Algebra 2
COURSE OVERVIEW
Algebra 2 focuses on the development of abstract thinking and reasoning of algebraic concepts, continuing with the concepts introduced in Algebra 1. Areas of concentration will include, but not be
limited to the following: functions, equations, graphs, linear systems, quadratic equations and
functions, polynomials and polynomial functions, exponential and logarithmic functions, rational functions and quadratic relations.
- Compare and order any real numbers.
- Simplify square roots.
- Find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) for sets of monomials.
- Simplify expressions involving properties and laws of exponents, roots, and absolute values to solve problems.
- Evaluate expressions involving properties and laws of exponents, roots, and absolute values to solve problems.
- Use estimation to solve problems.
- Add, subtract, and multiply polynomial expressions and express answers in simplest form.
- Factor algebraic expressions, including difference of squares and trinomials.
- Simplify a rational algebraic expression.
- Write, solve, and apply a linear equation including problem situations.
- Use an algebraic property to justify any step in an equation-solving process.
- Interpret solutions to problems in the context of the problem situation.
- Solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination.
- Interpret solutions to problems in the context of the problem situation.
- Solve compound inequalities and graph their solution sets on a number line (may include absolute value inequalities).
- Identify and graph the solution set to a linear inequality on a number line.
- Interpret solutions to problems in the context of the problem situation.
- Write and solve a system of linear inequalities using graphing.
- Analyze a set of data for the existence of a pattern and represent the pattern algebraically and graphically.
- Determine whether a relation is a function given a set of points or a graph.
- Identify the domain or range of a relation.
- Create, interpret, and use the equation, graph, or table of a linear function.
- Translate from one representation of a linear function to another.
- Identify, describe, and use constant rates of change.
- Apply the concept of linear rate of change (slope) to solve problems.
- Write or identify a linear equation when given the graph of the line, two points on the line, or the slope and a point on the line.
- Determine the slope and y-intercept represented by a linear equation or graph.
- Draw, identify, find, and write an equation for a line of best fit for a scatter plot.
- Calculate and interpret the range, quartiles, and interquartile range of data.
- Estimate and calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation.
- Analyze data, make predictions, and answer questions based on displayed data.
- Make predictions using the equations or graphs of best-fit lines of scatter plots.
- Find probabilities for compound events and represent as a fraction, decimal, or percent.
Numbers and Operations
CC.2.1.8.E.1:Â Distinguish between rational and irrational numbers using their properties.
CC.2.1.8.E.4: Estimate irrational numbers by comparing them to rational numbers.
CC.2.1.HS.F.1: Apply and extend the properties of exponents to solve problems with rational exponents.
CC.2.1.HS.F.2: Apply properties of rational and irrational numbers to solve real-world or mathematical problems.
CC.2.1.HS.F.3: Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.
- CC.2.1.HS.F.4: Use units as a way to understand problems and to guide the solution of multi-step problems.
CC.2.1.HS.F.5: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Algebraic Concepts
CC.2.2.8.B.1: Apply concepts of radicals and integer exponents to generate equivalent expressions.
CC.2.2.8.B.2: Understand the connections between proportional relationships, lines, and linear equations.
CC.2.2.8.B.3: Analyze and solve linear equations and pairs of simultaneous linear equations.
CC.2.2.HS.C.1: Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.2.HS.C.2:Â Graph and analyze functions and use their properties to make connections between the different representations.
CC.2.2.HS.C.3:Â Write functions or sequences that model relationships between two quantities.
CC.2.2.HS.C.4: Interpret the effects transformations have on functions and find the inverses of functions.
CC.2.2.HS.C.5:Â Construct and compare linear, quadratic, and exponential models to solve problems.
CC.2.2.HS.C.6:Â Interpret functions in terms of the situations they model.
CC.2.2.HS.D.1: Interpret the structure of expressions to represent a quantity in terms of its context.
CC.2.2.HS.D.2: Write expressions in equivalent forms to solve problems.
CC.2.2.HS.D.3: Extend the knowledge of arithmetic operations and apply to polynomials.
CC.2.2.HS.D.5:Â Use polynomial identities to solve problems.
CC.2.2.HS.D.6:Â Extend the knowledge of rational functions to rewrite in equivalent forms.
CC.2.2.HS.D.7: Create and graph equations or inequalities to describe numbers or relationships.
CC.2.2.HS.D.8: Apply inverse operations to solve equations or formulas for a given variable.
CC.2.2.HS.D.9:Â Use reasoning to solve equations and justify the solution method.
CC.2.2.HS.D.10: Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
Measurement, Data, and Probability
CC.2.4.HS.B.1:Â Summarize, represent, and interpret data on a single count or measurement variable.
CC.2.4.HS.B.2:Â Summarize, represent, and interpret data on two categorical and quantitative variables.
CC.2.4.HS.B.3:Â Analyze linear models to make interpretations based on the data.
CC.2.4.HS.B.4:Â Recognize and evaluate random processes underlying statistical experiments.
CC.2.4.HS.B.5:Â Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
CC.2.4.HS.B.7:Â Apply the rules of probability to compute probabilities of compound events in a uniform probability model.
Unit: Â Real Numbers and Equations
Lessons
- Real Numbers and Their Properties
- Simplifying Square Roots
- Evaluating Expressions
- Solving Equations
Unit: Â Inequalities and Absolute Value
Lessons
- Solving Inequalities
- Solving and Graphing Compound Inequalities
- Solving Absolute Value Equations
- Solving Absolute Value Inequalities
Unit: Â Functions and Rate of Change
Lessons
- Relations and Functions
- Domain and Range
- Function Notation
- Slope and Rate of Change
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Unit: Â Linear Equations
Lessons
- Graphing linear equations
- Parallel and Perpendicular Lines
- Writing Equations of lines
- Linear Models
- Direct Variation
- Scatter Plots and Line of Best Fit
Unit: Â Linear Systems
Lessons
- Solving a System by Graphing
- Solving a System by Substitution
- Solving a System by Elimination
- Applying Linear Systems
- Systems of Inequalities
- Inconsistent Systems
Unit: Â Exponent Properties
Lessons
- Applying Exponent Properties
- Zero and Negative Exponents
- Simplifying Rational Expressions
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Unit: Â Polynomials and Factoring
Lessons
- Adding and subtracting Polynomials
- Multiplying and Dividing Polynomials
- Finding GCF and LCM for Monomials
- Special Product Polynomials
- Factoring Polynomials
Unit: Â Data Analysis and Sequences
Lessons
- Probability       Â
- Central Tendency
- Box and Whisker
- Interpreting Data       Â
- Making Predictions       Â
- Arithmetic and Geometric Sequences       Â