Gummy Bears - A graduated jellybean

Arithmatic Sequences

2007-01-16T19:01:00.000-06:00

Monday, January 15, 2007.

Sorry everyone, I wasn't able to blog last night because my internet wasn't working. But we had someone come over tonight & fix it so, yay! :)

So far during this unit we've looked at:

Relations ; "Any set of Ordered Pairs." Example: (0,1) (2,3) (2,7) (-3,9) ...
Functions ; " (A type of Relation) Each x value can only have one corresponding y value."
Sequences ; " (A specific type of function) A list of numbers that have a particular pattern."

Today, we looked at Arithmatic Sequences.

Arethmatic Sequences are a list of numbers where the difference between consecutive terms is the same.

Example: 10 , 12 , 14 , 16 , 18 . . .

Since 10 is the first number in the sequence, it is called Term One or T1. 12 is the second number in the sequence, so it is called Term Two or T2.

With this sequence, there is a difference of 2 between each term. All Arithmatic Sequences create a straight line. ie: A Linear Equation. ( y = mx + b )

mx = The difference between consecutive terms

b = T1. ( Term One. )

d = The difference between terms.

tn = The Nth Term.

Here are some more examples that we did together in class...

For the following Arithmatic Sequences, determine the function that represents the list of munbers...

1.) 3 , 6 , 9 , 12 . . .

There is a differnce of 3 between each term, so d = 3

This means that the slope (or mx) is equal to 3/1

f(x) = 3x [ (x) is the term number. ]

f(1) = 3(1)

f(2) = 3(2) . . . (FUNCTION)

2.) 5 , -3 , -11 , -19 . . .

There is a differnce of -8 between each term, so d = -8.

This means that the slope ( or mx ) is equal to -8/1

So, starting at 5... take the difference (-8)

-8 --->5 = 13. (5 - -8 = 13)

f(x) = -8x+13. (IS NOT A DIRECT FUNCTION)

Now, to find the Nth Term...

tn = t1 + (n-1)d

t1 = First Term

n = Unknown Number

d = The Difference

Here are some examples...

1.) 8 , 16 , 24 . . . What is the 11th Term? (t11)

There is a difference of 8, so d = 8

So.. t11 = 8 + (11-1) 8 ... 8 + (10) 8 = 88 t11 = 88

2.) 2.2 , 1.1 , 0 , -1.1 . . . What is the 19th Term? (t19)

There is a difference of 1.1, so d = 1.1

So... t19 = 2.2 + (19-1) 1.1 ... 2.2 + (18) 1.1 = 17.6 t19 = 17.6

Homework was Excercises 58 (1-8) & 59 (1-11)

The next person to blog is Edward. :P

Relation

2007-01-15T22:51:00.000-06:00

To late for posting.lol!Well this is last mondays lesson.Relation(Domain and Range)

"Relation"

A relation is any subset of a Cartesian product. For instance, a subset of , called a "binary relation from to ," is a collection of ordered pairs with first components from and second components from , and, in particular, a subset of is called a "relation on ." For a binary relation , one often writes to mean that is in .

Eg.

(2,0),(1,5),(3,8),(4,1) ...(any set of ordered pairs are "relation")

The concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order, denoted by the sign "<" in a statement like "5 < 12". the concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order, denoted by the sign "<" in a statement like "5 < 12".

Relations are classified according to the number of sets in the cartesian product, in other words the number of terms in the expression:

Unary relation or property: L(u)

Binary relation: L(u, v) or u L v

Ternary relation: L(u, v, w)

Quaternary relation: L(u, v, w, x)

Domain and Range

Domain:

For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.

Range:

The range of f is the set of all values that the function takes when x takes values in the domain.
The y-values.

This list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. You list the values without duplication:
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} This are the set of numbers.

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

You can see how we put the numbers in domain and range. All the x were put to domain and all y were put in range..

Well i hope this things will help you:)Good luck

Graphing Data & Direct Variation

2007-01-14T18:54:00.000-06:00

On Friday's math class, we went through three things, graphing data, direct variation and Go For Gold.

Graphing Data

Ms. Armstrong took the guesswork out of deciding which information from a table of values is the dependent variable, and which is the independent variable. Even though we know that the dependent variable "relies" on the independent variable (eg. time and speed ; in this case, time would be the independent variable since the speed depends on the time that has elapsed), we learned that the first column of a table of values is always the independent variable.

Direct Variation
Definition:
A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first.

When two variable quantities have the the same ratio, they have what is called direct variation.

(This is the diagram/example we were given.)

So, in the diagram, ' p= 8h ', making it a linear function, since it's the same as ' y = mx+b ' but in
' p = 8h ' b = 0 This means that whenever b = 0, you have direct variation.
We were given other examples, too.

p = 6t + 2 <-- NOT direct variation y = 3x <-- direct variation y = -2x + 0 <-- direct variation To connect the previous lesson with this one, it is possible to write, what is called, a direct variation function. How? y = kx *In this equation, 'k' stands for 'constant' We were asked to write an equation for the following statement: The cost of selling items at $0.25 varies directly with the number of items sold.
c -> cost n -> number of items sold
c varies directly with n (this means that the cost is always determined by how many items are sold)
So, the equation would be: c = 0.25n

Exercise 46 #1-9
Exercise 57 #1-14, 17

* * * For extra help, visit this link: http://www.freemathhelp.com/direct-variation.html * * *

Go For Gold

The last part of the class was taken up by receiving our Go For Gold booklets. It consists of 25 pages, and has multiple choice, short answer and long answer questions. Basically, we were told:
- it's worth 10% of our mark, and it's either 0% or 100%.
- even though you can ask for help, Ms. Armstrong will check your booklet ONCE, and only once. - you can ask others for help, compare and work together in a study group.
- you must show your work for EVERY question.

- last, but definitely not least, DUE DATE: Monday, January 22nd

The next blogger is Christine.

More On Functions

2007-01-14T10:18:00.000-06:00

Today we did more on functions

What Is a Function you ask?

A function is a special type of relation where each x-value in the domain corresponds to ONLY 1 y-value in the range.

example: Graph f(x)= x-1 means the same as y=x-1

D:{xER}
R:{xER}

y-intercept --> f(0)=x-1
=0-1
=-1

the zeros of the function are the x-intercept(let y=0)
f(x)=x-1
0=x-1
1=x

to find zero let F(x)= 0

Graph, find D and R and the zeros for f(x)=3/2x-3

D:{xER}
R:{xER}

zeros: f(x)=3/2x-3
0=3/2x-3
2(3)=(3/2)2x
6=3x
2=x

f(x)=1/2x-3
0=1/2x-3
2(3)=(1/2)2x
6=x

linear functions f(x)=mx+b
constant functions f(x)=b <-- has no x value

will always be a straight line.
f(x)=-4

HOMEWORK: ex. 54 # 1-9, 12
55 # 1-7

Functions and Function Notation

2007-01-11T19:27:00.000-06:00

Ok...this is what happened on Wednesday. Functino and Function Notation.

What is a Function?

A Function is a special type of relation where each x-value in the domain corisponds to only 1 y-value in the range.

EG.

2 ==>8
0 ==>4
==>6
6 ==>3

Ordered Pairs: (2,8),(0,4),(0,6),(6,3)

As you can see in the ordered pairs the x-value of 0 has two different y-values. THIS IS AN EXAMPLE OF A RELATION, NOT A FUCTION.

That was an example of using the ordered pairs. What if we were given a graph? Why use the Vertical Line Test!

What is the vertical line test? Well its the test used on graphs to see if it is a function or a relation. If the line passes through two points or more on the graph then it is a relation. If it passes through only one point then it is a Function.

Here are a few Examples from class.

You know that this is a function right? The vertical line test shows it is. Anywhere on the graph if you drew a vertical line there it would only go through one point.

On to the next graph.

This is also a function. No line going through two points

This is a relation. Not a function. As you can see there is a vertical line in the graph. If you put a vertical line through that it over laps. Which means that its going through more then one point. If you drew it anywhere else it would not hit more then two points, but because of that vertical line the graph made it is considered a relation.

This one is in the same boat as the last one. It is a relation becaues there are three points in a line. If you drew a vertical line there it would hit all three. Therefore it is a relation.

Okay I know that this is gettign repetitive right about now, but now moving on to the other topic that was covered on wednesday.

Function Notation

Functions are usually represented with the letters "F" or "G"

Eg. f (x) = x + 2

This reads "The value of the function at this value of x is x +2"

Lets try doing a question from class , the one above. Well i think there is suppose to be a stament about what you switch f (x) with...but it seems i dont have it, I am very sorry for this. I do have the work though

f (x) = x + 2
f (3) = 3 + 2 ====> What ever you switch the x with on the right side you switch all the x's on the left side with the same thing and just evaluate left side. I am really sorry for how i said that and i know it should be something else mathematical, but i really dont know any other way to day it. ANYWAYS...continuing on.
f (3) = 5

Okay that was the easy one. Now we go into Compound Functions.

Let f (x) = x² / x + 1 and g (x) = 4 / x²

1.f (g⁽²⁾)

This may seem confusing at first but it really isnt that hard. You work your way inside out. You start with the g (2) function and find that. the you use that in the f function. Heres the work.

Oh we are replacing the x value with 2

g (x) = 4 / x²
g (2) = 4 / 2²
g (2) = 4 / 4
g (2) = 1

After you get that done just your answer you got from the g function and use it in the in function.

so instead of this.

f (g⁽²⁾)

It will be this.

f (1)

To finish the problem your going finish with the f function

f (x) = x² / x + 1
f (1) = 1² / 1 + 1
f (1) = 1 / 2
f (g⁽²⁾) = 1 / 2

And thats Wednesday's class. I picked don already to scribe and it should be up today too so i dont need to pick one again.

Function Jeopardy...sounds like FUN to me (hahaha)

2007-01-11T12:08:00.000-06:00

Hey Gummy Bears,
I thought you might enjoy this Jeopardy Game that quizzes you on relations, functions, and direct variation. Make sure you use function notation when typing in your answer or it will mark you incorrect. For example...If it asks what is the function, you can't type in 2x+3 . You must type f(x)=2x+3.

What comes after trillion ?

