- Level: International Baccalaureate
- Subject: Maths
- Word count: 700
IB Math Portfolio Investigating Ratios
Extracts from this document...
Introduction
Investigating Ratios of Areas and Volumes
The aim of this portfolio is to investigate the ratio of areas form when is graphed between two arbitrary parameters and such that .
- Given the function, consider the region formed by this function from to and the x-axis. This area is labeled B. The region from and and the y-axis is labeled A.
Finding the ratio of area A: area B:
The ratio of area A: area B is 2:1.
Calculate the ratio of the areas for other functions of the type , between and .
Let ,
Finding the ratio of area A: area B:
The ratio of area A: area B is 3:1.
Let ,
Finding the ratio of area A: area B:
The ratio of area A: area B is 4:1.
Let ,
Finding the ratio of area A: area B:
Middle
The conjecture is not true to negative integers.
Irrational Numbers:
Let ,
Finding the ratio of area A: area B:
The ratio of area A: area B is :1. This means the conjecture is true to irrational values of n.
- This conjecture is further tested for areas not only limited between and .
, for region formed by this function from to and the x-axis. This area is labeled B. The region from and and the y-axis is labeled A.
Finding the ratio of area A: area B:
The ratio of area A: area B is 2:1.
, for region formed by this function from to and the x-axis. This area is labeled B. The region from and and the y-axis is labeled A.
Finding the ratio of area A: area B:
Conclusion
Then take into account the function , and the region formed by this function from to and the x-axis (Area A). To find the area formed on the y-axis (Area B), substitute and values as 1 and 2, into the equations and , making and .
Calculating the ratios of areas A:B:
The ratio of area A: area B is 4:1.
Next take into account the function , and the region formed by this function from to and the x-axis (Area A). To find the area formed on the y-axis (Area B), substitute and values as 1 and 2, into the equations and , making and .
Calculating the ratios of areas A:B:
The ratio of area A: area B is 3:1.
From the above three trials we can successfully conclude that my conjecture is true for the general case from and and for the regions stated.
To further support the conjecture:
This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.
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