Math songs
Below are the math songs we sang in class, hope you get to sing them to someone else!
June 15, 2007
More logic problems
You can see some more logic problems (with a ranking for difficulty) by following the link below.
http://www.geocities.com/Heartland/Plains/4484/logic.htm#xpls
May 3, 2007
Review material
I have a list of topics for the exam prepared. I will give you a paper copy of it tomorrow, but you can download a copy of it to start your revision tonight if you wish. I will try and give you some questions you can work on (for the topics from the 2nd semester since I have given you a list of questions for the first semester already in preparation for your midyear exams).
About 70% of the material will be questions from this semester and about 30% will be questions from first semester.
March 21, 2007
Vector Summary (March 21, 2007)
Today in math we learned about vectors. Vectors are defined as a way of assigning a single object to represent a magnitude (size) and a direction. We write them using components (or more commonly known as coordinates). A vector is also known as a directed line segment. The notation for a vector is similar to that of the matrix, in fact a matrix notation with 1 column and 2 rows is always a vector. For example: 
To graph this vector, keep in mind that 2 is the x value and 3 is the y value. However, the vector does not necessarily begin at 0. The direction of the vector can also be changed. 
, this is the inverse of the original notation. 
and 
. Direction of vector is known as the gradient. 
. 
. 
and 
have the same direction. You can also make triangles with vectors, calculating the sides with the pythagorean theroem. I was going to add an example, however I thought it would not be very descriptive without a graph. The next presenter is : eleova. I don't know if she has gone already. xxxx
March 14, 2007
12 March 2007
This class we learned how to solve exponential equations using logarithms. Mr Wees gave such examples:
ex1)
To solve you multiply by
on each side
To receive x on its own
Then use logarithm rule #6:
ex2)
To solve we subsituted
for y, to receive a quadratic equation
We then factor the equation
(y-3)(y-2)=0
Then resubsituted
And then solve for x which gives us
ex3) This example was solved in terms of logx and logy
We then used the logarithms rules #1 and #3
Then we applied logarithm rul #2 to remove the exponents
=4logx + 6logy - 5logx
And combined like terms for our result
=6logy - logx
The remaining time of this class we worked on a worksheet.
I nominate mikbin to make the next class entry.
xoxoxo
February 27, 2007
Exponential Functions - Monday February 26, 2007
On monday in class we began to look at exponential functions by dropping a basketball. We saw that the highest height the basketball reaches each time it bounces after being dropped is a decrease in a gemoetric sequence. However we also saw that the graph could be written as an exponential function. We were told the formual for an exponential function was:
[tex]y=Ka^\lambda^(^x^-^b^)+C[/tex]
We then started work to find out how each variable in the formula effected the function. We discoverd that [tex]a^x[/tex] is the center of the equation therefore most changes that occur will change that figure thus changing the function. We found the following:
[tex]C[/tex] changes the Y-Intercept, the larger [tex]C[/tex], the larger the Y-Intercept
[tex]K[/tex] changes the Slope because it makes [tex]a^x[/tex] a larger number
[tex]K[/tex] muliplies the slope by [tex]K[/tex]
[tex]\lambda[/tex] changes the Slope
When [tex]\lambda[/tex] is increased by a factor of 1 the slope increases by a ratio of 2
[tex]b[/tex] shifts the function Left or Right, the larger [tex]b[/tex] is the farther right the function is when graphed
[tex]y=Ka^\lambda^(^x^-^b^)+C[/tex] is a combination of all these changes, depending on the values of the different variables.
That was basically the lesson for Monday February 26, 2007. The next person is Daaman. Sorry
Matein
February 9, 2007
Bouncing ball Java Applet
Check out this bouncing ball applet.
http://www.jensign.com/JavaScience/www/bounce/bounce.html
How does this resemble a geometric series?
Can you estimate the value of r for the heights of this series?
How would you find the distance the ball has travelled?
Flash application for sequences
If you want some practice with arithmetic sequences, check out the link below.
http://www.interactivestuff.org/sums4fun/sequences.html
Also, for a link to many different examples of fun interactive web mathematics, check out this page.
November 29, 2006
Solving systems of equations
I'm collecting some resources we can use to solve systems of equations.
Here is a tutorial that explains how to solve a system of equations using your TI graphing calculator.
