In general it is

__a+b__=

__a__+

__b__

c c c

After you have divided the question then you had to check for restrictions like, x cannot = 0 or other certain numbers since you can't divide a number by zero.

Homework:p. 152 39-63 odd

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## Wednesday, April 30, 2008

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Apr 29, 2008

## Sunday, March 23, 2008

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Monomials and Polynomials

## Saturday, March 22, 2008

On thursdsay, March20th in PRECAL20s the only thing we did for notes was:

Example:Factor

xsquared-4x-12

=(x+2)(x-6)

xsquared+6x-16

=(x+8)(x-2)

xsquared+1-20

=(x+5)(x-4)

There were two assignments handed out on thursday they were PAGE:120,37-44, and the class had to finish the rest of the orange booklet.

Thise post was added by Dustin G. Woods
## Wednesday, March 19, 2008

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March 18/08

## Wednesday, March 12, 2008

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Products of a Monomial and a Polynomial -March 12

## Wednesday, February 20, 2008

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Operations with radicals

## Thursday, February 14, 2008

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February 14, 2008

## Wednesday, February 13, 2008

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simplifying radicals

## Tuesday, February 12, 2008

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February 8, 2008

## Friday, February 8, 2008

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Feb.4/5

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February 7 - Real Numbers and Absolute Value

## Sunday, February 3, 2008

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deSCRIBE

## Sunday, January 27, 2008

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Welcome to PreCal 40S!

Learning to Think, Thinking to Learn

We took notes on the long divison of polynomials, it is the oppiste of facoring, you undo the facoring by division.

In general it is__a+b __= __a __+ __b__

c c c

After you have divided the question then you had to check for restrictions like, x cannot = 0 or other certain numbers since you can't divide a number by zero.

Homework:p. 152 39-63 odd

In general it is

c c c

After you have divided the question then you had to check for restrictions like, x cannot = 0 or other certain numbers since you can't divide a number by zero.

Homework:p. 152 39-63 odd

In PreCal20S, on March 11th,

we learnt that**Monomials** are:

- A number

- A product of one or more variables

- The product of a number and one or more variables

Monomials consist of a numerical coefficient and a variable.

**Polynomials**

*Are algebraic expressions formed by adding or subtracting monomials.*

*Each monomial is a term of the polynomial.*

x + 17

Binomial = two terms

x² + 4x - 3

Trinomial = three terms

**Evaluating Polynomials**

Evaluate the expression for the given value of the variable:

x² + 4x - 3 for x = 2

= (2)² + 4(2) -3

= 4 + 8 - 3

= 9

__Mathematical Convention__

The terms of a polynomial are usually written so that the exponents of the variable are in descending order or ascending order.

If there is more than one variable, then it is written in ascending or descending order of one od the variables.

__Ex. __**Write the polynomial in ascending order of x :**

5x³y + 4xy³ -3 + 4x²y²

= -3 + 4xy² + 4x²y² + 5x³y

__Adding Polynomials__

(x² + 4x - 2) + (2x² -6x +9)

= x² + 2x² + 4x - 6x -2 +9

= 3x² - 2x + 7

__OR__

x² + 4x - 2

+ 2x² - 6x + 9

_____________

= 3x² - 2x +7

__Subtracting Polynomials__

(6a² - ab + 4) - (7a² + 4ab - 2)

= 6a² - 7a² - ab + 4ab + 4 - 2

= -a² + 5ab + 2

__OR__

4y² - 2y + 3

- (3y² + 5y -2)

___________

= y² - 7y + 5

And for our assignment we just finished off the math booklet.

Taylor Wigston

we learnt that

- A number

- A product of one or more variables

- The product of a number and one or more variables

Monomials consist of a numerical coefficient and a variable.

x + 17

Binomial = two terms

x² + 4x - 3

Trinomial = three terms

Evaluate the expression for the given value of the variable:

x² + 4x - 3 for x = 2

= (2)² + 4(2) -3

= 4 + 8 - 3

= 9

The terms of a polynomial are usually written so that the exponents of the variable are in descending order or ascending order.

If there is more than one variable, then it is written in ascending or descending order of one od the variables.

