Reflection

hi to all (:

I just want to remind everyone that its our LOGIC TEST tomorrow!!
I'm kinda nervous about the test tomorrow because I have some difficulties understanding some topics.

I don't get these following topics:

=counterexample
=proof of contradiction (esp solving problems using graphs)

And that's everything:)..I hope everyone will do great on the test tomorrow!good luck!!

Logic

Today in class we learn about Conditional Statement.

Conditional Statement = is a statement having a "if" and "then".
= it consist of an Hypothesis "if" and a Conclusion "then".

Example: "If two lines are parallel then they do not intersect".

There are 3 Related Conditionals:

1. Converse = is formed by interchanging the hypothesis and conclusion of the original statement.
Ex. "If two lines do not intersect then the lines are parallel.

2. Inverse = is formed by negating the hypothesis and conclusion of the original statement.
= the word "not" is added to both parts of the sentence.
Ex. "If two lines are not parallel then they do intersect.

*note: In algebra we also use Inverse, remember when we subtract positive we get negative and when we add both negative we get positive, well its the same thing in Logic. It is easy to remember Inverse if we know this.

3. Contrapositive = is formed by negating the hypothesis and the conclusion and interchanging the resulting negative.
Ex. "If two lines do intersect then the lines are not parallel.

In class we also talk about biconditional.

Biconditional = it is a logical operator connecting two statements if and only if, where hypothesis and conclusion. Its like they are both going on the same direction.

-more information-

Logical Relationships Between Conditional Statement

Watch Video on Conditional Statements

Conditional Statements - Converse and Biconditional

and that`s it for today, don`t forget to do the homework Exercise 49 and finishing the homework from the blog.

next scribe is Jeamille.

Welcome back Mr. K!!

hi everyone!

today is a fresh start for each of us! Mr. K just arrived and i know were all excited to see him:))

today we have an assembly which means we had a short class.

our today's class was divided into three points:

1. Reintroduction - which means going over our previous topic, the quadratic function, triginomentry (sin, cosine, tangent and ambiguous triangles), analytic geometry.

2. Blogs, Scribe Post, Digital Ethics - Mr. K mention that we need to blog every single day means that everyone should participate, because its also important that everyone knew what's going one in class and if someone is absent in our class they can go to blog and check what they missed. And its worth 5% of our class mark, so we better do it:D.

3. Where we at! - where on analytic geometry right now and were almost done with this topic and soon were going to write our pre-test and test.

Before the assembly Mr. K give us the homework which we have to blog and tell him if we need extra help with the previous lessons or topic, so he will have an idea where we are at. So we better do it because its our chance to review some stuff.
He also gave us our homework for tonight. We need to solve this equation

(x-2)squared+(y+1)squared=25 (equation of a circle)

2x+y=5 (equation of a line)

Mr. K said we need to find a points of intersection where the circle and the line intersect. the point is (2, -1), the 2x+y=5 we need to change it to a standard form of equation and substitute those points. These are just some clues to solve the given equation.

I think that's about it!..

Don't forget to do the homework and don't forget to arrive on class early tomorrow!!(so no lates)

Cheers:D

next blogger is NOHOM..:)

I'm thinking!

hello Mr. K welcome back!!.And good to see you:))

i need some help with these following topics..

-ambiguous triangles
-imaginary roots
-some trigonometry functions
-quadratic inequality

i think thats it..thank you...

Linear Inequalities / Quadratic Inequalities

hello there!

first off we hand in our homework due today!Ex 27 #11

=The sum of two numbers is 181. Three times the larger plus twice the smaller equals 459. Find the numbers

1. we need to set up the equation
x + y = 181
3x+2y=459
2. eliminate by multiplying x + y = 181
2(x + y)=2(181)
2x+2y=362
3. subtract
3x+2y=459
-2x+2y=362
so you'll get x = 97
4. substitute the x=97 to the equation 2x+2y=362 and find y
2(97)+2y=362
194 + 2y=362
2y=362-194
2y=168
y=84

1. we were given an example

x+y>6
2x+2y<5>

"and" means intersection
=we have to look for x and y plane where both equations are true.

the red broken line represents the 1st equation.
the black broken line represents the 2nd equation.


if we were to check the intersection of the points we need to find a points that satisfy the 2 equation.
(0,0) is the easiest point to check if the line is not touching it!


so if we substitute that in the solution we will get:

0+0>6 that's true
2(0)+2(0)<5>the shaded part represents the intersection of the 2 equation.

*remember that ><>/\<>and included*









"or" means union
=we have to find solution that satisfy 1 of the equation

x-2y<5>3

(again this line will be excluded and will be broken line)

the green line represents the 1st equation.

the blue line represents the 2nd equation.

we need to find each quadrant were one of the points satisfy one equation.
we also need to check each quadrant. we use the points (1,-5) where only one of the equation was satisfied.

we are finished on this topic. Now were moving on to the new one, its all about Quadratic Inequalities.

Speaking of quadratic, what image do you think will be using??the answer is the parabola.

equation will be *y=axsquared+bx+c*

1st step is to graph:
this is a general parabola, we have to take a point inside and outside the parabola so we know which part should be shaded.
















we are given an example:

y>/x(squared)-2x-8

-we have to find the vertex
b/2a=-2/2=-1
x=1

-then substiture
y=1-2-8
y=-9

so the vertex will be (1,-9)

then we need to find the intercepts
x(squared)-2x-8
(x+4)(x-2)
intercepts are (4,-2)


then we need to find a point inside and
outside of the parabola. (0,0) for inside, and (5,0) for the outside.

check:
0>/0-8(inside)
5>/5-8(outside)

next example is x(squared)-2x-8>/0

we use solid circle because the points are included, we use this in set notations.

*the blue line represents the outside points. [-2,-infinity] and [4,infinity].

*the maroon line represents the inside points, points between -2 to 4.

In this case we only have one dimension (x-axis) so you can drop the y-axis. We don't have to worry about it.

Again we always have to check if were right, we have to find a point that satisfy the equation.

(0,0) can't be the right point because if we substitute it we'll get 0-0-8>/0. Its wrong!

(5,0) we'll get 5+10-8>/0. Its right!

(6,0) we'll get 36-12-8>/0. Its right too!

So either one of the two points can be use to satisfy the equation but not (0,0)

____________________________________________________________________

Sorry because I'm not sure how to do the uppercase of 2 so i put squared!
The shaded part represents the intersection.

Oh don't forget we have homework to do! Exercise 28 # 1-3

hope you did learn something on my blog!!..good luck to everyone!!:))

cheers!!!


the next scribe will be Kim C.:D..

September 5, 2008

Hi there... Today, Mr. K. was away, and we didn't expect it because we're all expecting to learn our new topic about Quadratic Function. Basically, we have a substitute and gave us our seat work which became our homework. It's all about Domain and Range. *Interval, and Set Notation*... I also posted the Homework for the week so everyone will see it.


and that's all for today..we're all expecting that everyone will finish their homeworks:D...

Next Scribe: Jeamille