tag:blogger.com,1999:blog-40700938988603448892024-03-14T12:32:44.124+08:002013 S3-05 Maths BlogJemaimahhttp://www.blogger.com/profile/09590012484957429518noreply@blogger.comBlogger149125tag:blogger.com,1999:blog-4070093898860344889.post-53362074726335115462013-10-23T07:00:00.000+08:002014-07-01T12:35:07.031+08:00MATHEMATICAL MODELLING 1 (INTRODUCTION)<h2>
<span style="color: blue; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-large;">SETTING THE CONTEXT</span></h2>
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<span style="font-size: large;">The following photos were taken along pavements and roads. </span><br />
<span style="font-size: large;">They show 'cracks' or 'gaps'. </span><br />
<br />
<ul>
<li><span style="font-size: large;">Are these cracks common phenomena? </span></li>
<li><span style="font-size: large;">Do they serve specific functions?</span></li>
</ul>
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi75Qqqcihker3W9Sm-oDP8e5uHZzbsN4dM20RrerRE1HwNwww-ICiBNo4CUyra2MM8gsMJ2wiQT7QcT4eXWz_YyvpaTlrOOT9msGlKC2LhES6_9FrfoJI_w5ijsB8oR9U-9ZxITrDaZ0mr/s1600/photo+4.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi75Qqqcihker3W9Sm-oDP8e5uHZzbsN4dM20RrerRE1HwNwww-ICiBNo4CUyra2MM8gsMJ2wiQT7QcT4eXWz_YyvpaTlrOOT9msGlKC2LhES6_9FrfoJI_w5ijsB8oR9U-9ZxITrDaZ0mr/s400/photo+4.JPG" height="400" width="301" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">PICTURE 2</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6Tmp7VciGM8Sy4Mbv1MWGWwtQR4sfLsa_CK3nsEt2J0vhLXuqUzyhpDGL3jfYscCISK2I93gRyEO4sdOLm4gwc0sKtPNLggcGE7vOsrwP5saWqB9b8I801xy202QYDvBt0SD-JL41p2uz/s1600/photo+3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6Tmp7VciGM8Sy4Mbv1MWGWwtQR4sfLsa_CK3nsEt2J0vhLXuqUzyhpDGL3jfYscCISK2I93gRyEO4sdOLm4gwc0sKtPNLggcGE7vOsrwP5saWqB9b8I801xy202QYDvBt0SD-JL41p2uz/s400/photo+3.JPG" height="400" title="picture 1" width="300" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">PICTURE 1</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQSAxLQe9T9KMEBYFrYJJoKJbyecCbT7z6PzSkgj1J0Ed_DlswsRfUgN8k7wTdyfN2omtL5oEtIsfsasPLD6iQ-GplLEmE8CU-YkC9ORWfEVSjYS-Ljwhuyh1SpFxIRf0ixdbJsM5qmLqe/s1600/photo+2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQSAxLQe9T9KMEBYFrYJJoKJbyecCbT7z6PzSkgj1J0Ed_DlswsRfUgN8k7wTdyfN2omtL5oEtIsfsasPLD6iQ-GplLEmE8CU-YkC9ORWfEVSjYS-Ljwhuyh1SpFxIRf0ixdbJsM5qmLqe/s400/photo+2.JPG" height="400" width="301" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">PICTURE 3</td></tr>
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<span style="color: blue; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-large;">REVISIT THE CONTEXT</span></h2>
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<span style="color: red;"><a href="http://nptel.iitm.ac.in/courses/105104098/TransportationII/lecture6/5slide.htm" target="_blank">joints in concrete pavements</a></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAwPsJWQobU_cBH9d7VuUL8Tmin0EGSUqYF21_66PQuLdJYnpMnkmL7yDXCx3adNbQbX74iArqDwenqb_yTl6UeY3H78fTtSHStNXSv2YSqApqsPeX6zRczzDh4EwGxHfRtEFzrYL9MD8G/s1600/Screen+Shot+2013-10-23+at+5.11.13+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAwPsJWQobU_cBH9d7VuUL8Tmin0EGSUqYF21_66PQuLdJYnpMnkmL7yDXCx3adNbQbX74iArqDwenqb_yTl6UeY3H78fTtSHStNXSv2YSqApqsPeX6zRczzDh4EwGxHfRtEFzrYL9MD8G/s640/Screen+Shot+2013-10-23+at+5.11.13+AM.png" height="292" width="640" /></a></div>
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<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-43692590613355647342013-10-23T06:00:00.000+08:002013-10-23T19:48:07.950+08:00MATHEMATICAL MODELLING 2 (OBJECTIVES)<br />
<h2>
<span style="color: blue; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-large;">OBJECTIVES</span></h2>
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<span style="font-size: large;">Understand the facets of <a href="http://sst2013-s305maths.blogspot.sg/p/math-framework.html" target="_blank">Applied Learning</a> through a Mathematics Lesson</span><br />
<span style="font-size: large;"><u><br /></u></span>
<span style="font-size: large;"><b>Authentic (Real World Application) </b></span><br />
<span style="font-size: large;">The focus on a science experiment as a basis to gather data and information</span><br />
<span style="font-size: large;"><br /></span>
<span style="font-size: large;"><b>Active & Relevant</b></span><br />
<span style="font-size: large;">Students will be engaged throughout the process as they are the co-constructors of knowledge (making <b><span style="color: red;">Prediction</span></b>, <span style="color: red;"><b>Observing</b></span> patterns and <b><span style="color: red;">Explaining </span></b>the final outcome(s))</span><br />
<span style="font-size: large;"><br /></span>
<span style="font-size: large;"><b>Integration (through inter-disciplinary approach)</b></span><br />
<span style="font-size: large;">Learning of cooling curve and using the Mathematical modeling to draw conclusion.</span><br />
<br /><span style="font-size: large;"><br /></span><br />
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-10837726830952264552013-10-23T05:00:00.001+08:002013-10-24T08:49:37.425+08:00MATHEMATICAL MODELLING 3 (POE)<br />
<h2>
<span style="color: blue; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-large;">RECALL - REVIEW - REFLECT</span></h2>
<span style="font-size: large;"><u>ACTIVITY </u></span><br />
<br />
<span style="font-size: large;">Measuring of body<b> temperature</b> against <b>time</b></span><br />
<br />
<span style="font-size: large;"><b><span style="color: red;">P</span></b>REDICT</span><br />
(before the experiment)<br />
<span style="font-size: large;">What do you think will be the characteristics of the <b>temperature</b> against <b>time</b> graph of this experiment?</span><br />
<span style="font-size: large;"><br /></span>
<span style="font-size: large;"><span style="color: red;"><b>O</b></span>BSERVE</span><br />
(during and after the experiment)<br />
<span style="font-size: large;">What do you notice about the graphical function(s) obtained?</span><br />
<span style="font-size: large;">Describe the characteristics?</span><br />
<span style="font-size: large;">Any unusual / distinct patterns observed?</span><br />
<span style="font-size: large;"><br /></span>
<span style="font-size: large;"><span style="color: red;"><b>E</b></span>XPLAIN</span><br />
(after experiment)<br />
<span style="font-size: large;">Are the experimental observations similar to the prediction? Why?</span><br />
<span style="font-size: large;">Can the outcome(s) be generalised for all cases?</span><br />
<span style="font-size: large;"><br /></span>
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkQ2BVzVqHat1SxfkJsjBH5dLnwLi2SzBv1_64WF__BECKIFcy_qSQXHIhwQsNJGn_1cefwxu-r2ay1835eMorIkbUZlcI_lLWIyIwO3iXVI5ZeXtAxbG9QN8TlzqYiE4aT9YkiX6q49xW/s1600/Photo1.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkQ2BVzVqHat1SxfkJsjBH5dLnwLi2SzBv1_64WF__BECKIFcy_qSQXHIhwQsNJGn_1cefwxu-r2ay1835eMorIkbUZlcI_lLWIyIwO3iXVI5ZeXtAxbG9QN8TlzqYiE4aT9YkiX6q49xW/s640/Photo1.jpeg" width="484" /></a></div>
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<h2 style="text-align: start;">
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<span style="color: blue; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-large;">RECALL - REVIEW - REFLECT</span></h2>
<h2 style="text-align: start;">
<b style="font-size: x-large; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">TYPES OF GRAPHS </span></b></h2>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8oyLmCYSU9rN7_Y9A7rinlJq_VnT_kWasD5FH1U1yQZZKHLMunJqxs0k3tKxkL7CRZJe50tXhrqGLjhfxZhWkY9L44BJ7SjnfnxgJHgJ5m-XF4TMQR-5rsJBhYMxLckMJAhAKzwtsQIkd/s1600/Screen+Shot+2013-10-23+at+5.49.57+AM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="336" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8oyLmCYSU9rN7_Y9A7rinlJq_VnT_kWasD5FH1U1yQZZKHLMunJqxs0k3tKxkL7CRZJe50tXhrqGLjhfxZhWkY9L44BJ7SjnfnxgJHgJ5m-XF4TMQR-5rsJBhYMxLckMJAhAKzwtsQIkd/s640/Screen+Shot+2013-10-23+at+5.49.57+AM.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Graphs</td></tr>
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<span style="font-size: large;"><u><br /></u></span>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-89383395196155795912013-10-23T05:00:00.000+08:002013-10-24T09:21:00.616+08:00MATHEMATICAL MODELLING 4 (ROUTINE)<br />
<h2>
<span style="color: blue; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-large;">CLASS LEARNING ROUTINE</span></h2>
<div class="separator" style="clear: both; text-align: center;">
<span style="color: red;"><br /></span></div>
<span style="color: red; font-size: large;"><b>Task in a Collaborative learning environment</b></span><br />
<span style="font-size: large;">You will be working in groups of 4 with the following roles:</span><br />
<ul>
<li><span style="font-size: large;">Student 1: Leader (lead the task and present findings)</span></li>
<li><span style="font-size: large;">Student 2: Scribe (capture learning and post in Mathematics Blog)</span></li>
<li><span style="font-size: large;">Students 3 & 4: Researchers (set-up apparatus for activities</span><span style="font-size: large;">)</span></li>
<li><span style="font-size: large;">All members will be involved in the activities through</span></li>
<ul>
<li><span style="font-size: large;">Group discussion</span></li>
<li><span style="font-size: large;">Prediction Making</span></li>
<li><span style="font-size: large;">Conduct of Experiment</span></li>
<li><span style="font-size: large;">Data Gathering (recording observations)</span></li>
<li><span style="font-size: large;">Presentation of Findings (explain the Mathematics model - graphical functions)</span></li>
</ul>
</ul>
<div>
<span style="color: red; font-size: large;"><b>Use of Apparatus / Equipment</b></span></div>
<div>
<span style="font-size: large;">Each group will have</span></div>
<div>
<ul>
<li><span style="font-size: large;">Learning Devices (for recording, researching, presenting)</span></li>
<li><span style="font-size: large;">One beaker</span></li>
<li><span style="font-size: large;">One TI-Nspire Calculator </span></li>
<li><span style="font-size: large;">One temperature probe</span></li>
</ul>
<div>
<span style="color: red; font-size: large;"><b>Set-up</b></span></div>
<div>
<br />
