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 Cca2= b2+ c22bc 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 triangle, I have found the ∠O in both triangles, allowing me a complete ration to perform the sine law. Side Note: All Final Answers are rounded to 3 Significant Figures. For the first calculations, r=1 and OP =2. By finding the ∠O in one triangle, I have found the ∠O in both triangles, allowing me a complete ration to perform the sine law. Side Note: All Final Answers are rounded to 3 Significant Figures. When a triangle has all three sides given and an angle needs to found, the Cosine Law can be used. By finding angle O in ∆OPA, a complete ratio...
...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...
...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....
...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...
...MathSLPortfolio – 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...
...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 the sense that, unlike day schools, offers an intense interaction with other students and teacher, and the...
...Taipei European SchoolMath Portfolio

VINCENT CHEN 
Gold Medal Heights
Aim: To consider the winning height for the men’s high jump in the Olympic games
Years  1932  1936  1948  1952  1956  1960  1964  1968  1972  1976  1980 
Height (cm)  197  203  198  204  212  216  218  224  223  225  236 
Height (cm)
Height (cm)
As shown from the table above, showing the height achieved by the gold medalists at various Olympic games, the Olympic...
...SL TYPE 1LACSAP’S FRACTIONS
* INTRODUCTION
This investigation is going to do research patterns relates to the Lacsap’s Fractions. For its external structure, Lacsap’s Fraction is analogous to Pascal’s Triangle. Lacsap’s Fraction presents the way of generating and organizing the binomial coefficients. Within this investigation, the work is planning to be divided into two parts. In the first part, the content will relate to the pattern of numerators. In the second part, I...