PC.PCN.2 Understand and use complex numbers, including real and imaginary numbers, on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number.
PC.PCN.4 State, prove, and use DeMoivre's Theorem.
PC.F.1 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
PC.F.2 Find linear models by using median fit and least squares regression methods. Decide which among several linear models gives a better fit. Interpret the slope and intercept in terms of the original context.
PC.F.4 Determine if a graph or table has an inverse, and justify if the inverse is a function, relation, or neither. Identify the values of an inverse function/relation from a graph or a table, given that the function has an inverse. Derive the inverse equation from the values of the inverse.
PC.F.5 Produce an invertible function from a non-invertible function by restricting the domain.
PC.F.6 Describe the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative). Find the value of k given the graph f(x) and the graph of f(x) + k, k f(x), f(kx), or f(x + k). Experiment with cases and illustrate an explanation of the effects on the graph using technology. Recognize even and odd functions from their graphs and algebraic expressions.
PC.F.7 Decide if a function is continuous at a point. Find the types of discontinuities of a function and relate them to finding limits of a function. Use the concept of limits to describe discontinuity and end-behavior of the function.
PC.F.8 Define arithmetic and geometric sequences recursively. Use a variety of recursion equations to describe a function. Model and solve word problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable.
PC.F.9 Use iteration and recursion as tools to represent, analyze, and solve problems involving sequential change.
PC.F.10 Describe the concept of the limit of a sequence and a limit of a function. Decide whether simple sequences converge or diverge. Recognize an infinite series as the limit of a sequence of partial sums.
PC.QPR Quadratic, Polynomial, and Rational Equations and Functions
PC.QPR.1 Use the method of completing the square to transform any quadratic equation into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
PC.EL.3 Graph and solve real-world and other mathematical problems that can be modeled using exponential and logarithmic equations and inequalities; interpret the solution and determine whether it is reasonable.
PC.EL.4 Use technology to find a quadratic, exponential, logarithmic, or power function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient.
PC.PE Parametric Equations
PC.PE.1 Convert between a pair of parametric equations and an equation in x and y. Model and solve problems using parametric equations.
PC.PE.2 Analyze planar curves, including those given in parametric form.