Mathematics AA HL IA Samples
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Comparative study on dimensions of cuboidal and cylindrical blocks placed inside a sphere
Exploring the mathematical and economic aspects of showpiece creation, this assessment dives into various factors like materials and manufacturing processes, seeking to understand and perhaps optimize them within the context of aesthetic and market value.
Comparing the suitability of Encryption algorithm using Iterative procedure in Discrete Mathematics
An exploration into cybersecurity and ethical hacking, this study embarks on understanding and resolving personal website data leak issues by navigating through the intricate world of data encryption and website certification for secure data transmission.
Investigating optimized dimensions for cylindrical packages in a manner such that containers’ environmental costs do not outweigh their aesthetic value
Exploring the optimal dimensions of cylindrical packaging, this research balances minimizing production and environmental costs with maintaining aesthetic appeal, using mathematical investigation and considering real-world applications with Pepsi Co. examples.
Importance of angle of release on a 3-point shot in basketball
Using projectile motion concepts, this study determines the optimal release angle for a successful 3-point basketball shot, assumes a throw velocity, and analyzes how release angle uncertainties affect shot success percentages for various player heights.
Determining the processing speed of a Rice Cooker by the investigation of the transfer function (output response with respect to input response) of a Rice Cooker obtained in two different methods (Integrating Factor Method and Laplace’s Method).
Emphasizing the synergy between theory and application, this study journeys through the student's intrinsic curiosity and mathematical upbringing to explore a topic beyond curriculum confines, illuminated by the pragmatic aspects of mathematical application.
Determination of shortest path using Dijkstra’s Algorithm and Kruskal’s Algorithm
Exploring shortest-path determination, this IA utilizes and compares Dijkstra's and Kruskal's Algorithms in weighted graph models derived from navigation data, aiming to discern efficiency and applicability in real-world routing and machine learning.
Investigation on the effect of angle of projection, wind current and air resistance in the game of javelin throw
Investigating the impact of projection angles on javelin throw distances, this study leverages motion equations to explore the interplay between initial velocity and angular trajectory, aiming to pinpoint the optimal angle for maximal throw range.
Investigation on N – queen’s problem using backtracking algorithm
Exploring chess through a mathematical lens, this study delves into the rich, strategic complexity of the ancient game, seeking to uncover and understand its inherent mathematical structures and combinations, intertwining strategy with numerical analysis.
Determination of optimized shape of Skyscrapers considering the cost of cleaning the outer wall be minimum.
Exploring the economic implications of skyscraper maintenance, this study delves into minimizing external cleaning costs via architectural optimization, navigating the interplay between structural design and its consequent financial burden post-construction.
Derivation of nth term of fibonacci series using the first two terms
Inspired by a family background in mathematics and computing, this exploration intertwines the student's personal journey with a mathematical investigation, initiating a deeper dive into numerical sequences and computational applications in mathematics.
Optimization of soft-beverage bottle such that it occupies maximum volume but incurs minimum manufacturing cost.
Blending personal interest and calculus, this study explores optimizing bottle design for minimal manufacturing cost and maximal volume, intertwining practical industry applications, particularly within the soft-beverage sector, with theoretical mathematics.