MATHEMATICAL MODELLING IN YOUR IB MATH IA
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Gather data and plot on a graph. Be sure to note if the data is discrete or continuous as
this may affect your axes.
Look at the pattern in points of the graph. What sort of curve do you think would best
fit? Think of all the types of functions we have learned in class. (Linear, polynomial,
rational, log, sinusoidal, etc.). If one type of functions best fits part of your data, but
other function fits better for a different part, consider a piecewise function.
This is an example of a BAD FIT of a model.
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This is an example of a GOOD FIT of a model.
Pick a general function and explain why you chose it.
Define the variables and describe what each of the parameters of the general function
does.
Solve for the parameters of your function. This is called your model. (See your teacher
if you need help in solving for the parameters!)
Graph your model on top of your data points and comment on the fit. Is the fit close, or
do you need to “tweak” any of the parameters to get a better fit?
Note: A Correlation Coefficient (r-value) is only used for linear models! If you use it for
non-linear data, this shows a lack of understanding of modelling and will result in a low
mark for criterion E.
Do not stop at just finding the model. Models are calculated for a reason!
Possible extension: Find the regression equation to match your model using technology.
How does it differ from your model? What might this mean in terms of the context of
your exploration? Which is a better predictor of the future? Why? Etc.
NOTE: If you only use technology to find a regression equation and do not find a model
analytically, you can score a max of 2 for criterion E.
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