IBDP Mathematics Applications & Interpretations HL Chapter 8 Notes
modelling real life phenomena
STUDY NOTES FOR MATHEMATICS – CHAPTER 8 – MODELLING REAL LIFE PHENOMENA
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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.
This chapter explains how we can apply mathematics to real-world problems to help us understand the world better. A mathematical model is a simplified description of a real system using mathematical concepts and language. The process of developing this model is called mathematical modelling. The modelling cycle involves five steps. First, pose a real-world problem. Then develop a model which represents the problem with mathematics. Test the model by comparing its predictions with known data. Reflect and apply to the original problem and finally extend it. The second topic is linear models. This topic shows how two variables are linearly related if the graph connecting them is a single line. The third topic is a piecewise model. This involves dividing the domain into smaller subintervals, and building a function using a separate formula for each subinterval, rather than using one single formula as it can be insufficient. In the final topic, we solve for unknown parameters by substituting points from known data values to construct a system of equations. By solving these systems of equations, we obtain the parameters which complete the model.
We learn to model various types of functions such as quadratic, cubic and linear. In exponential functions you will learn to graph exponential equations on a graphing calculator, you will learn about asymptotes and investigating slopes. Growth and Decay will look at situations where quantities are either increasing or decreasing exponentially. You will also come to understand that logarithmic functions are used for graphing.
- Chapter 1 Basic Geometry and Mathematics
- Chapter 2 Functions
- Chapter 3 Sequences and Series
- Chapter 4 Geometry and Trigonometry
- Chapter 5 Complex Number
- Chapter 6 Matrix Algebra
- Chapter 7 Vectors
- Chapter 8 Probability
- Chapter 9 Descriptive Statistics
- Chapter 10 Probability
- Chapter 11 Differential Calculus
- Chapter 12 Probability Distribution
- Chapter 13 Integral Calculus
- Chapter 14 Testing For Validity
- Chapter 15 Graph Theory