2007-01-10T00:12:00.000-06:00

It's quite facinating actually, there are a lot of numbers that come after "trillion". I searched it up on google and luckily I found a site where it gives a whole bunch of numbers that come after trillion. Here see for yourself:

thousand 1,000
1. million
1,000,000
2. billion
1,000,000,000
3. trillion
1,000,000,000,000
4. quadrillion
1,000,000,000,000,000
5. quintillion
1,000,000,000,000,000,000
6. sextillion
1,000,000,000,000,000,000,000
7. septillion
1,000,000,000,000,000,000,000,000
8. octillion
1,000,000,000,000,000,000,000,000,000
9. nonillion
1,000,000,000,000,000,000,000,000,000,000
10. decillion
1,000,000,000,000,000,000,000,000,000,000,000
11. undecillion
1,000,000,000,000,000,000,000,000,000,000,000,000
12. duodecillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000
13. tredecillion
write 1,000 followed by 13 groups of three zeros
14. quattuordecillion
1,000 followed by 14 groups of three zeros
15. quindecillion
1,000 followed by 15 groups of three zeros
16. sexdecillion
1,000 followed by 16 groups of three zeros
17. septendecillion
1,000 followed by 17 groups of three zeros
18. octodecillion
1,000 followed by 18 groups of three zeros
19. novemdecillion
1,000 followed by 19 groups of three zeros
20. vigintillion
1,000 followed by 20 groups of three zeros
21. unvigintillion
1,000 followed by 21 groups of three zeros
22. duovigintillion
1,000 followed by 22 groups of three zeros
23. trevigintillion
1,000 followed by 23 groups of three zeros
24. quattuorvigintillion
1,000 followed by 24 groups of three zeros
25. quinvigintillion
1,000 followed by 25 groups of three zeros
26. sexvigintillion
1,000 followed by 26 groups of three zeros.
27. septenvigintillion
1,000 followed by 27 groups of three zeros
28. octovigintillion
1,000 followed by 28 groups of three zeros
29. novemvigintillion
1,000 followed by 29 groups of three zeros
30. trigintillion
1,000 followed by 30 groups of three zeros
31. untrigintillion
1,000 followed by 31 groups of three zeros
32. duotrigintillion
1,000 followed by 32 groups of three zeros
33. tretrigintillion
1,000 followed by 33 groups of three zeros
34. quattuortrigintillion
1,000 followed by 34 groups of three zeros
35. quintrigintillion
1,000 followed by 35 groups of three zeros
36. sextrigintillion
1,000 followed by 36 groups of three zeros
37. septentrigintillion
1,000 followed by 37 groups of three zeros
38. octotrigintillion
1,000 followed by 38 groups of three zeros
39. novemtrigintillion
1,000 followed by 39 groups of three zeros
40. quadragintillion
1,000 followed by 40 groups of three zeros
41. unquadragintillion
1,000 followed by 41 groups of three zeros
42. duoquadragintillion
1,000 followed by 42 groups of three zeros
43. trequadragintillion
1,000 followed by 43 groups of three zeros
44. quattuorquadragintillion
1,000 followed by 44 groups of three zeros
45. quinquadragintillion
1,000 followed by 45 groups of three zeros.
46. sexquadragintillion
1,000 followed by 46 groups of three zeros
47. septenquadragintillion
1,000 followed by 47 groups of three zeros
48.octoquadragintillion
1,000 followed by 48 groups of three zeros
49. novemquadragintillion
1,000 followed by 49 groups of three zeros
50. quinquagintillion
1,000 followed by 50 groups of three zeros
51. unquinquagintillion
1,000 followed by 51 groups of three zeros
52. duoquinquagintillion
1,000 followed by 52 groups of three zeros
53. trequinquagintillion
1,000 followed by 53 groups of three zeros
54. quattuorquinquagintillion
1,000 followed by 54 groups of three zeros
55. quinquinquagintillion
1,000 followed by 55 groups of three zeros
56. sexquinquagintillion
1,000 followed by 56 groups of three zeros
57. septenquinquagintillion
1,000 followed by 57 groups of three zeros
58. octoquinquagintillion
1,000 followed by 58 groups of three zeros
59. novemquinquagintillion
1,000 followed by 59 groups of three zeros
60. sexagintillion
1,000 followed by 60 groups of three zeros
61. unsexagintillion
1,000 followed by 61 groups of three zeros
62. duosexagintillion
1,000 followed by 62 groups of three zeros
63. tresexagintillion
1,000 followed by 63 groups of three zeros
64. quattuorsexagintillion
1,000 followed by 64 groups of three zeros
65. quinsexagintillion
1,000 followed by 65 groups of three zeros
66. sexsexagintillion
1,000 followed by 66 groups of three zeros
67. septensexagintillion
1,000 followed by 67 groups of three zeros
68. octosexagintillion
1,000 followed by 68 groups of three zeros
69. novemsexagintillion
1,000 followed by 69 groups of three zeros
70. septuagintillion
1,000 followed by 70 groups of three zeros
71. unseptuagintillion
1,000 followed by 71 groups of three zeros
72. duoseptuagintillion
1,000 followed by 72 groups of three zeros
73. treseptuagintillion
1,000 followed by 73 groups of three zeros
74. quattuorseptuagintillion
1,000 followed by 74 groups of three zeros
75. quinseptuagintillion
1,000 followed by 75 groups of three zeros
76. sexseptuagintillion
1,000 followed by 76 groups of three zeros
77. septenseptuagintillion
1,000 followed by 77 groups of three zeros
78. octoseptuagintillion
1,000 followed by 78 groups of three zeros
79. novemseptuagintillion
1,000 followed by 79 groups of three zeros
80. octogintillion
1,000 followed by 80 groups of three zeros
81. unoctogintillion
1,000 followed by 81 groups of three zeros
82. duooctogintillion
1,000 followed by 82 groups of three zeros
83. treoctogintillion
1,000 followed by 83 groups of three zeros
84. quattuoroctogintillion
1,000 followed by 84 groups of three zeros
85. quinoctogintillion
1,000 followed by 85 groups of three zeros
86. sexoctogintillion
1,000 followed by 86 groups of three zeros
87. septoctogintillion
1,000 followed by 87 groups of three zeros
88. octooctogintillion
1,000 followed by 88 groups of three zeros
89. novemoctogintillion
1,000 followed by 89 groups of three zeros
90. nonagintillion
1,000 followed by 90 groups of three zeros
91. unnonagintillion
1,000 followed by 91 groups of three zeros
92. duononagintillion
1,000 followed by 92 groups of three zeros
93. trenonagintillion
1,000 followed by 93 groups of three zeros
94. quattuornonagintillion
1,000 followed by 94 groups of three zeros
95. quinnonagintillion
1,000 followed by 95 groups of three zeros
96. sexnonagintillion
1,000 followed by 96 groups of three zeros
97. septennonagintillion
1,000 followed by 97 groups of three zeros
98. octononagintillion
1,000 followed by 98 groups of three zeros
99. novemnonagintillion
1,000 followed by 99 groups of three zeros
100. centillion
1,000 followed by 100 groups of three zeros

One GOOGOL is a ONE followed by 100 zeroes.
One GOOGOLPLEX is a ONE followed by one googol zeroes
(you can't write a googolplex, even in a million years)

this information was taken off of this site: http://utterlyboring.com/archives/2003/09/10/what_comes_after_trillion.php I'm not quite sure if this is very accurate but it's pretty neat huh?

So the question now is, what comes after googoplex? Infinity?

Solving algebraic rational equations

2006-12-18T22:35:00.000-06:00

Solving Algebraic rational equations

Step 1 - Factor all denominators

Step 2 - State the restriction(s)

Step 3- Multiply both sides of the equations ( every term) by the LCD.

Here's a websites that might help you . Rational equations

Adding / Subtracting

2006-12-12T21:04:00.000-06:00

Adding / Subtracting

a few practice Questions
We started the notes we an example - Probably to see what we knew about the topic.

To simplify algebraic Fractions:
1)Factor/ Find the LCD (lower common denominator)
*multiply the denominators together to find a common denominator
2)Change both fractions to have the same denominator
3)Find the restrictions
4)Add/subtract
5)Simplify
6)Re-check Restrictions

eg)

eg)

Ex 44 is homework

omit 20

Cont'd Reducing Algebraic Fractions & Non Permissible Values

2006-12-12T17:59:00.000-06:00

The connection between numbers (fractions) and reducing expressions

-Factor it
-Cancel factors found in the numerator and the denominator
-Multiply / Simplify

Reduce the following fraction

Reduce the following expression

*When we Reduce and simplify algebraic fractions follow the following 5 steps:

1) Factor the numerator and the denominator
2) State the restrictions.
*What would make the denominator have a value of zero?
3) Reduce by any common terms
4) Factor out -1 if necessary
* (a - b) = -1(b - a)
5) Simplify

Eg)

Eg)

Sorry for being SO late in blogging, Its just that I wasnt feeling very good all weekend. To make up for me being late I will do December 12/06 also

Reducing algebraic fractions

Sorry Couldn't find a link forNon Permissible Values

Do exercises:

42 omit 12

43 omit 11

Reducing Algebraic Fractions

2006-12-07T20:36:00.000-06:00

Today in class we had time to finish up our tests from yesterday. After that we began a new unit called...

Rational Expressions and Equations

OK, so a rational expression can be expressed in the form of..

Where A, and B are polynomials and B does NOT equal zero. (if it did then it would be undefined)

Therefore, we have to state restrictions on x or any value that would not be permitted. (Anything that would make the denominator have a value of zero).

We ran out of time before we could finish the notes so this will continue on tomorrow.
Oh and no homework today but we have to do TWO exercises tomorrow.

The next blogger is Cory

Rational Algebraic Expressions

2006-12-07T12:27:00.000-06:00

Here is an interactive site that explains, shows examples, and provides practise with algebraic expressions.

Give it a go!!
Ms. Armstrong

The Problem with Parallelograms

2006-12-04T21:08:00.000-06:00

Hey Gummy Bears,
Here is a parallelogram problem for you to work on together. You can post comments, solutions, questions, ideas all in the interest of progressing the solution to the problem. Don't forget to use mathematical vocabulary so that everyone will know exactly what you are referring to. (No saying things like the number beside the thingy with the little side. ;^)

If a parallelogram is a non-rigid figure, find the minimum and maximum values for each of the diagonals if the lengths of the sides are 5 and 12.

For anyone wanting extra study tools, don't forget to try the multiple choice quizzes that I posted earlier this month.

2006-12-04T17:02:00.000-06:00

Friday, December 01, 2006

In class, we did an exercise were we had to decide whether point A(5,2), point B(1,9), point C(-3,2) and point D(1,-5) is a rectangle, rhombus, a square or a parallelogram.

First, we figure out the distance of AB, AD, DC, and BC by using the distance formula.

By doing the same thing, we found out that the distance of AD, DC, and BC are all

which means that the diagram can not be a parallelogram or a rectangle because all 4 sides are equal length. A parallelogram and a rectangle only have equal opposite sides.

Secondly, we can also find the slope of the line to figure out if the diagonals are perpendicular to each other by using the slope formula.

By doing that we figured out that the diagonals are not perpendicular to each other, therefore it can not be a square or a rectangle.
Which leaves us with a RHOMBUS.

And don't forget about our homework, Exercises 28 and 31.

And by the way, sorry for posting last fridays lesson late.

