Today we learned about:

Graphing Linear Equation - a linear equation in two variables is an equation whose graph in the co-ord plane is a straight line.

Here' is today's assignment.

Go to Exercise 6 in your book and do odd numbers from 1-9 and 10, 11, 12.

1. y = 2x + 2

3. y = 5x + 5

5. 3x - 2y = 6

7. x = 3

9. y = 1

10. Simplify: (2x^4y)²(3xy³) / 6xy^5

11. Solve for x: 3 - [2 - (x - 2)] = 2x

12. Solve for x: 3x + 1 / 2 + 3 = x

Tommorows scribe is MARK E.


Today Ms. Eviatar went over the questions that students were having trouble on. She also showed us that the tan of one of the angle is equivalent to the slope.

Here is the activity that we did just in case you missed it.

Just don't forget that .

Tommorows scribe is ICON.

Slides September 29th

Here they are ....

Pre-

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Friday, September 26th, 2008

Heey, today Dr. Eviator went over Excercise 7: Ques 1-3, 5-7 with the class. Our assignment is to do whatever we were supposed to finish today and also Excercise 7: 11, 16, 17 and Excercise 8: 6, 7. Here they are:

Excercise 7: 11, 16, 17:

11) AB = 3, BC = 4, DE = 10
How long is DC?

16) Find the length and midpoint of segment PQ given P(3, 2) and Q(-1, 4).

17) The midpoint of AB is M(1/2, 6). Given A(3, 7), find the coordinates of B.

Excercise 8: 6, 7:

6) Select any point on a sheet of graph paper, and call it A. Move two units to the left to point B. From there move five units up to point C and three units right to point D.

a) Find the slope of AD.

b) Find the distance between A and D.

7) What is the slope of

a) the x-axis?

b) the y-axis?

annnnd the next scirbe for monday is . . . arvee.

Slides September 26th

Here they are ....

Pre-Cal 0

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September 25, 2008

Here is today's assignment.
Go to Exercise 7 in your book and do questions 1-7, skipping number 4.

1. Find the slope of each segment:

2. Find the slope of each line:

3. On a sheet of graph paper locate the points P(-2, 3) and Q(4, -1). Find the slope of PQ.

5. Describe in words the difference between a positive slope and negative slope.
What kind of line has a zero slope?

6. Without drawing the line, find the slope of the line given the two points on the line:

a. (1, 2) and (6, 4)
b. (-1, 3) and (4, 2)
c. (-2, -3) and (1, 1)
d. (4, 3) and (-1, 2)

7. Find the area of triangle ABC.
(Hint: First find the altitude.)

AND THE NEXT SCRIBE IS.... ARJEL !

Slides September 25th

Here they are ...

Pre-Cal 20S Slides September 25th

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September 24, 2008

Here is today's assignment.

Go to exercise 5 and do question's 1-3 and 15-16 in your exercise book.

1. Determine the coordinates of the midpoint of the segments with endpoints given below:

a. A(4, 2), B(6, 4)

b. C(-3, 7), D(5, 7)

c. P(10, -5), Q(8, 8)

d. M(9, 6), N(3, 5)

2. A circle has a diameter with endpoints A(-3, -2) and B(5, 2). Determine the coordinates of its centre.

3. The midpoint of AB is M(5, 2). Given A(8, 3), find the coordinates of B.

15. Find the distance AB in each of the following:

a. A(-4, 1), B(-1, -3)

b. A(2, -5, B(1, -1)

16. Find the perimeter of the figure below.
















Please try your best to answer all the questions. If I missed anything please feel free to look at today's slide, or ask Dr.Eviatar for any questions.

TOMORROW'S NEXT SCRIBE CHEMUTAI !

Slides September 24th

Here they are .....