<ul>
<li><span style="font-size: large;">Go to your </span><b style="font-size: x-large;">Class Math Blog.</b></li>
<li><b style="font-size: x-large;">Set up </b><span style="font-size: large;">and </span><b style="font-size: x-large;">connect</b><span style="font-size: large;"> the TI-Nspire Calculator to the Local network. Refer to the instructions given. (ensure that your group appears on the teacher's screen)</span></li>
</ul>
</div>
</div>
<div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-h-sv8-eIAmy6BpiAb8F6iLAwfOh4aMFciCzyIo3lUyY5YSnx_gh1tvvsC0J36AN34VvoB_tarMBgNIMwL6zJBMMg9bDz1Db0l8Zi0Vj1R0hCKkwmrmt8DAQtwZ8wl8HkV5fC0zsrWb9z/s1600/Screen+Shot+2013-10-24+at+8.54.19+AM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="207" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-h-sv8-eIAmy6BpiAb8F6iLAwfOh4aMFciCzyIo3lUyY5YSnx_gh1tvvsC0J36AN34VvoB_tarMBgNIMwL6zJBMMg9bDz1Db0l8Zi0Vj1R0hCKkwmrmt8DAQtwZ8wl8HkV5fC0zsrWb9z/s320/Screen+Shot+2013-10-24+at+8.54.19+AM.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Class Math Blog</td></tr>
</tbody></table>
<br /></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-83628284906216067262013-10-23T03:00:00.000+08:002013-10-24T08:52:49.301+08:00MATHEMATICAL MODELLING 5 (STUDENT CENTRED EXPERIMENT)<h2>
<span style="color: blue; font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-large;">STUDENT-CENTRED ACTIVITY </span></h2>
<div class="separator" style="clear: both;">
<br /></div>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><u>STUDENT-CENTRED ACTIVITY </u></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">In this experiment, You have to use the
POE thinking routine approach to learn about the temperature change in 2
scenarios.</span></span><br />
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<span lang="EN-GB" style="font-family: Arial; font-size: 12.0pt; mso-ansi-language: EN-GB; mso-bidi-font-weight: bold; mso-bidi-language: AR-SA; mso-fareast-font-family: SimSun; mso-fareast-language: ZH-CN;"><span style="font-size: small;"><span lang="EN-GB" style="font-family: Arial; font-size: 12.0pt; mso-ansi-language: EN-GB; mso-bidi-font-weight: bold; mso-bidi-language: AR-SA; mso-fareast-font-family: SimSun; mso-fareast-language: ZH-CN;"><span style="font-size: small;"><br /></span></span></span></span></div>
<span lang="EN-GB" style="font-family: Arial, Helvetica, sans-serif; font-size: 12.0pt; mso-ansi-language: EN-GB; mso-bidi-font-weight: bold; mso-bidi-language: AR-SA; mso-fareast-font-family: SimSun; mso-fareast-language: ZH-CN;"><span style="font-size: small;">
</span><b style="color: red; font-size: x-large;">TASK STRUCTURE</b></span><br />
<div>
<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><b>in brief</b></span></div>
<div>
<div class="MsoCommentText">
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Predict by sketching the possible relationships between Temperature against time for BOTH scenarios. Indicate any intersections, turning points and any other possible characteristics based on your prediction.</span></li>
</ul>
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">You are given <u>40 minutes to do prediction, experiments, discussions and uploading of presentation on the S3-05 class Math blog (<span style="background-color: #fff2cc;">create a new page</span>).</u> You have to decide on the time and task management. </span></li>
</ul>
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Follow the format of your Presentation for BOTH scenarios as shown below.</span></li>
</ul>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b style="color: red;"></b><br /></span>
<b style="color: red;"><span style="font-family: Arial, Helvetica, sans-serif;">in detail</span></b><br />
<ol>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Post your</span><span style="font-family: Arial, Helvetica, sans-serif;"> </span><b style="font-family: Arial, Helvetica, sans-serif;"><span style="color: blue;">PREDICTION</span></b><span style="font-family: Arial, Helvetica, sans-serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif;">in the Class mathematics blog. </span></li>
<ol>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Include a Sketch (you may use any sketching tools) and </span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">a brief writeup of the Predicted mathematical model Example. Quadratic with a maximum turning point at ...(<span style="background-color: yellow;">BEFORE THE EXPERIMENT</span>)</span></li>
</ol>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Conduct the scenario and</span><span style="font-family: Arial, Helvetica, sans-serif;"> </span><span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><b>OBSERVE</b></span><span style="font-family: Arial, Helvetica, sans-serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif;">patterns, unusual phenomena /patterns /observations (if any). You may repeat it a few times. </span></li>
<ol>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Do a screen capture and post your experimental findings and </span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">identify the Mathematical model(s) that best suit the graphical function(s). example Linear from 0-4 s and then Quadratic etc. </span></li>
</ol>
<li><b style="color: blue; font-family: Arial, Helvetica, sans-serif;">EXPLAIN </b>your Prediction and Observations by posting the following in your blog.</li>
<ol>
<li><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -14.15pt;">Compare and contrast the predictions with the actual results, are there any significant differences? Why?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-GB" style="text-indent: -14.15pt;"> </span></span><span lang="EN-GB" style="text-indent: -14.15pt;">What are the characteristics of the graphs?</span></li>
</ol>
<ul><ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-indent: -18pt;">a. </span></span><span style="text-indent: -18pt;">the slope from start to finish (steeper, gentler)</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-indent: -18pt;">b. </span></span><span style="text-indent: -18pt;">intersections with axes (if any)</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-indent: -18pt;">c. </span></span><span style="text-indent: -18pt;">possible turning point (if any)</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-indent: -18pt;">d. </span></span><span style="text-indent: -18pt;">any asymptote?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-indent: -18pt;">e. </span></span><span style="text-indent: -18pt;">And any other evidence</span></li>
</ul>
</ul>
<li><span lang="EN-GB" style="font-family: Arial, Helvetica, sans-serif; text-indent: -14.15pt;">What are the assumptions you have to make for this experiment? What are the sources for discrepancies?</span></li>
</ol>
</div>
<div>
<b style="color: red; font-family: Arial; font-size: x-large;"></b>Sample format:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfFffYtVneDZKtxzA3Tj1v3Pg5YpyMTDcl_UwagmhNHtrvh8lBmrk_1ilOlM3KdMm1wykcECs31uYJl4AVW03jB8VdF3_1SFA5rO0kuU7jLWoxF-VP2nDcBNW7xvrYCZeFMfEhpSjuDvVe/s1600/Screen+Shot+2013-10-23+at+11.26.43+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="614" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfFffYtVneDZKtxzA3Tj1v3Pg5YpyMTDcl_UwagmhNHtrvh8lBmrk_1ilOlM3KdMm1wykcECs31uYJl4AVW03jB8VdF3_1SFA5rO0kuU7jLWoxF-VP2nDcBNW7xvrYCZeFMfEhpSjuDvVe/s640/Screen+Shot+2013-10-23+at+11.26.43+PM.png" width="640" /></a></div>
<br />
<br />
<hr />
<b style="color: red; font-family: Arial; font-size: x-large;">SCENARIO 1</b><span style="font-family: Arial;"> </span><br />
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<span lang="EN-GB" style="font-family: Arial; mso-bidi-font-weight: bold; mso-fareast-language: ZH-CN;">Start with your prediction:
Predict the relationship between <b>temperature</b> against <b>time </b>when you place the
probe in <u>hot water ONLY</u>. </span></div>
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<br /></div>
<div class="MsoNoSpacing">
<span lang="EN-GB" style="font-family: Arial; mso-bidi-font-weight: bold; mso-fareast-language: ZH-CN;"><b style="color: red; font-size: x-large;">SCENARIO 2</b> </span></div>
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<span lang="EN-GB" style="font-family: Arial; mso-bidi-font-weight: bold; mso-fareast-language: ZH-CN;">Predict the relationship between<b> temperature</b> against <b>time</b> when you <u>add few ice cubes</u> into the <u>hot water</u>. <o:p></o:p></span></div>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-64896970305899900432013-10-23T02:00:00.000+08:002013-10-23T18:54:00.010+08:00MATHEMATICAL MODELLING 6 (POST ACTIVITY REFLECTION)<iframe frameborder="0" height="1300" marginheight="0" marginwidth="0" src="https://docs.google.com/a/sst.edu.sg/forms/d/175cETEIxd5-Jd3ubxjFwVM2pWjgEA_w3BTK3CmRCGTA/viewform?embedded=true" width="760">Loading...</iframe>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-25039367995992710222013-09-20T10:47:00.001+08:002013-09-20T10:47:40.201+08:00TI84 exercise<div class="separator" style="clear: both; text-align: center;">
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-51244829276292964182013-09-18T05:34:00.004+08:002013-09-18T05:34:39.055+08:00Finding the centre of the circle — Aziel and Charlene<b><span style="font-family: Arial, Helvetica, sans-serif;">Finding the centre of the circle</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">We drew two long arcs with the same radius from opposite sides of the circle, making a line that passes through where the arcs intersected. This finds the perpendicular bisector of the undrawn line connecting the two points the arcs originated from.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">We turned the paper a rough 90° and repeated the same process. The instance where the two perpendicular bisectors intersect was the centre of the circle.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Proof of how we found the centre of the circle</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">The perpendicular bisector of any chord in a circle would be its diameter if extended from one point of the circumference to the other. This is because a line connecting the centre of the circle to a chord is perpendicular to the chord it connects the centre to.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">What we have done is find the perpendicular bisector of two chords and, since the diameters would intersect in the centre, hence have used this method to find it.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Finding the diameter and radius of the circle</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Extending or limiting the line drawn by the arc intercepts to exactly at the circumference and measuring this line, we found that the diameter was approximately 10.25 cm and that the radius was approximately 5.125 cm.</span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-39863044278512632022013-09-17T22:14:00.004+08:002013-09-17T22:14:50.228+08:00Finding the centre of a circle - Esther, Dawn & Dylaine<div class="separator" style="clear: both; text-align: left;">