Monday, December 04, 2006

For todays class, it started by Ms. Armstrong reminding us about couple of things. Then we started our lesson by doing a little activity to prepare us for our Trigonometry/ Geometry Test which is on Wednesday.
Todays activity was a green worksheet, were we had to choose whether the following statements were True or False.
1.) The consecutive angles of a parallelogram are congruent.
2.) Opposite angles of a parallelogram are congruent
3.) A rhombus has 4 congruent sides.
4.) A rectangle has congruent diagonals.
5.) If a quadrilateral is a rectangle, then it is a parallelogram.
6.) If a quadrilateral is a square, then it is a rhombus.
7.) If a parallelogram is a rectangle, then it is a rhombus.
8.) If a quadrilateral is a parralelogram, hten it is a rhombus.
Then at the bottom of the paper was a word problem that Ms. Armstrong will post seperately and everybody will have to work together through the blog to figure out the answer.

We also had some notes on HIERACHY QUADRILATERAL.

The diagram above shows that a square can be a rhombus or a rectangle. And a rhombus or a rectangle are both parallelogram. It also shows that a parallelogram is a trapezoid and a trapezoid is a quadrilateral. The kite on the other hand is a different type of a quadrilateral.
***But dont forget that it has to start on the square going up, it can not start from the quadrilateral.

And todays homework is Exercise 29 and 32.

Also, dont forget to study for our Trigonometry/ Geometry Test which is on Wednesday.

Words to define...

2006-11-29T17:57:00.000-06:00

Hiya!!! We didn't do much today in class. We just had a quiz on trigonometry (including sine and cosine laws) and went to the computer lab to find the definitions of the following words:

- complementary angles
- supplementary angles
- consecutive
- polygon
- quadrilateral
- congruent
- diagonal
- bisect

I guess we're doing this to have a heads-up on the geometry section of this unit.

For HOMEWORK ... fill up your Three Point Approach for Words and Concept sheets if you didn't get to finish it in class today.

If you're having any trouble with the definitions, you can go to this >>website<<. (I know the site says "for kids" but I think the activities are pretty cool and helpful.)

Next blogger is Christine !!!

Relationships in Similar Figures

2006-11-28T16:22:00.000-06:00

Today in class, we started working on SIMILAR FIGURES. We also worked on SURFACE AREA and VOLUME.

*REMINDER: The quiz is moved to tomorrow!*

Class was started off today with Ms. Armstrong drawing a little man on the board...

In the second picture, the length and the width has been doubled. Does that mean that we have doubled the size of the whole picture? Not quite, because we have doubled BOTH the length and the width, the size is actually quadrupled.

Next, instead of doing the rest of the notes, we did a worksheet on area and volume...

We had to find the surface area and volume of 2 cubes. I have tried to upload them, but it is not working, so the first cube was Length=2, width=2, depth=2. The second cube was length=6, width=6 and depth=6.

1) Surface area: 6(LW)

=24cm²

Volume: 2x2x2

=8cm³

2)Surface Area: 6(LW)

=216cm²

Volume: 6x6x6

=216cm³

The next part of the sheet was:

How many times bigger are the sides in the bigger cube? 3

*NOTE: when it says side, it means length of a side, not the whole side.*

How many times bigger is the surface area of the bigger cube compared to the smaller one?

9 times or 3²

How many times bigger is the volume of the bigger cube compared to the smaller one?

27 times or 3³

HINT: notice that when change change the answer into an exponent, the exponent for surface area is 2, and the exponent for volume is 3.

That's what we did for this sheet. The other side we have for homework.

Okay, now to continue on with some more notes:

To find the "new area or volume"

area= (scale factor)²x(old area)

volume=(scale factor)³x(old volume)

ex. The area of a region is 10cm²

by what factor must each dimension be multiplied to increase the area by 20cm²?

New area is 20+10=30cm²

30cm²=k²(10)

30 k²(10)

__= ____

10 10

3=k² square root of 3=k

wow... okay, thats it for what we did in class today. Sorry about the pictures, it wasn't working very well. I hope this helped anyway though.

HOMEWORK!

finish the other side of the worksheet

exercise #24

STUDY! There's a quiz TOMORROW!

Trigonometry Multiple Choice Review

2006-11-27T20:54:00.000-06:00

Hey there Gummy Bears...

Here are some multiple choice quizzes to help you review.
Law of Sines
Law of Cosines
Right angle Triangles
A Challenge

I also came across an interesting question to challenge your brains and stimulate your competitive nature. I would like you to 'discuss' the solution to this question through the comment box. If each person adds their ideas, I would bet that you can get it.

Solve the equation for A and B.

Good luck, have fun, and happy solving :)

Sine & Cosine Laws

2006-11-21T16:18:00.000-06:00

Tuesday, November 21, 2006;

Today in class, we were taught the Sine & Cosine Laws. We first started out with an activity. Mrs. Armstrong had us create a triangle that had one Obtuse Angle (more than 90 degrees). She then told us to measure each side of the triangle to the exact millimeter, & then find each angle of the triangle. Once we were done, she showed us the Sine Law.

Sin A = Sin B = Sin C
_____ _____ _____

a b c

*You can use the Sine Law whe you are given;

1) SSA ( Side , Side , Angle )
(notice the angle is not inbetween the two sides)

Example:

It cannot look like this:

2) AAS ( Angle , Angle , Side )
* Must have one complete ratio.

Example:

Here's an example of how to use the formula:

Solve for x and b:

First you can find angle B:

Angle B = 180 - ( 37+54 )

= 180 - 91

= 89 degrees / Angle B = 89 degrees

Now you can plug in the numbers that you have so far :

Sin 37 = Sin 89 = Sin 54

______ ______ ______

41 b x

Then you can find out what side b is equal to:

Sin 37 = Sin 89

_______ _______ } Cross - multiply

41 b

Sin 89 x 41

____________ = b So, side b is equal to 68.

Sin 37

So, now you should have : Sin 37 = Sin 89 = Sin 54

_______ _______ _______

41 68 x

Now you can find out what side x is equal to:

Sin 37 = Sin 54

_____ ______ } Cross - multiply

41 x

Sin 54 x 41

___________ = x So, side x is equal to 55.

Sin 37

The Cosine Law:

* You need at least two sides for the cosine law to apply to a problem.

a² = b² + c² - 2bcCosA

OR: [ b² = a² + c² - 2acCosB ]

OR: [ c² = a² + b² - 2abCosC ]

Here's an example of how to use the fromula:

Solve the triangle WTV.

w² = v² + t² - 2vtCosW

w² = 7.8² + 9² - 2 ( 7.8 x 9 ) Cos112

w² = 60.84 + 81 - ( - 52.59 )

w² = 194.43

The square root of 194.43 is 13.94

w = 13.94

--Now you can the same thing that you did when you were using the Sine Law:

Sin 112 = Sin T

_____ _____ } Cross - mulitply

13.94 9

Sin 112 x 9

_________ = T

13.94

Then do Inverse Sine to get the angle ( Depending on what type of calculator you have, the way of doing this may vary... On my calculator, I press the 2nd function button, then Sin ^-1, then the number I got from the last equation. ) .

T = 36.7 degrees.

To get angle V, all you do is: 180 - (112 + 36.7) = 31.3 V = 31.3 degrees

Our homework was Excersize # 19 & # 25

If you are still having trouble with the Sine & Cosine Laws, here is a website that should help you to better understand it. =)

Just a few reminders:

- There will be a quiz on Monday on what we've covered on Trigonometry .

& if anyone would like to contribute to sending flowers to Chris showing us our support, bring $2.00 to Mrs.Armstrong. She will then go & buy the flowers.

Well, I did my best. Lol. I hope this blog was helpful. The next person to blog is.. Meagan. =)

( I apologise if my images don't show up on the blog. I seem to be having some trouble uploading them. =( )

Determining Angles

2006-11-20T21:25:00.000-06:00

Today's class was pretty easy and hard at the same time. Easy because we only had one lesson to think about. Hard because the lesson that we learned was a little too difficult for me (I don't know about you guys). But I'll try my best to make this post as understandable as possible. Okay, here it goes.

Ms. Armstrong gave us a yellow sheet of paper with 2 questions on it. The first question didn't make sense at all so even Ms. Armstrong had some confusion. So we'll omit that so we can focus on the more important stuff.

The second question was to determine the angles that would produce the following ratios:
a) sin(x) = .707 acute angle = ___ obtuse angle = ___
b) cos(x) = .940 acute angle = ___ obtuse angle = ___
c) tan(x) = 11.43 acute angle = ___ obtuse angle = ___
d) cos(x) = -.970 acute angle = ___ obtuse angle = ___
e) sin(x) = -.5 acute angle = ___ obtuse angle = ___
f) tan(x) = -1.43 acute angle = ___ obtuse angle = ___

Note: It's not as easy at it looks. Here's how you solve each of the above questions but first, keep in mind to round all of your degrees to a whole number.

1) To find the acute angle, punch in the equation in your calculator:
2nd function > SIN/COS/TAN button = SIN/COS/TAN^-1 (given ratio).

Let's use letter a) for an example.
So, 2nd funct. > SIN button = SIN^-1 (.707) : the answer is 45^o.
The degree that comes out of this equation is your acute angle.

2) Now let's find the obtuse angle. To find the obtuse angle, you will need to know which quadrant does the given ratio belongs to.

The positive sine ratio belongs to the the first & second quadrants.

The positive cosine ratio belongs to the first and fourth quadrants

And the positive tangent ratio belongs to the first and third quadrant.

Since the positive sine ratio lands on the 2nd quadrant, you have to subtract your acute angle from 180 degrees since the acute angle is the measurement of how far is your hypoteneuse from the 2nd quadrant's degree (which is 180 degrees).

When finding the positive cosine ratio, subtract the acute angle from 360 degrees since it lands on the 4th quadrant.

Lastly, if you're finding the positive tangent ratio, subtract the acute angle from 270 degrees or add the acute angle to 180 degrees.

And now you're done your positive ratios! Here's how I solved the first three questions:

a) sin(x) = .707 which is 45^o.

Now, follow the rules above: 180 - 45 = 135^o

acute angle = 45^o

obtuse angle = 135^o

b) cos(x) = .940 which is 20^o

360 - 20 = 340^o

acute angle = 20^o

obtuse angle = 34^o

c) tan(x) = 11.43 which is 85^o

acute angle = 85^o

obtuse angle = 265^o

_______________________

Now the negatives (questions 4 - 6). The negative ratios are a little bit different.

1) To find the acute angle of a negative ratio, do the same thing as how you would find the acute angle of a positive ratio, here's a refresher:

punch in the equation in your calculator:

2nd function > SIN/COS/TAN button = SIN/COS/TAN ^-1 (given ratio).

Let's use letter d) for an example.

So, 2nd funct. > SIN button = COS^-1 (-.970)

When I used my scientific calculator, what I got was -166 degrees. But that's the not the final answer. Remember, the acute angle should be positive. So the answer will be 166 degrees (yes, just randomly take out the negative sign because I don't think that there is a mathematical format for how to change a negative degree to a positive degree).

