tag:blogger.com,1999:blog-6771772639456198562024-02-19T16:20:40.600+08:002011 S2-01 Maths BlogJason_Inghamhttp://www.blogger.com/profile/18134700146375885379noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-677177263945619856.post-55617734260309726042011-01-31T21:27:00.000+08:002011-01-31T21:27:31.938+08:00Week 4 learning pointsConcepts:<br />
-When moving the parabola up or down, the Line of Symmetry(LoS) remains the same.<br />
-Negative Square Root = NO SOLUTION!<br />
-It is possible for a parabola to have equal roots= 1 root OR 1 line OR never intercept at all which is no solution<br />
-Solving a parabola = finding the point where 2 intercepts Or where it intercepts the x -axis<br />
-Not rational number cannot be solved by factorisation <br />
<br />
<br />
When completing a square, you are trying to make the equation into (a+b)^2 or (a-b)^2<br />
So for example: x^2+ 2x+ 2=0<br />
x^2 +2x = -2<br />
So, multiply the coefficient of 2x which is 2 so = 4<br />
Then square it so its 4^2<br />
Then add it to the other side to equal the equation out. <br />
Thus,<br />
x^2 + 2x + 4^2 = -5 +4^2<br />
Then solve for x normally.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-677177263945619856.post-53332836270054757772011-01-31T18:10:00.005+08:002011-02-12T17:04:02.392+08:00Learning points in Term 1 Week 2/3<div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Types of solving equations: </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><ol style="list-style-type: decimal;"><li style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Factorisation</span></span></span></li>
</ol><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Example: y = x^2 + x - 6 </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> Factorise by trial and error </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> You should get y = (x+3)(x+2)</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">-------------------------------------------------------------------------</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">However there is another type: what happens when x^2 + x -6 = 0</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> </span></span></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> The method will be the same as the factorisation </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> </span></span></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> Except that the equation will be shown as (x+3)(x-2) = 0</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> Therefore if this equation is equivalent to zero, either (x+3) = 0 or (x-2) = 0 as something-zero multiplied by something is zero. </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> </span></span></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> Hence, x = -3 OR x = 2 because if x is 3, (x+3) is 0 and if x is 2, (x-2) = 0. </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><ol style="list-style-type: decimal;"><li style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">General formula</span></span></span></li>
</ol><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">y = -(b) ± √ (b)^2 - 4(a)(c) / 2(a)</span></span></span><br />