Pre-Cal 20S Slides September 24

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this scribe is from Franny

kk i just got my account. dr eviatar ask us to do questions 1-3 just to get us started on our new subject

1.a.A(2,1),B(5,5) 1.b.A(-5,0),B(1,-4) 1.c.A(7,-2),B(-3,0)

2. find the radius of the circle with diameter AB, where A(-3,5) and B(1,-1)

3. Find the perimeter of (a triangle)ABC is right angled, given A(2,3),B(-4,-3),C(6,-1)

The next ScRiBe will be from CASEY :)

Homework for September 23rd

I noticed that the slides aren't very clear on what your homework is. So, just to be sure everybody knows, here it is:

Exercise 4 on page 7, do questions 2 and 3, and also 1 if you didn't do it in class.

Remember - homework is your own responsibility, if you don't do it, you won't pass this class!

Slides September 23rd

Here they are ....

Pre-Cal 20S Slides September 23rd

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Do you have what it takes?

Take this survey and find out if your math study habits will carry you through high school!

http://www.purplemath.com/stdysrvy.htm

Monday, 22nd of September.

Well.. I haven't actually been on the computer lately. To be honest, I totally forgot about this blogger thing. Anyways, I know I'm late for this and I apologize.

Today, we got our tests back. We were suppose to correct them together as a class but Dr. Eviatar decided that it's best if she corrected it herself.

On the 18th which is last Thursday, we had our pretest and shared our answers in groups of three. The following day we had our actual test.

Here's the test that we did:
1. Multiply the following:
a. 12(2b²-3b+9)
b. 3a(-7a+2)

2. If x = 4 and y = -2, fine the values for the following:
a. 3x²-(2y-6)
b.(4x^-1)(x²y)

3. Solve the following equations for x:
a. x over 2 + 6 = x-1
b. 5x-1 over 3 = x + 3

4. Multiply the following polynomials:
a. (7+3x-5x²)(-3x²+2)
b.(2y+3)(6y-5)

5. Factor the following polynomials if possible:
a. 6b²-3b+12
b. x²+14x+24
c. 16-81y²
d. 8a²-24a+18
e. x^4-13x²+36

6. Divide the following polynomials and provide the division statement in either form:
a. (x^3-5x²+10x-15) by (x-3)
b. (x^3-12x-20) by (x+2)

7. The area of a rectangle is (10+25x²-33x+4x^4)m². If the length is (2x-1) find the width of the rectangle.



In case you didn't do well in this test, you just have to try harder next time!
& Tomorrow we will be starting a new unit, so be prepared!

. . . And the next scribe will be, FRANCIS :)

Link to Course Outcomes and Fixing Marks

Here is the Government of Manitoba website that tells you exactly what you need to know when you finish this course:

http://www.edu.gov.mb.ca/k12/cur/math/outcomes/s2pre-calculus_outcomes.html

Also, I wrote down two people who needed their mark fixed, but there was a third person whose name I didn't write down. I'm sorry, I don't know all your names yet! Please come to me first thing tomorrow morning with your test and I'll fix it for you.

Cheers, Dr. Eviatar.

Slides September 22

Here they are ...

Test Polynomials and Factoring

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Important notice about the test tomorrow!

The test will cover ALL the material you did with Mrs. Ingram and me, even if it was not on the pre-test. This includes solving for x, multiplying polynomials and finding the values of polynomils for different values of x.

Good luck and take it easy!

Dr. Eviatar.

Slides September 18

Here they are ...

Pre-Cal 20S September 18, 2004

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September 17, 2008

Well for today, Dr. Eviatar helped us with some questions we didnt quite understand on Exercise 10 - Factoring Difference of Squares.

She did some questions with us and here they are:

3. a.
a² - b²
(a - b) (a + b)
81 - (x + 7)²
9² - (x + 7)²
↑
a² - b²
[9 - (x + 7)] [9 + (x + 7)]
[9 - x - 7] [9 + x + 7]
(2 - x) (16 + x)

b.
(x - 1)² - (x + 1)²
(x - 1) (x - 1) - (x +1)(x + 1)
(x² - 2x + 1) - (x² + 2 + 1)
x² - 2x + 1 - x² - 2x - 1
-2x - 2x
= -4x

4. a.
x^8 - y¹²
(x^4)² - (y^6)² =
(x^4 - y^6) (x^4 + y^6) =
(x² - y³) (x² + y³) (x^4 + y^6)
x² - 16
x² - 0x - 16
(x - 4) (x + 4)

5. a.
4m² - 25y^4
↑
(2m)² - (5y²)²
121x² - 196y²
(11x)² - (14y)

Before classes ended, she told us to study the stuff we learned to be prepared for our Pre-Test tomorrow.
Now get studying for the REAL TEST on Friday to be ready.
- Good Luck!