5x³y + 4xy³ -3 + 4x²y²

= -3 + 4xy² + 4x²y² + 5x³y

(x² + 4x - 2) + (2x² -6x +9)

= x² + 2x² + 4x - 6x -2 +9

= 3x² - 2x + 7

x² + 4x - 2

+ 2x² - 6x + 9

_____________

= 3x² - 2x +7

(6a² - ab + 4) - (7a² + 4ab - 2)

= 6a² - 7a² - ab + 4ab + 4 - 2

= -a² + 5ab + 2

4y² - 2y + 3

- (3y² + 5y -2)

___________

= y² - 7y + 5

And for our assignment we just finished off the math booklet.

Taylor Wigston

Example:Factor

xsquared-4x-12

=(x+2)(x-6)

xsquared+6x-16

=(x+8)(x-2)

xsquared+1-20

=(x+5)(x-4)

There were two assignments handed out on thursday they were PAGE:120,37-44, and the class had to finish the rest of the orange booklet.

Thise post was added by Dustin G. Woods

Today March 18/2008 in pre cal 20s we learned how to do factoring.

Factoring:

We now begin a discussion of the algebraic operation called factoring. Factoring an expression is to rewrite the expression entirely as a polynomial product.

Factoring Over the Integer:

A polynomial is considered completely factored when there are no more variable factors can be removed. No more integer factor, other than 1 or -1 can be removed. The steps for this process is 1. find the GCF (greatest common factor). 2. What is the GCF of the coefficients (exponents)? 3. What is the GCF of the variables (letters)? 4. Check: Multiply and see if you get the same expression that you started with.

Factoring by Grouping?

Some polynomials do not have a common factor in all their terms. These polynomials can sometimes be factored by grouping terms that do have a common factor.

The assignments we had assigned to us today are: page 120 #11-22 and page 120 #30-36

Factoring:

We now begin a discussion of the algebraic operation called factoring. Factoring an expression is to rewrite the expression entirely as a polynomial product.

Factoring Over the Integer:

A polynomial is considered completely factored when there are no more variable factors can be removed. No more integer factor, other than 1 or -1 can be removed. The steps for this process is 1. find the GCF (greatest common factor). 2. What is the GCF of the coefficients (exponents)? 3. What is the GCF of the variables (letters)? 4. Check: Multiply and see if you get the same expression that you started with.

Factoring by Grouping?

Some polynomials do not have a common factor in all their terms. These polynomials can sometimes be factored by grouping terms that do have a common factor.

The assignments we had assigned to us today are: page 120 #11-22 and page 120 #30-36

Today in class we learnt how to multiply monomials and polynomials. Basically all you have to do is multiply the monomial outside of the brackets by the polynomial inside the brackets.

Ex: Expand

3a(4a-3b)

=12a²-9ab

We also learnt how to simplify these expressions. To simplify an expression you, first, expand the expression like we have already done and then, secondly, collect like terms.

Ex: Expand and Simplify

4x(2x²+ 5x -3) –(2x²-7)

=8x³+20x²-12x-2x²+7

=8x³+18x²-12x+7

The final thing that we learnt to do today was multiplying binomials. When multiplying binomials you use the F.O.I.L. method. The F.O.I.L. method stands for multiplying the**F**irst two terms, then multiplying the **O**utside two terms, then multiplying the **I**nside two terms, and, finally, multiplying the **L**ast two terms.

Ex: Find the product of the binomials

(x+6)(x+8)

=x²+8x+6x +48 <----(F.O.I.L. method)

=x²+14x+48 <----( you have to collect like terms here too.)

The assignment for today was:

pg.107, questions 1-29 odd and pg.108, questions 32-43 and 45-67

Ex: Expand

3a(4a-3b)

=12a²-9ab

We also learnt how to simplify these expressions. To simplify an expression you, first, expand the expression like we have already done and then, secondly, collect like terms.

Ex: Expand and Simplify

4x(2x²+ 5x -3) –(2x²-7)

=8x³+20x²-12x-2x²+7

=8x³+18x²-12x+7

The final thing that we learnt to do today was multiplying binomials. When multiplying binomials you use the F.O.I.L. method. The F.O.I.L. method stands for multiplying the

Ex: Find the product of the binomials

(x+6)(x+8)

=x²+8x+6x +48 <----(F.O.I.L. method)

=x²+14x+48 <----( you have to collect like terms here too.)