To find the <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="26657306-5940-43e1-ba50-2c4abbde0f89" ginger_sofatware_uiphraseguid="8533236e-63da-4c26-ae8f-6e2428e32863" grcontextid="centre:0">centre</span> of the circle, we drew a chord of the circle, then drew an arc from each of the two end points of the chord of the same radius length. From the two intersecting points formed by the arcs, we were able to construct a diameter of the circle, from the Bisecting Chord Theorem (<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c7aa64c1-d95d-4953-aac9-3217805576ec" ginger_sofatware_uiphraseguid="a589698a-b195-4833-a936-0b6668c21ebd" grcontextid="perpendicular bisector:0">perpendicular bisector</span> of <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="65f3b785-0146-4645-af1d-71950bfbf79b" ginger_sofatware_uiphraseguid="a589698a-b195-4833-a936-0b6668c21ebd" grcontextid="chord:1">chord</span> is <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5075eaf4-ee04-4b87-ba6a-1f41697cb089" ginger_sofatware_uiphraseguid="a589698a-b195-4833-a936-0b6668c21ebd" grcontextid="diameter:2">diameter</span>).</div>
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This was repeated to find another diameter, in which the intersection with the first diameter is the <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0aaf4ee6-472d-43a1-8f22-ff8ba08c1943" ginger_sofatware_uiphraseguid="67e1c80b-4019-40fe-9aa6-1194f33d7e45" grcontextid="centre:0">centre</span> of the circle.</div>
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<br /><br />Anonymoushttp://www.blogger.com/profile/11048163135680307869noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-37986158036276200212013-09-17T22:11:00.003+08:002013-09-17T22:11:23.232+08:00Finding the center and radius of a circle (Guo Jin, Luke, Jerome)<b>1) How to find the center of a circle:</b><br />
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Assume we have a circle</div>
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We will use the property: angles in a semicircle = 90º.<br />
This property shows that if a triangle is drawn inside a semicircle, the angle opposite the diameter will be 90º.<br />
With this property in mind, let us draw a 90º angle at a point on the circumference of the circle.<br />
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The 2 lines from the 90º angle form 2 sides of a triangle inscribed inside a semicircle. This can be derived by working backwards from the property of angles in a semicircle. Since the triangle is inscribed inside the semicircle, the 3rd side of the triangle is the diameter of the semicircle, and thus the diameter of the circle itself.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO7FZ_0fCaHCGUDMGJLJe0JUXuBoR3OEjwFkrPGAcYcwIx2AJWDlWykzYG8uE7j0qLfiudmBuwKPd7af2YuUHG_ZOIg9oyjE-N3Th6WodG_dcQXkdnTEK6CeuAIaX739avREKc4EFFy5ae/s1600/Transmutation_circle_Template_by_Notshurly.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO7FZ_0fCaHCGUDMGJLJe0JUXuBoR3OEjwFkrPGAcYcwIx2AJWDlWykzYG8uE7j0qLfiudmBuwKPd7af2YuUHG_ZOIg9oyjE-N3Th6WodG_dcQXkdnTEK6CeuAIaX739avREKc4EFFy5ae/s320/Transmutation_circle_Template_by_Notshurly.jpg" width="320" /></a></div>
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We can repeat the process again, and draw another right angle. By extending the lines formed by the right angle, another triangle inscribed in the semicircle is formed. Again, the 3rd side of this triangle is the diameter.<br />
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The point where the two diameters intersect is the center of the circle. (All diameters pass through the center, and all diameters intersect only at the center.)<br />
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<b>2) How to find the radius of a circle </b><br />
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<u>Method 1</u><br />
Assuming we have another circle<br />
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Draw 2 lines of the same length joined at a 90º angle at the circumference. Join the lines with another line.<br />
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These lines form the 2 sides of an inscribed triangle in the semicircle (the semicircle is the circle divided in half). The third side of the triangle would be the diameter of the semicircle which the triangle is inscribed in. The semicircle's diameter is the diameter of the circle itself.<br />
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Draw another line down from the point where the lines meet. Since the lines are of equal length, the line drawn here will bisect the diameter, forming 2 radii. The line that is drawn down to meet the diameter is also another radius.<br />
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Therefore, the radius can be determined.<br />
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<u>Other Methods:</u><br />
If the center has already been found, using methods such as in the previous part,<br />
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Draw a line from the center to the circumference, on one side. This line is the radius.<br />
This method can be used for any other circle which the center is already known.<br />
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Otherwise, calculation can be used. If the diameter, circumference or area of the circle is known, their respective formulas can be applied to obtain the radius.<br />
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Measurement can also be used.<br />
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Anonymoushttp://www.blogger.com/profile/06905317595557509399noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-78361902909206953952013-09-16T22:55:00.001+08:002013-09-16T23:07:52.181+08:00Circle Circle Circle<br />
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<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">3A</span></span></b></div>
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<span style="font-size: large;">introduction to task</span></div>
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<span style="font-family: Arial; font-size: 14pt;"><b>TASK:</b></span><br />
<span style="font-family: Arial;"><span style="font-size: 19px;">this a group task.</span></span><br />
<span style="font-family: Arial;"><span style="font-size: 19px;">Post your responses of the following:</span></span><br />
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<li><span style="font-family: Arial; font-size: 19px;">Why is a circle a 'circle' and why it is NOT a triangle? </span><span style="font-family: Arial; font-size: 19px;">Describe its characteristics.</span></li>
<li><span style="font-family: Arial; font-size: 19px;">Give at least 2 examples of daily objects, figures, shapes that could be classified as a circle.</span></li>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com21tag:blogger.com,1999:blog-4070093898860344889.post-80980541781899712232013-09-16T22:51:00.000+08:002013-09-16T23:13:40.493+08:00Find my Centre - Authentic Task<br />
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<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">3</span></span></b></div>
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<b>Objective: </b></div>
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This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.</div>
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<b>ICT tools:</b> </div>
your choice (Geogebra, Geometer Sketch Pad etc)<br />
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<a href="http://www.delcam.tv/delcam-video.asp?VideoId=17" target="_blank"><img border="0" height="235" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAIWMGZ2UC9OMEJBVPeYoLU-NUfCNYDhUOFN_L9uys9BwdY_OYpZTeRqIYIIwPHOIkPAm-jmqO3x9682P8FH_xxaSFNQPUJCcUOzMxU3o85qvGVCqekH9PQdUSeNcgclUf7LoUqxm8x8Si/s320/Screen+Shot+2013-09-16+at+11.00.58+PM.png" width="320" /></a></div>
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<a href="http://mould making process" target="_blank">mould making process</a></div>
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<span style="font-family: Arial; font-size: 14pt;">TASK:</span><br />
<span style="font-family: Arial;"><span style="font-size: medium;">You are a mechanical engineer that is supervising a mould making process. You have just been tasked to replicate a circular object in your production line. The products must be precise (congruent of the highest degree) and must be mass produced efficiently at the shortest possible time with </span><span style="font-size: 19px;">minuscule</span><span style="font-size: medium;"> margin of error. </span></span><br />
<span style="font-family: Arial;"><span style="font-size: medium;"><br /></span></span>
<span style="font-family: Arial;"><span style="font-size: medium;">The first task is to produce a mould by which all the objects will be replicated from. </span></span><br />
<span style="font-family: Arial;"><span style="font-size: medium;"><br /></span></span>
<span style="font-family: Arial;"><span style="font-size: medium;">To facilitate the process, you are required to first determine how you would determine the following</span></span></div>
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<ol>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">centre of the circle</span></li>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">radius of the circle / sphere</span></li>