& the next scribe will be : Lia! :)

Slides September 17

Here they are ...

Pre-Cal 20S September 17, 2008

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Slides September 16

Here they are ....

Pre-Cal 20S September 16, 2008

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Today in class Dr. Eviatar gave us Exercise 10: Factoring Difference of Squares questions 1-20. DO NOT do questions 8, 9, 12 -16 and 18. If you weren't in class today and you forgot your textbook in your locker here are the questions:

1.a.) x² - 16
b.)36t² - 1


2.a.) 4a² - b²
b.) 8c² - 72


3.a.) 81 - (x + 7)²
b.) (x - 1)² - (x + 1)²


4.a.) x^8 - y^12
b.)4x² - 1


5.a.) 4m² - 25y^4
b.) 121x² - 196y²


6.Simplify: [(3x²)(4x³)]²

7.Simplify: x³ + x³ + x³


10. How many rectangles occur in this figure?



11. Solve for x:
a.) x / 2 + 1= x / 3 - x - 1 / 2


b.) (x + 2 )(x + 3) = x² + x


17. If the area of a rectangle is (x³ - 1) square units and one side is (x + 1) units, what is the length of the other side?

19. Divide: (5x³ + 1 - 10 x) by (5 + 5x)

20. Factor Completely:
a)15x² + 37x +20
b) 9y² + 12xy + 4x²
c) 20a² + 20a -75



The next scribe is going to be Madelyn.

Slides September 15

Here are today's slides ...

Slides September 15th Factoring and Polynomials

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September 15, 2008

Excercise 9 : Factoring ax² + bx +c

For each question 1 to 5, factor each expression and write "prime" if not factorable.

1. a.) 2x² + 5x + 3
b.) 5x² + 6x + 1

2. a.) 5a² - 16a + 3
b.) 3y² + 4y + 1

3. a.) 24x² + 2x - 1
b.) 6y² + 20 + 23y

4. a.) 10 + y - 2y²
b.) 60y² - 27y - 60

5. a.) 15x² + 37x + 20
b.) 15a² + 8a - 12

6.) Solve for x: 6 - 2 [x - (3 + 4x) } = 8

7.) Solve for x: 4 - x -1 / 2 = x

8.) A square is inscribed in a circle. If the area of the circle is 100pi cm², what is the are of the square?




So this is everything we did in class. .
PLEASE DO ANY HOMEWORK YOU DIDN'T FINISH :)
THANK YOU!!
feel free to comment if I made any mistakes or forgotten anything. .
happy math, bye!


THE NEXT SCRIBE IS JEYSON SACEDA :) !!!

Today in class Dr.Eviator gave us Exercise 2: Factoring Review (Common, Simple Trinomial) questions 1-20. DO NOT do questions 14 and 18. If you weren't in class today and you forgot your textbook in your locker here are the questions: .

Exercise 2: Factoring Review (Common, Simple Trinomial)