<span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"> </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">This is an ellipse. Example: x^2 + y^2 = 9</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikxwcXDcl9-aIcMU-kA0D0ZaIIp6G7Jlewx89edsh7KlPtkAVubRWgKUUsMFT3tb5jg6CbLSexauM6DheV2GBVbKKjdJrNjk2NHHkm3ddsLRNBax2XEFVhyphenhyphenUxE2_YKrifFLnzGlt89C3U/s1600/Screen+shot+2011-01-30+at+17.02.58.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><img border="0" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikxwcXDcl9-aIcMU-kA0D0ZaIIp6G7Jlewx89edsh7KlPtkAVubRWgKUUsMFT3tb5jg6CbLSexauM6DheV2GBVbKKjdJrNjk2NHHkm3ddsLRNBax2XEFVhyphenhyphenUxE2_YKrifFLnzGlt89C3U/s320/Screen+shot+2011-01-30+at+17.02.58.png" width="320" /></span></span></a></div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Question 5 of homework 2-solving quadratic equations Tier C</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Given that the roots of the equation 2x^2 - 6x - k = 0 differ by 5, find the value of k. </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">First, we ask ourselves what can be the lowest value of k. </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Lowest value of k: 0</span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">So if we input y = 2x^2 - 6x - 0 into Geogebra we will get this (if not through factorisation) : </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDGTYV5tOSFHhbWyIOiOFTrTZLi1-CcSVBuMjuy7xTkPpDezCM2GR1AREMgrsMQbaq7r44zLYWxiQqnVhBuj9K2wbpPYxcnvvrUb-I9JxESb34eu08CGtyBzzUkCb3UnBUuhTkbn3ViXE/s1600/Screen+shot+2011-01-30+at+18.33.10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDGTYV5tOSFHhbWyIOiOFTrTZLi1-CcSVBuMjuy7xTkPpDezCM2GR1AREMgrsMQbaq7r44zLYWxiQqnVhBuj9K2wbpPYxcnvvrUb-I9JxESb34eu08CGtyBzzUkCb3UnBUuhTkbn3ViXE/s320/Screen+shot+2011-01-30+at+18.33.10.png" width="234" /></span></span></a></div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">As we can see, the roots of this equation only differs by 3, not 5. <span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">So we work on the line of symmetry </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIuppJxpYk9MyEFxqS-dGbVtldL5XozE0A1S2N80ghqXggPAbsZhhOuGKbfbSrYCh1U8tN3CKr6L4pqtWEv7X5HoOQDDJ03dOONEbNi8C8evVxKNbJeUMokOGKPNrvLlK-ldUoWObC8TM/s1600/Screen+shot+2011-01-31+at+21.15.11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIuppJxpYk9MyEFxqS-dGbVtldL5XozE0A1S2N80ghqXggPAbsZhhOuGKbfbSrYCh1U8tN3CKr6L4pqtWEv7X5HoOQDDJ03dOONEbNi8C8evVxKNbJeUMokOGKPNrvLlK-ldUoWObC8TM/s320/Screen+shot+2011-01-31+at+21.15.11.png" width="236" /></span></span></a></div><div class="separator" style="clear: both; text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">The parabola can be moved up and down the same line of symmetry. </span></span></b></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">So we look for the next set of numbers that differ by 5, -1 and 4.</span></span></b></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">As a result we will get this: </span></span></b></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><b></b></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><b></b></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6VGoH6Zo8B7V1XI9tg1HG290fWWc_u-BTS5ra2GJzrZ5ymJjSZZArbwpdlmrtn-lF9CY2z827fgUNuKPFUYFUI31MIxSU0TzukK3oVBudooaNrqQ9JcwxBM8eyeqn8bD0mxak_L7Bdi4/s1600/Screen+shot+2011-01-30+at+17.08.19.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><img border="0" height="245" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6VGoH6Zo8B7V1XI9tg1HG290fWWc_u-BTS5ra2GJzrZ5ymJjSZZArbwpdlmrtn-lF9CY2z827fgUNuKPFUYFUI31MIxSU0TzukK3oVBudooaNrqQ9JcwxBM8eyeqn8bD0mxak_L7Bdi4/s320/Screen+shot+2011-01-30+at+17.08.19.png" width="320" /></span></span></a></div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><b></b></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><b></b></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><b></b></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><b></b></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Now the roots differ by 5. Note that they have the same line of symmetry </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTV_pMzJ4016mWxMCwi76xhE1YjOMS39_1peh8YkQ7OjCqoeTyd0vzLAYzCk0GYM-uALwij-FrtW1QGrH8wp_TDBLSlPKga1Phdmwv6jjQ33RlU-SuAUASzY3rOgu3F-4YIfQYtYv3s1Q/s1600/Screen+shot+2011-01-31+at+21.16.51.