2) Then let's find the obtuse angle. Do the same thing as you did to the positive ratios.
d) cos(x) = -.970 which is 166 degrees
acute angle = 166 degrees
obtuse angle = 194 degrees

e) sin(x) = -.5 which is 30 degrees
acute angle = 30 degrees
obtuse angle = 330 degrees

f) tan(x) = -1.43 which is 55 degrees
acute angle = 55 degrees
obtuse angle = 235 degrees

And that's it! Sorry for the delay guys, there was too much in my head, although it's done now (: we also got our unit tests back then we went over some of the questions. Congratulations to the all stars! And oh yeah, I pick Desitini to blog next since the people I know didn't want to since they're "busy", haha. Oh yeah, and reminder to redo question #2 on exercise 18 using the above steps.

Ms. Armstrong, a video for this one is kind of hard to find. If anyone can help me , that'll be great :)

Cartesian Plane

2006-11-20T00:35:00.001-06:00

On Friday, Ms. Armstrong has us do a little activity to help us understand how the trig functions relate to the y and x axis'. Whether it has a positive or negative value.

Here are some examples, that might help you understand:

SOH CAH TOA

(sinØ= opp/adj)

The sine function means that you need to divide the opposite by the adjacent. But instead of using the terms opposite and adjacent, what if there wasnt a degree for us to determine which side would be the opposite? We could use the Cartesian plane.

This is how you would write it:
sinØ =

the "r" in the denominator means radius
and the "y" means the distance in the y axis

In the example below, shows the two quadrants that contain positive sine values:

SINE RATIO

What factor contributes to the ratio being positive in those 2 quadrants? (What do those 2 quadrants have in common?)

the Y AXIS: as you can see in the diagram above, the two shaded quadrants are the two quadrants where the y value is positive.

_______________________________________

SOH CAH TOA

(cosØ= adj/hyp)

The cosine functions means you need to divide the adjacent by the hypotenuse. How would that be done on a Cartesian plane?

cosØ=

the "r" in the denominator means radius
and the "x" means the distance in the x axis

In the example below, shows the two quadrants that contain positive cosine values:

COSINE RATIO

What factor contributes to the ratio being positive in those 2 quadrants? (What do those 2 quadrants have in common?)

the X AXIS: as you can see in the diagram above, the two shaded quadrants are the two quadrants where the x value is positive.

_______________________________________

SOH CAH TOA

(tanØ= opp/adj)

The tangent function means you need to divide the opposite by the adjacent. How would that be done on a Cartesian plane?

tanØ=

which can also be shown like this:

tanØ=

the "x" in the denominator stands for the cosine which is related to the x axis

the "y" in the numerator stands for the sine which is related to the y axis

In the example below, shows the two quadrants that contain positive tangent values:

TANGENT RATIO

What factor contributes to the ratio being positive in those 2 quadrants? (What do those 2 quadrants have in common?)

This is a tricky one. Both values have the same sign. If you look at the diagram above you'll see that they're either in both positive, or both negative, so either the the answer will end up being a positive because a postive divided by a positive is positive. And a negative divided by a negative is negative.

HEY! this guy is so old and he's doing the same math as we are, it makes me feel like a genius! HAHA. Here click here to watch this video

Here's another video, it's pretty long and boring but it kind of helped me because it reviews the simple formula's of algebra enjoy ! (it even the pythagorean theorem, the way Ms. Armstrong showed it)

Well that's my short review on Cartesian Plane. Hmm.. who to pick next ?

I think I pick JEFF. Yeah, you are the winkest link. hehe :)

.. For some of the stuff above i used Ms. Armstrong's worksheet questions and materials. And yahoo was my source to find those videos

Trigonometry Functions for Obtuse Triangles

2006-11-16T15:56:00.000-06:00

In today's class we fooled around with 30* triangles using SIN ratio. We drew three 30* triangles (1 small, 1 medium, and 1 big) See pictures below...

Small triangle

Note:
Mrs. Armstrong told us that when using a² + b ² = c² we should use Leg² + Leg² = Hyp² instead, unless it is labeled that way

Medium triangle

Since these are 30* triangles (using Sin) it will have a pattern in the measurements; in other words the hyp will be twice as big as the opp

Large triangle

The adj is effect by the opp of the triangle as you can see through these examples

Relations

Sin : Related to the Y axis

Cos : Related to the X axis

Tan : related to the Y axis divided by the X axis

Here is a chart that will show the relation of the trig ratios

Homework: exercise 18 and the next one to blog is..... Edward

Trigonometry with two right triangles

2006-11-16T12:38:00.000-06:00

In yesterday's class we learned how to find a side of two right triangles using trigononetry.

Review:SOH CAH TOA
S - sine
O - opposite
H - hypotenuese

C - cosine
A - adjacent
H - hypotenuese

T - tangent
O - opposite
A - adjacent

Example:
Find CD ( Hint: Fist find W )

tan 60 =W/2
(2)tan 60=W
W=3.5 cm

tan 60 =X/3.5
(3.5)tan 60=X
X=6.1 cm

Therefore CD=6.1 cm

Angle of Elevation

The angle between the line of sight and the horizontal.

Angle of depression

Homework:Exercise 17

Still need help? here's a site for you.

The next blogger is Shelly

Creating Triangles

2006-11-14T18:04:00.000-06:00

Today's class: The first 20 minutes were spent finishing our test from yesterday, "Rational Exponents & Radicals". As a reminder, our units were also due (10% deduction for everyday that it is late). Afterwards we started our new unit, which is going to be a mixture of Trigonometry and Geometry, beginning with Trigonometry.

Trigonometry is basically the computational component of geometry (to get technical), but to keep it within simpiler terms, it has to do a great deal wtih triangles and to start off our unit that is exactly what we created. In our groups, we were asked to make 3 right triangles with angles of 17degrees, 39 degrees and 54 degrees.

How do we create triangles?
let us use the example of creating a right triangle with a 17 degree angle.
STEP 1: On your piece of paper, use a ruler to make a straight horizontal line. (view image for further detail)

(To view image, hold shift and click on box)
STEP 2: Using a protractor, place the 90 degree point on one of the ends of your horizontal line.
Make a mark at the top and draw a straight vertical line going down from your mark to
the end point of your horizontal line. (view image for further detail)

(To view image, hold shift and click on box)
STEP 3: Place the protractor at the 90 degree point on the other end of the horizontal line. Make a
mark at the degree indicated in the instructions (in this case 17 degrees). Then draw a
line from the mark you've made to the end of the horizontal line. (view image for further
detail)

(To view image, hold shift and click on box)
STEP 4: Label the vertex with its degree (which happens to be 17 degrees in this case). (view
image for further details).

(To view image, hold shift and click on box)

After we were done making our triangles, we labelled the sides with hypotenuse, adjacent and opposite.

REVIEW: Hypotenuse - this is always the longest side, opposite of the right angle.
Adjacent - the side next to the angle you are refering to.
Opposite - the side opposite of the angle you are refering to .
* (depending on which angle you are refering to, the adjacent and opposite may change)

View diagram:

(To view image, hold shift and click on box)

The last thing we did was divide the sides as follows:
1. opposite/hypotenuese
2. adjacent/hypotenuese
3. opposite/adjacent
(round to 3 decimal places)

Still unsure about how to label a triangle? Then maybe this site will help, take a look.

Oh and btw, tomorrows blogger is Haiyan.

Multiplying + Dividing Radicals//Radicals w/An Irrational Denominator

2006-11-06T16:30:00.000-06:00

In today's class, we somehow fit two lessons in one day simply because I had to remind her that we didn't have math class tomorrow. Urgh... **groan** The mistake is mine, but the bad is not mine. Anyhow...in the first part of class, we learned about multiplying and dividing radicals. When multiplying radicals, here is one rule, or example to follow.

Ex. - √a × √b = √ab which also happens to equal (ab)^1/2.

That's easy enough to do though isn't it? Well of course, that example was just a review of what we've been doing in the previous days. It gets a little more complicated than that. Today, we also learned how to multiply radical binomials. Now this is pretty similar to the things we did in the first unit we did this year on polynomials and factoring them. In the following I will explain, [or try to...] the concept in a step-by-step process in the following example:

Simplify: 6√2 (√6 – 2√4)

1.) In order to simplify this, we must distribute the both the radical and the....oh...the other number, I don't quite know what the exact term is, but in this case it's the 6 right before the square root of 2. You multiply that with the same type of number of both sides of the binomial and then multiplying the radicals with the radicals resulting in...

6√2 (√6 – 2√4)

= 6√18 – 12√12

2.) After getting that answer, simplify the expression even more throughly, breaking it up bit-by-bit into more parts so that we are able to multiply it later on. [SiMpLiFy UnTiL yOu CaN nO lOnGeR sImPlIfY!!!]

6√2 (√6 – 2√4)

= 6√18 – 12√12

= 6√9√2 – 12√4√3

= 6 × 3 √2 -12 × 2 √3 = 18√2 – 24√3

Secondly, we were taught about radicals w/irrational denominators and what they had to do with dividing radicals-- which was pretty much everything...kind of. It was after all, in the form of a fraction, and a fraction is another expression of division. And this is what this might look like:

[click on box, because it's all screwed up.]

...where you divide the like terms [radicals with radicals] and then further simplify.

But when you are stuck in the situation where you have a radical binomial in the denominator, then it goes something like...

Ex
It is okay to have a radical in the numerator, but only then are numbers in their simplest form is when they do not have both a negative exponent and a radical in the denominator.

However, if there is a binomial in the denominator, the "difference of squares" must be multiplied. [REVIEW of DIFFERENCE OF SQUARES: Ex. (2x-3)(2x+3) = 4x² - 9]

An example of this might be...

[click on the box again. I don't know why the other diagram is goofing up.]

...where the terms with difference of squares cancel each other out because of the positive and the negative.

And yes...finally, it's the end for me. At least I think it is...but if you wish to tweak your "rationalizing" skills, I found a website that can give you some online practice where you could answer some questions by filling in the blanks and then check your answer.

I apologize if you didn't get some of the stuff, even though the post was incredibly lengthy. I tried though. And just a quick reminder just in case you missed it. The homework for the rest of the week is Exercise 37 [omit 10/11/16/17/18] and Exercise 38 [omit 11/14/16/18].

The next person to blog is Kim Tran.

--JhAyCaP--

Square Root Html and Multiple Choice Quizzes

2006-11-04T17:04:00.000-06:00

Hello Gummy Bears,
Here is the code that Chris used to create square root symbols. If you need to incorporate it into your post, my suggestion would be to do a copy and paste. The only thing that you will need to do is remove the *'s that I have added in.
x<*big>√<*/big><*span style="BORDER-TOP: white 1px solid">y<*/span>, x=Any number before the root sign and y=What is under the root sign.

