The aim of this investigation is to consider commercial fishing in a particular country in two different environments, that is from the sea and a fish farm (aquaculture). The following data provided below was taken form the UN Statistics Division Common Database. The tables gives the total mass of fish caught in the sea, in thousands of tones (1 tone = 1000 kilograms). Year| 1980| 1981| 1982| 1983| 1984| 1985| 1986| 1987| 1988| Total Mass| 426.8| 470.2| 503.4| 557.3| 564.7| 575.4| 579.8| 624.7 | 669.9|

Year| 1998| 1999| 2000| 2001| 2002| 2003| 2004| 2005| 2006| Total Mass| 487.2| 573.8| 503.3| 527.7| 566.7| 507.8| 550.5| 426.5 | 533.0| Table1. – The total mass of fish caught from 1980-2006

From the presented data, it is shown that in some years the amount of fish caught rises and on others the amount of fish caught in the sea decreases. The reason of the amount of fish to decrease can be influenced by ecological factors and weather phenomena’s or even the amount of fishermen on the particular area in the sea. Identifying variables: let y stand for the amount of fish caught from the sea and x stands for the years passed. It shows yx=amount of fish caught, so e.g. y1980=426.8. The set of possible values of the variable on the horizontal axis is called the domain. Therefore {x | 1980 < x ≤ 2006} is the domain of the amount of fish caught. The set which describes the possible y-values is called the range. Therefore the range of the fish caught is the total mass of fish from the sea.

...FISHPRODUCTION
Aim: This task considers commercial fishing in a particular country in two different
environments- the sea and fish farms (aquaculture). The data is taken from the UN Statistics
Division Common Database.
*The following table gives the total mass of fish caught in the sea, in thousands of tonnes
(1 tonne = 1000 kilograms)
Define suitable variables and discuss any parameters/ constraints. Using technology, plot the data
points form the table on a graph. Comment on any apparent trends in your graph and suggest
suitable models.
*Aquaculture pros and cons
Pros
Feeds the world's demand for seafood
Has a tremendous economic impact on world
GDP
Cons
Major impact it has on the ecology of the
oceans
Utilizes nets or traps may inadvertently capture
and kill other marine animals, including turtles,
dolphins or sharks.
70 percent of the world's fish species are
depleted" or "fully exploited."
"
Wild fish are usually healthier (higher in
Omega-3s) and less contaminated than farmed
fish.
Employs more than 200 million people around Overfishing
the globe
Many people prefer the taste of wild fish.
The shipping of fish all over the world uses
Farmed fish do not have as much room to
fossil fuels and pollutes the environment.
move which results in partial growth....

...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear,...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...Jonghyun Choe
March 25 2011
Math IB SL
Internal Assessment – LASCAP’S Fraction
The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern.
The presented pattern is:
Row 1
1 1
Row 2
1 32 1
Row 3
1 64 64 1
Row 4
1 107 106 107 1
Row 5
1 1511 159 159 1511 1
Step 1: This pattern is known as Lascap’s Fractions. En(r) will be used to represent the values involved in the pattern. r represents the element number, starting at r=0, and n represents the row number starting at n=1. So for instance, E52=159, the second element on the fifth row. Additionally, N will represent the value of the numerator and D value of the denominator.
To begin with, it is clear that in order to obtain a general statement for the pattern, two different statements will be needed to combine to form one final statement. This means that there will be two different statements, one that...

...Cindy Hwang
IB Math 11 SL 1-3
IB Math Portfolio
Gold medal heights
Aim:
The aim of this task is to consider the winning height for the men’s high jump in the Olympic Games.
Introduction:
The Olympic Games which are held in every four years have an event called Men’s High Jump and usually an athlete tries to jump over a bar which is set up in a certain range from1 meter to 3 meters. The table 1 shows the record of the gold medalists during the Olympic Games held during 1932 to 1980. Note: The Olympic Games were not held in 1940 and 1944.
Table 1
Year | 1932 | 1936 | 1948 | 1952 | 1956 | 1960 | 1964 | 1968 | 1972 | 1976 | 1980 |
Height(cm) | 197 | 203 | 198 | 204 | 212 | 216 | 218 | 224 | 223 | 225 | 236 |
Variables:
Independent Variables:
The heights that are achieved by the gold medalists
Dependent Variables:
The years of Olympic Games
Figure 1:
From the figure 1, the independent variables are the x axis which shows the years of the Olympic Games, and y axis is the dependent variables which represents the heights that are achieved by the gold medalists. Also it shows that it is not constant.
Linear Regression
To create a certain equation, you draw the best fit line on the graph.
The difference between the red graph and the linear function is that the red does not have a predictable pattern. When the best fit is drawn it is possible to find the equation of this graph. Though the equation that is made by...

...Winning Heights in the Men’s Olympic High Jumps
Introduction:
The Olympics are an international sporting event that is held every four years where people from around the world send their best athletes to compete and see who the best of the best is when it comes to sports. The Olympics date back to Ancient Greece where their basic events included track and field, which are like men’s high jump which is the topic of this report. In this problem we are looking at the data collected from the gold medalists in the men’s high jump in from the years 1932-1980, excluding the years 1940 and 1944 where the Olympics were not held due to World War II.
Below is the data for the gold medalists in the men’s high jump from the years 1932-1980 (again excluding 1940 and 1944).
Year | 1932 | 1936 | 1948 | 1952 | 1956 | 1960 | 1964 | 1968 | 1972 | 1976 | 198 |
Height (cm) | 197 | 203 | 198 | 204 | 212 | 216 | 218 | 224 | 223 | 225 | 236 |
Data:
The problem asks for the points in the table to be plotted and I chose to put them into a scatter plot because that is the most logical way of graphing the data shown in the table above. Because the data is not continuous you would not make a line graph.
The graph is shown below:
The graph shows that the data collected is for the most part an upward trend. You can tell this because most of the data goes up in a positive trend the majority of the time.
The problem asks for a function to describe the way that the graph moves up,...

...IB Mathematics SL Year 1
Welcome to IB Mathematics. This two-year course is designed for students who have a strong foundation in basic mathematical concepts. The topics covered in this course include:
* Algebra
* Functions
* Equations
* Circular functions
* Trigonometry
* Vectors
* Statistics
* Probability
* Calculus
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Resources:
* Textbook: Mathematics SL 3rd edition. Haese Mathematics 2012
ISBN: 978-1-921972-08-9
* Edmodo: A virtual learning website where students can get homework assignments, ask homework questions, access class documents, and communicate with peers. https://iam.edmodo.com/
* Class code: ybu2s4
* Quest: Virtual learning website where students will complete graded homework assignments. https://quest.cns.utexas.edu/
* Graphing Calculator. Recommended for this course and all subsequent math courses. The Ti-Nspire or Ti-84 plus silver edition are both good choices. http://education.ti.com
* Khan Academy: http://www.khanacademy.org. Will be used to provide students with alternative resources.
* Geometer’s Sketchpad: Graphing software. Will be installed on student computers. http://www.dynamicgeometry.com/
* Additional print, online resources and worksheets may be used.
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Assignments:
There will be several types of...