The assignment for today was:

pg.107, questions 1-29 odd and pg.108, questions 32-43 and 45-67

Today we were learning and recalling on radicals.

We didn't do much notes but more examples on how to:

Multiply a radical by a binomial && Radial Binomial Multiplication.

We also did 2 different assignments.

One was on -->*Page 23 # 9 - 28 odd*

and

the other was -->*Page 23 # 29 - 35*

- Ex. In order to add or subtract variables, the variable must be the same.
- The same is true when adding or subtracting radicals.
- The Part under th eradical must be
*exactly the same!!!*

We didn't do much notes but more examples on how to:

Multiply a radical by a binomial && Radial Binomial Multiplication.

We also did 2 different assignments.

One was on -->

and

the other was -->

Today we learned about rationalizing radicals when the radical sign

is in the demonimator. You do it by multiplying it by a form of 1 such as square 2 over square 2, to move the radical up top.

Its a pain in the butt, but its worth it. Todays assignment was page 19 #35-53 odd. Tomorrows scribe is Kara Lee Rae. Haha

is in the demonimator. You do it by multiplying it by a form of 1 such as square 2 over square 2, to move the radical up top.

Its a pain in the butt, but its worth it. Todays assignment was page 19 #35-53 odd. Tomorrows scribe is Kara Lee Rae. Haha

today in class we worked on simplifying radicals.

We lernt that we must lern numbers like 75 (sqaure root) and 2/9 (sqaure root) are called entire radicals

And numbers like 5 Sqaure 3 and 1/3 sqaure 2 are called mixed radicals

Joss Gowland

We lernt that we must lern numbers like 75 (sqaure root) and 2/9 (sqaure root) are called entire radicals

And numbers like 5 Sqaure 3 and 1/3 sqaure 2 are called mixed radicals

Joss Gowland

February 11, 2008

Today in class we learnt how to*Simplify Radicals*.

Mrs. Remple used a card game at first to help us understand the concept.

She handed everyone a few cards from her deck of cards. Everyone organized their cards into pairs of 2. We put all our pairs on the left side of our desk and our extra cards on the right. Then we repeated all this but making sets of 3. It helped show us what happens when we are simplifying radicals.

Here is an example:

²√ 16x³y¹z²

= 2∙2∙2∙2∙x∙x∙x∙y∙z∙z

There are two sets of 2s.

{2∙2}∙{2∙2}∙x∙x∙x∙y∙z∙z

There is one set of X’s and one X left over.

{2∙2}∙{2∙2}∙{x∙x}∙x∙y∙z∙z

There is only one Y, so it is just a left over.

There is one set of Z’s with 0 left over.

{2∙2}∙{2∙2}∙{x∙x}∙x∙y∙{z∙z}.

The simplified answer is:

2²xz√xy

Today in class we learnt how to

Mrs. Remple used a card game at first to help us understand the concept.

She handed everyone a few cards from her deck of cards. Everyone organized their cards into pairs of 2. We put all our pairs on the left side of our desk and our extra cards on the right. Then we repeated all this but making sets of 3. It helped show us what happens when we are simplifying radicals.

Here is an example:

²√ 16x³y¹z²

= 2∙2∙2∙2∙x∙x∙x∙y∙z∙z

There are two sets of 2s.

{2∙2}∙{2∙2}∙x∙x∙x∙y∙z∙z

There is one set of X’s and one X left over.

{2∙2}∙{2∙2}∙{x∙x}∙x∙y∙z∙z

There is only one Y, so it is just a left over.

There is one set of Z’s with 0 left over.

{2∙2}∙{2∙2}∙{x∙x}∙x∙y∙{z∙z}.

The simplified answer is:

2²xz√xy

Today we learnt about Real Number Stuff. We did questions from the overhead with groups.

Some examples of questions were:

State wheather each of the following is always true, sometimes true, or never true.