I am also putting in some links for reviewing material.

roots and radicals (videos)
rational exponents (tutorial with practice questions)
simplifying radical expressions (m/c quiz)
operations with radicals (m/c quiz)

Hope this helps and have fun!!!
Ms Armstrong

Adding and Subtracting Radicals

2006-11-04T14:17:00.000-06:00

Today in Friday's class, we learned about: Adding and Subtracting Radicals.

You can only add and subtract like terms.

Example: 4x+3x=7x
2√2 + 3√2 = 5√2
These two examples can be added together because
their bases are the same.

5x+3y=5x+3y
4√2 + 3√3 = 4√2 + 3√3

These two examples cannot be added together since their bases are not the same.

In order to add/subtract radicals you must first simplify.

Example: 2√12 - 3√48 (Starting problem)
2√4·3 - 3√16·3 (Break the problem up so there's a perfect square under the root)
4√3 - 12√3 (Solve the perfect square and multiply it with the number at the front, if there's no number in front, its considered to be a 1)
-8√3 (Combine like terms)

Example: √12 + 2√8 - 3√75 + √2(Starting problem)
√4·3 - 2√4·2 - 3√25·3 + √2 (Break the problem up with the highest perfect square that can be multiplyed into the original number)
2√3 - 4√2 - 15√3 + √2 (Solve the perfect square and multiply it with the number at the front, if there's no number in front, its considered to be a 1)
-13√3 + 5√2 (Combine like terms)

Note: The next example has the cube root represented by an upper 3.
Example: ³√24 + ³√81 + 2√12 - 3√48 (Starting problem)
³√8·3 + ³√27·3 + 2√4·3 - 3√16·3 (Break up the problem with the highest perfect cube that can be multiplyed into the original number)
2³√3 + 3³√3 + 4√3 - 12√3 (Solve the perfect cube and multiply it with the number at the front, if there's no number in front, it's considered to be a 1)
5·³√3 - 8√3(Combine like terms, remember to keep square, cube etc. roots seperated.)

Example: 6x√x - 7√x³ (Starting problem)
6x√x - 7x√x (Since this problem is rather easy, we can just look at it and take out x² from x³ which leaves us with x)
-x√x (Combine like terms)

Ms.Armstrong also gave us a Radical Puzzle(Square Root) which was to be put correctly into the shape of an equilateral triangle.

Homework was Exercise #34 omitting 10,16,18. If there's any questions feel free to comment. If you need any additional help, click here to view a page about radicals.

Originally posted by Jamie:

"The next person who will post will be "tall guy" Chris. Yes you. Haha. Mwahahahhaha.... =D"

The next person who will post will be the "small person" Jamie. Yes you. Haha. Mwahahahhaha....=D

Pi

2006-11-02T23:03:00.000-06:00

I finally found some information about pi. No one really knows who specifically figured out pi, but what we do know is that pi existed for over thousands of years and still today it is being used. In about 2000 BC, the babylonians used 3 1/4 as an approximation for pi and the egyptians used 256/81. Pi was used specifically for the measurements of a circle the old mathematicians used to measure really large circles to come up with the decimal numbers.

Radicals

2006-11-02T18:39:00.000-06:00

Today in class we got are quiz back from Ms.Armstrong and we got to see what are mark we have overall in precal...

After that she taught us about radicals and how to simplify them.

A radical is an expression under the square root, cubed root, or to the forth root... Our goal is to simplify radicals to their simplest form. Simplifying means to find another expression with the same value.

EG.

Rules for simplifying Radicals
1) Break up Whatever is under the root sign into a product of factors. Find the LARGEST PERFECT SQUARE.
2) Split up and simplify.

For homework exercise # 33 omit #5/12/17
For more help with radicals visit Radicals for you.

I pick Chris to scribe next.

Multiplying with rational exponents and more

2006-10-31T22:18:00.000-06:00

Today in class we learned how to multipy rational exponents.

There are three thinks you must konw [keep in mind], and they are.

1) Multiplying polynomials
2) Multiplying exponents iwht like bases. -add exponents
3) Adding fractions.

Now that you know the things to keep in mind lets do some examples.

The forth square root of 16x⁸y² multiplied by the square root of 9xy⁵

[I know that the <> and < / SQRT > arent working so I'll just type it out like you would say it, sorry if thats an a bit hard to do...And I really dont have time to make graphx now.]

I cant write how the quesiton would look like at first but I can after the first step. The question is The forth square root of 16x⁸y² multiplied by the square root of 9xy⁵, so just visualize it for now would you?

After the first step:

(16x⁸y²)^1/4

Multiplied by

(9xy⁵)^1/2

After you clear the brackets it would looke like this:

16^(1/4)x^{8^(1/4)}y^{2^(1/4)}

Multiplied by

9^(1/2)x^1/2y^{5^(1/2)}

You know the original exponents that were there? Yeah well you have multiply them with the fractional exponent. You also have to square root or cube root or forth root, etc the whole number.

y^{5^(1/2)}

You Add the 5 with the 1/2. Remember that 5 is the same as 5/1 in fractional form. So multiply the tops and multiply the bottems.

5 x 1 = 5

1 x 2 = 2

Now if you've done that it should look like this:

2x^8/4y^2/4

Multiplied by

3x^1/2y^5/2

Did you see what I did? I just multiplied the original exponents with the rooted exponent, which in this case was 1/2.

After you do that you need do you remeber what to do next? Well if you dont then your suppose to make the x's and the y's exponent's denominator the same, so you can add them later.

After that step it should look like this:

2x^8/4y^2/4

Multiplied by

3x^2/4y^10/4

Again did you see the change? I changed the second term's x 1/2 and y 5/2 to 2/4 and 10/4. They are still the same fraction but they just have the same denominator.

Now that you;ve done that you should juts multiply the two terms and then your done.

If you do multiply the terms[Remeber to add the exponents (fractions)] you should end up with an answer like:

6x^10/4y^17/4

You see I multiplied the whole numbers and the fractional exponents were added. You know the product law right? Add the exponets when multiplying.

I hope that You all understood that...>_<

Tell me if theres any mistakes in there or if you dont understand something ^^

The next scribe is Dinh, the guy who started it all >:)

The Scribe List - Round 2

2006-10-30T21:54:00.000-06:00

Hey Gummy Bears,
This is The Scribe List - Round 2. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name on this list in Blue Font then you CANNOT choose them as the scribe for the next class.This post can be quickly accesed from the [Links] list on the right hand sidebar. Check the list before you choose a scribe for tomorrow's class when it is your turn to do so. At the end of your scribe post, let us know who will be scribing tomorrow.

Dinh--------------- Edward

Michele H. ----- Thamie---------

Xuan ---------- Christine ----------- Don

Donavon ------ Jeff -------------- Meagan

Jamie -------------- Kim T.

Destini -------- Alanna -------------- Emman

Kevin --------- Chris --------------- Cory

Shelly-------- Haiyan

Paulo ---------- Daureen ----------- Jhonaleen

simplifying Radicals to Rational

2006-10-30T18:36:00.000-06:00

eg. 1:

√25a³b⁴

(25a³b⁴)^1/2

25^1/2(a³)^1/2

5a^3/2b^4/2

5a^3/2b²

eg. 2:

√36√6

√36*6^1/2

(36*6^1/2)^1/2

36^1/2*6^1/4

6^4/4*6^1/4

=6^5/4

eg 3:

⁴√81xy⁵

(81xy⁵)^1/4

(81^1/4)x^1/4(y⁵)^1/4
3x^1/4(y^5/4)

* To solve an exponential equation, express both sides as powers with the same base and let the exponents equal each other.

eg. 9^x+1= 27

3^2(x+1)= 3³

2(x+1)=3

2x+2-2=3-2

2x=1

2 2

x= 1/2

4^2x+1=16^-3

4^2x+1=4^2(-3)

2x+1=2(-3)

2x+1-1=-6-1

2X=-7

2 2

x=-7/2

this is what we did in class today and h/w is Ex #26 (omit 8,9,12,15 & 19)

and tomorrow is halloween and if you come to class with costume you'll get candy and we have quiz on // and I and on the number of sets .

tomorrows scribe is PAULO

Can anybody help me??

2006-10-30T09:00:00.000-06:00

Hi Gummy Bears,
As you may have noticed the html code for 'square root' is not working. I have done some research on the internet and everything seems to indicate that I coded correctly. I have tried the code <&radic>, but it doesn't work either. Does anyone have any programming experience that could help us format a radical? 2 Bonus marks on the next test for the person that solves our trouble.
Ms. Armstrong

Pi

2006-10-28T23:36:00.000-05:00

Hey everyone ! I was on the internet and found this article about a man reciting Pi to 100,000 decimal places. I thought it would be nice to know something about Pi, since Edward had to find out about it. Here's the link http://news.asiantown.net/read/1713.html (Click!)

Common perfect 2s & 3s

2006-10-27T15:56:00.000-05:00

Today in class Mrs. Armstrong showed us how to use the html codes for this blog:

Exponents: x< .sup>1/2 (no spaces and periods)

Square root: < .sqrt >x+2< /sqrt > (no spaces and periods)

We also corrected some questions in Ex:21

Egs:

1) 38= what number times it self 3 times will give 8
³ 8 = 8^1/3
³ 8 = 2

6) 3⁴3 = 3^1/23^1/4
= 3^{2/4+1/4 = 3^3/4 = ⁴3³}^{How to do it on the calulator:

Option 1 8y^x 0.3333333 = 1.9999999.... (not accurate)
Option 2 8y^x 1 a^b/c = 2 (only if you have the a^b/c button on your calulator)}

^{COMMON PERFECT SQUARES AND CUBES TABLE}

^{Heres an link that will show you the laws of}^{rational exponents}

^{Homework: finishing the puzzle Mrs. Armstrong gave us

Important!!!! On Monday we have a Quiz!!}^{The person who is going to blog next is...... Eden!}

Rational Exponents

2006-10-27T13:04:00.000-05:00

1/2+1/2=1
x^1/2*x^1/2=x¹
x¹*x¹=x²
x*x=x²
x*x=x¹
x^1/2=x

x=square root of x=x^1/2
3x=cube root of x=x^1/3
4x=4^th root of x=x^1/4
5x=5^th root of x=x^1/5

Rational Form Radical Form
x^m/n nx^m
x^4/7 7x⁴
a^2/6 3a
b^3/5 5b³
Next:Shelly

Rational & Irrational Numbers

2006-10-25T15:24:00.000-05:00

The Number system

Rational numbers ---> any number written in the form of ratio a/b of 2 integer. a,b and b cannot be a zero.
Examples:
is a rational number because....

the numbers are written in a/b form and the decimals are repeating.

Example#2:

and are both rational because the 1st number repeats and the 2nd number terminates.

However, 7.23242526.......... -- > is not a rational number because the number does not repeat or terminate. This is an example of irrational number because the number never ends.

