IBDP Mathematics Applications & Interpretations SL Chapter 5 Notes
Modelling constant rate of change: linear functions
STUDY NOTES FOR MATHEMATICS – CHAPTER 5 – Modelling constant rate of change: linear functions
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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.
In this chapter, we explore what it really means for the relationships between two variables to be called a function. We will then explore properties of functions which will help us work with and understand them. A relation between variables x and y is any set of points in the (x,y) plane. We say that the points connect the two variables. The chapter later on discusses what a domain and range of a function is and how to calculate them. The domain of a relation is the set of values which the variable on the horizontal axis can take. The variable is usually x. The range of a relation is the set of values which the variable on the vertical axis can take. The variable is usually y. The domain and range of relation can be described using set notation, interval notation, or a number line graph. We then graph functions to model real world situations. We also learn about arithmetic sequences. A sequence is a list of numbers that is written in a defined order, ascending or descending, following a specific rule. It can also be defined as a function whose domain is the set of positive integers. Ex. (1,2,6,8…), (1,4,9,16).
- Chapter 1 Measuring space: accuracy and 2D geometry
- Chapter 2 Representing space : non right angled trigonometry and volumes
- Chapter 3 Representing and describing data: descriptive statistics
- Chapter 4 Dividing up space : coordinate geometry , lines , Voronoi diagrams
- Chapter 5 Modelling constant rate of change: linear function
- Chapter 6 Modelling relationships: linear correlation of bivariate data
- Chapter 7 Quantifying uncertainty: probability, binomial and normal distributions
- Chapter 8 – Testing for validity: Spearman’s hypothesis testing and x^2 test for independence
- Chapter 9 Modelling relationships with functions: power f unctions
- Chapter 10 Modelling Rates of change: Exponential and logarithmic functions
- Chapter 11 Modelling Periodic Phenomena: Trigonometric Functions
- Chapter 12 Analyzing Rates of Change: Differential Calculus
- Chapter 13 Approximating Irregular Spaces: Integration