Mathematical Modelling
Mathematical Modelling
In 1988, Natalya Lisovskaya (of the USSR) won the gold medal for the shot putt at the Olympics Games.
The height of the shot putt from the ground level, relative to the horizontal distance it travelled from the point where it left Natalya’s hand was recorded and tabulated.
(a) Plot these points on a set of axes
(b) (i) What type of curve would nest model this situation?
(ii) Determine the equation of such a curve
(c) (i) What is the maximum height reached by the shot putt
(ii) How far did Natalya throw the shot putt?
Ikast - Brande Gymnasium Pre-IB
Assignment 14
Group work: mathematical modelling
Due on Friday, May 23rd
Academic Integrity:
If you don’t complete this section, your assignment will not be marked. If you received
any help to complete this assignment you have to list it here. If you did not receive any
help, write “no help received”.
I received help from ... .
Instructions
In class you were given a problem to work with (if you need a new copy of your problem,
you can download it from Lectio, under “Dokumenter”, “Hold”, “Exploration”).
Your first goal is to solve the problem. Almost all the problems involve modelling using
quadratic equations, and you may want to use GeoGebra either to solve the problem or
to check your solution.
After you solve the problem, you need to write your solution so that someone (for
instance, a classmate from a di?erent group) not knowing neither the problem nor the
solution can understand them.
This step is optional. If you are done solving the problem, writing it down and editing
what you wrote down, you can propose one more question related to the problem and
answer it.
For example, we saw the following problem in class:
Florence purchased a number of hand-held games for $180. She decided
to keep one and sell the rest. She sells the remaining games for $1 more
than she bought them for. After keeping one game for herself, she made a
profit of $10. How many games did she purchase?
Some examples of further questions are the following:
• If she wishes to make a profit of $15, how many games should she purchase to
re-sell?
• She wishes to make a profit of $15 but can’t invest more than $300. Can she sell
the games for $1 more than she bought them? or does she need to set a new
price?
• She is planning to buy new games and sell all of them for $2 more than the original
price. She can loan money from a friend to buy as many games as she want. Her
goal is to make a profit of $50. How much does she need to loan from her friend?
Important! Your final work must be submitted as a pdf file via Lectio.