</ol>
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<span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">For the above activity, you are required to use the angles properties discovered in the topic. </span><br />
<span style="color: red; font-family: Arial; font-size: 14pt; text-indent: -18pt;">Do provide the logical reasoning in your answer.</span><br />
<span style="color: red; font-family: Arial; font-size: 14pt; text-indent: -18pt;">Post your solution in <u>blog page</u> assigned to you.</span><br />
<span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">Remember time is a factor so you have to plan your time very well.</span></div>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-5676079642035016952013-09-16T22:09:00.003+08:002013-09-16T22:09:42.538+08:00Assessment in Term 4 2013<span style="font-family: Arial, Helvetica, sans-serif;">Dear SSTudents,</span><br />
<span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">1. Performance Task 2 (in lieu of Elementary Mathematics)</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">As mentioned earlier the deadline of the PT2 is 16 September 2013 @ 2359. To date many students have submitted their products with high quality questions and 'proof's. Effective use of ICT tools (google, Blog, Geogebra, Keynote, Powerpoint, Pretzi etc) have further enhanced the final product.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">2. Paper 3 (in lieu of Additional Mathematics)</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">The assessment information will be as follows:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Date: <span style="color: red;"><b> 23 September </b></span> 2013 (Monday)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> (Please be punctual and ensure you have a heavier meal in the morning)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Time: 3.00 pm to 4.00 pm</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Venue: Auditorium</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Note that you are required to sit according to your classes and index numbers. The teachers will supervise you on this.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Logistic:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">TI84 Graphic Calculator (or other approved GC model)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">(no other calculator will be allowed)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Stationery - pen and ruler</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">3. Information on EOY</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Please refer to your class math blog or google site earlier entries on this.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<i><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">All the best - you can do it because we have faith in you but do you!</span></i>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-68434459559945113472013-09-15T22:51:00.004+08:002013-09-15T22:51:47.584+08:00Angles in a Circle - MULTIMODAL LEARNING<div class="separator" style="clear: both; text-align: left;">
<b><span style="color: #cc0000;">ACTIVITY 1</span></b></div>
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<b><br /></b></div>
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<b>Objective: </b></div>
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This is a self directed activity to consolidate the learning of angles in a circle. </div>
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<b><br /></b></div>
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<b>ICT tools:</b> </div>
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Math Blog for activity specifications</div>
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TI-Nspire CAS</div>
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tns file will be given at the beginning of session</div>
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<!--StartFragment-->
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<div class="MsoNormal" style="text-align: left;">
<br />
<div class="separator" style="clear: both;">
<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">2</span></span></b></div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>Objective: </b></div>
<div class="separator" style="clear: both;">
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz formative assessment. </div>
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Error analysis will follow the assessment.</div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
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<b>ICT tools:</b> </div>
<div class="separator" style="clear: both;">
TI-Nspire CAS</div>
<div class="separator" style="clear: both;">
tns -based poll will be used to assess learning.</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH-71GOE4rpqfbq1xeWAWwyr_r4Ui-jWeKhKbH6x9eO3kc_m5RCKv6nISypUTUwzNXD0b0GNc-iDGkVqZU0V2BGx9wgaf2BwkMtAORdddgoBJAUDjochmpb7KgAtXjrWNTE6PkdD-b81M/s1600/Screen+Shot+2013-09-15+at+10.45.53+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH-71GOE4rpqfbq1xeWAWwyr_r4Ui-jWeKhKbH6x9eO3kc_m5RCKv6nISypUTUwzNXD0b0GNc-iDGkVqZU0V2BGx9wgaf2BwkMtAORdddgoBJAUDjochmpb7KgAtXjrWNTE6PkdD-b81M/s320/Screen+Shot+2013-09-15+at+10.45.53+PM.png" width="320" /></a></div>
<div class="separator" style="clear: both;">
<br /></div>
</div>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<div class="MsoNormal" style="text-align: left;">
<div class="separator" style="clear: both;">
<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">3</span></span></b></div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>Objective: </b></div>
<div class="separator" style="clear: both;">
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.</div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>ICT tools:</b> </div>
TI-Nspire CAS<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFkx3VuQbUTIXyNsKc2WI8udi6BhV1nPIEdRG5Ntt1Q_eYIpczUyKS_tpBAvpCFCcM-hpzzvEArCfnqdEQHDvMbVMj6H9hO0uJTiIFZV4_ofJquzV-DN3EaQMNndW_8530-yjmKQb3qf8/s1600/Screen+Shot+2013-09-15+at+10.48.33+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFkx3VuQbUTIXyNsKc2WI8udi6BhV1nPIEdRG5Ntt1Q_eYIpczUyKS_tpBAvpCFCcM-hpzzvEArCfnqdEQHDvMbVMj6H9hO0uJTiIFZV4_ofJquzV-DN3EaQMNndW_8530-yjmKQb3qf8/s320/Screen+Shot+2013-09-15+at+10.48.33+PM.png" width="320" /></a></div>
<span style="font-family: Arial; font-size: 14.0pt; mso-bidi-font-size: 12.0pt;"><br /></span>
<span style="font-family: Arial; font-size: 14.0pt; mso-bidi-font-size: 12.0pt;">TASK:</span><br />
<span style="font-family: Arial; font-size: 14.0pt; mso-bidi-font-size: 12.0pt;">Given the object, determine how you would determine the
following</span></div>
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<ol>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">centre of the circle</span></li>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">radius of the circle / sphere</span></li>
</ol>
<div class="MsoNormal" style="text-align: left;">
<span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">For the above activity, you are required to use the angles
properties discovered in the topic. Do provide the logical reasoning in your
answer.</span></div>
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<div style="text-align: left;">
<br /></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-73296555477993832072013-09-04T13:42:00.001+08:002013-09-04T13:44:48.267+08:00Circle propeties<div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwZrx5i7MOfzQSF59vciRBxOtu7w3W9gvRpTjqv39Z3ZAxcz74yhHzsGGupdlJabQseOZOAQGtYagevmqRBLkpdS5x-17V6CE2kExU-onuxJFpsNvss7uahtQQtn4XVzUwoZRyienAxXI/s1600/DSC_0242.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwZrx5i7MOfzQSF59vciRBxOtu7w3W9gvRpTjqv39Z3ZAxcz74yhHzsGGupdlJabQseOZOAQGtYagevmqRBLkpdS5x-17V6CE2kExU-onuxJFpsNvss7uahtQQtn4XVzUwoZRyienAxXI/s640/DSC_0242.jpg"> </a> </div>Sim Bowenhttp://www.blogger.com/profile/14268203390199606308noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-75928897733940701702013-09-04T12:52:00.008+08:002013-09-04T12:52:55.723+08:00Circle - Alternate Segment Theorem<br />
<h4>
<span style="font-weight: normal;">source: http://www.onlinemathlearning.com</span></h4>
<h2>
The Alternate Segment theorem states</h2>
<blockquote style="background-color: #d6d2d2; color: #000066; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 20px; margin: 12px 56px;">
<div class="definition" style="color: #990000; font-weight: bold;">
An angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.</div>
</blockquote>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18416" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcBNAYy5p36u7acuEJhyNcwS4u4DHSqwqLPzcFS51V4XsLRHApPSSki3GBm7lPGgz2x2c0azBSt63LC3wNCw3TE9WuZ06R8GXSVLKwkJhYpkqkQTS6Bl_z40E7bRztgReW7CO6mIZqOTE/s1600/Screen+Shot+2013-09-04+at+8.14.58+AM.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18416" target="_blank">link to activity</a></div>
<br />
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
Recall that a chord is any straight line drawn across a circle, beginning and ending on the curve of the circle.</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
In the following diagram, the chord <em>CE</em> divides the circle into 2 segments. Angle <em>CEA</em>and angle <em>CDE</em> are <span class="definition" style="color: #990000; font-weight: bold;">angles in alternate segments</span> because they are in opposite segments.</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<img height="154" src="http://www.onlinemathlearning.com/image-files/alternate-segment-theorem1.gif" style="border: 0px solid rgb(221, 221, 221);" width="236" /> </div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
The <strong class="definition" style="color: #990000;">alternate segment theorem</strong> states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
In terms of the above diagram, the alternate segment theorem tells us that angle<em>CEA </em>and angle <em>CDE</em> are equal.<br /><br /><br /></div>
<div class="highlight-step" style="background-color: #d6d2d2; color: #008800; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<strong><em>Example:</em></strong></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
