Math Portfolio SL TYPE I
LACSAP’S FRACTIONS
Introduction
This assignment requires us to solve patterns in numerators and denominators in LACSAP’S FRACTIONS, and the first five rows look like:
Figure 1: Lacsap’s Fractions
1 1st row
1 3/2 1 2nd row
1 6/4 6/4 1 3rd row
1 10/7 10/6 10/7 1 4th row
1 15/11 15/9 15/9 15/11 1 5th row Then, let’s look at each part of the question.
Part 1: Numerator of the Sixth Row
Describe how to find the numerator of the sixth row.
For the first part of the question, we need to describe how to find the numerator of the sixth row. To begin with, let’s make all the numerators look the same in a row:
Figure 2: Lacsap’s Fractions
1/1 1/1 1st row
3/3 3/2 3/3 2nd row
6/6 6/4 6/4 6/6 3rd row
10/10 10/7 10/6 10/7 10/10 4th row
15/15 15/11 15/9 15/9 15/11 15/15 5th row Then, we can take out the denominator and go down by the row and just look at the numerator for this part of question, which will look like:
t1=1; t2=3; t3=6; t4=10; t5=15
We can investigate that the numerator starts with 1 in the first row, and the numerators are the same in one row. Each numerator after 1 is the sum of 1+2+…+n (n=row number) which forms an arithmetic series. For example:
When n=3, the numerator will be t3=1+2+3=6.
Table 1: Row Number and Numerator
Row NumberNumeratorInvestigation
11t1=1
23t2=1+2
36t3=1+2+3
410t4=1+2+3+4
515t5=1+2+3+4+5
Therefore, according to this arithmetic series tn=1+2+3+…+n, (n=row number), we can find out the numerator of the sixth row is t6=1+2+3+4+5+6=21
Part 2: General Statement for Numerator and Row Number
Using technology, plot the relation between the row number, n, and the numerator in each...
...especially triangles. Angles are mostly what decide the shape of triangles. This activity was about grouping similar angles from a set of parallel line with another line intersecting both of them. This activity had an important connection to figuring out the final shadows equation because we put the problems in terms of triangles and triangles are heavily linked with angles. After all, triangles do mean three angles.
Compared to math class back in elementary school, IMP is totally different. When I used to just solve given equations from a book and memorize methods to solve various problems. Now I actually have to create my own equation and work with that. But honestly speaking I preferred doing math the old way. It felt more normal and more like math. Since I started IMP, math has begun to feel more like science class, with different experiments and no real rules to solving the problems in front of you. At least now I have kind of adjusted to this new way but before it was quite overwhelming.
Since starting IMP, I have started disliking math more, but not really in a bad way. I think because I don't like it as much I spend more time doing the homework assignments trying to understand the material so I will not have problems and fall behind. So my goals have changed compared to what they used to be in eighth grade. Now I am more determined to do really well because I am in a class...
...function can fit the data, and better than the first function, but there is still some error between these two curves. New solution method or model should be advanced to describe tolerance of human beings to Gforces over time.
Then, we still found that some little error exist between real data and the function we got. Observe the time of the data, it is clear that there are large difference between the data, the scale of time is from 0.01 to 30, which is that uniformly distribute. So, logarithm axis is considered to scale the time. We can get new data table as follows:
Time (min)  Log Time (min)  Ln Time (min)  +Gx (g) 
0.01  2  4.61  35 
0.03  1.52  3.51  28 
0.1  1  2.3  20 
0.3  0.52  1.2  15 
1  0  0  11 
3  0.478  1.1  9 
10  1  2.3  6 
30  1.478  3.4  4.5 
Then we plot the graph of Log Time and Ln Time as follows:
From the graph, it can be seen that the shape of curve is similar with liner function. We assume the function form as follows:
So, we still use the new data to solve parameter k and b, we choose first and fifth group of data, second and the sixth group of data, third and seventh group of data, fourth and eighth group of data to solve parameters separately. Then we get the average of them as the final parameters.
To get k and b, I use the method of solving matrix which is:
Thus,
So, we plot the graph with new function as follows:...
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The Founding Father, the Propagandist, and a Wife
Daniel Boggs
(HST2011) – (U.S. History I)
Colorado State University – Global Campus
Dr. Bruce Ingram
August 19, 2014
The Founding Father, the Propagandist, and a Wife
Three people walked into a bar. They were a founding father, a propagandist, and a wife of a famous leader. The three introduced themselves as; Thomas Jefferson, Thomas Paine, and Abigail Adams. Ok, so they really did not meet in a bar. If they did they would have plenty of stories to share with each other about their childhood, their contributions to independence, and their influence on the United States. Maybe, they would talk about the legacy each would like to leave behind and how the world was forever changed. Regardless, they would have a lot to talk about. Back in the Revolutionary and Enlightenment era these three people overcame many obstacles in the name of independence. Each individual had a remarkable background that inspired them to be great leaders that contributed to the birth of the United States. The legacies that these three people have left behind still live on today.