Irrational Numbers ---> a number that cannot be put in the form of a/b where a,b is an element of Integers.

However, the decimal form of an irrational number will never end or repeat.

Examples:

If you still need help with rational and irrational numbers click here and here.

Don't forget to do your Homework!

Explain how to solve each of the following and state what exponent law you used.

1) 3⁶.3²

2) 3⁶divided by 3²

3) (3⁶)²

4) 3⁰

5) 3² divided by 3⁶

Concept of Numbers

2006-10-24T20:37:00.000-05:00

Hey guys!
It's the very beginning of our new unit "rational Exponents and Radicals". Remember, tommorow at lunch hour is your only chance to redo last weeks, end of unit test.
Anyways today we looked at different sets of numbers, and cool patterns of how they can be used.
If you look above I have the diagram of the notes that we copied.
It explains how Natural Numbers (called this because they come naturally to a person), are connected with zero. Which makes a new set of numbers. The Whole Numbers and Zero (Which are part of a whole), are connected with Negative Numbers (which are lesser than zero). Which makes Integers, (either positive or negative) are connected to Non-Integers (Basically fractions), to make Rational Numbers (a ratio of 2 integers).
The symbol of the type of #, an example of the #, and an explanation are all in the appropriate boxes above.
We were also given a worksheet to do in class, but was for homework if not finished.
It was just showing neat little tricks and patterns on the calculater, when turning fractions into repeating decimals.
So ask Ms. Armstrong for your homework.
And remember that when you round of any decimal, each place value will lose you accuracy in the actual number.

Analytic Geometry Test

2006-10-20T23:56:00.000-05:00

First of all, currently, Jamie's blog entry is not up on the main page (since it's saved as a draft at the moment) but you can view it by clicking on this text and looking under the post title of 'Putting It All Together.'

Today in class, we had our Analytic Geometery Unit Test, which I'm sure we were all happy to do ;D. The test lasted for the whole period, and it was basically a small review on the unit. That's all we had a chance to do today, which means no notes or exercies.

Important Reminder

As Jamie mentioned in her post, our completed units are to be handed in on Monday, October 23^rd, 2006
With the following included:

A title page which is based on the unit. (Which means don't put something that has nothing to do with Analytic Geometry on it, Ex. Superman.)

A completed table of contents. (I'm pretty sure all exercises were posted up in previous blog entries so check them to see if you missed anything)

All of this unit's completed work/assignments and notes.

*Self-Reflection Tags which are required to be completed and included otherwise it will not be taken in.*

All of this presented in an organized duotang with your name on the cover.

This sums up my post and all we did in Friday's class (October 20^th, 2006), have a good weekend everybody and we'll see you on Monday.

Also, Monday's blogger will be: Kim D.

Putting It All Together

2006-10-19T17:49:00.000-05:00

Sorry I haven't been able to post, 'cause I have been having a hard time with my internet connection-- I have none right now whatsoever. And I'm using my neighbor's computer. But anyhow, for these past few days in math class, everyone has been fussing about the big math test coming up on Friday...at least I was.

No need to panic though. After yesterday's and today's class, it made things a lot easier. To clarify the concept of the parts some of us found confusing, the teacher had instructed us to make a table with four columns that explain the steps someone should go through when solving a problem-- any math problem at all. Personally, I thought this was a good process to go through, because this is the kind of thing that we should think about when analyzing problems.

After creating the chart, we were given an example, a problem to apply it to:
Ex. 1 - Find the standard form of the equation of the line containing (6, 1) and (-4, -3).

I can't put in the picture...why?? I'll just save this as a draft and continue.

We did this for yet another example, which is Ex. 2 Find the equation in slope-intercept form of a line which passes through (-4, 2) and has the same y-intercept as 2x -y = 3.

(diagram.)
'
And that is what we did for today's and yesterday's class. I say that this helps a lot. I'm sorry if I missed anything. Please tell me if I did, or what mistakes I made, so that I could do better next time-- because this is my first ever time blogging.

** Just another reminder. Friday is the unit TEST!! So that means the completed unit is due the next class after the test-- which is on Monday! Don't forget to include your completed assignments, your table of contents, your self-evaluations and an appealing title page!**

I guess that concludes this for me. The next person who will post will be "tall guy" Chris. Yes you. Haha. Mwahahahhaha.... =D

Parallel and Perpendicular Lines

2006-10-17T17:09:00.000-05:00

*** Click image to Enlarge ***

- all lines are declining
- negative slope
- slope exactly the same
- they are parallel lines

-when lines have the same slopes they are parallel

ex. // = parallel

Today we got our "Analytic Geometry Graphing Equations" quiz back. We went over quiz. Took some notes and made some perpendicular and parallel lines. Our homework for today is Excercise 14 - Parallel and Perpendicular Lines.

to my group...

2006-10-16T18:36:00.000-05:00

a message to my group (meagan, kriszelle, daureen, xuan)...

i finished the distances and stuff w/ the slide and made a title page just in case...i didnt do the write up but im sure meagan's doing it...right?

Another question...^_^"

2006-10-15T11:15:00.000-05:00

I have questions about the "Bulid a Slide" project.

I dont know who in our group is doing the one page write up so I thought that I should try it in case no one does it. First of all is anyone in my group doing it? I heard Cory is doing it but he wasn't there on friday so I don't know for sure.

For the write up (Letter G) does the whole thing have to be one page that would be including the diagrams or does the writing have to be one page?

Thanks.

Test Review

2006-10-11T18:13:00.000-05:00

Todays math class we talk about the 3 methods in graphing. Im here to explain again this methods so that we can all understand it.

Graphing Method #1 (Table of Values)

- "table of values" shows the relationship between x and y given by any equation.

We can pick any value for x and use the equation to solve y.

y=x+1 (y is equal to the value of x plus one)

let x = 1

y=x+1 Each one of this pairs values represents

y=1+1 a points on our line. These are then easily

y=2 graph.

let x = 2

y=x+1

y=2+1

y=3

let x = 3

y=x+1

y=3+1

y=4

Graphing Method # 2 (Intercept)

- When you speak of intercepts, it helps to know which one you're referring to.

In the plane, unless a line is parallel to either the x-axis or the y-axis, it will intersect

both axis sometime. We know this because two non-parallel lines in the same plane

will intersect sometime.

x-intercept
The x-intercept is where the graph crosses the x axis.

The word 'intercept' looks like the word 'intersect'.

Think of it as where the graph intersects the x-axis.

With that in mind, what value is y always going to be on the x-intercept? No matter

where you are on the x-axis, y’s value is 0, that is a constant.

eg.

y-intercept
If the x-intercept is where the graph crosses the x-axis where do you think the graph crosses for the y-intercept? If you said the y-axis, you are absolutely right.

This time it is x’s value that is 0. Any where you would cross the y-axis, x’s value is always 0.

eg.

Graphing Method #3 (Slope-Intercept)

- The slope of a line measures the steepness of the line.

- Most of you are probably familiar with associating slope with "rise over run".

Rise means how many units you move up or down from point to point.

On the graph that would be a change in the y values.

Run means how far left or right you move from point to point. On the graph,

that would mean a change of x values.

*equation: slope = y=mx+b

eg.

Every straight line can be represented by an equation: y = mx + b.

The coordinates of every point on the line will solve the equation if you substitute

them in the equation for x and y.

The slope m of this line - its steepness, or slant - can be calculated like this:

m = change in y-value

change in x-value

*if theirs question ask me..

next one to blog is jessica

Graphing Method # 2 and 3

2006-10-10T20:36:00.000-05:00

Graphing Method # 2
Using the Intercept Form

There are two intercept for any linear equation.

x intercept => where the line crosses the x axis.

y intercept => where the line crosses the y axis.

eg. graph the equation

* substitute 0 for x and then substitute 0 for y.

Using the intercept method.

Method # 3

Slope- Intercept Form

Step :
1.) Equation must be put into y= mx + b form.
ex. graph x- 2y = 2 ( using the intercept form.)

m = 1/2 = slope
b = -1 y intercept

2.) Plot the y intercept.
3.) Use the slope rise/run to find the second point from "b".

- and when graphing it, from point "b" rise 1/2 then run 2 place.

Homework:

Exercise # 11 and 12

And dont forget about the following dates:

October 13, 2006 - Quiz- 3 Graphing Methods.
October 17, 2006 - Slide project is due. (Ms. Armstrong changed it due to not having enough time because of the fire drill incident.)
October 19, 2006 - Analytic Geometry

And the next blogger is Emman.

Analytic Geometry Review

2006-10-10T12:45:00.000-05:00

Hey Gummy Bears,
Here are some online multiple choice questions to help you determine which topics you may need to focus on while you're studying. You can try a quiz more than once because most of the quizzes have a data base of several extra questions.

Slope
Writing Equations
Writing Equations in slope intercept form
Graphing Equations
Parallel and Perpendicular lines
Midpoint of a Line Segment

Hope this helps.
Ms. Armstrong

Build A Slide

2006-10-07T15:50:00.000-05:00

Okay, yesterday's math class, October 6th wasn't much of a math class. First, the whole school was really confused, because of the whole fire drill situation. We ended up spending about a third of the class standing outside in the cold. But when we did end up being allowed back inside the school, Ms. Armstrong told us we'd get the class to work on our "Build A Slide" project. For those of you who don't remember what the project is, or didn't recieve a hand out, here it is:

OUTLINE :
A) Using household items, you task is to build a model of a playground slide (5 marks)

B) Once you have completed the model, you will draw a labelled diagram of your model. Be sure to include an origin and (x,y) values for the height and base of the slide. Let 1cm represent 1 unit on the Cartesian plane. (5 marks)

C) CALCULATE the length of the slide using the DISTANCE FORMULA (on the orange sheet). Be sure to show all of your work and don't forget to include appropriate units (5 marks)

D) Measure the length of the slide. How does the measured length differ from the calculated length of the slide? Provide possible explanations for any discrepancies between the 2 values (5 marks)

E) Using TRIGONOMETRIC RATIOS, calculate the angle of inclination for your slide. Then use a protractor and measure the angle of inclination on your model. How do the 2 values compare? Provide possible sources of error to explain any difference in values. (5 marks)

F) CALCULATE the slope of the slide using the SLOPE FORMULA (on the orange sheet). (3 marks)

G) In proper paragraph format, DISCUSS how a change in the height of the staircase leading up to the slide would affect the slope of the slide. Be sure to include safety considerations as well as the enjoy ability for children using the slide. Diagrams and additional calculations may be useful to illustrate your position and understanding of the concepts. This portion must be at least 1 page. (20 marks)

FINISHED PRODUCT
You will need to hand in:
- Your model
- A neatly organized package of diagrams, calculations and write ups that follows the sequence of the outline
- The package must also include a visually stimulating and approriate title page. Don't forget to put your names, class and due date on the title page.

