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.

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

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!!!!!

Oliver

This week I had spent 2 days visiting colleges. On monday In visited Fordam in Manhattan, there I saw a very good place for me to find my career. For example Fordham is a very good college, it is still in New York City and it is a very challenging school and is a place of higher learning.Next day i visited SUNY Purchase a college locted in Westchester County and is a college dedicated to students who are artistic and want to chase an artistic career. SUNY is also very diffrent to Fordham in location. Fordham is located in Manhattan and is deep inside the city. SUNY Purshase is more suburben and is surrounded by trees and grass. I think its is a very good college for students who are searching fame and fortune. Also it is a very peaceful and beautiful campus

City College and Fordham University experience

The two college trips we went to were good. City College is a CUNY in Manhattan, and Fordham is a private college. I didnt really like City college becuase it was small and in Harlem. I rather go to a bigger school like G.W. I liked the dorms that Fordham has and the security looks top notch. Im looking foward to doing something in Engineering, or archetecture. I have to start working on doing my homework more and study more to show im commited.

College Trips

During this week, I have visited two different colleges. One was City College of New York, and the other one was Fordham University. Both of them are very great schools and are similar, but they are also diefferent ways. City College is located in the Harlem section of Manhattan. It is a very large place and the population is very diverse, with about 94 languages spoken on campus. Fordham University is also a large area located on the Bronx. The population is not very diverse, with the majority of students being white. The things i liked about CCNY was their large gym, their weight room their indoor and outdoor track field, and their buffet. I also liked Fordham University's library. I didnt like CCNY's large classrooms, though, but Fordham's small classrooms were just right for me. I know that in order for me to get into any colleges, I need to stay on top of my assignments and try my best to do well in my classes. I've decided that I want my majors to be biology and computer technology. In the future, I would like to visit Vaughn College and NYU. Johns Hopkins University.

my college trip

For my college trip I went to Fordham University. The trip to Fordham made me think more of going to this particular university. The reason why is because you can do art, dance, theater, and have classes on your religion. Even if this university is a catholic school. You have Christians, Muslims, and Jewish religions. Also that some of you classes will be graded for one your major subject like math, literature, biology, etc. For now in the 9th grade I will participate in many events the will boost up my opportunity to get in to Fordham University. But not only would I like to get into to Fordham, I would also like to get into NYU, Syracuse, John Hopkins, George .W, Clemson, Nyack and/or U.mass. These colleges have very good qualities that make them each unique that made me look at them. For now I don't know what majors I would like to consider. But I will find one.

College Trips: Fordham University

This week I visited Fordham University at the Lincoln Center. Some things that stood out to me were the variety of classes that the students were able to take, the opportunities that they had, and the building they took classes in. I liked the dorms and the numerous classes and groups you can participate in. The only thing that I did not like about the school is that it is local because I want to be able to experience going away for college.
As a 9th grader now I think that I need to make sure I stay focused and don't let my grades slip and also I need to maintain a positive attitude towards other people because they may be people I need to get into a good college. A major that I am considering for college is law or physcology. Some colleges I would like to visit in the future would include Spellman, GMU , Yale , Princeton , and many others.

College Visits :)

I was able to attend one of the two college visits that Bronx Prep had planned for us to go to. I wanted to go to the second college as well but was not able to. On October 22nd I went to Fordham University which was located in lower Manhattan and it was a private school. It was in a different area of the city and it was full of different cultures. When i went into the college campus I liked how we were treated by the tour guides. We were separated into groups with tour guides. They were very friendly and helped us out with any questions we wanted answered. We were able to see all different types of classrooms and dorms as well as lounge areas for the students attending. There isn't really anything i disliked about the college because they represented it very well. I didn't see anything wrong i just saw how positive it was that they can show off their artistic skills and express themselves. Some things you can do as a 9th grader to prepare for college is start obtaining independance skills. You would be on your own for the most part and have to work hard for yourself. Another thing you can learn now that would benefit in the college life is starting a friendly relationship with your professors so that your class can go smoother. I'm not sure yet on what i want to major in, but I do want to be sucessful which i have to work towards now. Some colleges i would like to visit in the future is Princeton, and other Suny and private colleges.

College Visit to fordham

On Monday October 22 ,2007 I attended Fordham University. Fordham was located in Manhattan and next to a public park. Fordham has many compartments and a large campus. Dorm rooms were like suites and contained 3 bedrooms, a bathroom, and a kitchen. Fordham also contained an art room, music room, lunch room, study hall area, law room, theatre area, and a large libary. Fordham university is a private school, which means it isn't a SUNY or a CUNY school. Becuase Fordham is a private school it can be a little pricey. For a dorm with 3 bedrooms it cost $7,000. For a single room you have to pay $12,000. I liked Fordham's "green area" and all the law rooms and law material they had. I also how roomy the dorm was. The only reason I wouldnt apply for Fordham is becuase i would like to go away from home when i attented college. I would like to majow in Law or Pyhscogoly and Fordham contains many materials for law. Another college I would like to vist might be Morgan or a school like Princeton. Right now as a 9th grader I need to be more into my work. I cant be lazy and do the work juss to pass. I have to apply my self.

college trip reflection

on the 22rd and the 23rd of october i visited two colleges in the city. when I visted the colleges I came with an open mind to see how I wanted to spend my future. The colleges I visted was ccny his college was better than i expected it to be. It was larger than I thought other city colleges were. The part that I liked the most was the amount of space that I would have access to. I was happy to see that they had computer labs for students who needed it and you were able to print any information you needed. The only reason i wouldn't attend ccny is because it did not have any majors i am interested in. I am interested in fashion design and sewing for fashion designers. The colleges I am interested in are parsons and the fashion institute of technology. The other college I visted was fordham university in the bronx on rose hill. I enjoyed seeing the amount of dorm space that was available to freshmens. The only thing is that I wouldn't want to live in dorm in the bronx when I live in the bronx already. I also liked the selection of food given in the cafeteria. I was happy to see a big library and small classes instead of large lecture halls like some colleges have. I hope to visit more colleges in the future so I have a variety of choices to chose from.

College Visits =]

On October 22nd and October 23rd I visited two different universities in the bronx. One of the universites I visted was City College. City college is a public universtiy located in Harlem, New York. It is refered to a CUNY school. I learned that CUNY stands for City University of New York. The university was very big and it had a large popularity of diverse people. What i really enjoyed about the College was that it had nice dorm rooms. They had varity of different type of dorm rooms to chose from. I also liked the size of the gym because it was very large and various excerizing machines.

On october 23rd I visited Fordham University at Rose Hill. I learned that Fordham university is neither a CUNY or a SUNY school but it is a private school. Unlike City College, Fordham University is a private school which means you have to pay more intuition. Many people attend Fordham because they wont like to get lost or not find thier way to their dorm room in a large campus. I liked Fordham University better than City college because it had a nice library and a very nice campus where you can relax in the spring and study for midterms or finals.

College Trips

My group had gone to City College of New York and Fordham University. Each college had something unique about them. About 75% of those who attended City College went on to Med School and about 85% went to Law School. Fordham University, I found, was based more around business. The percent of students who went to Med School was what really caught my attention at City College. There was nothing I didn't like at City College. I wasn't as interested in Fordham as I was in City College because I'm not looking to get into business. I want to start reaching for my highest potential here, in 9th grade, so that I now what I can do and where I can go when I'm looking for a college. For example, I would look to do some community service in places like hospitals. I'm looking to getting into the medical field. I hope I can visit colleges that can help me with that.