2020 May Mathematics HL Extended Essay – Grade A (28/34)

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2020 May Examination에서 A를 받은 Extended Essay입니다. Math 과목에 대해 작성하였고 주제는 ““What is the simplest pathway that a roller coaster must travel between two distinct points, taking into account the forces of friction and gravity, in order that the time taken be a minimum?” 입니다.






The roller coaster is originated in Russia from ice sliding in 1400s. People constructed hills, made from snow and ice, wooden stairways to reach the top of the hill and enjoy the ride. In
1700s, some people come up with an idea to construct wooden hills as a means of promoting people’s ride. (Cartmell, Robert, 1987) This leads to the construction of the first modern roller coaster, called the Promenades Aériennes. Later, it was adopted by Russian soldiers who conquered France in 1817. This roller coaster is referred as to the first complete roller coaster.

The modern appearance of roller coaster was revealed to the public in 1886, when Phillip Hinkle invented the first roller coaster with a lift hill. (Steven J. Urbanowicz, 2002). After his
invention, riding the roller coaster become a part of leisure activities in the amusement park. People nowadays ride more dynamic roller coasters, resulting from the development of the
safety equipment. Roller coasters can now keep contact with rails consistently throughout the ride, thanks to the invention of ‘underfriction wheel’. Underfriction wheel is a type of rail that makes sure that the roller coaster keeps contact with the rail. (Encyclopædia Britannica).




1. Describing the situation
The main aim of roller coaster makers is to provide the highest speed on the first slope of roller coaster, which is the highlight of the overall journey. This is because people ride roller
coasters to gain positive feelings from the combination of conquering fear and a rise in psychological arousal, originated from the high speed of the roller coaster on the first slope (Stephens, Richard, 28 Dec. 2018). To increase the speed of the roller coaster, the slope of roller coasters becomes steeper and steeper over time and now top 10 roller coasters in the world reaches the height approximately between 300 feet (91.44m) and 400 feet (122 m). (Statista, 2018)…


  • 총 페이지수: 26 pages
  • 과목명: Extended Essay (Mathematics)
  • 주제: The exploration of how to construct the route of the roller coasters
  • The file is in PDF format. 
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2020 May Mathematics HL Extended Essay – Grade A (28/34)

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