tag:blogger.com,1999:blog-10006934760511684562021-12-13T22:05:05.736-06:00JabbaMatheez 40S (Winter 2008)A window through the walls of our classroom. This is an interactive learning ecology for students and parents in my Pre-Cal Math 40S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.comBlogger265125tag:blogger.com,1999:blog-1000693476051168456.post-77367443516016100872008-06-23T10:30:00.000-05:002008-06-23T10:58:18.162-05:00So Long ...<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://farm1.static.flickr.com/36/79811964_33754e8586_d.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 320px;" src="http://farm1.static.flickr.com/36/79811964_33754e8586_d.jpg" border="0" alt="" /></a><br />And so we begin where we left off ... don't let the sky be your limit. ;-)<br /><br /><b><i>I'm so glad we've had this time together,<br /><br />Just to have a laugh or learn some math,<br /><br />Seems we've just got started and before you know it,<br /><br />Comes the time we have to say, "So Long!"</b></i><br /><br />So long everybody, I'll see you in September! Watch this space for pointers to new blogs for each of my classes. <br /><br />Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-17183622740814919602008-06-16T08:54:00.005-05:002008-06-16T13:52:33.668-05:00Class SurveyThe exam is over and we did a little survey in class. The results are below; 13 students participated. If you'd like to add another comment on what you see here <a href="mailto:dkuropatwa@wsd1.org?subject=Pre-Cal 40S Survey June 2008&body=Hi there, I'd like to comment on the survey. Here are my thoughts:">email me</a> or leave a comment below this post.<br /><br />Without any further ado, here are the results of our class's survey. Please share your thoughts by commenting (anonymously if you wish) below .....<br /><br /><b><i>Classroom Environment</i></b><br />The questions in this section were ranked using this 5 point scale:<br /><br /><table border="3" bordercolor="green"><tr align="center"><td>Strongly Disagree</td><td>Disagree</td><td>Neutral</td><td>Agree</td><td>Strongly Agree</td></tr><tr align="center"><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr></table><br /><br />The <b>bold</b> numbers after each item are the average ratings given by the entire class.<br /><br />1. The teacher was enthusiastic about teaching the course. <b>4.92</b><br /><br />2. The teacher made students feel welcome in seeking help in/outside of class. <b>4.69</b><br /><br />3. My interest in math has increased because of this course. <b>4.23</b><br /><br />4. Students were encouraged to ask questions and were given meaningful answers. <b>4.38</b><br /><br />5. The teacher enhanced the class through the use of humour. <b>4.46</b><br /><br />6. Course materials were well understood and explained clearly by the teacher. <b>4.31</b><br /><br />7. Graded materials fairly represented student understanding and effort. <b>3.85</b><br /><br />8. The teacher showed a genuine interest in individual students. <b>4.38</b><br /><br />9. I have learned something that I consider valuable. <b>3.50</b><br /><br />10. The teacher normally came to class well prepared. <b>4.54</b><br /><br /><b><i>Overall Impression of the Course</i></b><br />The questions in this section were ranked using this 5 point scale:<br /><br /><table border="3" bordercolor="green"><tr align="center"><td>Very Poor</td><td>Poor</td><td>Average</td><td>Good</td><td>Very Good</td></tr><tr align="center"><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr></table><br /><br />1. Compared with other high school courses I have taken, I would say this course was: <b>4.77</b><br /><br />2. Compared with other high school teachers I have had, I would say this teacher is: <b>4.77</b><br /><br />3. As an overall rating, I would say this teacher is: <b>4.77</b><br /><br /><b><i>Course Characteristics</i></b><br /><br />1. Course difficulty, compared to other high school courses:<br /><br /><table border="3" bordercolor="green"><tr align="center"><td>Very Easy<br>0%</td><td>Easy<br>0%</td><td>Average<br>23.1%</td><td>Difficult<br>61.5%</td><td>Very Difficult<br>15.4%</td></tr></table><br /><br />2. Course workload, compared to other high school courses:<br /><br /><table border="3" bordercolor="green"><tr align="center"><td>Very Easy<br>0%</td><td>Easy<br>7.7%</td><td>Average<br>61.5%</td><td>Difficult<br>30.8%</td><td>Very Difficult<br>0%</td></tr></table><br /><br />3. Hours per week required outside of class:<br /><br /><table border="3" bordercolor="green"><tr align="center"><td>0 to 2<br>23.1%</td><td>2 to 3<br>23.1%</td><td>3 to 5<br>38.5%</td><td>5 to 7<br>15.4%</td><td>over 7<br>0%</td></tr></table><br /><br />4. Expected grade in the course:<br /><br /><table border="3" bordercolor="green"><tr align="center"><td>F<br>7.7%</td><td>D<br>7.7%</td><td>C<br>38.5%</td><td>B<br>30.8%</td><td>A<br>15.4%</td></tr></table><br /><br /><b><i>Specific Feedback</i></b><br />[<b>Ed. Note:</b> Numbers in parentheses indicate the number of students, over 1, that gave the same answer.]<br /><br />What was your best learning experience in this course? <br /><br /><center><table border="3" bordercolor="green"><tr align="center"><td>Workshop classes (4)<br />Explaining our work on the SMARTboard (2)<br />Confidence<br />Great teaching with humour<br />Understanding math concepts instead of just using formulae (2)<br />Being comfortable with everyone<br />Learning the language of mathematics<br />SMARTboard (2)<br />Interaction (2)<br />Humour<br />Learning not to be afraid of making mistakes<br /><a href="http://expertvoices08.blogspot.com">Developing Expert Voices</a> project (2)<br />Getting feedback<br />This blog<br />Learning in other ways than with a textbook<br />Learning to solve problems (2)<br />Learning innovatively in many ways<br />Mathematics</td></tr></table></center><br /><br />What was your worst learning experience in this course?<br /><br /><center><table border="3" bordercolor="green"><tr align="center"><td>None (5)<br />More 1 on 1 help in class<br />Class kept getting unfocused (3)<br />Graphing<br />Circular Functions Unit<br />Sometimes had to rush<br />Not asking questions<br />Logarithms</td></tr></table></center><br /><br />What changes would you suggest to improve the way this course is taught?<br /><br /><center><table border="3" bordercolor="green"><tr align="center"><td>Fewer SMARTboard technical difficulties<br />Notes<br />Better scribe posts<br />Show formulae (how to "plug in values") first then explain or derive them<br />Mr. K. did an incredible job<br />I was motivated by Mr. K's enthusiasm<br />Laptops<br />Wanted to hear the "Mr. K. Quote" just before the exam<br />Study periods for tests<br />More workshop classes<br />More group work<br />More guidance for <a href="http://expertvoices08.blogspot.com">Developing Expert Voices</a> project<br />None<br />Wanted to hear about <a href="http://goldennumber.net/">The Golden Ratio</a><br />Give homework for marks<br />Too much humour<br />Make Developing Expert Voices projects simpler and more straight forward<br />We were occasionally distracted — could have got more done<br />Course was better than I expected<br />For once I actually enjoyed math<br />Stay on task<br />Don't get off topic (2)<br />Have an alternative to blogging</td></tr></table></center><br /><br />It's interesting to compare the items that were considered both the worst and best learning experiences. Also, take a look at the list of worst learning experiences compared to suggestions for next year. Help me do a better job next year by commenting on what you see here ....Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-52662465545992167572008-06-15T23:02:00.005-05:002008-06-15T23:12:16.544-05:00Student Voices Episode 4: Justice, Lawrence, and Richard<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://farm2.static.flickr.com/1162/1390706332_8572d1c1f8_d.jpg"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 320px;" src="http://farm2.static.flickr.com/1162/1390706332_8572d1c1f8_d.jpg" alt="" border="0" /></a>First an update on this podcast: While we have received few comments on this or any of our class blogs the number of times the audio files have been downloaded is remarkable ...<br /><br /><blockquote><a href="http://adifference.blogspot.com/2008/04/student-voices-episode-1-jessie.html">Episode 1: Jessie</a> 2440 downloads<br /><br /><a href="http://adifference.blogspot.com/2008/04/student-voices-episode-2-timmathy.html">Episode 2: Tim_MATH_y</a> 1766 downloads<br /><br /><a href="http://adifference.blogspot.com/2008/05/student-voices-episode-3-chris-craig.html">Episode 3: Chris, Craig, Graeme</a> 1367 downloads</blockquote><br /><br />Thanks to all our listeners. We might get one more published during this school year but this may be the last until September. In any case feel free to let us know your thoughts about what you heard; every comment is appreciated.<br /><br />In this episode of <a href="http://adifference.blogspot.com/search/label/Student%20Voices">Student Voices</a> Justice, Lawrence, and Richard talk about how they put together <a href="http://expertvoices08.blogspot.com/2008/06/team-lrj-studios-present.html">their Developing Expert Voices project</a> and what they learned in the process: how they they best learn math, how it can best be taught, and many other incidental things like team work and organizational skills.<br /><br />They have titled their project with one of my favourite reminders to all my students: Mathematics is the Science of Patterns. If you watch any of the video content they created you'll hear several "in jokes", listen for them. Without any further ado, here is the podcast. A copy of the poster they made for their work is below.<br /><br /><center><embed src="http://www.archive.org/download/DarrenKuropatwaStudentVoices_Episode4Justice_Lawrence_andRichard/SV04JusticeLaurenceRichardPC40SW08.mp3" type="audio/mpeg" autostart="false" loop="false" bgcolor="#ffffff" height="74" width="144"></embed><br />(<a href="http://www.archive.org/download/DarrenKuropatwaStudentVoices_Episode4Justice_Lawrence_andRichard/SV04JusticeLaurenceRichardPC40SW08.mp3">Download File</a> 12.2Mb, 25 min. 30 sec.)<br /></center><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_tlF3qs3v9cw/SFXm56L5XhI/AAAAAAAAAXY/6BZ6-EQewm8/s1600-h/Poster.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;" src="http://4.bp.blogspot.com/_tlF3qs3v9cw/SFXm56L5XhI/AAAAAAAAAXY/6BZ6-EQewm8/s400/Poster.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5212326026297302546" /></a><br /><br /><div align="right">Photo Credit: <a href="http://www.flickr.com/photos/zhzheka/1390706332/">Shadow singer</a> by flickr user EugeniusD80</div>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-21805942560286317452008-06-08T20:16:00.007-05:002008-06-08T20:55:10.804-05:00Judgement Day in Less Than Half a DayHi friends,<br /><br />Provincials are coming. It is TOMORROW!!! But don't fret, it is nothing bad. I believe that the reason why people do bad on the exams is because they are nervous or scared and that there isn't sufficient time. The exams are just longer tests. It isn't much more difficult than a test but a bit more tedious because of the lengthy and copious amounts of queBenofschool here. Seeing that my good ol' buddy m@rk didn't scribe I decided to do it for him. What we did TWO (YES TWO [2]) days ago was study for the provincial exams coming up. Thestions in under 3 hours. All that you have to do is just relax, feel confident in all of the studying you did (Don't be over confident because the will backfire. Just be enough that you are beginning to feel comfortable.) Studying would be the best way to cope with that pre-exam fear. Hopefully everybody asked others for help because listening to a peer is just as good if not better than asking a teacher. The voice of a peer is very valuable. There are many ways to be prepared for the exam and it varies among students. So there isn't a right way but only a wrong way to prepare. It all depends on you and what makes you feel comfortable in situations like tomorrow Provincial Math Exam. My method for studying might not be good for others but it makes me feel comfortable. Hopefully everybody has that comfort zone in their studying.<br /><br />Remember that time is a major issue for many people. That is why studying helps. Studying helps us all see the path to solving that problem quicker, more elegantly, and most of all more efficiently. The exam may play around with words or problems. They might word it differently, so just take your time in reading the questions carefully. If it helps, read the questions out loud but quietly because when you read with just your eyes your brain doesn't register it like when you read it with sounds being heard.<br /><br />To end this scribe as well as ending the final scribe I tell you this. Sorry if I can't be poetic like my friend Francis but I can be positive. Good Luck at the exam and remember not to be scared. Just feel comfortable and everything will be fine. Drink lots of water, bring water to the exam, bring pencils (note the plural), erasers (again the plural), and a lucky charm that are magically delicious. You can even bring a real rabbit's foot but not a real rabbit's foot because that is CRUEL!<br />Mr. K I have one favor to ask you. Could you use that before test line I just said above before the exam. I'm sure everybody will be happy when they hear that.<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_pdyr-lSHTaA/SEyMHkdqlPI/AAAAAAAAAFY/Pv-xFfrICeI/s1600-h/141900792_db0270a9f8.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://3.bp.blogspot.com/_pdyr-lSHTaA/SEyMHkdqlPI/AAAAAAAAAFY/Pv-xFfrICeI/s200/141900792_db0270a9f8.jpg" alt="" id="BLOGGER_PHOTO_ID_5209692930635896050" border="0" /></a><a href="http://flickr.com/photos/hamed/141900792/">Tehran Sky by flickr user Hamed Saber</a><br /><br /></div>Don't let the sky be the limit. Surpass the sky. And like what my good friend Andrew says, "Carpe Diem!" Which means seize the day. Hope to see everyone again in Calculus!!!