COMPUTER ALGEBRA SYSTEMS - TECHNOLOGY IN MATHEMATICS EDUCATION

IB HIGHER LEVEL MATHEMATICS Portfolio

IB portfolio:

Website of International Baccalaureate: www.ibo.org

Part 1:

Given the function y = x². Consider the region from x = 0 to x = 1 and the x-axis. Label this area B. Label the region from y = 0 to y = 1 and the y-axis area A.

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Part 3:

Can you prove your conjecture(s) for the general case from x = a to x = b such that a < b and

the regions are defined as:

Area A: y = xⁿ, y = aⁿ, y = bⁿ and the y-axis

Area B: y = xⁿ, x = a, x = b and the x-axis

Part 4:

Investigate the areas of the volumes of revolution formed by rotating region A about the y-axis and region B about the x-axis. Is there a relationship between these volumes? Can you state a conjecture and prove it.

The ideas here are based on an article written by Michael Meagher for

the Derive User Group Journal. Michael is currently finishing his doctoral

degree in Mathematics Education at Ohio State University.

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alternative assessment

External Examinations

Final Internal Examinations

- Advanced Placement Calculus

- International Baccalaureate