A little irrelevant

The United States is home to the greatest education institutions in the world. Nobody is going to argue that MIT, Caltech, Harvard, Princeton, Cornell, Yale,  and Harvard are the top dog institutions on our planet. And, given our increasingly technologically oriented society, the need for students who are technically adept is absolutely necessary. 

Yet, the trends in education is disturbing. Some highschools grad cannot even grasp basic algebra:

http://www.nydailynews.com/ny_local/education/2009/11/12/2009-11-12_cunys_got_math_problem_many_freshmen_from_city_hs_fail_at_basic_algebra.html

In my opinion, math is as important as English for university. If highschool grads are ill-equipped for the rigor of university, what then? Will the university be forced to water down their curriculum in response to the influx of bad students?

Not to imply that our curriculum is bad; it isn't.  But when the United States decides to walk down a new path, Canada isn't very far behind. This article addresses those issues:

http://www.osstf.on.ca/Default.aspx?DN=76e080a5-0ec6-4448-8bba-67494d2add93

More conics!

Assignments: exercises 37, 38, 39. This was assigned previously, but after today's lesson, we can do more.

Today, Mr Max expanded our knowledge on conics. The central idea of today's lesson is that we can change general form conics into standard form conics.


Conversion between general form conic and standard conics.

Ax^2 + Bxy + Cx^2 + Dx + Ey + F = 0


Remember how to complete the square?

Take: x^2 + 4x + 4

We can take a square and
(x+2)(x+2)
(x+2)^2

or:
How do we find x? Well, take b/2, and square the result. sqroot(3/2)







If we try to enter (X^2 + y^2 + 6x - 8y) = 11 into graphimatica directly, it fails to map the equation because it cannot parse the data. So, we use this form after we complete the square

(X^2 + y^2 + 6x - 8y) = 11
(x^2+6x+9)(y^2-8y+16) = 11 + 9 + 16
(x+3)^2 + (y - 4)^2 = 36

Using the general form:

(x-h)^2+(y-k)^2= r^2
(h,k) = center; r = radius
we enter (x+3)^2+(y-4)^2= 36
and get:








c)4x^2 - y^2 - 8x - 4y - 16 = 0
4x^2-8x -y-4y = 16 + 4 -4
4(x^2-2x+1) -1(y^2+4y+4) = 16 + 4 - 4
(4(x-1)^2 / 16) - ((y+2)^2 / 16) = (16 /16)
(x-1)^2/(2^2) - (y+2)^2/(4^2) = 1
(x-h)^2 / a^2 - (y+2)^2/b^2 = 1








The final is only ~27 days away. I'm going to start studying today! Yes, that sounds crazy, but the exam is difficult, and this class is pretty well perpetration for the exam.