I am a passionate, persistent individual who wills to become a bachelor in British Law, in order to, further on, exert the profession of a lawyer. I am and have always been deeply interested in the principles of justice, which I try to put into action in my everyday life. My intention on entering a Law School is acquiring a deeper knowledge on the subject which has always been my main interest, both in my social and in my personal life. One might perhaps marvel that a Brazilian would rather join an British law school rather than one in his home country; the main reason why I am convinced that studying law in the United Kingdom, more precisely in England, is the absolute passion and interest I have always had for this country throughout my whole life, also extending to the field of law. My interest in Law and Rights first blossomed at the age of seven, when problems like alimony and share of goods showed up after my parents’ divorce, raising my interest to the mutual dissatisfaction of each with different matters concerning law, which made me wonder to what extent Divorce Law in Brazil was fair to both sides of the divorce. Moreover, I also have been told the basics of the profession by uncles - who are bachelors in Brazil – and about how time-demanding and complex it can be. My uncle also told me, though, that as long as it is exerted for passion, and not for other reasons, the high charge of work and responsibility are not a burden, but a pleasure. So high was my interest in analyzing processes and things alike that I got to spend hours with these uncles, asking questions about their procedures and their opinion about processes. I believe that my differential contribution to the university is based on the cultural interchange interchanged I have been through between the years 2011 and 2013, during which I have been living in Germany in a boarding school, understanding the functionality of a community in...

...MATHS PORTFORLIO SL TYPE I
CIRCLES
In this portfolio I am investigating the positions of points in intersecting circles. (These are shown on the following page.
The following diagram shows a circle C1 with centre O and radius r, and any point P.
The circle C2 has centre P and radius OP. Let A be one of the points of intersection of C1 and C2. Circle C3 has the centre A, and radius r. The point Pʹ is the intersection of C3 with (OP). This is shown in the diagram below.
As shown on the assignment sheet, r=OA. We therefore need to find the values of OPʹ when r=OA=1 for the following of the values of OP: OP=2, OP=3 and OP=4.
We first of all extract the triangle OPA from the above diagram and since we have the values for all the three sides we can finds the angle AOP which will later on help to get the value of length OPʹ. The circle C2 and triangle OPA are shown below with all side of OPA indicated.
OP=AP since they are the radii of the same circle, C2. Having all the three sides, we can now calubulate the angle AOP using the cosine rule. Angle AOP is calculated below:
Cos...

...OPA Circle Style
The three circles; O, P and A intersect to create an interesting investigation regarding circles. Since this is a Calculus course, the investigation does have to deal with Derivatives. The most important and the focus of this portfolio is the line segment, OP’. Using the given diagram above, this investigation consists of finding the general equation for discovering OP’.
The values that are given are that r, is the radius of C1 and C2. OP and AP are the radii of C3. This information allows for the information to be manipulated too create two isosceles triangles. The first triangle and the one that is given, ∆OPA is an isosceles triangle therefore it can be concluded, thanks to the Isosceles Triangle Theorem that angle O and A are congruent to each other in this triangle. ∆OPA is not the only triangle that can be created, ∆OP’A is the second triangle created with a radius from C2. Therefore ∆OP’A is also an isosceles triangle. Now in both the triangles stated above, they share a common angle, O. With the help of this information we can analyze the preliminary relationship between OP and OP’.
We can find OP’, we have the tools. The two tools that we will be using mainly are the sine law and cosine law (respectively);
Sin Aa = Sin Bb = Sin Cc a2= b2+ c2-2bc cosA
and the two triangles that are going to be used;
For the first calculations, r=1 and OP =2. By finding the ∠O in one...

...Luna
Math IA (SL TYPE1)
CirclesCircles
Introduction
The objective of this task is to explore the relationship between the positions of points within circles that intersect.
The first figure illustrates circle C1 with radius r, centre O, and any point P. r is the distance between the centre O and any point (such as A) of circle C1.
Figure 1
The second diagram shows circle C2 with radius OP and centre P, as well as circle C3 with radius r and centre A. An intersection between C1 and C2 is marked by point A. The intersection of C3 with OP is marked by point P’.
Figure 2
Through this investigation I will examine how the r values correlate with the values of OP in determining the length of OP’ when r is held as a constant variable and the value of OP is the variable that is subject to change. I will then venture on to study the inverse, the relationship when the r values becomes the variable that is changed and the OP value is held constant.
r as a Constant
If we let the value of r be equal to 1, we can use that information to find the length of OP’ when OP=2, 3, and 4. The first thing one can deduce is that by using the points A, O, P’, and P two isosceles triangles can be formed; ∆AOP and ∆AOP’. To rationalize this assertion...

