IBDP Mathematics Analysis & Approaches HL Chapter 1 Notes

Algebra and Function Basics

STUDY NOTES FOR MATHEMATICS – CHAPTER 1 – Algebra and Function Basics

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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 deals with the fundamental topics that form the basis of algebra and functions such as the equation of a line and finding the gradient and intercept. In the next topic, 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. Finally, we graph functions to model real world situations.