In the following diagram, <em>MN</em> is a tangent to the circle at the point of contact <em>A.</em>Identify the angle that is equal to <em>x</em></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<br /></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<img height="160" src="http://www.onlinemathlearning.com/image-files/alternate-segment-theorem2.gif" style="border: 0px solid rgb(221, 221, 221);" width="229" /> </div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<br /></div>
<div class="highlight-subheading" style="background-color: #d6d2d2; color: #009933; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<strong><em>Solution:</em></strong></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
We need to find the angle that is in alternate segment to <em>x.</em></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<em>x</em> is the angle between the tangent <em>MN</em> and the chord <em>AB.</em></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
We look at the chord <em>AB</em> and find that it subtends angle <em>ACB</em> in the opposite segment.</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<img height="128" src="http://www.onlinemathlearning.com/image-files/alternate-segment-theorem3.gif" style="border: 0px solid rgb(221, 221, 221);" width="177" /> </div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
So, angle <em>ACB</em> is equal to <em>x</em>.</div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-9506649272361981282013-09-04T12:52:00.004+08:002013-09-04T12:52:19.087+08:00Circle - Cyclic Quadrilateral<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 1.75em; margin-bottom: 0.5em; margin-top: 0.4em; padding: 0px; text-align: -webkit-auto; vertical-align: baseline;">
source: <a href="http://www.artofproblemsolving.com/">http://www.artofproblemsolving.com/</a></div>
<div style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 1.75em; margin-bottom: 0.5em; margin-top: 0.4em; padding: 0px; text-align: -webkit-auto; vertical-align: baseline;">
A <b>cyclic quadrilateral</b> is a <a href="http://www.artofproblemsolving.com/Wiki/index.php/Quadrilateral" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Quadrilateral">quadrilateral</a> that can be inscribed in a <a href="http://www.artofproblemsolving.com/Wiki/index.php/Circle" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Circle">circle</a>. They have a number of interesting properties.</div>
<center style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 12px; line-height: 16px;">
<a class="image" href="http://www.artofproblemsolving.com/Wiki/index.php/File:Cyclicquad2.png" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="Cyclicquad2.png" height="241" src="http://www.artofproblemsolving.com/Wiki/images/3/3e/Cyclicquad2.png" style="border: none; vertical-align: middle;" width="248" /></a></center>
<h2 style="background-color: white; background-image: none; border-bottom-color: rgb(170, 170, 170); border-bottom-style: solid; border-bottom-width: 1px; font-family: Verdana, Geneva, sans-serif; font-size: 18px; font-weight: normal; line-height: 1em; margin: 0px 0px 0.6em; padding: 0.5em 0px 0.17em; vertical-align: top;">
<span class="mw-headline" id="Properties">Properties</span></h2>
<div style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 1.75em; margin-bottom: 0.5em; margin-top: 0.4em; padding: 0px; text-align: -webkit-auto; vertical-align: baseline;">
In cyclic quadrilateral <a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=fb2f85c88567f3c8ce9b799c7c54642d0c7b41f6&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="ABCD" class="latex" src="http://data.artofproblemsolving.com/images/latex/f/b/2/fb2f85c88567f3c8ce9b799c7c54642d0c7b41f6.gif" style="border: none; margin: 0px; vertical-align: 0px;" title="ABCD" /></a>:</div>
<ul style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 12px; line-height: 16px; list-style-image: url(http://www.artofproblemsolving.com/Wiki/skins/aops/bullet.gif); list-style-type: square; margin: 0.3em 0px 0px 3em; padding: 0px; text-align: -webkit-auto;">
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=91604050363ceb3b5be3dd2c59c930a2e3fa6a55&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle A + \angle C = \angle B + \angle D = {180}^{o}" class="latex" src="http://data.artofproblemsolving.com/images/latex/9/1/6/91604050363ceb3b5be3dd2c59c930a2e3fa6a55.gif" style="border: none; vertical-align: -2px;" title="\angle A + \angle C = \angle B + \angle D = {180}^{o}" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=cd0aba64745c5b558af5554556133da238c47242&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle ABD = \angle ACD" class="latex" src="http://data.artofproblemsolving.com/images/latex/c/d/0/cd0aba64745c5b558af5554556133da238c47242.gif" style="border: none; vertical-align: -1px;" title="\angle ABD = \angle ACD" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=77e6bcfc5538d8ed952df2a3385ffd9ed630b21a&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle BCA = \angle BDA" class="latex" src="http://data.artofproblemsolving.com/images/latex/7/7/e/77e6bcfc5538d8ed952df2a3385ffd9ed630b21a.gif" style="border: none; vertical-align: -1px;" title="\angle BCA = \angle BDA" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=ece76b3f12dea4aed5e214281185b56411f6e62a&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle BAC = \angle BDC" class="latex" src="http://data.artofproblemsolving.com/images/latex/e/c/e/ece76b3f12dea4aed5e214281185b56411f6e62a.gif" style="border: none; vertical-align: -1px;" title="\angle BAC = \angle BDC" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=c0e409f526db77b37478a0aa9d992e2431394236&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle CAD = \angle CBD" class="latex" src="http://data.artofproblemsolving.com/images/latex/c/0/e/c0e409f526db77b37478a0aa9d992e2431394236.gif" style="border: none; vertical-align: -1px;" title="\angle CAD = \angle CBD" /></a></li>
</ul>
<h2 style="background-color: white; background-image: none; border-bottom-color: rgb(170, 170, 170); border-bottom-style: solid; border-bottom-width: 1px; font-family: Verdana, Geneva, sans-serif; font-size: 18px; font-weight: normal; line-height: 1em; margin: 0px 0px 0.6em; padding: 0.5em 0px 0.17em; vertical-align: top;">
<span class="mw-headline" id="Applicable_Theorems.2FFormulae">Applicable Theorems/Formulae</span></h2>
<div style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 1.75em; margin-bottom: 0.5em; margin-top: 0.4em; padding: 0px; text-align: -webkit-auto; vertical-align: baseline;">
The following theorems and formulae apply to cyclic quadrilaterals:</div>
<ul style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 12px; line-height: 16px; list-style-image: url(http://www.artofproblemsolving.com/Wiki/skins/aops/bullet.gif); list-style-type: square; margin: 0.3em 0px 0px 3em; padding: 0px; text-align: -webkit-auto;">
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a href="http://www.artofproblemsolving.com/Wiki/index.php/Ptolemy%27s_Theorem" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Ptolemy's Theorem">Ptolemy's Theorem</a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="mw-redirect" href="http://www.artofproblemsolving.com/Wiki/index.php/Brahmagupta%27s_formula" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Brahmagupta's formula">Brahmagupta's formula</a></li>
</ul>
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<a href="http://www.geogebratube.org/student/m18415" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKYZYr1dfyT0v61cykBE5uvw598NSfb0s5hNZ5y1MNzfQ1Nw2t_qYLs1-w9IgPjPxA98KU-8-aK3nEY6jLhr0Q2oUtOvEEDyLrjFSFG5q05Lu7hHk10D44TwBzu8Dc_s_5BV2meEsJl4M/s1600/Screen+Shot+2013-09-04+at+8.14.17+AM.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18415" target="_blank">the link</a></div>
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<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-88130288485227976962013-09-04T12:51:00.003+08:002013-09-04T12:51:27.538+08:00Circle - angles @ centre & angles in same segment<h2>
<b>Class based activity:</b></h2>
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<b>Objectives: </b></div>
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to proof the validity of the following theorems through geometrical manipulations using Geogebra.</div>
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Theorem 1: Angle at the centre theorem</div>
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Theorem 2: Angle in a semi circle theorem</div>
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Theorem 3: Angles in the same segment</div>
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<b><span style="color: purple;">Activity 1:</span></b></div>
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Using the attached links explore the following:</div>
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a. the various permutations of Angle at the centre theorem</div>
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b. the relationship between Angle at the centre theorem and Angle in a semi circle theorem</div>
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<br /></div>
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<span style="color: purple;"><b>Activity 2:</b></span></div>
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Using the attached links explore the limitations of Angles in the same segment theorem.</div>
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<a href="http://www.geogebratube.org/student/m18414" target="_blank"><img border="0" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_3Zq9o1E1Xsu3bZ-C2_XmD5xkzAnfHDkNhKfJfG-D0xNEj49d6uHO9T2ohMEVmC2ohVhyphenhyphen4q9OTQm6ZFco0y-Q-YEEJ-dqB54OMpLIvUqgFUkcp9qN3wkGIG37sGyZU67uhlJQPvhp3FY/s320/Screen+Shot+2013-09-03+at+6.03.56+PM.png" width="320" /></a></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18414" target="_blank">link to activity</a>1</div>
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<a href="http://www.geogebratube.org/student/m18418" target="_blank"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjm7pkb1Rnbi2QcMi5auKY6XiLbm5MXyBP4C9Srp6Xt4h0Kh6Qw_ug7sNOeCmzEdxc3tP9X4j2jL4sRgZ3PMj8Gj9-z5G554laoTeVHVaePUo_Gb-zEbbAeTLMBBprXV9-1G9fxGJ7kbWQ/s320/Screen+Shot+2013-09-03+at+6.05.36+PM.png" width="320" /></a></div>
