwMzYtZjc0My00NmUyLTlmYmMtNWNjNTc1NGI2Mjk3">here</a> for Further Math 2003 Answers</div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-74156776985126994432012-01-26T06:44:00.000-08:002012-01-26T06:44:23.197-08:00Further Math 2002 Answers<div dir="ltr" style="text-align: left;" trbidi="on">
Click <a href="https://docs.google.com/open?id=0B3NUi_7xrhYgNmJkMDk1YmQtYzYwMy00ZTllLWFlY2QtZDYxNjhhMDVmZWM1">here</a> for Further Math 2002 Answers</div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-74857139577522868822012-01-26T06:12:00.000-08:002012-01-26T06:12:14.562-08:00Further Math 2011 Answers<div dir="ltr" style="text-align: left;" trbidi="on">
Click <a href="https://docs.google.com/open?id=0B3NUi_7xrhYgNDE0M2U3ZmQtYzk3OS00MjU2LWJkZTctYmI4M2IwODU5ODcx">here</a> for answers to STPM Further Math 2011 Answers</div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-79778770387822484702012-01-07T19:14:00.000-08:002012-01-07T19:38:45.227-08:00Teaching MathematicsTeaching Mathematics In the Higher Forms<br /><br />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.<br /><br />Teaching definitions using one word helps many students understand definitions such as<br />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?<br /><br />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.Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com2tag:blogger.com,1999:blog-28487404.post-86650009511669815832011-02-07T07:11:00.000-08:002011-02-07T07:22:04.625-08:00Greater Appreciation of Math for Pre-U Students<a href="https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B3NUi_7xrhYgY2U2ZGNlZjYtNDQwNS00N2M3LWE3YzQtZTI4YmZmMTIxZGVh&hl=en">Greater Appreciation in Mathematics For Pre-U Student</a><a href="https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B3NUi_7xrhYgY2U2ZGNlZjYtNDQwNS00N2M3LWE3YzQtZTI4YmZmMTIxZGVh&hl=en">s</a><br /><br />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.Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com2tag:blogger.com,1999:blog-28487404.post-42639652297178729472011-01-26T17:16:00.000-08:002011-01-26T17:24:37.152-08:00Olympiad Training Question On Algebra<a href="https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B3NUi_7xrhYgNmM5YTQyODctZTBkYy00ODUxLTlmZTEtZmFiMzcxOWNlNmI4&hl=en">An Exercise on Algebra</a><br /><br />The question rephrase can be rephrase as follows.<br /><br />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.Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com27tag:blogger.com,1999:blog-28487404.post-33410874842232868172011-01-26T17:06:00.000-08:002011-01-26T17:11:46.166-08:00Deductive Geometry - Olympiad Training Question<a href="https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B3NUi_7xrhYgZmU5ZGM3YTktMTgyMC00YmFiLWFhNGYtODU3MDhmODI4MTBl&hl=en">A Deductive Geometry Question involving Circle Properties</a>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com1tag:blogger.com,1999:blog-28487404.post-46053404314549621982010-11-04T07:57:00.000-07:002010-11-04T08:02:16.737-07:00Why (-1)(-1) = 1?<a href="https://docs.google.com/fileview?id=0B3NUi_7xrhYgZTg5OTc0ZTMtZmJlOC00YTA2LWJiNWYtZTQzNDBkYzQ2ZDUx&hl=en">Why (-1)(-1) = 1?</a><div><br /></div><div>Two methods shown.</div><div>1. Use of distributive law</div><div>2. Use of the Rule of Indices</div><div><br /></div><div>Some discussions are given to illustrate the use of negative numbers. </div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-50220056979696743302010-11-04T07:03:00.000-07:002010-11-04T07:10:01.089-07:00Polygons<a href="https://docs.google.com/fileview?id=0B3NUi_7xrhYgZDgxYzVjNjMtMTk3Zi00Nzg3LTljMDQtOWJkZGYwNWRhZTc3&hl=en">Sum of Interior Angles of A Polygons</a><div>There are 4 different proofs shown here. I am sure students will enjoy them.</div>Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-63999036181972040922010-07-23T13:52:00.000-07:002010-07-23T13:56:30.697-07:00International Standard Book Number<a href="http://docs.google.com/fileview?id=0B3NUi_7xrhYgMzlkOWJhMWYtZmNmMC00NzdiLWFiM2UtOWI2ZjgxMjc4N2Fi&hl=en">International Standard Book Number</a><br />This article is written for Thai students of Prichai Ratanakorn School from Ranong.Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0tag:blogger.com,1999:blog-28487404.post-78414662258879163562010-06-02T06:31:00.000-07:002010-06-02T06:36:16.989-07:00Square root of Complex Nos with Pythagorean Triples<a href="http://docs.google.com/fileview?id=0B3NUi_7xrhYgYTRiMmE0YzUtMDRjMy00NGU4LWE2MTQtNjIzMzkzNjM2ZWIz&hl=en">Square root of Complex Numbers with Pythagorean Triples</a><br /><br />This post is dedicated to Lower Six B of Penang Free School (Year 2010).Khor BHhttp://www.blogger.com/profile/16363531337170852655noreply@blogger.com0