The sum of a rational number and an irrational number is:

a) Positive: Sometimes True

b) Irrational: Always True

c) A fraction: Never True

d) Rational: Never True

e) Negative: Sometimes True

f) A whole number: Never True

If you took the absolute value of every number in each of the following sets of numbers, which set of numbers would you obtain?

a) Integers: Whole numbers

b) Negative integers: Natural numbers

c) Whole numbers: Whole numbers

d) Real numbers: Positive real numbers and zero

I learnt alot this day ha thanks to Ms. Remple she gave us no homework!

Some examples of questions were:

State wheather each of the following is always true, sometimes true, or never true.

The sum of a rational number and an irrational number is:

a) Positive: Sometimes True

b) Irrational: Always True

c) A fraction: Never True

d) Rational: Never True

e) Negative: Sometimes True

f) A whole number: Never True

If you took the absolute value of every number in each of the following sets of numbers, which set of numbers would you obtain?

a) Integers: Whole numbers

b) Negative integers: Natural numbers

c) Whole numbers: Whole numbers

d) Real numbers: Positive real numbers and zero

I learnt alot this day ha thanks to Ms. Remple she gave us no homework!

In pre-cal today we started unit 1 (Radicals and Rational Exponents)

Lesson 1-**Math 10F Review**

** Mental Math**

Multiply Polynomials

Ex.1 Expanding

**a)** **3(a+4)** Ex.2

**3a+4 a) (x+4)(x+3)-Used FOIL Method **

x^2+3x +4x +12

**b) x(x+3) x^2 + 7x +12**

**x^2 -3x**

**c)-5(y-2) **

**-5y + 10**

**Those were some examples of what we did the first day of pre-cal 20s.**

Lesson 1-

Multiply Polynomials

Ex.1 Expanding

x^2+3x +4x +12

Today, February 7th, in PreCal 20S, we learned about **real number lines**.

Every real number corresponds to a point on the real number line. There is a one-one correspondence between real numbers and the points on the line. In this real number line, there are no gaps, the line is complete throughout. Example:

_________________________________________

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

When Graphing on a Real Number Line - An open dot means that the point does not include the real number. A closed dot means that the point includes the real number.

**Absolute Value**

Also, today in class, we learned about absolute value.

The absolute value of a real number is the distance from zero to the position of the number on the real number line. When finding the absolute value of a real number, ignore the signs.

The notation for absolute value is x

Example: -2 = 2 , 2 = 2

Example: 2 - -5 , 2 - 5 = -3

Every real number corresponds to a point on the real number line. There is a one-one correspondence between real numbers and the points on the line. In this real number line, there are no gaps, the line is complete throughout. Example:

_________________________________________

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

When Graphing on a Real Number Line - An open dot means that the point does not include the real number. A closed dot means that the point includes the real number.

Also, today in class, we learned about absolute value.

The absolute value of a real number is the distance from zero to the position of the number on the real number line. When finding the absolute value of a real number, ignore the signs.

The notation for absolute value is x

Example: -2 = 2 , 2 = 2

Example: 2 - -5 , 2 - 5 = -3

Until the invention of the printing press, scribes were the people that were paid to write or copy books by hand. These were the educated people of their civilizations. In our class, the scribes will be the ones writing the customized textbook for our course.

A Scribe post is a summary of what happened in class. It is filled with enough detail that someone who missed class will be able to catch-up on what they missed. As you are writing your posts ask yourself **"Is this entry worthy to be included in our textbook? Would a graphic or example help clarify this topic?"** At the end of your scribe post you will name the next scribe and you will tag your post with the date and unit.

I learned about scribe posts from Mr. Kuropatwa at Daniel Mac and Mr. Harbeck at Sargent Park (both schools are in Winnipeg). Once I have learned how to include links, I will give the links to their blogs! The blogs that their students have created have impressed me to the point of making scribe posts a mandatory part of PreCal 20S at Ste. Anne Collegiate.

We will also have pre-service teachers from the University of Regina reading and commenting on your posts. This blog will be as rich and useful as **you** make it. This will be a place for you to think about your learning and to ask questions of your fellow classmates, the pre-service teachers, me (Mrs. Remple), and the world outside of the halls of SAC.

Labels:
deSCRIBE,
Mrs. Remple

This blog is a space for you to discuss what was learned in class and to reflect on your own learning.

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