1. a. 12m-2p
b. a - ar³y

2. a. 2a² - 12ab +ac
b. 6x² - 18z^6y - 6ax³z

3. a. 3r² - 15rh
b. 4n³ - 4n²

4. a. 32xy + 4x³y
b.3mn + 6n²m²

5. a. x² - 7x + 12
b. x² - 10x - 24

6. a. x² + 25 + 24
b. x² - 4x - 12

7. a. x² + x - 72
b. c² - 4c - 12

8. a. 4 - 5c + c²
b. x² - x - 6

9. If x = -3 and y = 4, find the valube of

a. 2x + 3y - xy b. x²y + xy²

10. Solve the equation: 3 - 2(x+1) = 5x + 4

11. Solve the equation: x/2 + 1 = x/3

12. Simplify the following expressions:

a. (3x)³
b. (4x²y)(3xy²)
c. 16x²y/ 4xy

13. If AB = 6 and BC = 10, find

a. the length of AC

b. the measure of angle B accurate
to the nearest degree

15. Find the Value of x to two decimal places.

16. Simplify: 3(x + 2) - 2(x + 3)

17. Simplify: (x + 2)(x + 1) - x(x + 3)

19. Simplify: 2[2x - (3 - x)]

20. The side of a square is (x + 4) cm. Find an algebraic expression for its area.

These questions are all due for Monday. Try to do all the questions. And the next scribe is....

LEVINIA!!!

Today Mrs.Ingram gave us work to do once we got into class and here are the questions if you didn't happen to get them EVEN though everyone got a text book, but here are the questions:

Exercise 3: Division by Binomials -1 ( 13-18 )

13)Simplify:

a) (x²)³ + (x³)²
b) (x+x+x)²

14)Simplify:

a)3-2[x-(4)]

15)A carpenter takes a piece of plywood measuring 10 units by 10 units and cuts out a letter T as shown. If the T is of a uniform width, x, write an algebraic expression for its area.



16)ABCD is divided into 4 rectangles as shown. The areas of three rectangles are given. What is the area of the fourth rectangle?



17)Simplify the expression:
a)(x+2)² - x²

18)Multiply:
a) 2x(x+1((x-3)

Exercise 8: Division by Binomials -2 (1-4)

1. Divide: 3x³+3x+2 by (x+3)

2. Divide: (4x³-1+8x) ÷ (4+4x)

3. Divide: (3x³+1+3x) by (6+3x)

4. Divide: (2x³+x+6) ÷ (x+1)


Please try your hardest to answer all these questions! If you have any question about THESE questions please ask tomorrow in class! AND ... the next scribe will be ..




...KIMBERLY.

September 10th 2008

Today in class, Mrs. Ingram showed us how to divide polynomials and what not. Here is an example that she gave us in class:

1.) HINT: When dividing, subtract the exponents






She went through a couple of example with us, then Mrs. Ingram told us to do questions 1 though 12. If you don't have your booklet w/ you. Here are the questions.

1. Divide: (x² + 6x + 5) ÷ (x + 1)

2. Divide: (x² + x - 20) ÷ (x + 5)

3. Divide: (x³ + 3x² + 3x + 1) ÷ (x + 1)

4. Divide: (x³ + 6x² + 2x +12) ÷ (x + 6)

5. Divide: (3x² + 12x + 12) ÷ (3x + 6)

6. Divide: 8x² - 2x - 15 / 4x - 5

7. If the area of a rectangle is x² + 9x + 18 units² and the length is x + 6 units, what is the width?

8. If x = 3, find the value of 6x - 1 + 3x°.

9. Solve the equation: 4 - 3(x - 2) = 7x + 6

10. Solve the equation: x/3 + 2 = 6 - x/6

11. The three doors were side by side, labeled with three consecutive numbers. Could this be the place? Thor stared at them intently. Little Peter handed him a notepad. He multiplied the largest of the three numbers by ten and he subtracted twice the smallest number. The result was a disappointing 124. What were the three numbers on the doors?

12. Triangle ABC has a right angle at C. If AB = 6cm and AC = 4cm,
a. find the length of BC
b. find the measure of angle A to the nearest degree.


Tomorrow's scribe will be Shawn, aka POGIshawn.

Not much happened during class today, although we did continue with Exercise 1 from #10 and on. If for some reason you don't have the questions, here they are:



"11- If x = 2 and y = -3, find the values for the following:

A) x + y (x + y) B) 2x² + 3xy


12- Solve these equations:

A) 3 (x - 2) = 4 - (x - 2) B) x [over] 3 + 1 = x - 4


13- Simplify the following expressions:

A) (3x²)(5x³) B) (3x^4)² C) 12x^5 [over] 3x²


14- How many triangles are in this diagram?




15- The area of a triangle is A. If the base is of length b, express the length of the altitude in terms of A and b.


