tag:blogger.com,1999:blog-67813976029258987222018-03-05T14:09:28.635-08:00Ste. Anne Collegiate PreCal 20S - 2008Learning to Think, Thinking to LearnSte. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-6781397602925898722.post-53778958018584561512008-04-30T10:13:00.001-07:002008-04-30T10:23:35.623-07:00Apr 29, 2008We took notes on the long divison of polynomials, it is the oppiste of facoring, you undo the facoring by division.<br /><br />In general it is <u>a+b </u>= <u>a </u>+ <u>b</u><br /> c c c<br /><br />After you have divided the question then you had to check for restrictions like, x cannot = 0 or other certain numbers since you can't divide a number by zero.<br /><br />Homework:p. 152 39-63 oddSte. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com35tag:blogger.com,1999:blog-6781397602925898722.post-7037871606270760682008-03-23T20:13:00.000-07:002008-03-23T20:56:35.354-07:00Monomials and PolynomialsIn PreCal20S, on March 11th,<br />we learnt that <strong>Monomials</strong> are:<br /><span style="font-size:85%;">- A number</span><br /><span style="font-size:85%;">- A product of one or more variables</span><br /><span style="font-size:85%;">- The product of a number and one or more variables</span><br /><br />Monomials consist of a numerical coefficient and a variable.<br /><br /><u><strong>Polynomials</strong> </u><br /><u></u><br /><span style="font-size:85%;"><em>Are algebraic expressions formed by adding or subtracting monomials.</em></span><br /><em><span style="font-size:85%;">Each monomial is a term of the polynomial.</span></em><br /><em><span style="font-size:85%;"></span></em><br /><span style="font-size:85%;">x + 17</span><br /><span style="font-size:85%;">Binomial = two terms</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">x² + 4x - 3</span><br /><span style="font-size:85%;">Trinomial = three terms </span><br /><span style="font-size:85%;"></span><br /><u><strong>Evaluating Polynomials</strong></u><br /><span style="font-size:85%;">Evaluate the expression for the given value of the variable:</span><br /><span style="font-size:85%;">x² + 4x - 3 for x = 2</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">= (2)² + 4(2) -3 </span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">= 4 + 8 - 3 </span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">= 9</span><br /><span style="font-size:85%;"></span><br /><strong><u>Mathematical Convention</u></strong><br /><br />The terms of a polynomial are usually written so that the exponents of the variable are in descending order or ascending order.<br /><br />If there is more than one variable, then it is written in ascending or descending order of one od the variables.<br /><br /><u>Ex. </u><strong>Write the polynomial in ascending order of x :</strong><br /><br /><span style="font-size:85%;">5x³y + 4xy³ -3 + 4x²y²</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">= -3 + 4xy² + 4x²y² + 5x³y</span><br /><span style="font-size:85%;"></span><br /><strong><u>Adding Polynomials</u></strong><br /><br /><span style="font-size:85%;">(x² + 4x - 2) + (2x² -6x +9)</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">= x² + 2x² + 4x - 6x -2 +9</span><br /><span style="font-size:85%;">= 3x² - 2x + 7</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;"><strong><u>OR</u></strong></span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;"> x² + 4x - 2</span><br /><span style="font-size:85%;">+ 2x² - 6x + 9</span><br /><span style="font-size:85%;">_____________</span><br /><span style="font-size:85%;">= 3x² - 2x +7</span><br /><span style="font-size:85%;"></span><br /><strong><u>Subtracting Polynomials</u></strong><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">(6a² - ab + 4) - (7a² + 4ab - 2) </span><br /><span style="font-size:85%;">= 6a² - 7a² - ab + 4ab + 4 - 2 </span><br /><span style="font-size:85%;">= -a² + 5ab + 2</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;"><strong><u>OR</u></strong> </span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">4y² - 2y + 3 </span><br /><span style="font-size:85%;">- (3y² + 5y -2)</span><br /><span style="font-size:85%;">___________</span><br /><span style="font-size:85%;">= y² - 7y + 5</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:85%;">And for our assignment we just finished off the math booklet.