12.M.TMS.RN Number and Quantity - The Real Number System
12. Extend the properties of exponents to rational exponents.
12.M.TMS.RN.1 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.
12.M.TMS.APR Algebra - Arithmetic with Polynomials & Rational Expressions
12. Perform arithmetic operations on polynomials
12.M.TMS.APR.1 Understand 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.
12.M.TMS.APR.3 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
12.M.TMS.APR.4 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
12. Create equations that describe numbers or relationships
12.M.TMS.ACE.1 create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
12.M.TMS.REI.3 solve quadratic equations in one variable. 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. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
12. Represent and solve equations and inequalities graphically
12.M.TMS.REI.5 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, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
12. Understand the concept of a function and use function notation
12.M.TMS.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
12. Interpret functions that arise in applications in terms of the context
12.M.TMS.IF.3 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.
12.M.TMS.BF.2.d Produce an invertible function from a non-invertible function by restricting the domain.
12. Trigonometric Functions
12.M.TMS.BF.3 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.
12. Apply geometric concepts in modeling situations
12.M.TMS.MG.1 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
12.M.TMS.SPI Statistics and Probability - Interpreting Categorical & Quantitative Data
12. Summarize, represent, and interpret data on two categorical and quantitative variables
12.M.TMS.SPI.1 represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Interpret linear models