912.A-APR Arithmetic with Polynomials and Rational Expressions
912.A-APR.1 Perform arithmetic operations on polynomials
912.A-APR.1.1 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.
912.A-APR.4.6 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.
912.A-CED.1 Create equations that describe numbers or relationships
912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.
912.A-REI Reasoning with Equations and Inequalities
912.A-REI.1 Understand solving equations as a process of reasoning and explain the reasoning
912.A-REI.1.1 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. Construct a viable argument to justify a solution method.
912.A-REI.2 Solve equations and inequalities in one variable
912.A-REI.2.4 Solve quadratic equations in one variable.
912.A-REI.2.4.a 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.
912.A-REI.2.4.b 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.
912.A-REI.4 Represent and solve equations and inequalities graphically
912.A-REI.4.11 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.
912.F-BF.2 Build new functions from existing functions
912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
912.F-IF.2 Interpret functions that arise in applications in terms of the context
912.F-IF.2.4 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.
912.F-TF.1.2 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.
912.N-RN.1 Extend the properties of exponents to rational exponents.
912.N-RN.1.1 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.
912.S-CP Conditional Probability and the Rules of Probability
912.S-CP.1 Understand independence and conditional probability and use them to interpret data
912.S-CP.1.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
912.S-CP.1.2 Understand 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.
912.S-CP.1.3 Understand the conditional probability of a given b as p(a and b)/p(b), and interpret 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.
912.S-CP.1.4 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.
912.S-ID Interpreting Categorical and Quantitative Data
912.S-ID.1 Summarize, represent, and interpret data on a single count or measurement variable
912.S-ID.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.