IBDP Mathematics Applications & Interpretations HL Chapter 2 Notes
STUDY NOTES FOR MATHEMATICS – CHAPTER 2 – 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. Finally, we graph functions to model real world situations.
We look at how an object point is moved to an image point by using matrices; these are called linear transformations, which include stretches, rotations, reflections and any composition of these. Affine transformations include translation, as well. In translation, a translation vector provides the x and y components of the translation, where every point on the object moves the same distance in the same direction. Rotations about the origin through an arbitrary angle theta will be discussed to find the transformation matrix of the rotation. Stretches will look at both horizontal and vertical with scale factors of k, where the image formed is k times the distance from the y-axis. In enlargements, the scale factor k used for the enlarged image and the transformation matrix will be looked at. Composite transformations are when we apply one transformation after another.
- 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