# Academic standards list

### Algebra 2 — Mathematics

### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### The Real Number System

TSS.Math.A2.N.RN — Conceptual Category: Number and Quantity

Extend the properties of exponents to rational exponents.

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for…

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

### Quantities

TSS.Math.A2.N.Q — Conceptual Category: Number and Quantity

Reason quantitatively and use units to solve problems.

Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. ♦

### The Complex Number System

TSS.Math.A2.N.CN — Conceptual Category: Number and Quantity

Perform arithmetic operations with complex numbers.

Know there is a complex number i such that r^2 = -1, and every complex number has the form a + bi with a and b real. ♦

Know and use the relation r^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. ♦

Use complex numbers in quadratic equations.

### Seeing Structure in Expressions

TSS.Math.A2.A.SSE — Conceptual Category: Algebra

Interpret the structure of expressions.

Use expressions in equivalent forms to solve problems.

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

*There are 1 components within this standard*.Recognize a finite geometric series (when the common ratio is not 1), and know and use the sum formula to solve problems in context.

### Arithmetic with Polynomials and Rational Expressions

TSS.Math.A2.A.APR — Conceptual Category: Algebra

Understand the relationship between zeros and factors of polynomials.

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (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…

Use polynomial identities to solve problems.

Rewrite rational expressions.

### Creating Equations

TSS.Math.A2.A.CED — Conceptual Category: Algebra

Create equations that describe numbers or relationships.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

### Reasoning with Equations and Inequalities

TSS.Math.A2.A.REI — Conceptual Category: Algebra

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

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…

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

Solve equations and inequalities in one variable.

Solve quadratic equations and inequalities in one variable. ♦

*There are 1 components within this standard*.Solve systems of equations.

Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. ♦

Represent and solve equations graphically.

### Interpreting Functions

TSS.Math.A2.F.IF — Conceptual Category: Functions

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

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch…

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

Analyze functions using different representations.

Graph functions expressed symbolically and show key features of the graph, by hand and using technology. ♦

*There are 3 components within this standard*.Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. ♦

*There are 1 components within this standard*.Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). ♦

### Building Functions

TSS.Math.A2.F.BF — Conceptual Category: Functions

Build a function that models a relationship between two quantities.

Write a function that describes a relationship between two quantities.

*There are 2 components within this standard*.Know and write arithmetic and geometric sequences with an explicit formula and use them to model situations.

Build new functions from existing 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… ♦

### Linear, Quadratic, and Exponential Models

TSS.Math.A2.F.LE — Conceptual Category: Functions

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

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or… ♦

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the… ♦

Interpret expressions for functions in terms of the situation they model.

### Trigonometric Functions

TSS.Math.A2.F.TF — Conceptual Category: Functions

Extend the domain of trigonometric functions using the unit circle.

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures… ♦

Prove and apply trigonometric identities.

Know and use trigonometric identities to to find values of trig functions. ♦

*There are 2 components within this standard*.### Interpreting Categorical and Quantitative Data

TSS.Math.A2.S.ID — Conceptual Category: Statistics and Probability

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

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. ♦

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

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. ♦

*There are 1 components within this standard*.### Making Inferences and Justify Conclusions

TSS.Math.A2.S.IC — Conceptual Category: Statistics and Probability

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

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context

### Conditional Probability and the Rule of Probability.

TSS.Math.A2.S.CP — Conceptual Category: Statistics and Probability

Understand independence and conditional probability and use them to interpret data.

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or… ♦

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… ♦

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… ♦

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. ♦

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

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 model. ♦

Know and apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. ♦

♦ Academic Standards marked with a diamond are "

*Supporting Content*" within the grade level or course.

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