<br /><br />Good Bye and Good Luck! =)Benofschoolhttp://www.blogger.com/profile/10547772016514296237noreply@blogger.com2tag:blogger.com,1999:blog-1000693476051168456.post-38281750225957784612008-06-06T13:00:00.001-05:002008-06-06T13:07:24.723-05:00Today's Slides: June 6Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_451876"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080606-1212775587869016-9"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080606-1212775587869016-9" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-june-6-2008?src=embed" title="View Pre-Cal 40S Slides June 6, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-31961912741378472362008-06-05T19:27:00.007-05:002008-06-05T22:59:47.795-05:00Last Class of the Jabbamatheez.Today was the end of of our classes together. It's been quite fun learning about everything from circular functions to Geometric sequences, especially because of all the skits Mr. K put in.<br /><br />Well, we started the class by solving a geometric sequence, given the 2nd and 3rd term. We had to find the 8th term given this. Since it was a geometric sequence, we know that there's a common ratio. To find this common ratio, we found the product of the 2 terms. Which was 12/24 = 1/2. We then found where y = 0, if we were to graph this. We found the 1st term by going backwards, which means you would have to multiply the 2nd term (24) by 2. 24 x 2 = 48. Then to find the term of 0, we would double that, which was 96. We then multiplied 96 by (1/2)<sup>8</sup> because we need to find the 8th term, and it had a common ratio of 1/2. The answer was 0.375<br /><br />Last class we found out where the infinite geometric sequence came from, but today we learned that when the common ratio is greater than 1, then it is a diverging series, because it will keep going on and on, thus meaning it is infinity. So when |r| > 1 then r<sup>∞</sup> = ∞<br />When the common ratio is less than 1, it's called a converging series, because it hones in on one value, which is 0. So when |r|<>∞ = 0.<br /><br />This was pretty much all we learned, so we did some questions after. There was a question about a super ball. At this point Paul pulled out a super ball for Mr. K to use, and it gave the class a little interaction. The ball would start at 200 cm and drop to the ground, it would rebound 3/4 of the distance it fell. We had to then find the total distance travelled by the 4th bounce. This question was easily accomplished using a diagram.<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_Dn_sslJIj9w/SEil1RHFvjI/AAAAAAAAAFY/MAssXPqh0sc/s1600-h/Bounces.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://1.bp.blogspot.com/_Dn_sslJIj9w/SEil1RHFvjI/AAAAAAAAAFY/MAssXPqh0sc/s320/Bounces.bmp" alt="" id="BLOGGER_PHOTO_ID_5208595303598767666" border="0" /></a><br />The initial distance being 200 cm, we can multiply by 3/4 to find the distance it bounces back up, then multiply that distance by 2, because it travels that distance twice, bouncing up and falling down, then we multiply the distance from the second bounce by 3/4 (150 x (3/4) = 112.5) to get the distance going up, then multiply by 2 for it going up and down,(150 x (3/4) = 112.5 x 2 = 225 cm) then multiply the distance from the 3rd bounce by 3/4 again (112.5 x (3/4) = 84.375) then multiply that by 2 because it goes up that distance and down hat distance, so it would be (84.375 x 2 = 168.75) add all the values together to get 893.75<br />You can also use the geometric sequence equation to find this also.<br />After this we had to find the distance travelled until the ball stopped, so we used the infinite geometric series which was 1200, given all the variables, and you would add the initial value which was 200, and that would be 1400 cm. This was the last question.<br /><br />That was all we did for our last class. I know, we need something special, because I'm the last scribe and this whole course has been oh so special, because of this reason, I wrote a poem. It's a Kyrielle poem. With 8 syllables each line, and rhyming scheme being aabB ccbB ddbB. Enjoy.<br /><br />One More Step<br /><br />Unluckily today's the last,<br />Of this most enjoyable class.<br />Though it's not the end for us yet,<br />As we move on just one more step.<br /><br />Mr. K, we give you homage,<br />For expanding on our knowledge.<br />Never dull, you were fun instead.<br />As we move on just one more step.<br /><br />Leaving with a fantastic smile,<br />As every thing's been so worthwhile.<br />Now to continue, and to prep.<br />As we move on just one more step.<br /><br />-Francis BowersAnonymousnoreply@blogger.com5tag:blogger.com,1999:blog-1000693476051168456.post-87179770853294334782008-06-05T19:26:00.000-05:002008-06-06T00:15:47.434-05:00er... Scribe List<p align="center"><span style="font-family:trebuchet ms;font-size:180%;color:#cc0000;">What Am I even doing this for? There's no more scribing! XD</span></p><p>Quote of the Cycle ;</p><p style="FONT-WEIGHT: bold"><em>"There's no such thing in the world as absolute reality. Most of what they call real is actually fiction. What you think you see is only as real as your brain tells you it is."</em></p><br /><center></center><p align="left"><span style="font-size:100%;">Stay Phi everyone,<br /><br />Rence ~ Out</span></p><p align="left"> </p><em><span style="font-family:times new roman;">... and I wonder, if you know... what it means, to find your dreams come true...</span></em>Rencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-3791311810764783972008-06-05T12:42:00.002-05:002008-06-16T23:29:54.671-05:00Today's Slides: June 5Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_449979"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080605-1212698865569874-9"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080605-1212698865569874-9" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-june-5-2008?src=embed" title="View Pre-Cal 40S Slides June 5, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-49332476151032471442008-06-04T23:27:00.002-05:002008-06-04T23:31:55.665-05:00Scribe List<div align="left">Cycle 6</div><table><tbody><tr><td width="120"><br />Francis<br />Joyce<br />Eleven<br />benofschool<br />roxanne<br /></td><td width="120"><br />JamieNeRd123C<br /><s>zeph</s><br />Richard<br />Hi I'm Justus<br /></td><td width="120"><br /><s>nelsa</s><br />Rence<br />kristina<br />Paul<br /></td></tr></tbody></table><p>Quote of the Cycle ;</p><p style="font-weight: bold;"><em>"There's no such thing in the world as absolute reality. Most of what they call real is actually fiction. What you think you see is only as real as your brain tells you it is."</em></p><br /><center>I don't know about you guys, but honestly, I'm scared of the exam.