</span><br /><span style="font-size:85%;"></span><br /><span style="font-size:130%;">Taylor Wigston</span>Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com2tag:blogger.com,1999:blog-6781397602925898722.post-64416735726223347412008-03-22T16:23:00.000-07:002008-03-22T16:37:46.786-07:00On thursdsay, March20th in PRECAL20s the only thing we did for notes was:<br /> Example:Factor<br /> x<span style="font-size:78%;">squared</span><span style="font-size:100%;">-4x-12</span><br /> =(x+2)(x-6)<br /> <br /> x<span style="font-size:78%;">squared</span><span style="font-size:100%;">+6x-16</span><br /> =(x+8)(x-2)<br /><br /> x<span style="font-size:78%;">squared</span><span style="font-size:100%;">+1-20</span><br /> =(x+5)(x-4)<br /><br />There were two assignments handed out on thursday they were PAGE:120,37-44, and the class had to finish the rest of the orange booklet.<br /><br /> Thise post was added by Dustin G. WoodsSte. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com2tag:blogger.com,1999:blog-6781397602925898722.post-69896325464544846952008-03-19T15:01:00.000-07:002008-03-19T15:15:37.142-07:00March 18/08Today March 18/2008 in pre cal 20s we learned how to do factoring.<br />Factoring:<br />We now begin a discussion of the algebraic operation called factoring. Factoring an expression is to rewrite the expression entirely as a polynomial product.<br />Factoring Over the Integer:<br />A polynomial is considered completely factored when there are no more variable factors can be removed. No more integer factor, other than 1 or -1 can be removed. The steps for this process is 1. find the GCF (greatest common factor). 2. What is the GCF of the coefficients (exponents)? 3. What is the GCF of the variables (letters)? 4. Check: Multiply and see if you get the same expression that you started with.<br />Factoring by Grouping?<br />Some polynomials do not have a common factor in all their terms. These polynomials can sometimes be factored by grouping terms that do have a common factor.<br />The assignments we had assigned to us today are: page 120 #11-22 and page 120 #30-36Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com2tag:blogger.com,1999:blog-6781397602925898722.post-80263723882640836402008-03-12T19:23:00.000-07:002008-03-12T19:58:12.821-07:00Products of a Monomial and a Polynomial -March 12Today in class we learnt how to multiply monomials and polynomials. Basically all you have to do is multiply the monomial outside of the brackets by the polynomial inside the brackets.<br /> Ex: Expand<br /> 3a(4a-3b)<br /> =12a²-9ab<br /><br /> We also learnt how to simplify these expressions. To simplify an expression you, first, expand the expression like we have already done and then, secondly, collect like terms.<br /> Ex: Expand and Simplify<br /> 4x(2x²+ 5x -3) –(2x²-7)<br /> =8x³+20x²-12x-2x²+7<br /> =8x³+18x²-12x+7<br /> <br /> The final thing that we learnt to do today was multiplying binomials. When multiplying binomials you use the F.O.I.L. method. The F.O.I.L. method stands for multiplying the <strong>F</strong>irst two terms, then multiplying the <strong>O</strong>utside two terms, then multiplying the <strong>I</strong>nside two terms, and, finally, multiplying the <strong>L</strong>ast two terms.<br /> Ex: Find the product of the binomials<br /> (x+6)(x+8)<br /> =x²+8x+6x +48 <----(F.O.I.L. method)<br /> =x²+14x+48 <----( you have to collect like terms here too.)<br /><br /> The assignment for today was:<br /> pg.107, questions 1-29 odd and pg.108, questions 32-43 and 45-67Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com2tag:blogger.com,1999:blog-6781397602925898722.post-78790546177191936602008-02-20T11:07:00.000-08:002008-02-20T11:29:34.615-08:00Operations with radicalsToday we were learning and recalling on radicals.<br /><br /><ul><li>Ex. In order to add or subtract variables, the variable must be the same.</li><li>The same is true when adding or subtracting radicals.</li><li>The Part under th eradical must be <em>exactly the same!!!</em></li></ul><br />We didn't do much notes but more examples on how to:<br />Multiply a radical by a binomial && Radial Binomial Multiplication.<br /><br />We also did 2 different assignments.