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<a href="http://www.geogebratube.org/student/m18418" target="_blank">link to activity</a>2</div>
<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-86737937945140111332013-09-02T22:52:00.002+08:002013-09-02T22:59:59.765+08:00Circle - angle propertiessource: <a href="http://www.onlinemathlearning.com/angles-circle.html">http://www.onlinemathlearning.com/angles-circle.html</a><br />
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<iframe allowfullscreen="" frameborder="0" height="415" src="//www.youtube.com/embed/H2d3uVdFNmU" width="620"></iframe>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrQlhIQKoNL32-jleBixapo3Xxw2bhX6T231qKYr67lcgTdTLgZR-N_ayRBnfhTZqQm3pZShExq-wrqJd7WrnGOTlSnR23Nobkxe7hOgljuD2ONQcUkT4g5zUD2IMO7mlb-YpSjeI34GI/s1600/Screen+Shot+2013-09-02+at+10.46.22+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><br /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrQlhIQKoNL32-jleBixapo3Xxw2bhX6T231qKYr67lcgTdTLgZR-N_ayRBnfhTZqQm3pZShExq-wrqJd7WrnGOTlSnR23Nobkxe7hOgljuD2ONQcUkT4g5zUD2IMO7mlb-YpSjeI34GI/s1600/Screen+Shot+2013-09-02+at+10.46.22+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><br /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrQlhIQKoNL32-jleBixapo3Xxw2bhX6T231qKYr67lcgTdTLgZR-N_ayRBnfhTZqQm3pZShExq-wrqJd7WrnGOTlSnR23Nobkxe7hOgljuD2ONQcUkT4g5zUD2IMO7mlb-YpSjeI34GI/s1600/Screen+Shot+2013-09-02+at+10.46.22+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;">source: http://www.bbc.co.uk<img border="0" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrQlhIQKoNL32-jleBixapo3Xxw2bhX6T231qKYr67lcgTdTLgZR-N_ayRBnfhTZqQm3pZShExq-wrqJd7WrnGOTlSnR23Nobkxe7hOgljuD2ONQcUkT4g5zUD2IMO7mlb-YpSjeI34GI/s640/Screen+Shot+2013-09-02+at+10.46.22+PM.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhDBadd4JdANf1xhMYtMSyfQJ7GgThMXni9ph7WwYdCjCejXUdt-wwASTW2PCpavndXRN8f3ykc2YRVUy-M_jb_J_A5yR_cfbnHEALrryPjXLmHyonlpbK3hmf5v10xsADX0sYAp6FJwc/s1600/Screen+Shot+2013-09-02+at+10.47.20+PM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhDBadd4JdANf1xhMYtMSyfQJ7GgThMXni9ph7WwYdCjCejXUdt-wwASTW2PCpavndXRN8f3ykc2YRVUy-M_jb_J_A5yR_cfbnHEALrryPjXLmHyonlpbK3hmf5v10xsADX0sYAp6FJwc/s640/Screen+Shot+2013-09-02+at+10.47.20+PM.png" width="632" /></a></div>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-45828019532011393092013-09-02T22:51:00.001+08:002013-09-02T22:51:41.234+08:00Circle - Chord Properties<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUjfEbtCcUscrW_1X4aB11GdRpcr08bmPo4hwek1VAMWORu5EmHHgLW5GkSyyVq-aL6qeO0kxJcSlVbmajV51dew-_7-8sq8drYAlWO88a66mZ5SX2v4TrqWW3-_J69RGdC4bU1tnJfQM/s1600/Screen+Shot+2013-09-02+at+10.41.45+PM.png" imageanchor="1"><img border="0" height="530" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUjfEbtCcUscrW_1X4aB11GdRpcr08bmPo4hwek1VAMWORu5EmHHgLW5GkSyyVq-aL6qeO0kxJcSlVbmajV51dew-_7-8sq8drYAlWO88a66mZ5SX2v4TrqWW3-_J69RGdC4bU1tnJfQM/s640/Screen+Shot+2013-09-02+at+10.41.45+PM.png" width="640" /></a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv3xZdyr_5WoVREtOOFp1SdrxiLrVIryA8rJsni58KlZqdzH_5x4pYv71vf6c_pJV5TjFRjqNHlAnwRlDfPL3Yxo0UNGNqjmPfM689ICuTgIuLHAaLXdGgCOzh5zkTuCbvZLVzUYdF5xI/s1600/Screen+Shot+2013-09-02+at+10.40.36+PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv3xZdyr_5WoVREtOOFp1SdrxiLrVIryA8rJsni58KlZqdzH_5x4pYv71vf6c_pJV5TjFRjqNHlAnwRlDfPL3Yxo0UNGNqjmPfM689ICuTgIuLHAaLXdGgCOzh5zkTuCbvZLVzUYdF5xI/s640/Screen+Shot+2013-09-02+at+10.40.36+PM.png" width="640" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin8X1_TKhbMpPam1Y44CAvPwkxuAYYgRT_eyqCX2bpnVgT5tNiHbpkijRFEXLw5LwC04gWr-Ze_8CGP3RK9p6iH7yYVUJSYTMMBLKBSwUs-zfzSkXU-mCpGv_7_MsAXQjAFcxUqQhlKwM/s1600/Screen+Shot+2013-09-02+at+10.40.28+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin8X1_TKhbMpPam1Y44CAvPwkxuAYYgRT_eyqCX2bpnVgT5tNiHbpkijRFEXLw5LwC04gWr-Ze_8CGP3RK9p6iH7yYVUJSYTMMBLKBSwUs-zfzSkXU-mCpGv_7_MsAXQjAFcxUqQhlKwM/s640/Screen+Shot+2013-09-02+at+10.40.28+PM.png" width="640" /></a><br />
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<iframe width="560" height="315" src="//www.youtube.com/embed/KvaD0x8QdDA" frameborder="0" allowfullscreen></iframe>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-75502053600919340152013-09-02T22:30:00.003+08:002013-09-02T22:30:50.107+08:00Essential GDC Skills<!--[if gte mso 9]><xml>
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<b><span style="font-family: "Times New Roman";">Essential GDC Skills<o:p></o:p></span></b></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">View each video
carefully and learn these fundamental GDC skills.<o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman";">1. Basic Graphing Controls<o:p></o:p></span></b></div>
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<span style="font-family: "Times New Roman";">a. Zoom Options<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=r7DWbhWd9zE&list=PLB1A524363687A860"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=r7DWbhWd9zE&list=PLB1A524363687A860</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: "Times New Roman";">b. Setting the
Window<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";"><a href="http://www.youtube.com/watch?v=a_uJpI6LXr4">http://www.youtube.com/watch?v=a_uJpI6LXr4</a></span><span style="font-family: "Times New Roman";"><o:p></o:p></span><br />
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<b><span style="font-family: "Times New Roman";">2. Graphing Basics<o:p></o:p></span></b></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">a. Graph a line
and find the table of values:<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=3WctC2xCnI0"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=3WctC2xCnI0</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">b. Finding
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<a href="http://www.youtube.com/watch?v=pXRbQv8gauI"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=pXRbQv8gauI</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">c. Finding
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<a href="http://www.youtube.com/watch?v=M-1QUYQbYHM"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=M-1QUYQbYHM</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";">(comes with
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<br /></div>
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<span style="font-family: "Times New Roman";">d. Finding roots
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<br /></div>
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<br /></div>
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<b><span style="font-family: "Times New Roman";">3. PlySmlt2<o:p></o:p></span></b></div>
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<span style="font-family: "Times New Roman";">a. Using
PlySmlt2 for Solving Quadratic Equations<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=NBRzvsJ6ros"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=NBRzvsJ6ros</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">b. Using
PlySmlt2 to Solve a System of Equations<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=Dyox4aNR0Zc"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=Dyox4aNR0Zc</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: "Times New Roman";">c. Using
PlySmlt2 to Solve Polynomial Equations<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";"><a href="http://www.youtube.com/watch?v=3CoNcxnVbtY">http://www.youtube.com/watch?v=3CoNcxnVbtY</a></span><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/3CoNcxnVbtY" width="560"></iframe>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-17629107469026868622013-09-02T22:28:00.003+08:002013-09-02T22:28:19.379+08:00Angles in a Circle<div class="separator" style="clear: both; text-align: center;">
Angles properties <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgROf9jqVHkqQZ3rhyXNDEJ8ibAguNNkTWsICs9ydiO_bNmdFTMLsc2koTcg1dFK7n30Xt6AN81nX8aUPu4SgkyeRJgIvk9XUKyT8O7fGhLyDnNCytEKRlkgv_3tsQNEsz8cQruDbOGtNk/s1600/Screen+Shot+2013-09-01+at+10.52.19+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgROf9jqVHkqQZ3rhyXNDEJ8ibAguNNkTWsICs9ydiO_bNmdFTMLsc2koTcg1dFK7n30Xt6AN81nX8aUPu4SgkyeRJgIvk9XUKyT8O7fGhLyDnNCytEKRlkgv_3tsQNEsz8cQruDbOGtNk/s640/Screen+Shot+2013-09-01+at+10.52.19+PM.png" width="640" /></a></div>
<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-24054311702629645472013-08-31T22:24:00.000+08:002013-08-31T22:24:40.004+08:00Update on Assessment (i) PT2 (ii) P3 (iii) EOY<br />
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;">(1) Performance Task 2</b></span></div>
<div style="color: #222222; font-size: 13px;">
<span style="font-family: Arial, Helvetica, sans-serif;">This constitutes the Elementary Mathematics component of Assessment.</span></div>
<div style="color: #222222; font-size: 13px;">
<span style="font-family: Arial, Helvetica, sans-serif;">The performance task focuses on the topic of Geometrical Proof - Circle Properties. (please refer to Blog entry on <a class="GHUY-LPOB" href="http://www.blogger.com/blogger.g?blogID=1833288305023363886#editor/target=post;postID=3014593268360659227;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=0;src=postname" style="border: 0px; color: #1155cc; cursor: pointer; margin: 0px 10px 0px 0px; padding: 0px; text-align: -webkit-left; vertical-align: baseline;">Mathematics Performance Task 2</a>)</span></div>
<div style="font-size: 13px;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #222222;">Deadline for submission is </span><b><span style="color: red;">Term 4 Week 1 (first lesson)</span></b></span></div>
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;"><br /></b></span></div>
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;">(2) Paper 3</b></span></div>
<div style="background-color: white; font-size: 13px;">
<div style="color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif;">This constitutes the Additional Mathematics component of Assessment.</span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #222222;">This will be conducted in </span><b><span style="color: red;">Term 4</span></b><span style="color: #222222;">.</span></span></div>