<br /><br /></center> <p align="left"><span style="font-size:100%;">Stay Phi everyone,<br /><br />Rence ~ Out</span></p>Rencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-13028828456665861062008-06-04T18:35:00.004-05:002008-06-04T20:14:26.847-05:00Infinite Geometric Series<span style="font-weight: bold;font-family:georgia;" ><br />OVERVIEW:</span><br /><ul><li>Finding the Sum of Numbers in a Sequence</li><li>Sigma Notation</li><li>Infinite Geometric Series Formula<br /></li></ul><br /><span style="font-weight: bold;font-family:georgia;" ><blockquote>Finding the Sum of Numbers in a Sequence</blockquote></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_ugolG4Kchdw/SEcxjgNBHyI/AAAAAAAAAHU/77vJRGgAYqQ/s1600-h/2.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://1.bp.blogspot.com/_ugolG4Kchdw/SEcxjgNBHyI/AAAAAAAAAHU/77vJRGgAYqQ/s400/2.bmp" alt="" id="BLOGGER_PHOTO_ID_5208185980086984482" border="0" /></a><span style="font-weight: bold;">(a) What is the sum of the integers from 1 to 5000?</span><br /><br />Credit to Paul for being our Gauss today.<br /><br />We imagine the sequence of all the numbers 1 to 5000 in the top row while the bottom row has all the numbers from 5000 to 1.<br /><br />Example:<br />1, 2, 3, ... 5000<br />5000, 4999, 4998, ... 1<br /><br />We find the sum of each column in our table and see that they're all 5001. Refer to slide 4 of June 3's slide for a better understanding of what I'm talking about.<br /><br />We know that there are 5000 of these terms. We also know that if we want to find the sum of the integers between 1 to 5000, then we would have to multiply the number of terms by the total we have then divide by 2. We divided by 2 because there were two sequences we added.<br /><br />Example: 5000 * 5001 / 2 = 12 502 500<br /><br />Another way of solving this problem is to pull out the equation (found on June 3's slide #7) and plugging in the appropriate numbers, which Mr. K has a distaste for using this method because we're not really understanding the concept but just plugging numbers into an equation.<br /><br /><span style="font-weight: bold;">(b) What is the sum of all multiples of 7 between 1 & 5000?</span><br /><br />The lowest multiple of 7 between 1 and 5000 is 7.<br />The highest multiple of 7 between 1 and 5000 is 4998.<br />There are 714 terms that are multiples of 7 between 1 and 5000.<br /><br />We then imagine, again, that table, listing all the numbers in the sequence from 1 to 5000 (that are multiples of 7) in the top row and all the numbers in the sequence from 5000 to 1 (that are multiples of 7) in the bottom row, and find the sum of each column.<br /><br />Example:<br />7, 14, 21, ..., 4998<br />4998, 4991, 4984, ..., 7<br /><br />Add the top row and the bottom row, and you find that under each column in our imaginary table is 5005.<br /><br />We multiplied the number of multiples of 7 between 1 and 5000 by the sum of the first and last terms of the sequence and divided that by 2 because we've counted the sequence twice and we get 1 786 785.<br /><br /><span style="font-weight: bold;">(c) What is the sum of all integers from 1 to 5000 inclusive that are not multiples of 7?</span><br /><br />Well, we have the sum of all the integers from 1 to 5000. We have the sum of all the multiples of 7 between 1 and 5000. So if we find the difference of those two numbers, we find the sum of all the integers from 1 to 5000 inclusive that are not multiples of 7.<br /><br />12 502 500 - 1 786 785 = 10 715 715<br /><br /><blockquote><span style="font-weight: bold;font-family:georgia;" >Sigma Notation</span></blockquote><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_ugolG4Kchdw/SEcxj97ZV5I/AAAAAAAAAHc/cHwGxSeztm8/s1600-h/3.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://2.bp.blogspot.com/_ugolG4Kchdw/SEcxj97ZV5I/AAAAAAAAAHc/cHwGxSeztm8/s400/3.bmp" alt="" id="BLOGGER_PHOTO_ID_5208185988066138002" border="0" /></a>Left Question:<br /><ul><li>The k = 1 means that you start with 1 and evaluate 3k.</li><li>The number above the sigma symbol, 4, means to keep evaluating 3k until k = 4, then add all the terms.</li></ul><br />Right Question:<br /><ul><li>The k = 0 means that you start with 0 and evaluate 2^k.</li><li>The number above the sigma symbol, 3, means to keep evaluating 2^k until k = 3, then add all the terms.</li></ul><br />Then Mr. K says to find another sigma notation that is equivalent to the two questions on the slide. Of course, "mathematics is the science of patterns" is the common phrase that Mr. K always says, and yes, there're patterns here.<br /><br />Also, a quick way of figuring out the answer to the sigma notation in question is to add the first and last term, then multiply by 2. Example: In the left question, [3(1) + 3(4)] * 2 = 30<br /><br /><br /><span style="font-weight: bold;font-family:georgia;" ><blockquote>Infinite Geometric Series Formula</blockquote></span><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_ugolG4Kchdw/SEcxkQt2UhI/AAAAAAAAAHs/GC_hhnUewYo/s1600-h/5.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://1.bp.blogspot.com/_ugolG4Kchdw/SEcxkQt2UhI/AAAAAAAAAHs/GC_hhnUewYo/s400/5.bmp" alt="" id="BLOGGER_PHOTO_ID_5208185993109590546" border="0" /></a>The formula given in the above slide is something that we already derived from the previous class.<br /><br />To answer the question "why is that the formula?" let's first use an example to help better our understanding of infinite geometric series. We make a square, cut it in half, and shade the half. We take the unshaded region of the square, cut that in half, and shade the half. Then we take another unshaded region of the square, cut that in half, and shade that half, and so on. So, firstly, we got 1/2 of the square shaded, then 1/2 + 1/4 shaded, then 1/2 + 1/4 + 1/8 shaded, then 1/2 + 1/4 + 1/8 + 1/16 shaded, and so on. If we continue this pattern and keep cutting and shading the square in half an infinite number of times, then we would've a shaded square.<br /><br />1/2 + 1/4 + 1/8 + 1/16 + 1/32 ... = 1<br /><br />The formula that we derived from the previous class was<br /><br />Sn = t1*(1-r^infinity) / (1-r)<br /><br />If we take r and raise it to the power of infinity, that would equal zero.<br />Example: r = 1/2<br /><br />1/2 * 1/2 * 1/2 * 1/2 ... = 0<br /><br />So, in the part of the formula where it says (1-r^infinity), that part of the formula is going to equal (1-0) = 1 anyways, and multiplying a number by 1 won't really have a visible effect. It's more efficient to just not include the (1-r^infinity) into the formula.<br /><br />Plug in the numbers into the equation, BING! BANG! BOOM! you have the result. Have a nice day.<br /><br /><br /><span style="font-weight: bold;">END NOTES</span><br /><ul><li>Start on Exercise 47: Infinite Geometric Series. You should have finished all the questions in the exercise book up to 47.<br /></li><li>Tomorrow, we will finish off the lesson the infinite geometric series.<br /></li><li>Hopefully, we will be on task and finish the course tomorrow, and do a review on Friday.