IBDP Mathematics Applications & Interpretations SL Chapter 9 Notes

Modelling relationships with functions: power f unctions

STUDY NOTES FOR MATHEMATICS –Chapter 9 Modelling relationships with functions: power f unctions

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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.

A quadratic function is a relationship between two variables x and y which can be written in the form y= ax^2+bx+c. This forms the basis of this chapter. We then use the discriminant. b^2- 4ac, to determine the number of real roots of the equation. If we are given sufficient information on or about a graph, we can also determine the quadratic in whatever form required. We then learn problem solving in quadratics and optimization with quadratics. Lastly, the chapter deals with quadratic inequalities. This chapter also discusses the ways in which two variables can be related. Direct variation is when two variables are directly proportional as multiplying one of them by a number results in the other one being multiplied by the same number. However in many conditions, the variables we consider are not directly proportional, but there may be direction variation in their powers. This is dealt with in the second topic. Whereas two variables are inversely proportional, when one is multiplied by a constant, the other is divided by the same constant. The final topic under this chapter involves modelling direct and inverse variations. Variation models have equations in the form of y=ax^n. If n>0, we have direct variation. Contrarily, if n<0, we have inverse variation. We can also use technology to find variation models, which are also referred to as power models.