<div style="color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif;">Students are expected to familiarise themselves with GC-TI84+.</span></div>
<div style="color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif;">(please refer to your Math teacher on information on use of GC-TI84+)</span></div>
</div>
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;"><br /></b></span></div>
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;"><br /></b></span></div>
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;">(3) End-of-Year Examination: Mathematics</b></span></div>
<div style="background-color: white; color: #222222; font-size: 13px;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Information pertaining to the Maths exam has been communicated to the students in the GoogleSite (as well as the <a href="http://sst2013-s107maths.blogspot.sg/2013/08/end-of-year-exam-mathematics.html" style="color: #1155cc;" target="_blank">Maths blog</a>).</span></div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
<div style="background-color: white; color: #222222;">
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><u>Elementary Mathematics paper 1</u></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Date:<b><span style="color: red;"> <span class="aBn" data-term="goog_1508903472" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">27 September 2013</span></span> </span></b>(<span class="aBn" data-term="goog_1508903473" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Friday</span></span>)</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 1 hour 30 minutes</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
<div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><u>Elementary Mathematics paper 2</u></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Date:<b><span style="color: red;"> 30<span class="aBn" data-term="goog_1508903472" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;"> September 2013</span></span> </span></b>(Monday)</span></div>
</div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 2 hours</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
</div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><u>Additional Mathematics</u></span></div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Date:<b><span style="color: red;"> <span class="aBn" data-term="goog_1508903472" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">4 October 2013</span></span> </span></b>(<span class="aBn" data-term="goog_1508903473" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Friday</span></span>)</span></div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 2 hours 30 minutes</span></div>
<div style="background-color: white; color: #222222;">
<span style="font-size: x-small;"><br /></span></div>
<div style="background-color: white; color: #222222;">
<b><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Table of Specification</span></b></div>
<div style="background-color: white; color: #222222;">
<u><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">A. Elementary Mathematics</span></u></div>
<div style="background-color: white;">
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Numbers
and the four operations (moe 1.1)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Percentage
(moe 1.3)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Kinematics
/ speed (moe 1.4)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Algebraic
representation and formulae (moe 1.5)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Functions
and graphs (moe 1.7)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Algebraic
manipulation (moe 1.6)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Solutions
of equations and inequalities (moe 1.8)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Congruence
and similarity (moe 2.2)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Properties
of circles (moe 2.3)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Coordinate
geometry (moe 2.6)<span style="color: #1a1a1a;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">•
</span>Data
analysis (moe 3.2)</span></div>
<div class="MsoNormal" style="color: #222222; margin-left: 36pt; text-indent: -36pt;">
<span style="font-family: Arial, Helvetica, sans-serif; text-indent: -36pt;"><span style="font-size: x-small;"><br /></span></span></div>
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<u><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -36pt;">B. </span><span style="text-indent: -36pt;">Additional Mathematics</span></span></u></div>
<div>
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A1) Equations and inequalities </span></b></div>
<div>
<b style="text-indent: -24px;"><span style="color: blue;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Conditions for a quadratic equation</span></span></b></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -18pt;"> Solving</span><span style="text-indent: -18pt;"> </span><b style="text-indent: -18pt;"><span style="color: blue;">simultaneous equations</span></b><span style="text-indent: -18pt;"> </span><span style="text-indent: -18pt;">in two variables with at least one linear
equation, by substitution</span></span></div>
<div>
<span style="text-indent: -18pt;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Relationships between the <b><span style="color: blue;">roots and coefficients of a quadratic equation</span></b></span></span></div>
<div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -18pt;"> Solving</span><span style="text-indent: -18pt;"> </span><b style="text-indent: -18pt;"><span style="color: blue;">quadratic inequalities</span></b><span style="text-indent: -18pt;">, and representing the solution on the number line</span></span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A2) Indices and surds</span></b></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b style="text-indent: -24px;"><span style="color: blue;"> Four operations</span></b><span style="text-indent: -24px;"> on indices and surds, including rationalising the denominator</span></span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b style="text-indent: -24px;"><span style="color: blue;"> Solving equations</span></b><span style="text-indent: -24px;"> involving indices and surds</span></span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A3) Polynomials and Partial Fractions</span></b></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="text-indent: -24px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Multiplication and division of polynomials</span></span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -24px;"> Use of </span><b style="text-indent: -24px;"><span style="color: blue;">remainder and factor theorems</span></b></span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="text-indent: -24px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Factorisation of polynomials</span></span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<b style="text-indent: -24px;"><span style="color: blue;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Partial fractions</span></span></b></div>
<div class="MsoNormal" style="text-indent: 0px;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A4) Binomial Expansions</span></b></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A5) Power, Exponential, Logarithmic, and Modulus functions</span></b></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b>(G1) </b>Trigonometric functions, identities and equations.</span></div>
<div class="MsoNormal" style="text-indent: 0px;">
</div>
<div class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 10pt 29pt; text-indent: -18pt;">
</div>
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="font-size: x-small;">· Six trigonometric functions for angles of any magnitude (in degrees or radians)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Principal values</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> of sin</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: -6pt;">–1</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x, cos</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: -6pt;">–1</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x, tan</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: -6pt;">–1</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· Exact values of the trigonometric functions for </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">special angles</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">
</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: 1pt;">(</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">30°,45°,60°</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: 1pt;">) or </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">(π/6, π/4, π/3)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Amplitude, periodicity and symmetries </span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">related to the</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;"> sine and cosine</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> functions