<br /></li><li>Next scribe is <span style="font-weight: bold;">Francis</span>.</li></ul>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-28496623381777737922008-06-04T15:56:00.002-05:002008-06-04T15:58:46.323-05:00Today's Slides: June 4Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_447558"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080604-1212612816015646-8"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080604-1212612816015646-8" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-june-4-2008?src=embed" title="View Pre-Cal 40S Slides June 4, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-63315620021341699852008-06-03T17:42:00.007-05:002008-06-03T22:35:55.751-05:00Introducing SeriesThe first thing we did in class today is answer some simple questions. Pretty straight forward, should be easy to do. Even if you weren't in class yesterday. Noo excuses, 'cuz I wasn't in class yesterday.<br /><br />We also graphed the function <em>'y = [square root] x'</em>, which looks like half a sideways parabola.<br /><br />Next, we learned about 'young Gauss', who was a pretty clever seven-year-old. His teacher told the class one day to add up all the numbers from 1 to 100. Instead of writing it all out and adding it, he found a pattern.<br /><br /><br /><div><div><br /><div></div><img id="BLOGGER_PHOTO_ID_5207850148643592802" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://4.bp.blogspot.com/_7qjcZRxJPeI/SEYAHild2mI/AAAAAAAAAFk/mDRiQIAiESs/s400/sequences+I.jpg" border="0" /><br /><br /><div align="left">When the numbers are laid out like above, their sums equal 101. There should be a hundred 101's, hence the reason we multiply 100 and 101. We divide it because you added one hundred twice. That's what Karl Gauss figured out. If you want to know the details, you can go ahead and visit this link: <a href="http://www.sigmaxi.org/amscionline/gauss-snippets.html">http://www.sigmaxi.org/amscionline/gauss-snippets.html</a><br /><br /><br />Using the same idea as above, we found the formula for an arithmetic series.<br /><em>Sn = (n/2)[2a+(n-1)d]<br /><br /><img id="BLOGGER_PHOTO_ID_5207857832340085378" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://1.bp.blogspot.com/_7qjcZRxJPeI/SEYHGyld2oI/AAAAAAAAAF0/SiC-bLW1I2Q/s400/sequences+II.jpg" border="0" /></em></div></div></div><br />A <strong>series</strong> is the sum of numbers in a sequence to a particular term in a sequence (definition can be found on blog). You can't have a series if you don't have a sequence first, or else, what are you adding?<br /><br />We also found the formula for a geometric series.<br /><em>Sn = [a(1-r^n)]/(1-r)<br /><br /><img id="BLOGGER_PHOTO_ID_5207864270496062098" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://4.bp.blogspot.com/_7qjcZRxJPeI/SEYM9ild2pI/AAAAAAAAAF8/kApt9EV2hRY/s400/sequences+III.jpg" border="0" /></em><br /><br />Lastly, we touched a little bit on <em>'Sigma'</em>, which is located on the second-last slide (8).<br /><br /><br /><br />Mmm, yeah, that's it. I'm tired now, I'm sorry. Hahaha, next scribe is Joseph, since he asked.. again.nelsahttp://www.blogger.com/profile/14797016515149385545noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-27468961122779066162008-06-03T15:48:00.004-05:002008-06-03T16:26:33.573-05:00Scribe List<div align="left">Cycle 6</div><table><tbody><tr><td width="120"><br />Francis<br />Joyce<br />Eleven<br />benofschool<br />roxanne<br /></td><td width="120"><br />JamieNeRd123C<br />zeph<br />Richard<br />Hi I'm Justus<br /></td><td width="120"><br /><s>nelsa</s><br />Rence<br />kristina<br />Paul<br /></td></tr></tbody></table><p>Quote of the Cycle ;</p><p><em>"There's no such thing in the world as absolute reality. Most of what they call real is actually fiction. What you think you see is only as real as your brain tells you it is."</em></p><div align="center"><span style="font-family:Verdana;font-size:85%;">And remember to watch... </span></div><div align="center"><a href="http://teamlrjdev.blogspot.com/"><img id="BLOGGER_PHOTO_ID_5207769215160339362" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://2.bp.blogspot.com/_JkXkX0yuX_Q/SEW2gl3Yy6I/AAAAAAAAAE8/9Ui3CtsWHpo/s320/Poster.jpg" border="0" /></a> ... it's epic</div><p></p><p align="left"><span style="font-size:100%;">Stay Phi everyone,<br /><br />Rence ~ Out</span></p>Rencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-31239299992083000522008-06-03T13:09:00.002-05:002008-06-03T13:11:42.430-05:00Today's Slides: June 3Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_444866"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080603-1212516610481795-9"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080603-1212516610481795-9" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-june-3-2008?src=embed" title="View Pre-Cal 40S Slides June 3, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-62136778776088363692008-06-02T19:12:00.006-05:002008-06-02T22:20:34.759-05:00Geometric Sequences<blockquote>WARNING: The geometric sequences unit does not have any new material; rather the unit gives a new perspective to what we already know from previous learning.</blockquote><br /><span style="font-weight: bold;font-family:georgia;" >OVERVIEW:</span><br /><ul><li>What is a sequence?<br /></li><li>Recursive definition vs. implicit definition</li><li>Common difference vs. common ratio<br /></li><li>Determining any term (the nth term) in an arithmetic sequence vs. determining any term (the nth term) in a geometric sequence<br /></li></ul><br /><span style="font-weight: bold;">SLIDE 2<br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_ugolG4Kchdw/SESfP2G_V1I/AAAAAAAAAG0/5oGevlg4TkQ/s1600-h/2.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://1.bp.blogspot.com/_ugolG4Kchdw/SESfP2G_V1I/AAAAAAAAAG0/5oGevlg4TkQ/s400/2.bmp" alt="" id="BLOGGER_PHOTO_ID_5207462163718821714" border="0" /></a>An example of an arithmetic sequence is the first sequence of numbers found on SLIDE 2. Examples of geometric sequences is the second and the third sequence of numbers. Note that arithmetic sequences and geometric sequences aren't the only sequences that exists, such as the Fibonacci sequence, but the main scope of the unit focuses on geometric sequences.<br /><br />We find the next three terms by determining a rule for each sequence of numbers.<br /><ol><li>For the first sequence of numbers (4, 7, 10, 13...), we see that 3 is added to any term to get the next term. </li><li>For the second sequence of numbers (3, 6, 12, 24...), we see that 2 is multiplied to any term to get the next term. </li><li>For the third sequence of numbers (32, 16, 8, 4...), we see that 1/2 is multiplied to any term to get the next term. (Remember, in grade 12, we multiply by 1/2 instead of dividing by 2; it's to make our calculations easier to do.)<br /></li><li>For the fourth sequence of numbers (1, 1, 2, 3...), we see that we have to add the previous two terms to get the next term.