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTV_pMzJ4016mWxMCwi76xhE1YjOMS39_1peh8YkQ7OjCqoeTyd0vzLAYzCk0GYM-uALwij-FrtW1QGrH8wp_TDBLSlPKga1Phdmwv6jjQ33RlU-SuAUASzY3rOgu3F-4YIfQYtYv3s1Q/s320/Screen+shot+2011-01-31+at+21.16.51.png" width="192" /></span></span></a></div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><br />
</span> </span><span class="Apple-style-span" style="font-size: small;"> </span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Now having found the correct parabola that has roots that differ by 5, we should be wondering: how do we put this into an equation. </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px;"><span style="letter-spacing: 0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;">Well since we just “moved” the parabola, the ax^2 and bx should be the same. Only the c changes. </span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2Y0OQz2aT95qkViXI-0-KQwNkGFPrdcRjExYMm55JU2yPYVAwtjmHQsLyxUix4crxBo4iY1YiybeNinESFjdm1uvDLPPCrRFaJs5dJeMgcTCj_dbfj-kEQ0HuG23GsabQyP_IaV1DGUM/s1600/Screen+shot+2011-01-31+at+21.17.22.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><img border="0" height="233" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2Y0OQz2aT95qkViXI-0-KQwNkGFPrdcRjExYMm55JU2yPYVAwtjmHQsLyxUix4crxBo4iY1YiybeNinESFjdm1uvDLPPCrRFaJs5dJeMgcTCj_dbfj-kEQ0HuG23GsabQyP_IaV1DGUM/s320/Screen+shot+2011-01-31+at+21.17.22.png" width="320" /></span></span></a></div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: small;"><span style="letter-spacing: 0px;"></span></span></span></div><div style="font: 12.0px Helvetica; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 14.0px;"><br />
</div>t.jianhuihttp://www.blogger.com/profile/06354172526273501498noreply@blogger.com1tag:blogger.com,1999:blog-677177263945619856.post-52148504299335974572011-01-11T16:53:00.015+08:002011-01-14T19:14:22.907+08:00Things Learnt In Term 1 Week 2<span style=";font-family:trebuchet ms;font-size:85%;" ><span style="font-weight: bold;">Monday(10 January 2011)</span><br /><br />Ms Loh touched on fractional expressions and she also revised the topic of factorization briefly with us on Monday. The various methods of factorization are shown in the picture below.<br /><br /></span><span style="font-size:85%;"> <a style="font-family: trebuchet ms;" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj57qKpRu_eCp61BA33RmDNjqjYm3XgTFIP7O1m-jdAhHiRSCwvSTzfLgdQjfOw0J1Jx8ejO7wi66uwQQJ9hXZywq-dUwDLMHvR_qZuEXrGq1GBxBh2AyPJe6wAt8qsD0_j11xcsxqcMhVP/s1600/Screen+shot+2011-01-11+at+PM+04.57.07.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 400px; height: 309px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj57qKpRu_eCp61BA33RmDNjqjYm3XgTFIP7O1m-jdAhHiRSCwvSTzfLgdQjfOw0J1Jx8ejO7wi66uwQQJ9hXZywq-dUwDLMHvR_qZuEXrGq1GBxBh2AyPJe6wAt8qsD0_j11xcsxqcMhVP/s400/Screen+shot+2011-01-11+at+PM+04.57.07.png" alt="" id="BLOGGER_PHOTO_ID_5560849873060706946" border="0" /></a></span><span style="font-size:85%;"> </span><span style=";font-family:trebuchet ms;font-size:85%;" ><span style="font-weight: bold;">Tuesday(11 January 2011)</span><br /><br />Today, we covered topics like parabola, subject and algebraic fractions. One of the questions we encountered in the pre-quiz is shown below.<br /><br /></span><span style="font-size:85%;"><a style="font-family: trebuchet ms;" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGuNvRy2hFG_sEgBwcVWvdLTj8BkkgTAu6tzZVa07c6cx4UzAqu3RcJVPI0RAFLiPEkv_TxYPoh4TxzL4ZM4DlbyN6WmZ-ok9lZ3a70JDuFEa1_2Jd0O9FMLvznrsVYMVIDBQSaOp58gJE/s1600/Screen+shot+2011-01-11+at+PM+05.01.13.