And, don't forget about Ms. Armstrong's LEGO girl. She should be able to slide down your slide safely without falling, or breaking the slide.

** DUE DATE : Friday, October 13th. **

Ms. Armstrong also gave us the tip of using this blog as a way to communicate with other memebers of your group, but DO NOT GIVE EACH OTHER YOUR PHONE NUMBERS, or other personal information on here.

As far as the class itself, Ms. Armstrong had to leave early, yet again, because of another football game (which I'm wondering if we won), so Ms. Ingram came in and kept an eye over us. And don't worry Ms. Armstrong, we behaved. :)

The blogger for Tuesday will be Christine.

Today's class (continuation of slope of a line)

2006-10-05T20:03:00.000-05:00

Today we corrected the 4 graphs from yesterday:

(click to make it bigger)

We also continued the notes from yesterday:

m is the notation for slope: y= mx + b

If m is greater than zero, the line is diagonal and rises to the right.

If m is less than zero, the line is diagonal and falls to the right

If m is equal to zero, the line is horizontal.

If m is undefined, the line is vertical.

The larger the number, the steeper the slope, and the smaller the number, the less steep the slope is. Here is a neat video to explain slope and intercept

Our homework was Exercise 7.

Next blogger is Jhonaleen.

Slope of a Line

2006-10-04T19:53:00.000-05:00

October 4, 2006 : quiz - Distance Formula & Midpoint of a Segment
notes - Slope of a Line

homework - Slope of a line examples

*NOTES:
what is slope of a line?
Definition - a measurement of how much slant.

If you know 2 points on a graph you can determine the slope.

ex. A
(2,1)
B (-1,6)

what is the slope?

*HOMEWORK:

Plot thes coordinates on a grid and find the slope.
1. A (0,-4) B(2,3)
2. A (-1,6) B(3,0)
3. x = 3
4. y = -2

Graphing A line using a table of Values

2006-10-03T20:31:00.000-05:00

These or the notes from today's class(October 2/2006) just in case you weren't taking notes or weren't in class today at all:

*first of three ways to graph a line

Equations of straight lines can be written in three ways:
-1) Ax+By+C= 0
-2) Ax+By=C
*3) y=mx+b m=slope b=intercept

1) and 2) are standard form
3) is slope intercept form

-in order to graph from a T.O.V. (table of values), the equation must be in "slope intercept form"

while graphing the T.O.V. you should think:
a) is it in slope intercept form?
and make a:
b) two variable table

eg) graph y=2x+3 using a table of values
a) yes
b)

*you only need 3 pts. to graph a line*

eg) let x have a value of -1,0,1
graph 4x+2y=12 using T.O.V.

eg) graph y=-4+0x

eg)

Well that's all for notes, I hope they helped the people looking for notes

So we were assigned all of exercise 5 in our red duotang and we were also responsible for "marking" one of our class mates completed unit.

-base the marks on the title page (needs to contain diagrams appropriate to the unit in this case polynomials, color and creativity) out of 5

-table of contents (a complete list of notes and assignments covered in class, and if included in completed unit must have a checkmark) out of 5

-Completeness (all class work and noted included, assignments completed, organized in same order as stated on the table of contents)out of 25

-Neatness(all items are neat, legible, and organized)out of 5

-And last but certainly not least the most important of all, the self reflections(I'm proud, I've improved, I still need to work on and trash it tags are included, reflections show insight into self improvement and learning)out of 10

if you need more explanation on the completed unit go to "unit one" by Xuan

oh yeah, before I forget the next person to post will be Kimberley

Midpoint of a segment

2006-10-02T19:09:00.000-05:00

The midpoint of a line segment is the point directly in the center of the line. Here is the midpoint formula.

This is like finding the average of the x's and y's

Here are some examples:
1.) Find the center of a circle whos end points of the diameter are D(3,-2) and E (-2,4)

2.) (9,11) is the midpoint and the end points are at (x,12) and (B, y) find xy

It doesnt matter what variable is used. so dont get confused by that. Just remember to always plug in the information that you have.

Thats about all we learned on fridays class. exept that ms.Armstrong worked for her dad's candy company and her children slept in shopping carts. hehe.

Dont forget that the homework was exersise 5 and expect a quiz on midpoints and distance on wednesday. not on graphing.

Review of Today's Class

2006-09-28T18:52:00.000-05:00

Today (September 28th) we had a teacher come in to take over our class since Ms. Armstrong was with the football team. We were basically instructed to work on Exercise #4 from our red booklet during class, and if we could not possibly finish it during our given time then we were to take it home with us and finish it for homework.

Note: After doing all the questions, you can check over your work and see if your answers are correct or if you've made any mistakes by looking at the answer key in your blue booklet .

[I wish i could have written more, but this is basically all we did in class today. For those who were away or forgot what was for homework i hope this helps =) ]

and oh yeah!..the blogger for tomorrow is MEAGEN!!

Using Formulas

2006-09-27T23:31:00.000-05:00

This post was for Tuesday September, 26. Today in class we learned some easy steps to using formulas.

Step 1) Identify what you are asked to calculate.
Step 2) What info would you need to be able to use that formula.
Step 3) Are you given the info directly or do you need to do some calculations first?

eg.

In this example we would use the Pythagorean Theory.

Step 1) Identify what you are asked to calculate which in this case would be (x).
Step 2) We would need atleast two sides to use the formula, which are 10 m and 4 m. Step 3) We must make some calculations to find the value of (x).

Distance Between Two Points

2006-09-27T17:25:00.000-05:00

Hey! Today in class, we learned how to get the distance between two points. Basically, it's like the Pythagorean Theory but more easier to use if the distance you are trying to find is in the graph. The formula to get the distance between two points looks like this:Recall: A point on a graph is denoted by the coordinates (x,y)

If AB is 5 spaces high and BC is 7 spaces long, you would use the Pythagorean Theorem to get AC, right? Your work would look somewhat like this: But if you used the distance formula, you wouldn't need the 'spaces' because using this formula would give you the sides of all the area all in one equation.

1 is (-4, -1) and 2 is (3, 4)

It doesn't matter if you switched the 1 as (3, 4) and 2 as (-4, -1).

Well, that's what we learned today. It's kind of confusing at first and almost everybody has this "wha..?" face when Ms. Armstrong was explaining it to us...

oh yeah ... Kriszelle, your doing it next...

Missed date

2006-09-25T17:32:00.000-05:00

Well...I have a bad eye, I always seem to miss something. I went through my work and I missed something on the table of contents. Well I need to confirm the date we learned the "Group Method of Factoring". My writing isn't real messy that I need to ask about the date it's just that i missed the date altogether. And since I dont write the date on my work I am asking here.

By the way I think that it was Wed Sept 20 judging by my table of contents, just need to make sure.

So anyone willing to tell me...^_^;;

Unit One

2006-09-23T13:51:00.000-05:00

Well yesterday's class started with Ms. Armstrong explaining to us about the sheets that the sub gave out. They don't have to be done, the point of it was to get the sheet with things you are having trouble with, so it will help you on our TEST: Monday, September 25th, 2006.

Ms. Armstrong said that everytime we have a test on an unit, the next day is the due date for the Unit Books, so our Unit Books are due on Tuesday, September 26th,2006.

Ms. Armstrong gave us instructions on how to put together the Unit Book.

1. Title
When making your title page, think about math. The example below is showing you what NOT to do. Superman or other characters and pictures that have nothing to do with math, they're nice, but they don't relate to math, so don't waste your time on a picture that has nothing to do with mathematics. To receive the full 5 marks, it must include, Unit name, diagram, colour and creativity.

2. Table of Contents
The picture below represents the Table of Contents. It isn't really that colour, its a yellow sheet. The colours are only there so I can explain easier. The green column is where you put the date the assignment was given. The blue is where you put the name of the assignment. The yellow column is to help you know if you're done the assignment, for example, if you're done the assignment, then you would put a check on the yellow column next to the assignment. To receive the 5 full marks, you must include complete list of all items covered in class, and assignments that are finished should be checked off.

3. Completeness
To receive the full 5 marks, all of the notes and assignments should be included, they should also be in order to match the order of the Table of Contents. If the work isn't complete then don't put it in, and don't check it off on the Table of Contents.

4. Neatness
For the full 5 marks, everything should be neat, organized in correct order, and easy to read.

5. Self Reflection
The picture below is the self tags. You cut them out seperately on the dotted line. If you have am assignment or worksheet that you are proud of, you would attach the 'I'm Proud' tag to it. If you have something that you think you've improved, then you would attach the 'I've Improved' tag to it. If you have something you need work on, then attach the 'Still need work on' tag to it. And lastly, if you have something that you're not proud of at all, or you think it should be in the trash, attach the 'Trash it" tag on it. Reflections show insight into self improvement and learning.

I had lots of fun doing this scribe, even though it wasn't on a lesson, I hope this will help some people with their Unit One book thingys. haha.
PS. Mondays scribe is going to be .... Kevin, OH and everyone, don't forget there's a TEST Monday, September 25, 2006.
- Xuan

Factoring Trinomials When a > 1.

2006-09-21T20:44:00.000-05:00

Well gummy bears,
I would make a great detective. I knew that Destini wouldn't let us down, so it didn't make sense that her posting wasn't up on the blog. What she did was create an entirely new blog site instead of creating a new post. So I've copied what she wrote yesterday and here it is.

Factoring Trinomials When a > 1.
Wednesday, September 20, 2006 ;

Today in class, we touched on the subject of factoring trinomials when a is greater than 1. This method was called The Grouping Method. There are 5 steps to complete this method.

Step One; Find the Factors of a * c.
Example: 15x² - 4x - 4
**15 would be concidered a & -4 would be concidered c .
**(15) (-4) = -60.
Find the factors of -60;
-60, 1 or 60, -1
-30, 2 or 30 , -2
-20, 3 or 20, -3
-15, 4 or -4 , 15
-12, 5 or -5 , 12
-10, 6 or -6 , 10

Step Two; Find the combination whose sum is equal to b. ( b = -4 )
It would be ( 6, -10 ) because -10 + 6 = -4.