</li></ol><br /><span style="font-weight: bold;">SLIDE 3<br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_ugolG4Kchdw/SESfQI9jPhI/AAAAAAAAAG8/p0QCg-LGw9c/s1600-h/3.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://2.bp.blogspot.com/_ugolG4Kchdw/SESfQI9jPhI/AAAAAAAAAG8/p0QCg-LGw9c/s400/3.bmp" alt="" id="BLOGGER_PHOTO_ID_5207462168779505170" border="0" /></a>Let's take a closer look at the first sequence of numbers (4, 7, 10, 13...).<br /><br />How did we determine that the rule is to add 3 to any term to get the next term? We find that out by determining that the common difference is 3 (green font). We then find out that if we're given any term, n, then 3n+1 is the equation we use to get what n equals. For example,<br /><br />3n+1 = 3(1)+1 = 4.<br /><br />So if the rank (n) is 1, then its term is 4. If the rank is 2, then its term is 7. If the rank is 7, then its term is 22. This is expressed with the equation 3n+1.<br /><br />The rank represents the term. For example, in this sequence, the rank of the first term is 1, the rank of the second term is 2, the rank of the third term is 3, the rank of the nth term is 3n+1, and so on.<br /><br />Graph 3n+1, and we find that it is the equation of a line. Also, we can determine the 0th term by plugging 0 into the equation.<br /><br />3n+1 = 3(0)+1 = 1.<br /><br />For the zeroth term, the output 1. It is also the y-intercept of the graph.<br /><br />Term 1 (t1), or in some textbooks it's called a, equals 4. The common difference, d, is 3.<br /><br />The recursive definition, in this sequence of numbers, is to take a term and add 3 continuously.<br /><br />The implicit definition, in this sequence of numbers, is the equation of the sequence, tn = 3n+1.<br /><br /><br /><span style="font-weight: bold;">SLIDE 4<br /><br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_ugolG4Kchdw/SESfQSbUEwI/AAAAAAAAAHE/joRwZJz_HDc/s1600-h/4.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://4.bp.blogspot.com/_ugolG4Kchdw/SESfQSbUEwI/AAAAAAAAAHE/joRwZJz_HDc/s400/4.bmp" alt="" id="BLOGGER_PHOTO_ID_5207462171320259330" border="0" /></a>Let's take a closer look at the second sequence of numbers (3, 6, 12, 24...).<br /><br />How did we determine that the rule is to multiply 2 to any term to get the next term? Firstly, there isn't a common difference in this case but a common ratio. The common ratio is 2. We then find out that if we're given any term, n, then (3/2)(2^n) is the equation we use to get what n equals.<br /><br />tn = (3/2)(2^n) = [3 * (1/2) * 2^n] = [3 * 2^(n-1)]<br /><br />(Refer to the bottom-right corner of SLIDE 4.)<br /><br />So if the rank (n) is 1, then its term is 3. Similarly, if the rank is 2, then its term is 6. If the rank is 7, then its term is 192. Etcetera.<br /><br />Graph [3 * 2^(n-1)], and we find that it is the equation of an exponential function. Also, we can determine the 0th term by plugging 0 into the equation.<br /><br />tn = [3 * 2^(n-1)]<br />t(0) = [3 * 2^(0-1] = 3/2<br /><br />For the zeroth term, the output 3/2. It is also the y-intercept of the graph.<br /><br />The recursive definition, in this sequence of numbers, is to take a term and multiply it continuously by 2.<br /><br />The implicit definition, in this sequence of numbers, is the equation of the sequence, tn = 3*2^(n-1).<br /><br /><br /><span style="font-weight: bold;">SLIDE 5<br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_ugolG4Kchdw/SESfQvDPImI/AAAAAAAAAHM/kkL-XqVT4pg/s1600-h/5.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://4.bp.blogspot.com/_ugolG4Kchdw/SESfQvDPImI/AAAAAAAAAHM/kkL-XqVT4pg/s400/5.bmp" alt="" id="BLOGGER_PHOTO_ID_5207462179003900514" border="0" /></a>Let's take a closer look at the third sequence of numbers (32, 16, 8, 4...).<br /><br />The recursive definition, in this sequence of numbers, is to take a term and multiply it continuously by 1/2.<br /><br />The implicit definition, in this sequence of numbers, is the equation of the sequence.<br /><br /><br />VOCABULARY/SUMMARY is found on SLIDES 6 to 9.<br /><br /><br /><span style="font-weight: bold;font-family:georgia;" >HOMEWORK</span><br /><ul><li>Exercise 45: Geometric Sequences<br /></li></ul><br />Next Scribe is <span style="font-weight: bold;">Nelsa</span>.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-72374951122456130002008-06-02T15:53:00.002-05:002008-06-02T15:57:14.936-05:00Today's Slides: June 2Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_442793"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080602-1212439822058955-8"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080602-1212439822058955-8" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-june-2-2008?src=embed" title="View Pre-Cal 40S Slides June 2, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-89675169893149307652008-06-02T00:42:00.000-05:002008-06-02T00:43:50.861-05:00Scribe List<div align="left">Cycle 5</div><table><tbody><tr><td width="120"><br /><s>Francis</s><br /><s>Joyce</s><br /><s>Eleven</s><br /><s>benofschool</s><br /><s>roxanne</s><br /></td><td width="120"><br /><s>JamieNeRd123C</s><br />zeph<br />AnhThi<br /><s>Richard</s><br /><s>Hi I'm Justus</s><br /></td><td><br /><s>nelsa</s><br /><s>Rence</s><br /><s>kristina</s><br /><s>Paul</s><br /></td></tr></tbody></table><p></p><p></p><p>Quote of the Cycle ;</p><p><em>"We say we love flowers, yet we pluck them. We say we love trees, yet we cut them down. And people still wonder why some are afraid when told they are loved."</em></p><p><em></em></p><p><span style="font-family:verdana;font-size:180%;"><br />Stay Phi everyone,<br /><br />Rence ~ Out</p><br /></span>Rencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-25729738891585483462008-05-31T21:39:00.021-05:002008-06-01T20:03:34.623-05:00Probability: More Practice<span style="font-family:arial;">Instead of starting a new unit, we worked on Probability. Mostly we went over the practice sheet we were given on Thursday. The questions we reviewed were one, two, six and nine.<br /><br /><br /><strong><span style="font-size:130%;">Question One:</span></strong> </span><br /><div><div><div><div><div><div><div><div><ul><li><em><span style="font-family:arial;color:#006600;">The probability of a randomly chosen car being defective is 1/3. Four cars are chosen randomly in order. Given that at least two cars are defective, what is the probability that the first car is defective?</span></em></li></ul><p><span style="color:#000000;"><span style="font-family:arial;">The first thing we did, was figure out what the question was asking.<br /><em>P(1st is defective </em>I </span><span style="font-family:arial;"><em>at least two is defective)<br /><br /></em>Next we found the sample space. It's always easier if you think of it as a word, and then asking yourself how many times the letters in that word can be rearranged, like so:<br /></span><em><span style="font-family:arial;">DDGG -- meaning two of the cars are defective<br /></span></em></span><span style="color:#000000;"><span style="font-family:georgia;"><span style="font-family:arial;"><em>DDDG -- three cars are defective<br />DDDD -- all four cars are defective<br /></em>Then you can find the probability that the cars will be chosen that way, and that becomes your sample space, or denominator.