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 400px; height: 183px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGuNvRy2hFG_sEgBwcVWvdLTj8BkkgTAu6tzZVa07c6cx4UzAqu3RcJVPI0RAFLiPEkv_TxYPoh4TxzL4ZM4DlbyN6WmZ-ok9lZ3a70JDuFEa1_2Jd0O9FMLvznrsVYMVIDBQSaOp58gJE/s400/Screen+shot+2011-01-11+at+PM+05.01.13.png" alt="" id="BLOGGER_PHOTO_ID_5560850897441411890" border="0" /></a></span><span style=";font-family:trebuchet ms;font-size:85%;" >As you can see, we have to factorize the numerator and denominator, such that we can simplify the fraction in a more easier manner. It is encouraged write a statement like "<span style="color: rgb(0, 0, 0);">x ≠ -3/2</span>" behind the answer if there is a certain value that does not work on the fraction</span><span style="font-size:85%;"><span style="font-family:trebuchet ms;">.</span> <span style="font-family:trebuchet ms;"><br /><br />We also encountered another question like this in our pre-quiz. However, this time, we have to make <span style="font-style: italic;">t</span> as the subject of the equation.<br /><br /></span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc0hhn9tBoFcLD-dVTYjTeS10KHW2LjcV_MEjcbhvfnv06o1R2e_s-4Pc6rrN72NWZwGLDhv0OENim2lSIEAUfSCt3aOcIvt1zPRBmFoHHwiyxo32OgY2xqUmqNU3b3Cjf-LWDPZzbc_sU/s1600/Screen+shot+2011-01-11+at+PM+05.07.25.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 388px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc0hhn9tBoFcLD-dVTYjTeS10KHW2LjcV_MEjcbhvfnv06o1R2e_s-4Pc6rrN72NWZwGLDhv0OENim2lSIEAUfSCt3aOcIvt1zPRBmFoHHwiyxo32OgY2xqUmqNU3b3Cjf-LWDPZzbc_sU/s400/Screen+shot+2011-01-11+at+PM+05.07.25.png" alt="" id="BLOGGER_PHOTO_ID_5560852995068238562" border="0" /></a><br /><span style="font-size:85%;"><span style="font-family:trebuchet ms;">Apparently, if the question wants <span style="font-style: italic;">t</span> to be the subject of the equation, the answer should look something like this in the end:<br /><br /><span style="font-style: italic;">t</span> = ________ (devoid of <span style="font-style: italic;">t</span>; no <span style="font-style: italic;">t</span>s) <span style="font-family:trebuchet ms;"><br /><br />We also need to put the "±" sign behind the value, which has been square rooted. This is because the subject of the equation is squared. For example, we can say the value of </span><span style="font-style: italic;font-family:trebuchet ms;" >x</span><span style="font-family:trebuchet ms;"> squared is 16, so x can be -4 or 4. That is why we must not forget the "±" sign.<br /><br /></span><span style="font-family:trebuchet ms;">This brings us to parabolas. Parabolas have two roots and they are synonymous to the </span></span></span><span style=";font-family:trebuchet ms;font-size:85%;" >"±" sign</span><span style=";font-family:trebuchet ms;font-size:85%;" >.</span><span style="font-size:85%;"><span style="font-family:trebuchet ms;"> This brings us to a question. Let's say that the equation is y = x^2 and they also stated that y = 4. How can we go about solving this question? We can do this in a graphical perspective like this.<br /><br /></span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5cXXLCgjWI3Sdnp5coNN5LvwNH2wQTh7bkjggyjBYhpiwyG01-ws2I1OB8w35Sahr8Yp_UmA6nkOlfXsd8tPCpPcmVVcqB0qCxnvZSBzdcU0Uvp8RMIC8U5BtR3jg7mwYy9hCKJaY0P-h/s1600/Screen+shot+2011-01-11+at+PM+05.18.28.