16- The solution to the equation 2x + 3 = 3x + [ink blot] is x= -8 What number is under the ink blot?


17- Find the value of x.



18- Find the value of x. Express your answer to one decimal place.




19- Use trigonometry to find the value of x. Give the answer to two decimal places.



20- Use trigonometry to find x. Give the answer to two decimal places.

"



Tomorrow's scribe will be Rustine.

To my students ...

Hi,

By the time you read this you will already have heard from Mrs. Ingram that I will be away from school for an extended period of time. 10 weeks to be exact. I'll be back on November 17.

On August 18 we had our fourth child, a little girl. Her name is Sadie. My wife and I discussed this a lot. As this is our last child, late last week we decided together that I would take a parental leave of absence.

I must admit I had very mixed feelings about taking the leave of absence. We began learning together and were off to a wonderful start with much hope and promise for the semester ahead. That hasn't changed. You are all capable of being the person, learner, mathematician you imagine yourself to be.

I have always believed that anyone can learn math, even the most advanced math, as long as they see themselves as able to be successful. So much of your success, in school and in life, has to do with believing in yourself; having confidence in yourself. See yourself as a success and you will be successful; in this and in all things.

In my absence you will be learning from one of the finest teachers in our school, yet don't underestimate yourselves. You can also be the finest teachers of each other. Just making the effort to take on that role for each other will deepen your learning and make you better students. You are your own best teachers. Continue to work together. Teach and support each other. And watch yourselves grow into the finest mathematicians in the school.

Mrs. Ingram is a wonderful teacher, I've worked with her for years, I know. Trust and lean on her, and each other, and you'll go far together.

I'm going to spend the next little while just being a dad to my kids. In the meantime I'll be poking in on the blog to see how you're all doing.

Take care of each other. And learn hard.

Your Teacher,
Mr. K

Corrections/Riviewing Grade 9 Math, Multiplying Polynomials.

Today, we now have a different teacher for math class and her name is Mrs.Ingram. For the classmates who doesn't know, the reason why Mr.K is not showing up for class is because he is busy with his personal life outside of school and won't be coming back for awhile.

Today, we looked over our worksheet from last week homework, "Polynomials Exercise 1" and did corrections on it.

I will give you guys the correct answers for the questions below for the worksheet.

1.) Simplify each of the expressions below.

a) (a - 3b) + (2 + 2b)
answer:a+2-b

b) (8k + 3m) + (2k - 5m)
answer:10k-2m

c) (3a + 2b) - (a + 3b)
answer:2a-b

d) 3(2x^2y - 3xy + 7) + (xy - 3x^2y - 2)
answer:3x^2y-8xy+19

e) x(4x^2 + 5x) -2x^2(5x^2 - 2x)
answer:-10x^4+8x^3+5x^2

f) (1/2x + 1/3y) - (3/2x + 2/3y + 5) + (7/2x + 1/5y + 4)
answer:Confusing...ask teacher about this one

2. Find the sum of 7x^4y^3 - 3xy and 6x^5 - 5xy .
answer:6x^5+7x^4y^3-8xy

3. Wanda's age is (4x + 3y + 6) and her daughter's age is (2x - y - 4). Find the difference of their ages , expressing your answer in terms of x and y .
answer:2x+4y+10

Mrs.Ingram gived us examples "Multiplying Polynomials"
example- 3(x^2+6x+9)= 3x^2+18x+27

example- x(x^2+6x+9)= x^3+6x^2+9

example- (x+4)(x-2)= x^2-2x+4x-8= x^2+2x-8

Today homework is in our textbook.
"Multiplying Polynomials" Riviewing.
Exercise 1 questions#1-10
MUST BE DONE BY TOMORROW!

IF YOU EVER NEED HELP IN ANYTHING IN MATH!!
**REMEMBER TO ASK PEOPLE FOR HELP, DON'T BE SHY, YOU CAN ASK ME FOR HELP FOR EXAMPLE** & BE POSITIVE!! X)

Next Scribe is..........KRIS!?