Step Three; Break up the middle term using the factors from step two.
15x²-4x-4= 15x² -10x+6x-4

Step Four; Factor out a Greatest Common Factor (G.C.F.) from term 1,2 & 3,4.
15x² - 10 x + 6 x - 4= ( 5x ) ( 2 )= 5x(3x-2) + 2(3x-2)

Step Five; The 2 G.C.F.'s become the 1st factor and the brackets become the 2nd factor.
5x(3x-2) + 2(3x-2)= (5x+2) (3x-2)-

The assignment was Exersize #9. Questions 1 - 11 & 20. (omit questions 11-19)

P.S. - Xwan will be blogging next.. =)
posted by DestiniLyn

Factoring and Difference of Squares

2006-09-19T17:44:00.000-05:00

FACTORING

Okay everybody, today we started of class with a recap of yesterday's lesson on factoring. So here are the notes and examples:

1. Can I factor a GCF?

2. Is it a trinomial where a=1? ax² + bx +

eg. x² - 1x-6 (Hint: What combonations can I multiply to make 6?) -1,6 -6,1 2,-3 -2,3
2 and -3 is the correct combo, so the answer should look like this: (x+2)(x-3)

3. Only 2 terms, and they are separated by a - sign. eg. a²x²-b²y²

Okay, now here is the notes on differences of squares:

DIFFERENCE OF SQUARES

a,b,x, and y must be perfect squares which means that each has an integer square root.

eg. 4x²-y²

2 x y y
2 x

(2x+y)(2x-y)

(Remember! Use the
distributive property to check!)

eg. 1/16a⁴b¹⁰⁰-1/100x¹⁰y⁵⁰

(Hint: Find the square root of the bottom number of the fraction!)

It should turn out like this:

(1/4a²b⁵⁰+1/10x⁵y²⁵)(1/4a²b⁵⁰-1/10x⁵y²⁵)

Well that was all for the notes that we did, and after that we moved into a game.
Ms. Armstrong handed out a couple of cards for each table, each card having

I have...
and Who has the factors of the expression...

on each side of the card. Each card had an expression on the side, and you had to match it with other cards that other people had across the room.

Homework:

-Excersise 10, #1-7,11,17, and 19
-She also gave us a puzzle with expressions on it, where you have to match all of the sides together.

And tomorrow's scribe is. . . DESTINI!

Hoped this Helped!

COMMON FACTORS AND FACTORING SIMPLE TRINOMIALS

2006-09-18T20:57:00.000-05:00

Okay, so everybody remembers factoring from when you were in 7th grade
So a quick example would do:
18's factors are 1,2,3,6,9,18
24's factors are 1,2,3,4,6,8,12,24
so the greatest common factor (gcf) for 18 and 24 is 6

so when factoring a polynomial, we do almost the same: you find the GCF for the coefficient or constansts just as you would any other number, but you can have a variable also:
factor 6x-8y, it's factored 2(3x-4y). If you multiply 2 by 3x-4y you end up with the same as you started with! So another example is 25x2-15x is factored as 5x(5x-3).

Get It? Got it? Good, then we can go on to factoring simple trinomials

It's just like factoring before, except you have three terms so 3x3-9x2-30x is factored 3x(x-5)(x+2)

I hope that you guys learned from this, becuase this is my first blog post, and I had to use subscript for exponents, so they're a little low.
Oh, and today's assignment was EXERCISE 2, ALL QUESTIONS
GO MAROONS!!!

Activity for dividing polynomials

2006-09-17T19:59:00.000-05:00

On September 15(friday that just passed) basically all we did during class was get into groups of four and divided polynomials. Using the the white boards we tried to figure out the answers as fast as we could for points.
+ 3 if your answer was correct
and -2 if you got it wrong.
As for homework, I believe that we weren't assigned any for the weekend. Unless you did not have the opportunity to complete excercise one and three. Aside from that, I can't seem to remember anything else from friday's class :S. Sorrrrryyy.. Yes, I know my post seems ridiculously short compared to all the other postings.

Oh, btw .. This is Michelle S., I'm using Dinh's account because I couldn't post on my own :. I could only see last year's s1 posts. Anyways, Thanks Dinh for letting me use your account.

Answer Key - Grade 9 Review

2006-09-16T21:54:00.000-05:00

Hey Gummy Bears,
Here it is... the answer key that you have all been waiting for. Just click on the link and then download the document. It will open up in Microsoft Word. Let me know if there are any glitches since this is the first time I've tried this.
Ms. A

The Scribe List

2006-09-16T14:50:00.000-05:00

Hey Gummy Bears,

This is The Scribe List.
Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name on this list in Blue Font then you CANNOT choose them as the scribe for the next class.This post can be quickly accesed from the [Links] list on the right hand sidebar. Check the list before you choose a scribe for tomorrow's class when it is your turn to do so. At the end of your scribe post, let us know who will be scribing tomorrow.

Eden----------- Dinh--------------- Edward

Michele H. ----- Thamie---------Kim D.

Xuan ---------- Christine ----------- Don

Donavon ------ Jeff -------------- Meagan

Jessica -------- Jamie -------------- Kim T.

Destini -------- Alanna -------------- Emman

Kevin --------- Chris --------------- Cory

Shelly-------- Haiyan ------------- Stephanie

Paulo ---------- Daureen ----------- Jhonaleen

Multiplying and Dividing Polynomials

2006-09-14T19:46:00.000-05:00

First thing's first, we started the class by having Ms. Armstrong to post the answer key for the S1 Review at the back of the room. So if you need to correct your work, check it out sometime. Anyway, we were in groups once again. Ms. Armstrong turned on the projector and then we started taking down notes on "Multiplying Polynomials".

*Here are the notes incase you were lazy in class and didn't copy them :P

Multiplying Polynomials

= 12
Multiplying means "finding the area of a rectangle".

Example:
Find the area.
Now, there are 3 ways that you can do to find the area or to multiply the polynomials. It depends on which one you are most comfortable with:

The first way of multiplying polynomials is to use the "Tic Tac Toe" format. Using the above question, it will look like the image on the left. The yellow "x" is the multiplication sign. The "x+1" represents the width, and the "2x+2" represents the length of the rectangle. So it'll be like, (2x)(x) = 2x² and so forth. Then you add the like terms which are the ones that are circled.

The second way is using the "Algetiles". This format is like the Tic Tac Toe format except it is presented in images. If you don't know what the images represents, see the previous post.

The last one is everybody's favourite, the "Distributive Property". You first do the red one then the yellow then the green then the blue. So the answer would be:
= 2x² + 2x + 2x + 2
= 2x² + 4x + 2 (the like terms were added to simplify)

Dividing Polynomials

Dividing polynomials isn't that hard once you got how to do it properly. On an equation like this:

16x⁴y⁵ - 8x⁸y⁹
------------------------------
4xy⁴

Reminder that the denominator applies to all the polynomials on top. So here's how you divide polynomials:

i. Divide the coefficient (the number before the variable) on the denominator from the coefficient on the numerator. (Eg: 16 divided by 4)
ii. Subtract the exponents
iii. Then do the same thing with the second monomial.

**The final answer will look like this: 4x³y - 2x⁷y⁵

Like the multiplication of polynomials, dividing polynomials also have different ways to represent the equation:

i. (4x²+x³+5+2) division sign (x+2)
ii. (4x²+x³+5+2) / (x+2)
iii. Divide (4x²+x³+5+2) by (x+2)
iv. Find the length of a rectangle if the AREA is (4x²+x³+5+2) and the width is (x+2).

Long Division:
Before you solve an equation in long division, you must make sure that your terms are in descending order. If it's 4x²+x³+5+2, it should be x³+4x²+5+2, since the exponent "3" is higher than the exponent "2" even though it has a coefficient before it and the other one doesnt.

Long Division in polynomials is the same thing as dividing long division normally.

Between the notes, we've had an activity. The activity was to find the area of this:

Our Solution

My group started to find the area of the "whole rectangle" (on the left side, picture 2). Then subtracted the area of the small rectangle (in gray).

Our equation turned out to be like this:

The area of the "whole rectangle".
A = (4x - 1)(3x + 5)
A = 12x² 20x - 3x - 5

The area of the smaller rectangle (in gray).
A = (2x - 3)(3x - 1)
A = 6x² - 2x - 9x + 3
A = 6x² - 11x + 3

Subtract them together.
A = (12x² + 17x - 5) - (6x² - 11x + 3)

Note: To subtract polynomials, change the "-" sign (in the middle) to "+" then change the rest of the right side to it's opposite signs.
A = 12x² + 17x - 5 + (-6x²) + 11x - 3
A = 6x² + 28x - 8

Aaaand that's it. Pheew, did I do this blogging right?
Homework: Exercise #1 - If you're not done yet.
Homework: Exercise #3

NEW START : Polynomials

2006-09-13T20:01:00.000-05:00

Today Ms. Armstrong switched the unit, and so we are no longer learning the "variations and sequences" unit first but instead Ms. Armstrong decided that we were going to do the "Polynomials" unit first. We will still be including the work from earlier into this unit though, so don't throw those away!!

Then we corrected the worksheet called "PRE-CALCULUS 20S - creating and modifying tables", so get the right answers from a friend if you weren't there.

We also had a brief introductions on polynomials - REVIEW:

At the end of class Ms. Armstrong assigned all of "Exersize 1" in the red duotang (textbook) for homework

Oh, btw .. This is Michele, I'm just using dinh's account because i forgot my username and password.

-MICHELE H.

Creating and Modifying Tables

2006-09-12T22:52:00.000-05:00

On sept 11 we started with Creating and Modifying tables. We began with notes on patterns and recieved a worksheet on creating and modifying tables. We also learned that tables are a good way of organizing and summarizing information that is related. We also learned a little bit about non-recursive and recursive tables. A recursive table requires data from the previous term in order to find the successive term. A non-recursive table does not require the previous term in order to find the next successive term. Page 89 questions 1-7 and 9,10,11,16, and 19 was also homework as well as finishing up the booklet.

How To Spot Out The Right Graph

2006-09-09T20:59:00.000-05:00

On friday we began looking at graphs. The class had to choose between 4 graphs to see what graph best fits the question that is being asked. Ms.Armstrong also handed out slips so she could add students to the blog. She also handed us an assignment to do for the weekend and is due after the weekend. The assignment is called A Picture's Worth a Thousand Words. We also had to work as groups to help eachother out to pick what graph best answered the question be asked. That is what we basically did on friday. If im missing something leave a comment and i will add it into the blog.

The most obvious way to spot the wrong graph is if there is a loop in the graph because time cannot go backwards.

Grade 9 Review Booklet

2006-09-09T17:05:00.000-05:00

Hey Gummy Bears,
Thanks for all the positive comments about the blog, and the start of the new school year. I am looking forward to getting to know all of you over the semester. We are off to a terrific start. So far I am encouraged by the initiative that you are taking - getting to class on time, finding out when things are due, and getting yourselves signed up on the blog. I love seeing this much enthusiasm towards learning - keep it up.

Your first assignment (the grade 9 review) is due on Wednesday. You will be marking it yourselves, but I will be checking to see that you did as much as you possibly could do. Remember, this is a review. I expect that there are some topics that you need help refreshing your memory, while other topics may be new to you depending on where you went for grade 9. Don't fret - I will help you get through this but I want you to start by helping yourself. Try reviewing your notes from last year or work with a classmate. This is a really good opportunity to meet new friends - someone who went to a different school than you in grade 9 may be able to assist you with one topic while you might be able to help them with another.

Keep up the good work. It will all pay off in the long run.
Ms. Armstrong

Start Testing

2006-08-29T21:41:00.000-05:00

Time to change the template