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Math Portfolio Type II (HL)


charmainelee

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DESIGNING A FREIGHT ELEVATOR

- In this activity, you will first explore a possible model for the motion of a heavy-duty freight elevator

used to raise and lower equipment and minerals in a mineshaft. You will evaluate the model for its

strengths and weaknesses and then create a set of specifications to develop a model of your own.

MODELLING THE HEIGHTS OF SAPLINGS

- The following data come from a random sample of 1000 saplings collected from a representative 0.25 km2 area in a forest. Your job is to find a way to use this random sample to develop a probability density function (pdf) to model the population of all such saplings in the area in which the sample was taken.

MODELLING PROBABILITIES IN GAMES OF TENNIS

- The purpose of this task is to analyze the relationship between certain probability distributions and the process of match play in tennis. We will construct a probability model first for two players of predictable abilities. We will also investigate two models of resolving ties.

MODELLING THE COURSE OF A VIRAL ILLNESS AND ITS TREATMENT

- When viral particles of a certain virus enter the human body, they replicate rapidly. In about four hours, the number of viral particles has doubled. The immune system does not respond until there are about 1 million viral particles in the body. The first response of the immune system is fever. The rise in temperature lowers the rate at which the viral particles replicate to 160 % every four hours, but the immune system can only eliminate these particular viral particles at the rate of about 50 000 viral particles per hour. Often people do not seek medical attention immediately as they think they have a common cold. If the number of viral particles, however, reaches 1012, the person dies.

Those are the "introductions" to each task. If you pick one you seem interesting I'll post the whole task. Each task will take a whole post so I can't just post all 4 of them in their entirety.

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