Algebra II

Number and Quantity

Algebra

Functions

Statistics and Probability

The Real Number System

Quantities

Matrices

Seeing Structure in Expressions

Creating Equations

Reasoning with Equations and Inequalities

Interpreting Functions

Building Functions

Linear, Quadratic, and Exponential Models

Interpreting Categorical and Quantitative Data

Making Inferences and Justifying Conclusions

Conditional Probability and the Rules of Probability

Extend the properties of exponents to rational exponents.

Reason quantitatively and use units to understand problems.

Perform operations on matrices and use matrices in applications.

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Create equations that describe numbers or relationships.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve systems of equations.

Interpret functions that arise in applications in terms of the context.

Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Construct and compare linear, quadratic, and exponential models and solve problems.

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Understand independence and conditional probability and use them to create visual representations of data.

Understand and apply basic concepts of probability.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Extend the properties of integer exponents to rational exponents.

Use units as a way to understand real-world problems.

Use matrices to represent data in a real-world context. Interpret rows, columns, and dimensions of matrices in terms of the context.

Perform operations on matrices in a real-world context.

Create and use augmented matrices to solve systems of linear equations in real-world contexts, by hand and using technology.

Interpret expressions that represent a quantity in terms of its context.

Know and apply the Factor Theorem: For a polynomial p(x) and a number a, p(a) = 0 if and only if (x – a) is a factor of p(x).

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Create equations and inequalities in one variable and use them to solve problems in a real-world context.

Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations and inequalities with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

Solve radical equations in one variable, and identify extraneous solutions when they exist.

Write and solve a system of linear equations in a real-world context.

Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically, graphically, and using technology.

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.

Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.

Understand geometric formulas as functions.

Graph functions expressed algebraically and show key features of the graph by hand and using technology.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

Build a function that describes a relationship between two quantities.

Define sequences as functions, including recursive definitions, whose domain is a subset of the integers. Write explicit and recursive formulas for arithmetic and geometric sequences in context and connect them to linear and exponential functions.

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.

Find the inverse of a function.

Know the relationship between exponential functions and logarithmic functions.

Know that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or cubically.

Use statistics appropriate to the shape of the data distribution to compare center (mean, median, and/or mode) and spread (range, standard deviation) of two or more different data sets.

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.

Compute, interpret, and compare z-scores for normally distributed data in a real-world context.

Represent data from two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Recognize the purposes of and differences among sample surveys, experiments, and observational studies.

Identify potential sources of bias in statistical studies.

Distinguish between a statistic and a parameter. Evaluate reports based on data and recognize when poor conclusions are drawn from well-collected data.

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Categorize events as independent or dependent.

Apply statistical counting techniques.

Use the Law of Large Numbers to assess the validity of a statistical claim.

Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the given context.

Develop the meaning of rational exponents by applying the properties of integer exponents.

Explain why x^1/n can be written as the n^th root of x.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Choose and interpret the scale and the origin in graphs and data displays.

Use appropriate quantities in formulas, converting units as necessary.

Define and justify appropriate quantities within a context for the purpose of modeling.

Choose an appropriate level of accuracy when reporting quantities.

Multiply a matrix by a scalar to produce a new matrix.

Add and/or subtract matrices by hand and using technology.

Multiply matrices of appropriate dimensions, by hand in simple cases and using technology for more complicated cases.

Describe the roles that zero matrices and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real number system.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Rewrite quadratic functions to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a real-world context.

Know and use the properties of exponents to interpret expressions for exponential functions in terms of a real-world context.

Compare properties of two different functions. Functions may be of different types and/or represented in different ways.

Compare properties of the same function on two different intervals or represented in two different ways.

Combine standard function types using arithmetic operations.

Combine standard function types using composition.

Determine whether a function is one-to-one.

Find the inverse of a function on an appropriate domain.

Given an invertible function on an appropriate domain, identify the domain of the inverse function.

Solve exponential equations using a variety of strategies, including logarithms.

Understand that a logarithm is the solution to ab^ct = d, where a, b, c, and d are numbers.

Evaluate logarithms using technology.

Use the Fundamental Counting Principle to compute probabilities of compound events and solve problems.

Use permutations and combinations to compute probabilities of compound events and solve problems.