In today's class, we started off with the Pre-Test. When our time was up, we were put into groups. In our groups, we were given 15 minutes to work together in getting the best/right answer. We then worked together on the answers. One of the people from the group was to be the spy for a minute. The spy could go anywhere around the room and ask other groups about the questions they had difficulty on. When the minute was up, he gave up an extra 4 minutes to finish up the Pre-Test and hand in one paper from each group with all the people from the group's names.

The Answer for this was B.

3.5 x 4 x 1/4 = 3.5 cm

In the beginning, I actually thought that this question was easy. That I just had to multiply 3.5 cm by 4.0 cm and then divide it by a half because of the scale factor of 1:2 which I thought meant to just divide by 1/2. It actually means that the area changes by (1/2)^2.

The Answer for this was C.

Formula for the Surface Area of a Sphere: 4pr²

In this question, you should just know the formula for a Sphere which is 4pr². After that, you just plug in the radius. It is C because A is a Volume Formula for the Sphere. It cannot be B or D because B doesn't have the square after the radius and D has a cube instead of a square.

The Answer for this was 190 km.

There was not just one way this could have been done. The way that Mr. Kuropatwa did it was like this.

x = 19 000 000 cm
= 190 km

The way that I did it was what I learned in Science.

In 1 m, there is 100 cm.

In 1 km, there is 1 000 cm.

First, I multiplied 3.8 by 5 000 000 which equaled to 19 000 000 ( cm ).
I then divided 19 000 000 by 100 making me get 190 000 ( m ).
After that, I divided one more time. I divided 190 000 by 1 000 causing it to be 190 km.

Mr. Kuropatwa also thought us:
King Henry Died Mother Didn't Care Much.

Then he drew a staircase from top to bottom: K, H, D, M, D, C, M.

K: kilo

H: hecto

D: deca

M: meter

D: deci

C: centi

M: milli

The Answer for this was 22.62.

For the Last question, I understood it the same way we did it in class. It will be easier to check the blog so I'll be leaving it there. I apologize for not writing it down here. Well this is my scribe and I'm sorry that it's late.

Good Luck with the TEST TOMORROW!

Like Mr. Kuropatwa says, " You can have lucky charms ; they are magically delicious. You can also have a rabbit's foot ; but not a real rabbit's foot because that would be cruel. "

And so I end it here. The Next Scribe will be ANA!

Today's Slides: December 3

Here they are ...

Pre-Cal 20S December 3, 2008

View SlideShare presentation or Upload your own. (tags: geometry pc20sf08)

December 1, 2008

Today was a Workshop Class. Mr. K put a question on the smart board and one person from each group wrote an answer. We were only able to get two questions done and Mr. K went through the second one. Before all that, he showed us a picture. The picture had stairs that were consecutively getting bigger.

Each staircase represents an area of a rectangle and how each staircase above it is 4 times bigger then the one below it.

Question 1

The area of figure F is 30cm². If the dimensions of figure F are multiplied by a scale factor of 4, what is the area of the new figure?

Area = 30cm²

Scale Factor = 4² = 16

New Area = 30cm² x 16 = 480cm²

I am not quite sure what the diagrams and fractions represent but the question was to find the area of the new figure so I think this answer would give you full marks.

Question 2

Prove that if a parallelogram has one right angle, then all its angles are right angles, that is, the angles of a rectangle are all right angles.

Basically write reasons why the parallelogram is actually a rectangle because it has a right angle.

Statement 1:∟ABC = 90°

Reason: Because consecutive angles are supplementary.

Statement 2: ∟BCD = ∟BAD = 90°

Reason: Because opposite angles are congruent.

Statement 3: ∟CDA = 90°

Reason: Because all quadrilaterals equal 360°.

*Mr. K assigned the rest of the questions and Exercise 31 and 32 for homework.

*There won’t be a math class tomorrow.

*The pretest for this unit will be this Wednesday

And yeah. I think that was all we did today. Although this class seemed a bit longer then it usually is, this was all I got out of it. Write a comment if you have any questions or if I had forgotten something. The next scribe post will be from Madstaah. CHEYEAH!

Thursday's Class

Today Mr. K went over Quadrilateral Investigation. As Casey said on her scribe post, the properties on the chart : Opposite side are equal, all sides are equal, opposite angle are right angles, consecutive angels are supplementary, diagonals are congruent, diagonals bisect each other, diagonals bisect opposite angles and diagonals are perpendicular to each other.

