12.PC30.1.g Develop, explain, and apply strategies for determining the general form for all angles that are coterminal to a given angle (in degrees and radians).
12.PC30.1.h Explain the relationship between the radian measure of an angle in standard position and the length of the arc cut on a circle of radius r, and solve situational questions based on that relationship.
12.PC30.2.f Develop, generalize, explain, and apply strategies, including using the unit circle or a reference triangle, for determining the exact trigonometric ratios for angles whose measures are multiples of 0°, 30°, 45°, 60°, 90° (when expressed in degrees), 0, π/6, π/4, π/3, or π/2 (when expressed in radians).
12.PC30.2.g Explain and apply strategies (with or without the use of technology) to determine the measures, in degrees or radians, of the angles in a specified domain that have a particular trigonometric ratio value.
12.PC30.2.h Explain and apply strategies to determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain.
12.PC30.2.i Sketch a diagram to represent the context of a problem that involves trigonometric ratios.
12.PC30.2.j Solve situational questions using trigonometric ratios.
12.PC30.3.c Develop, generalize, and explain strategies for determining the transformational impact of changing the coefficients a, b, c, and d in y = asinb(x - c)+ d and y = a cosb (x - c) + d on the graph of y = sinx and y = cosx respectively, including amplitude, asymptotes, domain, period, phase shift, range, and zeros.
12.PC30.3.d Develop and apply strategies to sketch, without technology, graphs of the form y = asinb (x - c) + d or y = a cosb (x - c) + d.
12.PC30.3.e Write equations for given graphs of sine or cosine functions.
12.PC30.7 Extend understanding of transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, and horizontal and vertical stretches.
12.PC30.7.a Compare and analyze various graphs of transformations of the function y = f(x), and generalize about the effect of the placement of different coefficients on the original graph of y = f(x).
12.PC30.7.b Develop, generalize, explain, and apply strategies for sketching transformations of the graph of y = f(x) to give the graph of y - k = af(b(x - h)).
12.PC30.7.c Write the equation of a function that has undergone specified vertical translations, horizontal translations, vertical stretches, and/ or horizontal translations of the function y = f(x) for which the equation is given.
12.PC30.8.a Generalize and apply the relationship between the coordinates of an ordered pair and the coordinates of the corresponding ordered pair that results from a reflection through the x-axis, the y-axis, or the line y = x.
12.PC30.8.b Develop and apply strategies for sketching the reflection of a function y = f(x) through the x-axis, the y-axis, or the line y = x when the graph of f(x) is given but the equation is not.
12.PC30.8.c Develop and apply strategies for sketching the graphs of y = -f(x), y = f(-x), and x = -f(y) when the graph of f(x) is given and the equation is not.
12.PC30.8.d Develop and apply strategies for writing the equation of a function that is the reflection of the function f(x) through the x-axis, y-axis, or line y = x.
12.PC30.9.m Solve situational questions involving logarithmic scales, such as the Richter scale and pH scale.
12.PC30.9.n Analyze graphs of exponential functions of the form y = a to the x power, a > 0 and report about the relationships between the value of a and the domain, range, horizontal asymptote, and intercepts.
12.PC30.10.e Generalize, through inductive reasoning, the relationship between the remainder when a polynomial expression is divided by x-a, a∈I and the value of the polynomial expression at x = a (The Remainder Theorem).
12.PC30.10.f Explain and apply the factor theorem to express a polynomial expression as a product of factors.
12.PC30.10.g Categorize, with justification, a set of functions into polynomial functions and non-polynomial functions.
12.PC30.10.h Analyze graphs of polynomial functions to determine the impact of changing the values of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.
12.PC30.11.i Match a set of equations for rational and radical functions to their corresponding graphs.
12.PC30.11.j Describe the relationship between the roots of a rational equation and the x-intercepts of the graph of the corresponding rational function.
12.PC30.11.k Determine graphically an approximate solution to a rational equation.
12.PC30.11.l Critique statements such as "Any value that makes the denominator of a rational function equal to zero will result in a vertical asymptote on the graph of the rational function".
12.PC30.12 Demonstrate understanding of permutations, including the fundamental counting principle.
12.PC30.12.a Develop and apply strategies, such as lists or tree diagrams, to determine the total number of choices or arrangements possible in a situation.
12.PC30.12.b Explain why the total number of possible choices is found by multiplying rather than adding the number of ways that individual choices can be made.
12.PC30.12.c Provide examples of situations relevant to self, family, and community where the fundamental counting principle can be applied to determine the number of possible choices or arrangements.
12.PC30.12.d Create and solve situational questions that involve the application of the fundamental counting principle.
12.PC30.12.e Count, using graphic organizers, the number of ways to arrange the elements of a set in a row.
12.PC30.12.f Develop, generalize, explain, and apply strategies, including the use of factorial notation, to determine the number of permutations possible if n different elements are taken n or r at a time.