<br /><br />One was on --><em>Page 23 # 9 - 28 odd</em><br /> and<br />the other was --><em>Page 23 # 29 - 35</em>Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com1tag:blogger.com,1999:blog-6781397602925898722.post-87783803320592349632008-02-14T13:16:00.000-08:002008-02-14T13:21:56.578-08:00February 14, 2008Today we learned about rationalizing radicals when the radical sign <br />is in the demonimator. You do it by multiplying it by a form of 1 such as square 2 over square 2, to move the radical up top. <br />Its a pain in the butt, but its worth it. Todays assignment was page 19 #35-53 odd. Tomorrows scribe is Kara Lee Rae. HahaSte. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com0tag:blogger.com,1999:blog-6781397602925898722.post-51131388717957429322008-02-13T20:46:00.000-08:002008-02-13T20:56:10.664-08:00simplifying radicalstoday in class we worked on simplifying radicals.<br /><br />We lernt that we must lern numbers like 75 (sqaure root) and 2/9 (sqaure root) are called entire radicals<br /><br />And numbers like 5 Sqaure 3 and 1/3 sqaure 2 are called mixed radicals<br /><br /><br /><br /><br />Joss GowlandSte. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com0tag:blogger.com,1999:blog-6781397602925898722.post-5999732451007599112008-02-12T20:03:00.003-08:002008-02-12T20:05:58.246-08:00February 11, 2008<br /><br />Today in class we learnt how to <em>Simplify Radicals</em>.<br /><br /> Mrs. Remple used a card game at first to help us understand the concept.<br />She handed everyone a few cards from her deck of cards. Everyone organized their cards into pairs of 2. We put all our pairs on the left side of our desk and our extra cards on the right. Then we repeated all this but making sets of 3. It helped show us what happens when we are simplifying radicals.<br /><br />Here is an example:<br /><br />²√ 16x³y¹z²<br />= 2∙2∙2∙2∙x∙x∙x∙y∙z∙z<br />There are two sets of 2s.<br />{2∙2}∙{2∙2}∙x∙x∙x∙y∙z∙z<br />There is one set of X’s and one X left over.<br /> {2∙2}∙{2∙2}∙{x∙x}∙x∙y∙z∙z<br />There is only one Y, so it is just a left over.<br />There is one set of Z’s with 0 left over.<br />{2∙2}∙{2∙2}∙{x∙x}∙x∙y∙{z∙z}.<br />The simplified answer is:<br />2²xz√xySte. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com1tag:blogger.com,1999:blog-6781397602925898722.post-45278639191502642702008-02-12T17:42:00.000-08:002008-02-12T17:43:46.850-08:00February 8, 2008Today we learnt about Real Number Stuff. We did questions from the overhead with groups.<br />Some examples of questions were:<br />State wheather each of the following is always true, sometimes true, or never true.<br />The sum of a rational number and an irrational number is:<br />a) Positive: Sometimes True<br />b) Irrational: Always True<br />c) A fraction: Never True<br />d) Rational: Never True<br />e) Negative: Sometimes True<br />f) A whole number: Never True<br /><br />If you took the absolute value of every number in each of the following sets of numbers, which set of numbers would you obtain?<br />a) Integers: Whole numbers<br />b) Negative integers: Natural numbers<br />c) Whole numbers: Whole numbers<br />d) Real numbers: Positive real numbers and zero<br />I learnt alot this day ha thanks to Ms. Remple she gave us no homework!Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com0tag:blogger.com,1999:blog-6781397602925898722.post-33020990319986204722008-02-08T09:55:00.000-08:002008-02-08T10:08:01.512-08:00Feb.4/5<div>In pre-cal today we started unit 1 (Radicals and Rational Exponents)</div><br /><div>Lesson 1- <strong>Math 10F Review</strong></div><br /><div> </div><br /><div> <strong> Mental Math</strong></div><br /><div>Multiply Polynomials</div><br /><div>Ex.1 Expanding</div><br /><div><strong>a)</strong> <strong>3(a+4)</strong> Ex.2 </div><br /><div><strong><font color="#ff0000">3a+4</font> a) (x+4)(x+3)-Used FOIL Method </strong></div><br /><div> x^2+3x +4x +12</div><br /><div><strong>b) x(x+3) <font color="#ff0000">x^2 + 7x +12</font></strong></div><br /><div><strong><font color="#ff0000">x^2 -3x</font></strong></div><br /><div><strong></strong> </div><br /><div><strong>c)-5(y-2) </strong></div><br /><div><strong><font color="#ff0000">-5y + 10</font></strong></div><br /><div><strong></strong> </div><br /><div><strong>Those were some examples of what we did the first day of pre-cal 20s.