I hope you don't mind that I'm using your pictures, Casey |D

A parallelogram:

• opposite sides are equal
• consecutive angles are supplementary
• diagonals are congruent
• diagonals bisect each other

A trapezoid:

• opposite angles are right angles

A rectangle:

• opposite sides are equal
• opposite angles are right angles
• consecutive angles are supplementary
• diagonals are congruent
• diagonals bisect each other

A rhombus

• opposite sides are equal
• consecutive angles are supplementary
• diagonals bisect each other
• diagonals bisect opposite angles
• diagonals are perpendicular to each other

A right trapezoid

• consecutive angles are supplementary
  

A square

• opposite side are equal
  
• all sides are equal
• opposite angle are right angles
• consecutive angels are supplementary
• diagonals are congruent
• diagonals bisect each other
• diagonals bisect opposite angles
  
• diagonals are perpendicular to each other

Note that: A square is a special case of a rectangle, as it has four right angles and equal parallel side. It is also a special case of trapezoid, rhombus and parallelogram.

Transversal line is a line that passes through two or more lines at different points.









Later on in the class, Mr. K put us into groups to work on Problem Solving: Geometry 0 & 1 or The Proof is in the Parallelogram. We have to prove that ABRM is a parallelogram

First you have to look at the same sides:

Angle A = Angle R
Angle B = Angle M

Angle A + Angle B + Angle R + Angle M = 360°. That's because Angle A has 90°, angle B has 90°, angle R has 90° and angle M has 90°

2 Angle A + 2 Angle M = 360°. Why ? Because of Angle A = Angle R & Angle M = Angle B.
It's also similar to 2 Angle A + 2 Angle B = 360°
That is why, ABRM is a parallelogram AB // BR and AM // BR


Hopefully, I told you guys everything. I'm really sorry because I'm really bad at explaining stuff, I really tried my best. I'm really sorry that I posted my scribe late. Please, if you didn't understand anything, PLEASE ASK SOMEONE you know that can help you or Mr. K, himself.


MONDAY'S SCRIBE WILL BE .... MARKKKK !!!

November 27, 2008

Today's class, Mr.Kuropatwa put up 2 questions on the board to start off the class.


A. Find the surface area of a prism.







To find the surface area of a prism you have to find the congruent faces. Opposites that have the same area. Find the area of 2 sides (L*w), adjacent sides (w*h), then the two ends (l*w). Then add the total areas. Therefore the answer for the question should be:

SA = 2(2x3) +2 (5x2) +2 (3+5) = 62units²

B. If we triple all the dimensions, what will the new surface area be...Use the pattern we learned yesterday. Although I forgot what the pattern we learned from yesterday, I should of asked again. Answer for the question is:

9x62 = 558

Later on in the class, Mr.K put us into groups to work on a sheet on Quadrilateral. We had to identify figures of shapes with the proper names, examine each figure and identify properties it has in a chart.

The properties on the chart : Opposite side are equal, all sides are equal, opposite angle are right angles, consecutive angles are supplementary. diagonals are congruent, diagonals bisect each other, diagonals bisect opposite angles, diagonals are perpendicular to each other.

The word supplementary means is 2 angles that add up to 180 degrees.
The word congruent means is having the exact equal size and shape.
The word bisect means cutting into 2 congruent in halves.

Mr.K talked a little bit about Convex and Concave but we will be learning more about Convex. He also talked about the Trapezoid being a special quadrilateral ; 2 sides 1 pair parallel (//) *Remember the symbol for parallel* A Parallelogram ; 2 pairs opposite sides parallel. For a rectangle, all sides are congruent. Why? Because all sides are equal to 90 degrees.

Hopefully I covered most of today's scribe. Please bear with me though I'm not good at explaining everything. I tried my best! If you did not understand anything .. PLEASE ask questions in class; it will help you and everyone. :)

TOMORROW'S SCRIBE WILL BE ! ... i-i-i-i-i-i-i-i-i-i.. icon !