</span> </span></span><span style="color:#000000;"><span style="font-family:georgia;"><br /></p><img id="BLOGGER_PHOTO_ID_5207083033124788818" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://1.bp.blogspot.com/_7qjcZRxJPeI/SENGbild2lI/AAAAAAAAAFc/4oo2uNu9B70/s200/probability+I.jpg" border="0" /><br /><span style="font-family:arial;">Next we looked at all the possibilities that the first car will be defective using slots, which, if you remember, was from combinatorics.</span><br /><br /></span></span><img id="BLOGGER_PHOTO_ID_5207080529158855202" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://2.bp.blogspot.com/_7qjcZRxJPeI/SENEJyld2iI/AAAAAAAAAFE/gSKj8mRx-0M/s320/probability+II.jpg" border="0" /><span style="font-family:arial;">Put that numerator on top of the denominator that we found earlier, and you have your answer.<br /><br /><br /><br /><strong><span style="font-size:130%;">Question Two: </span></strong></span><br /><ul><li><em><span style="font-family:arial;color:#006600;">Two jars contain red and green marbles. Jar I contains 3 red and 2 green marbles. Jar II contains 4 red and 3 green marbles. A jar is picked at random and two marbles are picked out of that jar in order. If it is known that the first marble is red, what is the probability of the second marble being red?</span></em></li></ul><img id="BLOGGER_PHOTO_ID_5207026202117527970" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://1.bp.blogspot.com/_7qjcZRxJPeI/SEMSvild2aI/AAAAAAAAAEE/HpZibtoRWlk/s320/probability+III.jpg" border="0" /><span style="font-family:arial;">You can start this problem by drawing a tree, and writing down the probability that each possibility will occur - if that makes sense. For example, if you look at the picture above, you'll see that the first branch is <em>'Jar I'</em> followed by <em>'Jar II'</em>, the probability of choosing either jar is one half. The next branches are <em>'red' </em>and <em>'green'</em>, and the probability of choosing red in <em>'Jar I'</em> is 3/5, while the probability of choosing green is 2/5. So on and so forth. Keep in mind that the marbles are not replaced after you take it out, so the sample space is different everytime you draw.<br /><br />In this question, what we're looking for is the probability of getting a red after drawing a red marble first. That becomes the numerator, and the denominator consists of all the possibilities, as shown above. So you plug in the proper numbers in their proper places, and you have that question solved.<br /><br /><br /><br /><strong><span style="font-size:130%;">Question Six:</span></strong> </span><br /><ul><li><em><span style="font-family:arial;color:#006600;">Susan sees her friend, Tim, at his locker with a worried look on his face. She asks, "What's wrong?" Tim has to open his locker and change clothes within the next five minutes. However, he has forgotten the combination to his new lock. He knows that the lock requires three different numbers. He also remembers that all of the numbers are odd, and all of the numbers are divisible by seven. It takes 10 seconds to dial a locker combination and 1.5 minutes to change clothes. Is Tim likely to be ready for gym class on time?</span></em></li></ul><img id="BLOGGER_PHOTO_ID_5207043171533314514" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://4.bp.blogspot.com/_7qjcZRxJPeI/SEMiLSld2dI/AAAAAAAAAEc/sCyuzKkVWGM/s400/probability+IV.jpg" border="0" /><span style="font-family:arial;">I think you'll understand how we solved this problem just by looking at the above picture. The <em>'1 min 30 sec'</em>, written in pink, is how long it takes Tim to change.<br /><br /><br /><br /><strong><span style="font-size:130%;">Question Nine:</span></strong></span></div></div><ul><li><span style="font-family:arial;color:#006600;"><em>Three identical boxes each contain two drawers. In one box, each drawer contains a gold coin. In another box, each drawer contains a silver coin. The remaining box has a silver coin in one drawer and a gold coin in the other. One drawer is opened and a gold coin is found. What is the probability that the other drawer in that box also contains a gold coin.</em></span></li><li><span style="font-family:arial;color:#006600;"><em>Michael claims that the probability is 1/3. Jessica claims it is 1/2. Raymond says the probability is 2/3. Explain how each person may have arrived at their answer. Who is correct? Justify your answer.</em></span></li></ul><img id="BLOGGER_PHOTO_ID_5207054076455279090" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://3.bp.blogspot.com/_7qjcZRxJPeI/SEMsGCld2fI/AAAAAAAAAEs/TNyecaJXS50/s320/probability+V.jpg" border="0" /></div><p><span style="font-family:arial;">The probability of choosing the right box is 1/3, and the probability of choosing either a gold or silver coin is 1/2, since there's two drawers. Obviously if you get the box that only have two gold coins, you're not going to get a silver coin. But I'm sure we're all smart enough to realize that.<br /><br />The probability of getting a second gold coin is shown by:<br /></span><span style="font-family:arial;"><em>[P(IG)/(P(IIIG) + P(IG) + P(IG))] + [P(IG)/(P(IIIG) + P(IG) + P(IG))]<br /><br /></em>If we plug in the correct numbers, we have:<br /></span><span style="font-family:arial;"><em>[(1/6)/((1/6) + (1/6) + (1/6))] + [(1/6)/((1/6) + (1/6) + (1/6))]<br />[(1/6)/(1/2)] + [(1/6)/(1/2)]<br />(1/3) + (1/3)<br />2/3<br /><br /></em>Therefore, Raymond is correct. Michael could've gotten his answer by thinking that there's only one box that contains two gold coins, and the probability of choosing that box is 1/3. Jessica could've simply thought, well there's two drawers, so there's a 1/2 chance of getting a gold coin.<br /><br /><br /><br />So that's the end of that. There's also questions in the slides (9-18) that we could do for practice. In the afternoon class we had a pre-test that we're going to go over tomorrow. There isn't going to be a test for this unit because we don't have time. Soo.. we're starting a new unit next week.<br /><br />And that's that. The next scribe will be <span style="color:#6600cc;"><strong><span style="font-size:180%;">Joseph</span></strong><strong> </strong><span style="color:#000000;">because he asked me yesterday. Whoot. Good luck to everyone doing the English Provincial Exams tomorrow! Remember to pace yourself and.. uhh, I forgot what else Mr. V and Mrs. Strecker said.. but.. yes!