</strong></div><br /><div><strong></strong> </div><br /><div><strong></strong> </div>Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com0tag:blogger.com,1999:blog-6781397602925898722.post-64090193775670296222008-02-08T07:12:00.000-08:002008-02-08T07:14:40.149-08:00February 7 - Real Numbers and Absolute ValueToday, February 7th, in PreCal 20S, we learned about <strong>real number lines</strong>.<br /><br />Every real number corresponds to a point on the real number line. There is a one-one correspondence between real numbers and the points on the line. In this real number line, there are no gaps, the line is complete throughout. Example:<br />_________________________________________<br />-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10<br /><br />When Graphing on a Real Number Line - An open dot means that the point does not include the real number. A closed dot means that the point includes the real number.<br /><br /><strong>Absolute Value</strong><br /><br />Also, today in class, we learned about absolute value.<br />The absolute value of a real number is the distance from zero to the position of the number on the real number line. When finding the absolute value of a real number, ignore the signs.<br />The notation for absolute value is x<br />Example: -2 = 2 , 2 = 2<br />Example: 2 - -5 , 2 - 5 = -3Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com4tag:blogger.com,1999:blog-6781397602925898722.post-39376325357830125152008-02-03T16:57:00.000-08:002008-02-03T17:38:54.996-08:00deSCRIBE<a href="http://3.bp.blogspot.com/_-hfDXsWwBOQ/R6ZqFT2ZThI/AAAAAAAAAAU/IgMiHIgnQRA/s1600-h/arbron.jpg"><img id="BLOGGER_PHOTO_ID_5162930662287166994" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://3.bp.blogspot.com/_-hfDXsWwBOQ/R6ZqFT2ZThI/AAAAAAAAAAU/IgMiHIgnQRA/s320/arbron.jpg" border="0" /></a><br /><a href="http://4.bp.blogspot.com/_-hfDXsWwBOQ/R6Zpaj2ZTgI/AAAAAAAAAAM/3_JEHPPyZ4I/s1600-h/arbron.jpg"></a><div align="center"><a href="http://www.flickr.com/photos/arbron/923398621/">http://www.flickr.com/photos/arbron/923398621/</a><br /><a href="http://www.flickr.com/photos/arbron/923398621/"></a><br /></div><div><br /></div><div><br /></div><div>Until the invention of the printing press, scribes were the people that were paid to write or copy books by hand. These were the educated people of their civilizations. In our class, the scribes will be the ones writing the customized textbook for our course.<br /></div><br /><div><br /></div><div>A Scribe post is a summary of what happened in class. It is filled with enough detail that someone who missed class will be able to catch-up on what they missed. As you are writing your posts ask yourself <strong>"Is this entry worthy to be included in our textbook? Would a graphic or example help clarify this topic?"</strong> At the end of your scribe post you will name the next scribe and you will tag your post with the date and unit.</div><div><br /></div><div> </div><div>I learned about scribe posts from Mr. Kuropatwa at Daniel Mac and Mr. Harbeck at Sargent Park (both schools are in Winnipeg). Once I have learned how to include links, I will give the links to their blogs! The blogs that their students have created have impressed me to the point of making scribe posts a mandatory part of PreCal 20S at Ste. Anne Collegiate. </div><br /><br /><div><br /></div><div>We will also have pre-service teachers from the University of Regina reading and commenting on your posts. This blog will be as rich and useful as <strong>you</strong> make it. This will be a place for you to think about your learning and to ask questions of your fellow classmates, the pre-service teachers, me (Mrs. Remple), and the world outside of the halls of SAC. </div>Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com0tag:blogger.com,1999:blog-6781397602925898722.post-12325887787318296352008-01-27T16:10:00.001-08:002008-01-27T16:10:59.967-08:00Welcome to PreCal 40S!This blog is a space for you to discuss what was learned in class and to reflect on your own learning.Ste. Anne Collegiate - PreCal 20S 2008http://www.blogger.com/profile/15706648014875878787noreply@blogger.com0