M2.N.RN.A Extend the properties of exponents to rational exponents.
M2.N.RN.A.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.
M2.A.APR Arithmetic with Polynomials and Rational Expressions
M2.A.APR.A Perform arithmetic operations on polynomials.
M2.A.APR.A.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.
M2.A.REI Reasoning with Equations and Inequalities
M2.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
M2.A.REI.A.1 Explain each step in solving an 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.
M2.A.REI.B Solve equations and inequalities in one variable.
M2.A.REI.B.2 Solve quadratic equations and inequalities in one variable.
M2.A.REI.B.2.a Use the method of completing the square to rewrite 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.
M2.A.REI.B.2.b Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying 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.
M2.F.IF.A Interpret functions that arise in applications in terms of the context.
M2.F.IF.A.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.
M2.F.BF.B Build new functions from existing functions.
M2.F.BF.B.2 Identify 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 graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
M2.G.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; 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.
M2.S.ID Interpreting Categorical and Quantitative Data
M2.S.ID.A Summarize, represent, and interpret data on two categorical and quantitative variables.
M2.S.ID.A.1 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
M2.S.ID.A.1.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
M2.S.CP Conditional Probability and the Rules of Probability
M2.S.CP.A Understand independence and conditional probability and use them to interpret data.
M2.S.CP.A.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").
M2.S.CP.A.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.
M2.S.CP.A.3 Know and 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.