Here is a resource for playing around with Gaussian elimination and trying to figure out how to make it work.
and finally, here is a resource for solving systems of equations, quadratic equations, or normal one variable equations. It also shows most of the steps involved in solving the equations.
November 27, 2006
Résumé of class today
Today, we worked on how to solve 3 simultaneous equations. Mr Wees taught us 2 ways to do it.
Firstly, the method by gaussian elimination:
ex. -(1)- 3x + 4y + 3z = 10
-(2)- 2x - 3y + 2z = 6
-(3)- 1x - 1y + 10z = 20
Now, we simplify -(1)- and -(2)- : 3 *-(1)- + 4 *-(2)- => 17x + 17z = 54
Then, we simplify -(1)- and -(3)- : 1 * -(1)- + 4*-(3)- => 7x + 43z = 90
At this point, we have 2 equations with 2 unknowns, easily solvable.
Secondly by metrics, but I think it is just useful to know how our calculators proceed (because it's much more difficult than the first one!)
Each line constitutes an equation:
-(1)- 1 2 3 | 1
-(2)- 4 2 3 | 10
-(3)- 5 1 2 | 20
We simplify each one of them separately; such as:
-(2)- - 4 * -(1)- and -(3)- - 5 * -(1)-
which gives us
-(1)- 1 2 3 | 1
-(2)- 0 -6 -9 | 6
-(3)- 0 -9 -13 | 15
Then we multiply -(2)- by -1/6:
-(1)- 1 2 3 | 1
-(2)- 0 1 1.5 | -1
-(3)- 0 -9 -13 | 15
We simplify -(2)- and -(3)- together by doing -(3)- + 9 * -(2)-, which gives:
-(1)- 1 2 3 | 1
-(2)- 0 1 1.5 | -1
-(3)- 0 0 0.5 | 6
Then we do 2 * -(3)- to find z:
-(1)- 1 2 3 | 1
-(2)- 0 1 1.5 | -1
-(3)- 0 0 1 | 12
so z = 12
At this point, we do back substitution to find x and y (by replacing z by its value in the other equations) :
y + 1.5 (12) = -1
y = -19
x + 2(-19) + 3 (12) = 1
x - 38 + 36 = 1
x = 3
And we got the 3 unknowns :)
At the end of the period, we took different points from a video showing the different places of a ball being thrown. With the coordinates of 3 points, our homework assignement is to find the equation of the function (y = ax² + bx + c) using the tools we have learnt today.
I have no idea of who didn't get the chance to write a résumé yet, so perhaps we could sort it out on Wednesday ?!
-Origny
October 23, 2006
Alternatives to Equation Editor for Microsoft Word
There are some alternatives to Equation Editor you can use some of the following alternatives:
MathCast - This allows you to create equations, and then copy and paste the equations into Microsoft Word and other such applications. You can download this code from here. Make sure you extract the file you download into a new directory (otherwise you will end up with a mess of files on your desktop, which is never pretty). You then simply double click on MathCast.exe to run the file.
WebEq - You can use this program again, which comes with a 30 day evaluation version. Just download it from here.
Of course both of these options assume you are using a PC with Windows as your operating system. If you are using a Mac, you can use instead:
Actually I couldn't find any good solutions for the Mac. WebEq apparently (same download page as above) has a Mac version of their software. Your other option is to visit this page, but you will both have to download their software, and TeX for Mac OS X. You will ALSO need to use the TeX language to create the equations.
Your best bet, if you are using a Mac, is to have a window of http://www.forkosh.com/mimetex.html open, and just copy and paste the images that his Mimetex equation generator creates directly into your Word document.
September 18, 2006
Graphs and Equations
You can insert graphs into your entries like so:
And equations into your entries like:
For more information see:
My blog
My blog
August 31, 2006
Welcome to the 10th grade blog!
Here's a place where the students of the 10th grade Extended class can summarize their lessons. They will be able to include mathematical equations in their entries using [tex] and [/tex] tags. (see the tutorial here)
As the year progresses we hope the summaries get better. What will happen is that when one student posts, they get to choose the next student. However they cannot choose someone who has already done as many posts as they have done (so that each person get picked at some point).
This is the blog for Mr. Wees' classes. Here we will be able to include images, flash files, mathematical discussions, or whatever else is relevant to our discussions.
We can also include mathematical equations in our posts, like
.
You can also see a tutorial on how to include mathematical equations here