This Problem-solving and modelling task is to design a profile of a roller coaster and calculate its excitement factor. To come up with the design, a minimum of 3 types of functions including polynomial, trigonometric, exponential and logarithmic are used to generate the model. The excitement factor depends on the angle of steepest descent in each drop and the total vertical distance of the top. Both technological and mathematical procedures are used to design the profile, including simultaneous equation solving, calculus and trigonometry, and technology, for example Excel, graphic calculator and Desmos. The report also includes evaluation and recommendations to further discuss the strength and limitation of the model.