MPM 2D - Grade 10 Academic Mathematics - Culminating 2020 NAME: Section Detail Sheet Section A ~ line Slope Calculation y - intercept Calculation Coordinate Points: Length Calculation Equation of Line A: Section B ~ line Slope Calculation y - intercept Calculation Coordinate Points: Length Calculation Equation of Line B: Find the Point of Intersection of Section A and Section B Line Equations: Use SUBSTITUTION or ELIMINATION Point of Intersection: (MPM 2D Grade 10 Academic Mathematics - Culminating 2020 NAME: Culminating Task: Rollercoaster Canada's Wonderland, an amusement park in Toronto, has asked you to design a new rollercoaster for their park. They are asking you to sketch a 20 {Modimensional} path of a rollercoaster that will show the relation between the distance travelled in metres, and the height of the rollercoaster in metres. The park has the following conditions that must be met: 1. The path of the rollercoaster must be made up of 8 distinct sections or pieces that are joined together at EXACT points. {can't have gaps} A. Section A must be linear B. Section B must be linear C. Section (3 must be a Quadratic that opens down D. Section D must be a Quadratic that opens up E. Section E must be linear F. Section F must be a circle or a part of a circle. G. Section G and H are your choice Quadratics. 2. The rollercoaster must start at a height of 10 meters. 3. The rollercoaster must nish at a height of 2 metres. 4 The total length of the path must be between 300 400 metres. In order to input the design into the computerr all sections need to have proper equations and lengths. Quadratic sections will not need the exact lengths and could be estimated, as long as, the length you come up with is reasonable and justied. The engineers at Canada's Wonderland want to see how you have come up with your equations for each section, so please show your organized work. The engineers would like quadratic equations to be in ALL forms, and linear equations in the y=mx+b form. The calculations of the lengths of each sections should also be shown. Your work will be assessed using a rubric. It is a good idea to read that rubric first in order to know what it is that you are being marked on. Practice graph paper for sketches is provided. You will submit the following by Friday, June 12mr 2D2U at 3pm: 1] Hand Drawn Graph ofthe rollercoaster's path with axis and sections labelled clearly. 2] Desmos Screenshot of your rollercoaster path with the equations clearly visible. 3} Section Detail Sheet completed by hand. 4} Rubric with your Name on the top. MPM 2D - Grade 10 Academic Mathematics - Culminating 2020 NAME: Section E ~ Line Length Calculation Equation of Line E: Section F ~ Circle Equation of Circle F: Length Calculation (Circumference) Radius of your Circle: Section G ~ Quadratic Length Estimation Equation of Section G in Vertex From: Section H ~ Quadratic Length Estimation Equation of Section H in Vertex From:MPM 2D - Grade 10 Academic Mathematics - Culminating 2020 NAME: Section C ~ Quadratic Opening Down "a" Value Calculation Coordinate(s) Points Used: Equation of Section C in Vertex From: Length Estimation Equation of Section C in Factored From: Equation of Section C in Standard From: Section D ~ Quadratic Opening Up "a" Value Calculation Coordinate(s) Points Used: Equation of Section D in Vertex From: Length Estimation Equation of Section D in Factored From: Equation of Section D in Standard From: Converting Forms: Show your work going from your equation in STANDARD FORM for Section D to VERTEX FORM