9-12.1.1 The complex number system includes real numbers and imaginary numbers
9-12.1.1.a Extend the properties of exponents to rational exponents.
9-12.1.1.a.i Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
9-12.1.2.a.iv Describe factors affecting take-home pay and calculate the impact
9-12.1.2.a.v Design and use a budget, including income (net take-home pay) and expenses (mortgage, car loans, and living expenses) to demonstrate how living within your means is essential for a secure financial future
9-12.2 Patterns, Functions, and Algebraic Structures
9-12.2.1 Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables
9-12.2.1.a Formulate the concept of a function and use function notation.
9-12.2.1.a.i Explain that a function is a correspondence from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.
9-12.2.1.b Interpret functions that arise in applications in terms of the context
9-12.2.1.b.i 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.
9-12.2.1.f.ii Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
9-12.2.2.a.iii Use graphs and tables to describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
9-12.2.2.a.iv For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
9-12.2.3.c Perform arithmetic operations on polynomials
9-12.2.3.c.i Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
9-12.2.4.b Understand solving equations as a process of reasoning and explain the reasoning
9-12.2.4.b.i Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.
9-12.2.4.c.ii Solve quadratic equations in one variable.
9-12.2.4.c.ii.1 Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
9-12.2.4.e.ii Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately.
9-12.2.4.e.iii Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
9-12.3.1.a.iv Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages and identify data sets for which such a procedure is not appropriate.
9-12.3.1.a.v Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
9-12.3.1.b Summarize, represent, and interpret data on two categorical and quantitative variables
9-12.3.1.b.i Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
9-12.3.1.b.ii Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
9-12.3.1.b.ii.1 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
9-12.3.1.b.ii.2 Informally assess the fit of a function by plotting and analyzing residuals.
9-12.3.3.a.ii Explain that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
9-12.3.3.a.iii Using the conditional probability of A given B as P(A and B)/P(B), interpret the independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
9-12.3.3.a.iv Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
9-12.3.3.c Analyze the cost of insurance as a method to offset the risk of a situation
9-12.4 Shape, Dimension, and Geometric Relationships
9-12.4.1 Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically
9-12.4.1.a Experiment with transformations in the plane
9-12.4.1.a.i State precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
9-12.4.1.b.ii Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
9-12.4.1.b.iii Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
9-12.4.2.a.iii Explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
9-12.4.2.f Find arc lengths and areas of sectors of circles.
9-12.4.2.f.i Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality.