Friday, November 9, 2007

Foil Method - Diamond & Melanie

Melanie Mendez & Diamond Valles



The topic we are introducing is the FOIL Method. The FOIL Method is the multiplying of two binomials by distributing twice. FOIL stands for First Outer Inner Last. The meaning of this acronym is the steps used to successfully use the distributive property. First you multiply the outer terms of the binomials. Then you multiply the inner terms of each binomial. After you have gotten your products you combine like terms and you have completely distributed two binomials.

Examples:
1. (3x + 4) (2x-8) -> (3x+4) (2x-8) -> (3x+4) (2x-8) -> (3x+4) (2x-8)
V V V V V V V V
6x^2 + -24x + 8x -32
V
6x^2 + -16x + -32

2. (4x + 2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3)
V V V V V V V V
4x^2 + -12 x + 2x -6
V
4x2+ -10x + -6

3. (2x + 2) (2x +2) -> (2x + 2) (2x + 2) -> (2x + 2) (2x + 2) -> (2x + 2) (2x + 2)
V V V V V V V V
4x2 + 4x + 4x + 4
V
4x2+ 8x + 4

4. (Ax2 + B) (Bx2-C) -> (Ax2 + B) (Bx2 – C) –> (Ax2 + B) (Bx2 – C) –> (Ax2 +B) (Bx2 – C)
V V V V V V V V
ABx2 + _ACx2 + 2Bx2 + -BC
V
ABx2 + -ACx2 + 2Bx2 + -BC

5. (2x+ 2) (x + 2) -> (2x+2) (x+2) -> (2x+2) (x+2) -> (2x+2) (x+2)
V V V V V V V V

2x^2 + 4x + 2x + 4
2x^2 + 6x + 4

Class Examples: 1. (xt5) (x+5)
2. (3x+5) (6x-8)
3. (x+7) (4x-5)
4. (10x-45) (12x+34)
5. (-9c+7) (7c-2)
6. (18d-2) (-12d+7)
7. (x+4) (x-4)
8. (7x + 6) (8x+ 5)
9. (x-5) (9x+5)
10. (10x-10) (10x+10)
Conclusion:

The topic that we are explaining is the FOIL METHOD. The FOIL method consists of multiplying of two binomials by distributing twice. FOIL stands for First Outer Inner Last as we had explained before. The first thing we had done was remember the First Outer Inner Last. For instance, example # 2

2. (4x + 2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3) -> (4x+2) (x-3)
V V V V V V V V
4x^2 + -12 x + 2x -6
V
4x^2+ -10x + -6

The fist thing we did was notice the first two numbers in both parentheses. Then we multiplied 4x and x together giving us 4x^2. Then we took the first term from the first parentheses and the second term from the second parentheses and multiplied. Which had given us -12x. Then we took the second term from the first parentheses and the first term from the second parentheses and multiplied, which gave us 2x. We then took the last two terms and multiplied and had gotten -6. Therefore we had gotten 4x^2 + -12x + 2x - 6. Then our final answer is 4x^2 + -10x + - 6. We have introduced the FOIL method in a simple easy way to understand.

GPS

Marcus Smith

Given, Plan, Solve

My topic is the GPS method. This Stand for Given Plan Solve. When using this method you have to get your equation and break it down into coefficents, variables, constants etc. This is just showing you all your information broken up. The second step is to Plan out your sequence in solving the problem. You use steps such as divide, add, subtract etc. The final step in doing the GPS method is to solve. After the first two step you basically have planned out what you need to do to solve. Follow your steps from the plan part to solve the problem. For Example:

1.2y +12= 20
Y= variable
2= coefficient
12,20= constants

2y+12=20
-12 -12
2y= 8
2 2
Y=4

2. 21- 3x= 27
X=variable
3=coefficient
21,27=constant
21-3x= 27
-21 -21
-3x=6
3 3
X=2

3. 30k+15=75 4. 100b-10= 290 5.40i+12= 52
-15 -15 +10 +10 -12 -12
30k=60 100b=300 40i=40
30 30 100 100 40 40
K=2 b=3 i=1

Solve the following using GPS:
1. 12q-3=90
2. 27p- 3= 42
3. 14j-7=70
4. 20u+20=400
5. 90n+30=120
6. 45n=135
7. 50r=750
8. 10o-90=-10
9. 6*4t=48
10.50+40a=420

The GPS method system lets you plan out and split up the equation or expression before solving it. The 3 steps are to split up the expression in the Given section, explain the problem in the Plan section, then Solve the problem using your plan. This method can be used for addition, subtraction, division, and multiplication. This method is used for solving for variables and many equations and expression.

Thursday, November 8, 2007

Oliver Box Method

Oliver Askia October, 25, 2008
Math B Bronx Prep



Hello my name is Oliver I am going to walk you throught the steps of BOX method. My partner Brandon and I are going to guide you through the steps of solving the X value in an equation. The main goal is to find the X value and turn it into an equation that use the distributive property twice. The next steps will show you how as a diagram.


The First Step:

Here is the BOX that you will need in order to solve the equation:

x2 -10x+ 25



x2
25


--25Fill in the top left space with x2 and the bottom right with 25. Multiply both values to get 25x2 . now the space should look like this.


x2
25 ___x___ = 25x2 ___x___ = -10x


The next step is to find what multiples will have a product of 25x2 and a sum of -10x.



x2
-25
-5x
-5x

Now that you found your value (-5x) you can now began to solve the equation.

x2
-25
-5x2
-5x2 (-5x) x (-5x) = 25x2 (-5x) + (-5x) = -10x


Next step is for you to simplify the variables using the greatest common factor.

x2
-25
-5x2
-5x2 (-5x) x (-5x) = 25x2 (-5x) + (-5x) = -10x



x2 -10x+ 25 = ( x – 5)(x – 5)

1. y2 + 11y + 24 = ( y +8)( y+3)
2. c2 +6c + 5 = ( c + 5)(c + 1)
3. m2 + 10m + 9 = ( m + 9)( m + 1)
4. x2 + x – 6 = ( x + 3)(x – 2)
5. x2 + 2x + 1 = ( x + 1)( x + 1)








1. x2 + 7x - 30
2. 48x2 + 4x - 24
3.x2 - 31x - 140
4.2x2 - x - 6
5. -x2 - 2x + 3
6. x2 - 7x + 10
7. 10y4 + 50y3 - 500y2
8. y2 + 10y + 9
9. c2 + 6c + 5
10. x2 + 2 + 1

Equation of a Line



By Hayley & Cashel

Equation of Line


When dealing graphs we go through many methods. One common thing we do is find the relationship between the points on X axis and the points on Y axis. We can also use slope to help us understand a line. Slope is how many boxes on a graph goes up or down and how many boxes to the right of the graph. We can find slope using 3 methods: numerically, algebraically, and graphically. Finding an equation of a line means we already have slope. When finding plots on a line with slope we use the equation format m(x) +b= y. M=slope, and b= y-intercept.

Here are the ways to solve

Numerically: y pattern /X pattern

Ex- y pattern is -15
X pattern is + .5
Slope- x= +.5/ = -30
Y =-15

Graphically: units going up down
Units to the right

Algebraically: y2-y1
X2-x1

Ex- 6-18 = -12 = -2
6, 0 6


Examples

Ex#1: y=8x-5 M=8 B= (0,-5)

Ex#2: y=1/2x+3 m=1/2 B= (0, 3)

Ex#3:y=7x-7 M=7 B=(0,7)


Ex #4= x: 0,4,8,12
y: -2,0,2,4
+2/+4= M=0.5
Ex#5= x: 0,6,12,24
y: 4,8,12,14
+4/6=m
Independent problems:

For the following identify the slope and y intercept, then Graph

1: y=2x-3

2: y=1/2x-4

3: y=5x-3

4: y=8x-5

5: y=1/4+2

6: y=5x-1

7: y=6x-2

8: y=7x-5

9: x: 2,4,6,8
y: 10,20,30,40
10: x: 3,6,9,12
y: 6,12,18,24

In conclusion we’ve come to see how we’re able to graph a line using the equation m(x) + b = y. We also learned how to find slope using the 3 ways numerically, algebraically, and graphically. Each way is different but every answer will always come out the same.









Factoring Perfect squares & GCF

Factoring – GCF and Perfect Squares

By: Abenai Chatman and Rosalba Urena


On our math project we are working on the topic Factoring – GCF and Perfect Squares. Anytime you have the difference of two perfect squares, you’ll always have two binomials. One of the binomial terms has to have a negative sign in between. You should always check your work so that you could see if you got your answer is right because sometimes you can get confused with the negative and positive signs. To find the GCF of a polynomial, trinomial, or a binomial you have to look an each term and determine if all the terms in the expression have the same variable and/or number. If the expression does, then you take out the variable and/or number and put the other terms in side the parenthesis.

Example Problems:

1. 25x² – 36

= (5x-6)(5x+6)
= 25x² + 30x – 30x – 36
= 25x² - 36

2. t² -25

= (t+5)(t-5)
= t² - 5t + 5t - 25
= t² - 25


3. y² - 36

= (y+6)(y-6)
= y² - 6y + 6y - 36
= y² - 36

4. 63yr² - 28y
= 7y (9r²- 4)
= 7y (3r - 2)(3r + 2)
= 7y (9r² + 6r – 6r – 4)
= 7y (9r² - 4)
= 63yr² - 28y

5. x² + 14x + 40
= (x + 10)(x + 4)
= x² + 4x + 10x + 40
= x² + 14x + 40


Independent Problems:


GCF:

1. 4x + 10x

2. 10xy² – 5x

3. 9ym² + 9ym

4. 25x² + 5x

5. 18ym² + 45yx


Factoring Perfect Squares:

6. p² + 16p + 63

7. s² + 12s + 20

8. h² - 14h + 48

9. w² + 13x + 30

10. y² - 13y – 36

In my conclusion through the expressions that come before this we can recognize that when we are factoring these perfect square binomials we are Factoring the Difference of Two Perfect Squares. Such as the example y²-36 we understand from knowing that they are both perfect squares that the answer is going to be (y - 6)(y + 6) because y · y = y² and the other perfect square 36 = 6 · 6. What these two Perfect Squares have in common is that they both when factored pull out twins of that same number instead of a different number. We learned that through factoring perfect squares that are binomials you must always have a subtraction sign for the expression.

Solving Quadratic Equations (factoring)

Solving Quadratic Equations (Factoring)
Amaleen Gonzalez
Trevion Martin



A quadratic equation is an equation with the highest exponent of two. For example, x²+2x+5 is a quadratic expression. Factoring a quadratic equation is making it into two binomials, where you would use FOIL to return it to a quadratic equation. There are two ways to factor a quadratic equation. Each quadratic equation needs to be factored a different way.

One way to factor a quadratic equation is by using a perfect square. For example, x²+10x+25 has a perfect square of twenty-five. A square root of twenty-five is five. When you factor it, the equation becomes (x+5)². If the equation was x²-10x+25, you could still use the perfect square to factor. When factored, that equation becomes (x²-5)² because negative five times negative five equals twenty-five. You could also use the fact that twenty-five is a perfect square if the equation was x²-25. When factored, that equation becomes (x+5)(x-5).

The other way to factor a quadratic equation is by using Box Method. You use Box Method when the quadratic equation doesn’t have a perfect square or if the equation does have a perfect square but the coefficients don’t add up correctly. For example, x²+7x+10 needs to be factored using Box Method. Box Method is used by setting up a box with four equally smaller boxes inside.

The first term is put into the first box and the last term is put in the last box. Then you multiply the first and last term together, which in this case would give you 10x². Now you have to find two numbers that equal 10x² when multiplied and 7x when added.

____ · ____ = 10x² ____ · ____ = 7x
You would find that 2x and 5x fit in. You put 2x and 5x into the remaining boxes.

With these numbers plugged in, you find the GCF going down and across. You end up with (x+2)(x+5).
Sometimes there is a perfect square, but you still need to use Box Method. For example, x²+10x+16. If you do not use Box Method, you’d think it was (x+4)², but this is equal to x²+8x+16. Using Box Method, you’d have the correct answer, which would be (x+2)(x+8).
Quadratic Problems

5) 1. 2x²-8x+24 =0 2. 7x²-21x-18 =0

3. 9x² +3x-22 =0 4. 14x² +100x-25=0


5. 12x² +14x+4=0 6. 22x² +5x-30 =0

7. X² + 2x-8=0 8.4x²-10x = 7

9. 2x²-3x+ 12 =15(x² +4) 10. 40x²-28x-36=0


Quadratic Equations Continued

As my partner has stated a quadratic equation is a equation with the highest exponent is 2. One way to making it into two binomials is to use box method or find the perfect square of a number. If you want to check your answer just FOIL the problem which is the opposite of box method. Box method is only used when you don’t have a perfect square. This is a non quadratic equations like 5x³-30x+20 because the highest exponent is 3.
- Trevion

Solving Linear Equations

Xavier Richardson & Stephanie Gordon
Solving Linear Equations




Hello, my name is Xavier. Stephanie and I will be showing you how to solve a linear equation. A linear equation is an equation that creates a straight line when put on a graph. To solve a linear equation, take the smallest constant in the equation and use its opposite operation (ex: -3’s opposite operation would be +3) after you do that, bring down the remaining numbers so that you have a smaller equation. Next, find a greatest common factor, or GCF, between the remaining numbers. Divide the numbers by that GCF. You should now get the value for the exponent that you are looking for.