</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Graphs</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> of </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">sin(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">bx</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) , </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">sin(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x/b + c</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">), </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">cos(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">bx</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) , </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">cos(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x/b + c</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) and </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">tan(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">bx</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) , where a is real, b is a positive integer and c is an integer.</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="font-size: x-small;">· Use of the following</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">∗</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;"> (BASIC TRIG RULES)</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> sin A/cos A=tan A,</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> cos A/sin A=cot A, </span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> sin</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A+cos</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A=1,</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> sec</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A=1+tan</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A,</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> cosec</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A =1+cot</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> (DOUBLE ANLES)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> the expansions of </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">sin(A ± B), cos(A ± B) and tan(A ± B)</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> the formulae for sin 2A, cos 2A and tan 2A</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> (R-FORMULA) - </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">the expression for acosu + bsinu in the form </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">Rcos(u ± a) or R sin (u ± a)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">Simplification of trigonometric expressions</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Solution of simple trigonometric equations</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> in a given interval (excluding
general solution)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Proofs</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> of simple trigonometric identities</span></span></li>
</ul>
<br />
<br />
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(G2) Coordinate Geometry</span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Condition for two lines to be parallel or perpendicular</span></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(G2) Linear Law</span></b></div>
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</div>
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<span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;"><span style="color: blue;"><b> </b></span>Transformation of given relationships, including </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">y = ax</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: 0px; top: -6pt;">n </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">and y = kb</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: 0px; top: -6pt;">x</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">, to linear form to determine the unknown constants from a straight line graph</span></span></div>
<br />
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
</div>
</div>
<div style="background-color: white; color: #222222;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Resource and References</span></b></div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">The following would be useful for revision:</span></div>
<div style="background-color: white; color: #222222;">
<ul>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Maths Workbook</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Study notes</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Homework Handouts</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Exam Prep Booklets (that was given since the beginning of the year)</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Ace Learning Portal - where they could attempt practices that are auto-mark</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Past GCEO EM and AM questions (students were recommended to purchase these at the beginning of the year)</span></li>
</ul>
</div>
<div style="background-color: white; color: #222222;">
<div>
<b style="background-color: yellow;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></b></div>
<div>
<b style="background-color: yellow;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(4) General Consultation and Timed-trial during the school holidays</span></b></div>
</div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
<span style="background-color: white;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #222222;">During the school holidays, there would be a timed-trial on </span><b><span style="color: red;">Monday 9 September 2013</span></b><span style="color: #222222;"> (Monday). The focus would be on Additional Mathematics and students are strongly encouraged to attend.</span></span></span><br />
<div>
<span style="background-color: white; color: #222222;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 0800 - 1030 (2 hours 30 minutes) </span></span></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-56458155933099844322013-08-31T21:17:00.000+08:002013-08-31T21:17:38.002+08:00Mathematics Performance Task 2 <div class="separator" style="clear: both; text-align: center;">
<b><span style="font-size: large;">Due Term 4 Week 1 (first Mathematics Lesson)</span></b></div>
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<i>the file could be downloaded from google site.</i></div>
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<br /></div>
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<iframe frameborder="0" height="500" marginheight="0" marginwidth="0" src="https://docs.google.com/forms/d/1wRIgYkt1USpRFOxJOUurtpGFjTMl9oHNvnP0xg440aQ/viewform?embedded=true" width="760">Loading...</iframe>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-4070093898860344889.post-18296680453523033402013-08-26T09:59:00.002+08:002013-08-26T09:59:57.152+08:004. Uses of Binomial Theorem <div dir="ltr" style="text-align: left;" trbidi="on">
<u><b>Uses</b></u><br />
- It is used in statistics to calculate the binomial distribution.(Probability distribution is the probability distribution of the number of successes in a sequence of n independent in yes/no distribution)<br />
- This allows statisticians to determine the probability of a given number of favorable outcomes in a repeated number of trials.<br />
- Binomial expansion is also interesting from a mathematical point of view--it gives mathematicians insight into the properties of polynomials.<br />
- Used in the distribution of IP addresses<br />
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<u><b>Conceptual aspects</b></u><br />
-This is the formula.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDKVy9xVvCrRJaepU935PjIcDa6xDNHjDtSXh_0EDbVTgyGNNVS7V3rN8GqYYWV4LsN2FZFxs205XYibzYS0twMbPCTVyR7eoAUYDxWi2rCT3zIXmVNOIKeOKigoOKpB6EmSszgB_kS6AV/s1600/Screen+shot+2013-08-26+at+AM+09.39.54.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDKVy9xVvCrRJaepU935PjIcDa6xDNHjDtSXh_0EDbVTgyGNNVS7V3rN8GqYYWV4LsN2FZFxs205XYibzYS0twMbPCTVyR7eoAUYDxWi2rCT3zIXmVNOIKeOKigoOKpB6EmSszgB_kS6AV/s1600/Screen+shot+2013-08-26+at+AM+09.39.54.png" /></a></div>
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The way to derive the expanded form of a binomial with a exponential e.g. 4.</div>
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Lets just have the binomial be (a+b)</div>
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(a+b)^3 = a^3 + 3(a^2)b + 3ab^2 + b^3</div>
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As can be seen, the a exponents go from 3 to 0. (a^3, 3(a^2)b, 3ab^2, b^3)</div>
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The b exponents go from 0 to 3. (a^3, 3(a^2)b, 3ab^2, b^3)</div>
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The coefficients go 1,3,3,1 (3rd row of the Pascal triangle)</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJHsWDhZLEKityn-Gu0lZzow_lPe7sKSGFahLlgp1df4jU5M4EMSxYOpT32Pj4ORNZyDWJNPfJALKyOBv9RsnKI2Eai-fdrZx1WGNqQL52TWff4zcxdsYXQYwUeDw6x7Tk283v7jfwW-ky/s1600/Screen+shot+2013-08-26+at+AM+09.42.38.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJHsWDhZLEKityn-Gu0lZzow_lPe7sKSGFahLlgp1df4jU5M4EMSxYOpT32Pj4ORNZyDWJNPfJALKyOBv9RsnKI2Eai-fdrZx1WGNqQL52TWff4zcxdsYXQYwUeDw6x7Tk283v7jfwW-ky/s1600/Screen+shot+2013-08-26+at+AM+09.42.38.png" /></a></div>
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To get the coefficients, you can use the above formula. Factorial = !</div>
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k is the order of the terms (e.g. 2nd or 3rd term)</div>
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e.g. to get the coefficient of the 42nd term of a binomial to the power of 50 e.g. ( a+b )^50</div>
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50! / (42!)(50-42)! = 536878650</div>
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You can get the coefficient of any term using this formula. Used together with the pattern of the exponents of the a and b terms, you can get the expanded form. ( faster than expanding). It is still very slow.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSRR7cFE4TmRm7Lxw_S6Pl42MsiUTGcKQhNkiHecR_Je1i_p4LLFapeWYR6HeLM-rjdXKSzkfI__7a97Qec50uKCgnKZf2kDRYZuKWbDjea9PvlFXhWykf_BMIbp-IMkwjJ_PTjw6Tye-N/s1600/Screen+shot+2013-08-26+at+AM+09.41.22.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSRR7cFE4TmRm7Lxw_S6Pl42MsiUTGcKQhNkiHecR_Je1i_p4LLFapeWYR6HeLM-rjdXKSzkfI__7a97Qec50uKCgnKZf2kDRYZuKWbDjea9PvlFXhWykf_BMIbp-IMkwjJ_PTjw6Tye-N/s1600/Screen+shot+2013-08-26+at+AM+09.41.22.png" /></a></div>
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Below is an example of how to use the formula for binomial expansion to get the expanded form of the binomial cubed.</div>
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<u><b>How is it used in probability?</b></u><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihT-ZngsU3ATi4SKKQnmPnFH76HzWjDVejhyphenhyphenp1o223LC3oILAOmQyvXEx2u2vrCaBB1R474sCLWq1r2EvrRTXOPQlNha2OO3MURK0__xg43pfHxhQrXQyC_CWLIo3lSsXDSpny7nczKyQO/s1600/Screen+shot+2013-08-26+at+AM+09.36.06.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="376" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihT-ZngsU3ATi4SKKQnmPnFH76HzWjDVejhyphenhyphenp1o223LC3oILAOmQyvXEx2u2vrCaBB1R474sCLWq1r2EvrRTXOPQlNha2OO3MURK0__xg43pfHxhQrXQyC_CWLIo3lSsXDSpny7nczKyQO/s640/Screen+shot+2013-08-26+at+AM+09.36.06.png" width="640" /></a></div>
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