Note: The Olympic Games were not held in 1940 and 1944.

Using technology, plot the data points on a graph. Define all variables used and state any parameters clearly. Discuss any possible constraints of the task.

What type of function models the behavior of the graph? Explain why you chose this function. Analytically create an equation to model the data in the above table.

On a new set of axes, draw your model function and the original graph. Comment on any differences. Discuss the limitations of your model. Refine your model if necessary.

Use technology to find another function that models the data. On a new set of axes, draw both your model functions. Comment on any differences.

Had the Games been held in 1940 and 1944, estimate what the winning heights would have been and justify your answers.

Use your model(s) to predict the winning height in 1984 and 2016. Comment on your answers.

The following table gives the winning heights for all the other Olympic Games since 1896.

...Lacsap’s Fractions
IBMathSL
Internal Assessment Paper 1
Lacsap’s Fractions
Lacsap is Pascal spelled backward. Therefore, Pascal’s Triangle can be used practically especially with this diagram.
(Diagram 1)
This diagram is of Pascal’s Triangle and shows the relationship of the row number, n, and the diagonal columns, r. This is evident in Lacsap’s Fractions as well, and can be used to help understand some of the following...

...MathSL 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...

...Alma Guadalupe Luna
MathIA (SL TYPE1)
Circles
Circles
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...

...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...

...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...

...Lacsap’s Fractions
Laurie Scott
SLMath Internal Assessment
Mr. Winningham
9/5/12
Instructions: In this task you will consider a set of numbers that are presented in a symmetrical pattern.
Pascal’s Triangle
|n=0 |1 |
|1 |0 |
|2 |3 |
|3 |6...

...and numerator) must be compared. To find this equation, the relationship between the row number and numerator must be found, put it graph form, and the equation for the graph will be the equation needed.
Row Number, n | Numerator, N |
1 | 1 |
2 | 3 |
3 | 6 |
4 | 10 |
5 | 15 |
Numerator
Numerator
Row Number
Row Number
The equation for the numerator can be derived by using quadratic regression on a graphing calculator. The...

...SLTYPE 1-LACSAP’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...

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