Here are some examples:

27 = 5x -3
+3 +3
30=5x

divide the 30 and the 5x by its GCF. That should give you:
x = 6


5 = 5x + 4
-4 -4
1 = 5x
/1 /1
x = 1

14 = 7x – 21
+21 +21
35 = 7x
/7 /7
x = 5
4. 3x + 9 = 81
-9 -9
3x = 72
/3 /3
x = 24
5. 16 = 8x – 4
+4 +4
24 = 8x
/8 / 8
3 = x
1. 50=5x+15

2. 48= 54 -3x

3. 46 + 9x= 100

4. 10x- 20= 80

5. 36= 6x -6

6. 25= 3x+ 1

7. 27= 4x +3

8. 49= 21x – 7

9. 34= 6x+4

10. 76= 9x – 5

In conclusion, the linear equation can be very difficult to solve. But if you keep on practicing. You will be the greatest at solving a linear equation.

Instructions for Posting Algebra Project on the Blog

Once you have finished typing and saving your project in Microsoft Word, it is time to publish your project. Copy and paste all the work each team member did into ONE Word document. Make sure you have checked over your group’s work and that there are NO math or spelling mistakes. Only 1 team member should post your group’s project. To post your text on our Math B Blog, follow these steps:

1. Highlight your document text, excluding pictures and tables, and click ‘Copy’
2. Open up an Internet Explorer window and type the following:
www.blogger.com
3. Type in the Username and Password that you set up before
4. If you did this correctly, you should now be looking at the ‘Dashboard’. Click on the green cross that says ‘New Post’.
5. For the ‘Title’, type in the name of the math topic for your group (examples: Solving Linear Equations, Venn Diagram Comparing Rationals and Irrationals, etc.)
6. ‘Paste’ the work you copied before into the body of the ‘Posting’ window
7. Some words and numbers may not look right! Edit them right in that window.
8. If you have an image to add (table, box, picture, etc.), you should right click in the upper left corner of the image, hit 'Copy', and then 'Paste' the image into your blog post.
9. If everything looks good, click the ‘Publish Post’ button. You should view the blog and make sure your work appears in the right format.

KEEP IN MIND THAT THE PROJECT IS DUE THIS FRIDAY, NOVEMBER 9TH, at 4 PM!!!

So if you and your partner do not finish today, you need to work on the project in the laptop lab afterschool today or at home. NO LATE PROJECTS WILL BE ACCEPTED!!!

Happy Blogging!
Mrs. Collins and Mr. Glogower

Tuesday, November 6, 2007

Melnaie's Trip to fordam And CIty College

Over this last week the 9Th grade went to several colleges. The group I was in had went to City College a CU NY college in Manhattan and Fordam University a private in the Bronx. Both colleges are great and have lots of interesting courses to consider. In City College the things that stood out to me the most was the different majors. For example, this college has the opportunity to become and inter to become a nurse later on in my life. I also liked the campus, the way the buildings looked and were modern and closed off. I think the fact that the security is pretty tight is another interest I have in a college. I don't like the location of either colleges. But the campus is very beautiful. I Fordam because it made me more inspired to pursuit and thing i want by the time i decide what i want to do. I think I might major in business or the Arts like theater,etc. I would like to visit Princeton University or Yale University as well to see the expectations I need to do right now in order to attend a college that is that high on the list.

Melanie's first blog

Hey my name is Melanie! I am freshmen in High School. I am a Capricorn and is very friendly. I go to Bronx Prep Charter School. My hobbies are to hang out with my friends, talk on the phone, laugh, act, and sing. I like to do a lot of things that involve having fun with my friends and family. I am Dominican, Puerto Rican,Italian, And Haitian. As you can see I have a lot of different sides to myself. My favorite hobbies are to laugh. When you will see me in the halls you will usually find me laughing. My smile is something that is important to me in many different ways. It's apart of me that has been there since i was born! My favorite classes are math, science, and theater. I think this blogger will help my and my friends express our different views on different subjects in the mat world. I have a lot to learn and this will help me understand what other people understand in math. Its like picking a piece of each one of my friends minds and learning from each opinion!! This year is about new things to do, new mistakes and new things to learn. I would like to at least learn one huge lesson as this year grows more exciting and more interesting!!!!!