Thomas Jefferson
Thomas Jefferson had many accomplishments in his life. Most notably was that he was the one who wrote the Declaration of Independence and also the Statute of Virginia for Religious Freedom. After the American Revolution, Jefferson was elected the third president of the United States. Before he died on July 4, 1826, he also established...
...111 32 11 64 64 11 107 106 107 11 1511 159 159 1511 1
The aim of this task is to find the general statement for En(r). Let En(r) be the element in the nth row, starting with r = 0.
First to find the numerator of the sixth row, the pattern for the numerator for the first five rows is observed. Since the numerator is the same in each row (not counting the first and the last number in each row), I can observe the numerator in the middle of each row. The numerators from row 1 to row 5 are 1,3,6,10,15
Table 1: A table showing the relationship between the row number and the numerator. The table also shows the relationship between the numerators in each row.
Row  Numerator  1st differences  2nd differences 
1  1  2  1 
2  3   
  3  
3  6   1 
  4  
4  10   1 
  5  
5  15   
The difference between the numerator in row 1 and row 2 is 2, row 2 and row 3 is 3, row 3 and 4 is 4 and row 4 and 5 is 5. The second difference for each row number is 1; this shows that the equation...
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Math SL PortfolioLacsap’s Fractions 
Type1: Investigation Portfolio
Greenwood High (An International School) 




Table of Contents:
Introduction……………………………………………………………………………………………………..……..…...Page 2
Patterns in Numerator………………………………………………………………………………….………………Page 2 and Page 3
Plotting Graph of Row Number and Numerator……………………………………………………………Page 4 to Page 7
Finding Denominator………………………………………………….………………………………………..………Page 8 to Page 9
Finding Further Rows……………………………………………………………………..…………………………… Page 10
General Statement……………………………………………………………………………………………………….Page 10
Scope and Limitations…………………………………………………………………………………………………..Page 15
Conclusion…………………………………………………………………………………………………….………………Page15
Pascal’s Triangle, a graphical representation by the French mathematician, Blaise Pascal, is used to show the relationship of numbers in the binomial theorem. It is shown in Figure 1 below:
11 2 11 3 3 11 4 6 4 11 5 10 10 5 1
Fig. 1Pascal’s Triangle
This portfolio is on “Lacsap’s Fractions”, and finding a pattern in the numerators and denominators of the fractions, as well as creating a general statement for En(r)where r is the element in the nth row; I shall start with r=0.
Row...
...Higher Level Mathematics
Internal Assessment Type I
Shadow Functions
Contents
Introduction: Functions/Polynomials 3
Part A: Quadratic Polynomials 4
Part B: Cubic Polynomials 12
Introduction:
In mathematics, function is defined as a relationship, or more of a correspondence between the set of input values and the set of output values. Also, a rule is involved, or as it may be referred to, a ‘set of ordered pairs’ that assigns a unique output for each of the input. The output correspondence is usually defined as f and the output is x. The correspondence is denoted as f(x). All functions are mainly defined by two factors, as was mentioned before, set of inputs  which are called arguments; and outputs  which are oftenly called values. The set of all arguments is called domain; and the set of all the values is called range.
The graph on the left is just an example of a simple function f(x)=3x+2. As you can see it is a straight line.
Any function has an ability to be described through its relations to other functions, for example as an inverse function, or as a solution to a differential equation. Also, as we will see further, functions can be quadratic.
Quadratic function graph is simply a parabola. The equation of that function doesn’t contain any powers that are higher than 2. Basically, quadratic function is a polynomial of degree of 2.
There are different types of polynomials, but the most common ones...
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IB Math: Studies Statistics
Portfolio:
What is the relationship between the numbers of goals the top sixteen players of the FIFA world cup 2014 score with the height of the players?
Due date: Friday November 23, 2013
School Name: Franklin Delano Roosevelt
Course: IB Math Studies
Name: Valerie Philco
What is the relationship between football player’s height that is participating in FIFA and has scored more than fourteen goals with the number of goals they have scored?
Introduction
The FIFA world cup is one of the most celebrated soccer tournaments around the world today. Not only does it serve as entertainment to everyone that watches the tournament but to participate teams have to have play a game against every team of there area teams classified this year include country’s like Argentina, Spain, Bosnia, Brazil, USA, Italy, France and many more. This being said for teams to win games they have to score more goals than other teams in this investigation the purpose is to verify if there is a correlation between the height of soccer players and the amount of goals they score.
Statement of task
The main purpose of this investigation is to determine whether there is a relationship between the height of the player and the amount of scores that they scored through out the period of qualifications for the 2014 FIFA world cup Brazil. The...