Students apply and explain the method of mathematical induction to prove formulas and statements. Students perform operations with vectors in the coordinate plane and solve practical problems using vectors. 2.1 add, subtract, find scalar products, dot products, and norms of vectors noting the field properties which apply 2.2 determine, interpret, and use a unit directional vector, perpendicular components, and norms to express vectors in the coordinate plane 2.3 graph and interpret complex numbers as vectors and in polar form Measurement and Geometry 1. Students understand and use periodic functions and trigonometric relationships. 1.1 use similarity, right triangles, the Law of Sines, and the Law of Cosines to determine measurements of objects which are difficult to measure directly 2.
Students use vectors to represent and answer questions about quantities.
2.1 draw a system of vectors and find the resultant graphically 2.2 identify, create, and solve practical problems using a system of vectors and their horizontal and vertical components Functions 1. Students investigate, identify the characteristics of, and graph polynomial and rational functions. Students perform operations on functions and determine the domain and range of the results. 2.1 determine the composition of two or more functions and the composition of a function with itself and determine the domain and range of the resultant function 2.2 determine the inverse of a function given as an equation, a graph, or a set of ordered pairs, determine its domain and range and discuss the relationships among these representations 3. Students analyze and explain the reasons behind the effect changing coefficients, exponents, and other parameters has on functions and their graphs.