...Evaluate/Compare and Contrast/Discuss/Examine models or theories of one cognitive process with reference to research studies (22)
Human beings actively process information and it is cognitive processes that guide behavior. These cognitive processes are influenced by social and cultural factors. One of the cognitive processes is memory. Many researchers and psychologies have proved that the mind can be studies scientifically by developing theories and using a number of scientific research methods. This is demonstrated in theories and models of cognition which are discussed and continuously tested. The key characteristics of a good memory models are first, testability; second, simplicity; lastly, applicability. This essay looks at strength and limitation/similarities and differences/examine/discuss of models of one cognitive process, which is memory, with reference to research studies.
Not all of developing models have such characteristics above.
MSM by Atkinson and Shiffrin (1968)
* Sensory memory, STM and LTM as permanent structural components of the memory system.
* Rehearsal is a control process, which acts as permanent structural components of the memory system.
* Rehearsal is a control process, which acts as a buffer between sensory memory and LTM, and helps the transfer of information to LTM.
-Evidence
* H.M. Case studies by Milner (1966)
-Studies of brain-damaged, amnesic patients appear to support the STM-LTM distinction. While STM...

...Introduction
In this task, I will develop model functions representing the tolerance of human beings to G-force over time.
In general, humans have a greater tolerance to forward acceleration than backward acceleration, since blood vessels in the retina appear more sensitive in the latter direction.
As we all know, the large acceleration is, the shorter time people can bear. Using the data shown in the task and Mat lab analysis, we can get several model functions to represent the tolerance of human beings to G-force over time. Then the model functions are improved through further investigation. The validation result shows that the models represented are efficient for the tolerance of human beings to G-force over time.
Problem formulation
To define appropriate variables and parameters, and identify any constraints for the data and use technology plot the data points on a graph. Comment on any apparent trends shown in the graph. Find function to model the behavior of the graph and explain the reason to choose the function. Create an equation to fit the graph. On new set axes, draw the model function and the function of the original data points. Comment on any differences and revise the model if necessary. Discuss the implications of the model in terms of G-force acting on human beings. Use technology to find another function to model the data. On a new set of axes, draw the model function and comment on the differences. Then, check whether the first model fits...

...Math SL Portfolio – Tips and Reminders Checklist
Notation and Terminology
Check for the following:
• I did not use calculator notation. (I didn’t include things like ‘x^2’ for or Sn for Sn)
• I used appropriate mathematical vocabulary.
Communication
Check for the following:
• The reader will not need to refer to the list of questions in order to understand my work.
• My responses are not numbered.
• I have an introduction, conclusion, title page, and table of contents.
• All graphs are labeled – Each graph has a title, labeled axes, and appropriate scale.
• My graphs and tables are within the body of my work. They are not separate or in an appendix.
• I have explained why I made the choices I did when going through the task.
• I did not include key stroke sequences, e.g. “I pressed the 2nd key, then TRACE…”
• My tables do not straddle pages.
• My tables are labeled well, including my variable definitions in each column.
Use of Technology
Check for the following:
• I used technology to illustrate my points and ideas. I didn’t just “stick in” a graph.
• Each graph or table (or other piece of tech.) is accompanied by explanations and my ideas.
• I did not include too many graphs on the same axes – my graphs are easy to read.
Mathematical Process (Type 1)
Check for the following:
• I explicitly defined variables and parameters the first time I used them, even if they were
already defined in...

...Introduction: In this following assignment, I will be considering geometric shapes that lead to special numbers. The simplest examples of these are square numbers (1, 4, 9, 16, etc), which are derived from squaring 1, 2, 3, and 4. From this I got the equation y= x2. This equation is illustrated in the table below.
y=x2
|x |y |
|1 |1 |
|2 |4 |
|3 |9 |
|4 |16 |
In the table on the left, I observe that from the y value 1 to the y value 4 there is an increase of 3. From the y values 4 to 9, there is an increase of 5. From the y values 9 to 16, there is an increase of 7. This shows that it goes: +3, +5, +7, which is then increasing by 2 between each of those numbers.
Below, is the graph of y=x2
[pic]
The equation y=x2 comes from the general equation y= ax2-bx+c.
Y=x2 is the same as y=x2+0x+0. Therefore, a=1, b=0, and c=0.
The next example I am going to show you is similar to the one above. The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular numbers (1, 3, 6, 10, 15, 21, 28, 36).
|Tn |y |
|1 |1 |
|2 |3...

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