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 141px; height: 286px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5cXXLCgjWI3Sdnp5coNN5LvwNH2wQTh7bkjggyjBYhpiwyG01-ws2I1OB8w35Sahr8Yp_UmA6nkOlfXsd8tPCpPcmVVcqB0qCxnvZSBzdcU0Uvp8RMIC8U5BtR3jg7mwYy9hCKJaY0P-h/s400/Screen+shot+2011-01-11+at+PM+05.18.28.png" alt="" id="BLOGGER_PHOTO_ID_5560857231220739602" border="0" /></a><span style="font-size:85%;"><span style="font-family:trebuchet ms;"><br />Remember, we have to include the "±" sign behind the square rooted value of 4 as the x, the subject for the current equation, is squared. The picture below shows another approach of solving the same question.<br /><br /></span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9kR5oQEVwikv15BzCfMGS-0Rp_juZIRMInJ3A_LP5LlST1kVIDEc_muN4ld7nAcHChlPdWnA1yKs6lx6aD8294kRKZ3nZW6RMFaMm1fNgAmta1noAwKSvj5WlCb1tCHZhD2zbmkMZcqQG/s1600/Screen+shot+2011-01-11+at+PM+05.17.16.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 264px; height: 214px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9kR5oQEVwikv15BzCfMGS-0Rp_juZIRMInJ3A_LP5LlST1kVIDEc_muN4ld7nAcHChlPdWnA1yKs6lx6aD8294kRKZ3nZW6RMFaMm1fNgAmta1noAwKSvj5WlCb1tCHZhD2zbmkMZcqQG/s400/Screen+shot+2011-01-11+at+PM+05.17.16.png" alt="" id="BLOGGER_PHOTO_ID_5560856475461384322" border="0" /></a><span style="font-size:85%;"><span style="font-family:trebuchet ms;"><br />We have to put x, as well as the two other equations given to us, onto the table as shown above. We have to list the numbers out and find similar numbers for the two equations, and not x. After that, we will be able to identify the two differing values of x.<br /><br /><span style="font-weight: bold;">Friday(14 January 2011)<br /><br /></span><span>Today, we did some questions of factorization and algebraic fractions. This is one of the questions that we have done in our lesson today.<br /><br /></span></span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpC25XEaDccAu7CatM2ONg29bYUF7Rk0fyPqPX1G5LBYXyt6pLQ2t3QStQqDpQi2wIj_kHMtKGOTcZPre7Dqjm9VzCIM0qh6rfLK98LbpbdphVagT4brFOETCZ4FIUB1TTp1yt68YnU67N/s1600/Screen+shot+2011-01-14+at+PM+01.18.54.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 372px; height: 276px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpC25XEaDccAu7CatM2ONg29bYUF7Rk0fyPqPX1G5LBYXyt6pLQ2t3QStQqDpQi2wIj_kHMtKGOTcZPre7Dqjm9VzCIM0qh6rfLK98LbpbdphVagT4brFOETCZ4FIUB1TTp1yt68YnU67N/s400/Screen+shot+2011-01-14+at+PM+01.18.54.png" alt="" id="BLOGGER_PHOTO_ID_5561906915090315730" border="0" /></a><span style="font-size:85%;"><span style="font-family:trebuchet ms;"><br />As you can see, the first step of the solution has two fractions with different denominators. One of them is 3(x - 2), while the other denominator is (x + 3)(x - 2). We have to find the LCM in order to determine the denominator of the algebraic fraction, thus we have to list them out and try to find the desired equation.<br /><br />(3) (x - 2) (1)<br /> (1) (x - 2) (x + 3)<br /><br />Since we have to choose the largest number of each column to get the desired LCM, we must determine the denominator, which will be 3(x + 3)(x - 2) in this case. Then, we can proceed and try to solve the algebraic fraction after solving the numerator.<br /><br />Remember, if the question asks for simplification of the algebraic fraction, do not expand the solution. Otherwise, it is very hard to complete the equation because it is going around in circles. It is also important that we must not forget to write vital steps in our answers, otherwise our marks will be deducted during examinations.<br /><br />For example, if the question says that y = 2x - 1 and that x = 1, we cannot just answer straightaway. We must have y = 2(1) - 1, before getting 1, which is the answer for the equation.<br /></span></span>Torhttp://www.blogger.com/profile/02066068448375741081noreply@blogger.com0