There isn't much to talk about for Friday's class .
We had a substitute for the day ; Mr. Kuropatwa wasn't in class .
But he left us a worksheet to work on . It was still review of polynomials and such .
That's all we did for class .
I'm quite sure everyone got the worksheet but if you somehow misplaced it , here are the questions :

1. Simplify each of the expressions below.

a) (a - 3b) + (2 + 2b)

b) (8k + 3m) + (2k - 5m)

c) (3a + 2b) - (a + 3b)

d) 3(2x^2y - 3xy + 7) + (xy - 3x^2y - 2)

e) x(4x^2 + 5x) -2x^2(5x^2 - 2x)

f) (1/2x + 1/3y) - (3/2x + 2/3y + 5) + (7/2x + 1/5y + 4) *

2. Find the sum of 7x^4y^3 - 3xy and 6x^5 - 5xy .

3. Wanda's age is (4x + 3y + 6) and her daughter's age is (2x - y - 4). Find the difference of their ages , expressing your answer in terms of x and y .




* The reason why I starred " f) " was because that was the one that I had difficulty with . I'm sure there are others in the class who had difficulty with this question as well . If you understood how to do it , could you please explain and help us understand .


Monday's scribe will be Jessica .

Polynomials

Hello! Grade 10 Pre-Cal

Today in class we started with polynomials which is our first Unit of the course.

Mr. Kurapatwa thought as a little bit of Definition of Polynomials.

As we know that our first unit is polynomial, So we have to know the definition of polynomial!

1. Polynomials: is an algebraic expression of one or more terms

e.g. 2x+3y or x^2 - 5x+4

2. Monomial: is an algebraic expression of one term

e.g. 6x or 5ab or y

3. Binomial: is an algebraic expression of two terms
*We have to remember that any expression with two terms is a Binomial

e.g. x-y or x + 4

4. Trinomial: is an algebraic expression of three terms

e.g. 2x + 5y -4

*We also learn 5 other Definition*

1) Terms: is a symbol or group of symbols separated from other symbols bya plus or minus sign.
e.g. 3x - 5y + 7xyz in this expression we know that there are three terms, note that terms may contain several numbers and letters.

2) Coefficient: The numeric factor of a term (a number with a variable)
* for example 3x + 5y -4* the coefficient in this expression are 5 & 4

3) Sum: The result of Adding two or more number
e.g. The sum of 2 and 3 is? so we know that if we add 2 and 3 we get 5

4) Product: The result of Multiplying two or more numbers
e.g. the product of 7 and 3 is? so what we will do is to multiply 7 and 3, which will give us 49.

Time to Practice!!

Adding and Subtracting Polynomials
a. 7x-y-2x+3y? (when we are adding or subtracting polynomials we combine the like terms which looks the same.)

7x-2x are like terms

3y-y are like terms

so now it's easy for as to solve it!

the answer is 5x+2y

2. (4x-2y-4)-(-3x-2y+5) *i think this is little bit trickier*

What we will do hear is multiply the minus to each of the second expression on the right hand.

And now we remain with (4x-2y-4)+(3x+2y-5)

now the second expression is changed, what we will do is to take off the brackets and as i say we combine the like terms.

4x+3x-2y+2y-4-5

7x-9 ans

Multiplying and Dividing of Polynomials.

1. 2(x+y)

we just multiplied 2 to everything in the brackets

2.

Now what we have to is to divide
the coefficient and cancel the like terms
variable. Which Will give as 8x

For More Practice and Exercise:
Adding and Subtracting polynomial
Please Click

Multiplying Polynomial
Please Click

Next Scribe Blog Will be Rawena

I hope you guys will understand my blog
if not please live a comment for mistakes or anything

Thanks!!

Today's Slides: September 4

Here they are ...

Pre-Cal 20S September 4, 2008

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A New Beginning

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline); for parents to find out "How Was School Today;" to share your knowledge with other students. Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, contribute to the conversation and lets get down to some serious blogging!

Here are the slides from today (your homework is on slide #33):

September 3, 2008 Pre-Cal 20S First Class

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See you tomorrow.

Cheers,
Mr. K.