</span></span></span></p></div></div></div></div></div>nelsahttp://www.blogger.com/profile/14797016515149385545noreply@blogger.com2tag:blogger.com,1999:blog-1000693476051168456.post-10287919698456265502008-05-30T12:34:00.002-05:002008-05-30T12:37:51.965-05:00Today's Slides: May 30Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_437836"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080530-1212168670272737-8"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080530-1212168670272737-8" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-may-30-2008?src=embed" title="View Pre-Cal 40S Slides May 30, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-89641930087955418442008-05-29T23:45:00.004-05:002008-05-29T23:54:16.622-05:00Scribe List<div align="left">Cycle 5</div><table><tbody><tr><td width="120"><br /><s>Francis</s><br /><s>Joyce</s><br /><s>Eleven</s><br /><s>benofschool</s><br /><s>roxanne</s><br /></td><td width="120"><br /><s>JamieNeRd123C</s><br />zeph<br />AnhThi<br /><s>Richard</s><br /><s>Hi I'm Justus</s><br /></td><td><br />nelsa<br /><s>Rence</s><br /><s>kristina</s><br /><s>Paul</s><br /></td></tr></tbody></table><p></p><p></p><p>Quote of the Cycle ;</p><p><em>"We say we love flowers, yet we pluck them. We say we love trees, yet we cut them down. And people still wonder why some are afraid when told they are loved."</em></p><p><em></em></p><p>Reminder: Roxanne, Francis and Elven - Your D.E.V. Project is due <strong>FRIDAY</strong>, yeah that's right, <strong><em>FRIDAY</em></strong> by midnight. </p><p><strong><em>AND!</em></strong> </p><p><span style="font-family:verdana;font-size:180%;">If you haven't already, just give Mr.K a quick email to have him add you to the D.E.V. Blog. Do it now! 'Cause I know you want to.</span> </p><p>On a side note: That dot on the Visitor map is getting awfully large. Makes us seem like a big target =( Lol, just kidding.<br /></p><p><br />Stay Phi everyone,<br /><br />Rence ~ Out</p>Rencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-36001124331458587162008-05-29T22:17:00.005-05:002008-05-29T22:23:05.757-05:00Workshop PeriodOhhh my goodness. I nearly forgot I was scribe today because of the basketball game XD. (Go lakers!)<br /><br />So the title above describes todays class. Mr. K was away again but no worries, he'll be back tomorrow...i think. Anyways, we were given a worksheet that we worked on in our little groups for the whole class. I thought the sheet had some challenging question like 1 and 2. I hope we go over those tomorrow. Yeeaah it was a pretty uneventful period other than that.<br /><br />So I'll get to the point. Next scriibe is NELSA. "Beautiful" right Nelsa?Joycehttp://www.blogger.com/profile/13751916783945460043noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-42758216645931385972008-05-29T00:30:00.001-05:002008-05-29T00:31:51.290-05:00Scribe List<div align="left">Cycle 5</div><table><tbody><tr><td width="120"><br /><s>Francis</s><br />Joyce<br /><s>Eleven</s><br /><s>benofschool</s><br /><s>roxanne</s><br /></td><td width="120"><br /><s>JamieNeRd123C</s><br />zeph<br />AnhThi<br /><s>Richard</s><br /><s>Hi I'm Justus</s><br /></td><td><br />nelsa<br /><s>Rence</s><br /><s>kristina</s><br /><s>Paul</s><br /></td></tr></tbody></table><p></p><p></p><p>Quote of the Cycle ;</p><p><em>"We say we love flowers, yet we pluck them. We say we love trees, yet we cut them down. And people still wonder why some are afraid when told they are loved."</em></p><p><em></em> </p><p>AND NO, Unicorns aren't real. :) Sorry to burst your bubble guys. Lol.</p><p></p><p><br /><br />Stay Phi everyone,<br /><br />Rence ~ Out</p>Rencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-1209922301308941602008-05-28T17:58:00.002-05:002008-05-28T18:06:22.639-05:00DEV Work Period!<span style="font-family:arial;">Well, today we had Ms. Gonzaga come back as our substitute since Mr. K was away today. Surprisingly, and thankfully, there was no quiz or anything (which some of us may have been expecting since we usually get one when there's a sub). But anywho, who cares about that right?! So then, basically, this class was dedicated to working on our DEV projects. The due dates for them are <span style="font-style: italic;">really</span> close that's why. We were also told to work on Exercise 44 as well, and that's it! Same deal for the afternoon class! Okay, that's it!<br /><br />Aaaannnnd!!! Here's something Jamie is probably expecting (inside-outside joke?!)...she's not scribe by the way, <span style="color: rgb(255, 0, 0);">Joyce<span style="color: rgb(51, 51, 51);"> is, and no I did not mean harm to her by putting her name in red!<br /><br /></span></span></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://lilymichaud.files.wordpress.com/2007/09/unicorn.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 320px;" src="http://lilymichaud.files.wordpress.com/2007/09/unicorn.jpg" alt="" border="0" /></a><span style="font-family: arial;"><br />Well then, that's it for today!!!! Did I mention the next scribe? Well for those who don't care about reading scribe posts and just like scrolling RIGHT TO THE BOTTOM immediately, the scribe is <span style="font-weight: bold; color: rgb(255, 0, 0);">Joyce</span>.<br /></span>kristinahttp://www.blogger.com/profile/12365815325056314375noreply@blogger.com2tag:blogger.com,1999:blog-1000693476051168456.post-48116372667265589482008-05-27T23:42:00.003-05:002008-05-29T00:30:15.325-05:00Scribe List<div align="left">Cycle 5</div><table><tbody><tr><td width="120"><br /><s>Francis</s><br />Joyce<br /><s>Eleven</s><br /><s>benofschool</s><br /><s>roxanne</s><br /></td><td width="120"><br /><s>JamieNeRd123C</s><br />zeph<br />AnhThi<br /><s>Richard</s><br /><s>Hi I'm Justus</s><br /></td><td><br />nelsa<br /><s>Rence</s><br />kristina<br /><s>Paul</s><br /></td></tr></tbody></table><p></p><p></p><p>Quote of the Cycle ;</p><p><em>"We say we love flowers, yet we pluck them. We say we love trees, yet we cut them down. And people still wonder why some are afraid when told they are loved."</em></p><p></p><p><br /><br />Stay Phi everyone,<br /><br />Rence ~ OutRencehttp://www.blogger.com/profile/11112931316863902414noreply@blogger.com0tag:blogger.com,1999:blog-1000693476051168456.post-38023713660119677052008-05-27T22:51:00.001-05:002008-05-30T12:37:29.295-05:00Today's Slides: May 27Here they are ...<br /><br /><center><br /><div style="width:425px;text-align:left" id="__ss_437837"><object style="margin:0px" width="425" height="355"><param name="movie" value="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080527-1212168665570794-8"/><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slideshare.net/swf/ssplayer2.swf?doc=pc40sw0820080527-1212168665570794-8" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="font-size:11px;font-family:tahoma,arial;height:26px;padding-top:2px;"><a href="http://www.slideshare.net/?src=embed"><img src="http://static.slideshare.net/swf/logo_embd.png" style="border:0px none;margin-bottom:-5px" alt="SlideShare"/></a> | <a href="http://www.slideshare.net/dkuropatwa/precal-40s-slides-may-27-2008?src=embed" title="View Pre-Cal 40S Slides May 27, 2008 on SlideShare">View</a> | <a href="http://www.slideshare.net/upload?src=embed">Upload your own</a></div></div><br /></center>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0