IB Mathematics AI SL Modelling MAI Study Notes - New Syllabus

 The Modelling Process

Mathematical modelling involves the following steps:

1. Identifying the Problem
Understand the real-world situation to be modelled.

2. Making Assumptions and Defining Variables
Simplify the problem by making reasonable assumptions and define variables clearly.

3. Formulating the Model
Develop mathematical relationships (equations or functions) that represent the situation.

4. Solving the Model
Use appropriate mathematical methods to find solutions.

5. Interpreting the Solution
Translate mathematical results back into the context of the original problem.

6. Validating the Model
Compare model predictions with real data to assess accuracy.

7. Refining the Model
Adjust the model as necessary to improve its fit or applicability.

Types of Models
Common functions used in modelling include:

 Linear Models: Represent constant rate of change.
Quadratic Models: Model situations with acceleration or deceleration.
Exponential Models: Describe rapid growth or decay processes.
Trigonometric Models: Used for periodic phenomena.

Selecting the appropriate model depends on the nature of the data and the context of the problem.

Using Technology
Graphing calculators or software can assist in:

Plotting data points
Fitting curves to data
Calculating regression equations
Visualizing the model’s behavior

Technology aids in refining models and assessing their fit to real-world data.

 Evaluating Models
When assessing a model:

Appropriateness: Does the model suit the context?
 Accuracy: How well does the model fit the data?
Limitations: What are the constraints or assumptions of the model?
Predictive Power: Can the model reliably predict future outcomes?