CCSS.Math.Content.HSN-RN.A Extend the properties of exponents to rational exponents
CCSS.Math.Content.HSN-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.
CCSS.Math.Content.HSA-APR Arithmetic with Polynomials and Rational Expressions
CCSS.Math.Content.HSA-APR.A Perform arithmetic operations on polynomials
CCSS.Math.Content.HSA-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.
CCSS.Math.Content.HSA-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
CCSS.Math.Content.HSA-REI Reasoning with Equations and Inequalities
CCSS.Math.Content.HSA-REI.A Understand solving equations as a process of reasoning and explain the reasoning
CCSS.Math.Content.HSA-REI.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.
CCSS.Math.Content.HSA-REI.B Solve equations and inequalities in one variable
CCSS.Math.Content.HSA-REI.4 Solve quadratic equations in one variable.
CCSS.Math.Content.HSA-REI.4a 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.
CCSS.Math.Content.HSA-REI.4b 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.
CCSS.Math.Content.HSF-IF.A Interpret functions that arise in applications in terms of the context
CCSS.Math.Content.HSF-IF.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.
CCSS.Math.Content.HSF-IF.5 For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
CCSS.Math.Content.HSF-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
CCSS.Math.Content.HSF-IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
CCSS.Math.Content.HSF-BF.B Build new functions from existing functions
CCSS.Math.Content.HSF-BF.3 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.
CCSS.Math.Content.HSG-SRT.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.
CCSS.Math.Content.HSS-CP Conditional Probability and the Rules of Probability
CCSS.Math.Content.HSS-CP.A Understand independence and conditional probability and use them to interpret data
CCSS.Math.Content.HSS-CP.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").
CCSS.Math.Content.HSS-CP.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.
CCSS.Math.Content.HSS-CP.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.
CCSS.Math.Content.HSS-CP.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.