November 25, 2008 / Tuesday's Class

Yesterday we started the class of with finding the surface area and volume of each:

a. Sphere









To find the surface area of each sphere, you need to use the formula: 4pr²
(p= pi)

Sphere 1:
4p(1)² = 4p1
4x1xp = 4p

Sphere 2:
4p(2)² = 4p4
4x4xp = 16p

Sphere 3:
4p(3)² = 4p9
4x9xp = 36p

After doing this, you should notice a pattern or a relationship between the spheres above. The end result multiplied by pi have a perfect square in it. By noticing the pattern, you can jump to a sphere that has a radius of 10 instead of doing the formula one after another, after another and so on.
For example, if your trying to find the volume of a sphere that has a radius of 10, I think you have to square the radius and then multiply it by 4, after doing that you multiply it by pi or leave it with the pi sign beside it as your final answer.
*(This is where I personally feel lost, I am not sure how to explain it, hopefully this will help a little. I believe there is more to it, but this is where I am stuck.)*

Now you have to find the volume of each sphere using the formula: 4/3pr³
(p= pi)

Sphere 1:
4/3p(1)³ = 4/3p1
4x1xp divided by 3 = 4p/3

Sphere 2:
4/3p(2)³ = 4/3p8
4x8xp divided by 3 = 32p/3

Sphere 3:
4/2p(3)³ = 4/3p27
4x27xp divided by 3 = 108p/3


b. Cube












Now to find the surface area of each cube you have to use the formula: 6s²

Cube 1:
6x1² = 6x1 = 6

Cube 2:
6x2² = 6x4 = 24

Cube 3:
6x3² = 6x9 = 54

I think there is another pattern, but I am not sure. I have no idea, so I'm just going to leave it as it is.

Now find the volume of each cube using the formula: lwh
Cube 1:
1x1x1 = 1

Cube 2:
2x2x2 = 8

Cube 3
3x3x3 = 27

Since the length, width and the height are all equal, there isn't much to do but to cube the length, width or height.

So most of the class was talking about these questions above and trying to look for a relationship or pattern between them and then we ended the class with sitting in groups trying to figure out these questions below:

1. The area of a shape is 30 cm². If the dimensions of the shape are increased 4 times, what is the area of the new shape?
40 x 4² = 480 cm²

2. The volume of a solid is 24cm³. If the dimensions are tripled, what is the new volume?
24 x 3³ = 648 cm³

Hopefully this scribe helps whoever did not understand the work we did yesterday, I know I got lost in some parts but I didn't say anything.

Today's scribe post will be posted later on tonight by caseyh.

Friday, November 21st, 2008

Today Mr. K first off talked about the blog, telling us how to write label's properly because if you don't, then you won't get the mark's that you deserved for it. Then he moved on mentioning to us that since we were having difficulty with vocabulary, he now will add onto the blog something that will help us out. This is a site found in the right hand side of the blog with a link called "wordequationswiki" sort of like wikipedia, only this time we could add on word's that we don't understand, ourselves to this site.

Our next unit that we began since we had to move on, is called Geometry. For this unit we need to know volume of a cylinder and sphere formula's. There is also another one that we also need to know about, and it is called the baseball theorem. For example, if you take a baseball and cut all the stitches, and then unfold it, it would have 4 circles. And these 4 cirlcles is what is used to find out the surface of a sphere. This is because if you take the 4 circles multiply it by pie and also multiply the radius by itself 2 times, then you would get the surface of a sphere. Note when multiplying with pie you can't just multiply it with just "3.14". You can't just do that you have to use the whole thing because if you were to use "3.14" that'll only be close to pie unlike if you use the whole thing "3.141592654" your answers will be fully correct.

To get us started with Geometry Mr. K gave us an example:

EX) A sphere fits exactly inside a cylinder. Find the volume of each of the size's of cylinder's with spheres inside them. Is there a relationship or a pattern?

First off you have to find the height of the cylinder. You get the height of the cylinder by the diameter of the sphere. And then once that is settled, for all the 3 size's you plug in the measurement's in the formula. For the volume of cylinder formula this is what it would be like : . For the volume of sphere formula it would look like this :

Let's start off with the smaller size first to get you help started and to show you how to do it for the other sizes .

First find the volume of the cylinder:

VCYL =

=

=
= 50.2654

Then find the volume of the sphere inside :

VSPH =
=
=
= 33.5103

VCYL = = 50.26

VSPH = = 33.51

Now do the same method for the medium and the large sizes, which will give us:

Medium Sized:

VCYL =

VSPH =

Large Sized:

VCYL =

VSPH =

In conclusion, using the medium size one, one and a half spheres fit in each cylinders :

===

Our assignment for today was Excercise 23, Questions: All. A reminder on Monday, November 24th 2008, is our test on Radicals and Exponents, so study hard.

And our next scribe is caseyh.