```GSE Algebra I ``` `UNIT 1 - Relationships Between Quantities` `UNIT 2 - Linear Equations & Inequalities` `UNIT 3 - Modeling Quadratics` `UNIT 4 - Modeling & Analyzing Exponential Functions` `UNIT 5 - Comparing & Contrasting Functions` `UNIT 6 - Describing Data` `EOC Prep` ```GSE Geometry ``` `UNIT 1 - Transformations in the Coordinate Plane ` `UNIT 2 - Similarity Congruence, Proofs` `UNIT 3 - Right Triangle Trigonometry` `UNIT 4 - Circles & Volume` `UNIT 5 - Geometric & Algebraic Connections` `UNIT 6 - Applications of Probability` `EOC Prep` ```GSE Algebra II ``` `UNIT 1 - Quadratics Revisited` `UNIT 2 - Operations with Polynomials` `UNIT 3 - Polynomial Functions` `UNIT 4 - Rational & Radical Relationships` `UNIT 5 - Exponential & Logarithmic Functions` `UNIT 6 - Mathematical Modeling` `UNIT 7 - Inferences & Conclusions from Data` ```GSE PreCalc ``` UNIT 1 - Trigonometry of General Triangles UNIT 2 - Introduction to Trig Functions UNIT 3 - Trigonometric Functions `UNIT 4 - Trigonometric Identities` `UNIT 5 - Matrices` `UNIT 6 - Conics` `UNIT 7 - Vectors` `UNIT 8 - Probability` ```Other Courses ``` Calculus I ```Adv. Mathematical Decision Making ``` `UNIT 1 - Analyzing Numerical Data` `UNIT 2 - Probability` `UNIT 3 - Statistical Studies` `UNIT 4 - Recursion Models` `UNIT 5 - Trigonometry & Regression Models` `UNIT 6 - Financial Decisions` `UNIT 7 - Networks & Graphs` `UNIT 8 - Matrix Applications & Voting Methods` ```Analytical Geometry ``` `UNIT 1 - Similarity, Congruence, Proof` `UNIT 2 - Right Triangle Trigonometry` `UNIT 3 - Circles & Volumes` `UNIT 4 - Extending the Number System` `UNIT 5 - Quadratic Functions` `UNIT 6 - Modeling Geometry` `UNIT 7 - Applications of Probability` `EOC Practice Test` ```CP-Statistics ``` `All Units` ```Coordinate Algebra ``` `EOC Practice Test` ```Integrated Algebra I ``` `UNIT 1 - Function Families` `UNIT 2 - Algebra Investigations` `UNIT 3 - Geometry` `UNIT 4 - The Chance of Winning` `UNIT 5 - Algebraic Investigations` `UNIT 6 - Coordinate Geometry` `EOCT Prep` ```Integrated Geometry ``` `UNIT 1 - Quadratic Function` `UNIT 2 - Right Triangle Trigonometry` `UNIT 3 - Circles and Spheres` `UNIT 4 - Data Analysis & Probability` `UNIT 5 - Piecewise, Inverse, Exponential` `UNIT 6 - Find the Best Model` ```GPS Middle School Math ``` `6th Grade Math` `7th Grade Math` `8th Grade Math` Home > GSE Algebra 1 >Unit 2 - Reasoning with Linear Eq. & Inequalities

Search Site:

Review

 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 EOC

Georgia
Unit 2 Frameworks All of Unit 2
Unit 2-1 :
Solving Basic Equations (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.REI.1:Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.

MGSE9-12.A.REI.3:Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax+3=7, solve for x.

MGSE9-12.A.CED.4:rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.

Quick Example: Video

Video Lessons: (
p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF)

Unit 2-2 : Solving Equations Applications (Doc, PDF, Key)

Word List (Doc, PDF)

Georgia Standards of Excellence (Click to Expand)

MGSE9-12.A.CED.1:Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions.

MGSE9-12.A.REI.3:Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax+3=7, solve for x.

Video Lessons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF)

Unit 2-3: Basic Inequalities (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.REI.3:Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax+3=7, solve for x

Video Lessons: (p1, p2)

Sample Quiz: (Interactive, PDF)
Unit 2-4: System of Equations Graphing (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

MGSE9-12.A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

MGSE9-12.A.REI.11:Using graphs, tables, or successive approximations, show that the solutions to the equation f(x)= g(x) is the x-value where the y-values of f(x) and g(x) are the same.

Video Lessons: (p1, p2)

Sample Quiz: (Interactive, PDF)
Unit 2-5: System of Equations Algebra (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.A.REI.5: Show and explain why the elimination method works to solve a system of two-variable equations.

MGSE9-12.A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Video Lessons: (p1, p2, p3)

Sample Quiz: (Interactive, PDF)

Unit 2-6: System of Equations Application (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.F.BF.1 Write a function that describes a relationship between two quantities.

MGSE9-12.A.CED.2: Create linear equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Video Lessons: (p1, p2, p3, p4 )

Sample Quiz: (Interactive, PDF)
Unit 2-7: System of Inequalities Graphing (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.REI.12: Graph the solution set to a linear inequality two variables.

MGSE9-12.A.CED3:Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret data points as possible or not possible under establish constraints.

Video Lessons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF)

Unit 2-8: Introduction to Functions (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.F.IF.1: Understand that a function from one set to another set assigns to each element of the domain exactly one element of the range. If f is a function, x is the input and f(x) is the output. Graphically, the graph is y = f(x)

MGSE9-12.F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Video Lesons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF)
Unit 2-9: Building Linear & Exponential Functions (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

MGSE9-12.A.CED2:Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

MGSE9-12.F.BF.1:Write a function that describes a relationship between two quantities.

MGSE9-12.F.LE.1c:Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

MGSE9-12.F.LE.5:Interpret the parameters in a linear (f(x) = mx+b) and exponential (f(x) =a*d^x)function in terms of context. In context, students should describe what these parameters mean in terms of change and starting value.

Video Lessons: (p1, p2, p3)

Sample Quiz: (Interactive, PDF)

Unit 2-10: Domain & Range of Functions (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.F.IF.1: Understand that a function from one set to another set assigns to each element of the domain exactly one element of the range. If f is a function, x is the input and f(x) is the output. Graphically, the graph is y = f(x)

MGSE9-12.F.IF.5:Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Video Lessons: (p1, p2, p3)

Sample Quiz: (Interactive, PDF)
Unit 2-11: Describing Functions (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret key characteristics of functions which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MGSE9-12.F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph.

MGSE9-12.F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7a: Graph linear & quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

MGSE9-12.F.LE.1a:Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

MGSE9-12.F.IF.9:Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

MGSE9-12.F.LE.1b:Recognize situation in which one quantity changes at a constant rate per unit interval relative to another.

MGSE9-12.F.LE.3:Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or as a polynomial function.

Video Lessons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF)

Unit 2-12: Basic Transforms of Functions (Doc, PDF, Key)

Georgia Standards of Excellence (Click to Expand)
MGSE9-12:Identify the effect on the graph of replacing f(x) by f(x)+k, kf(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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Video Lessons: (p1a, p1b, p2a, p2b, p3, p4, p5)

Sample Quiz: (Interactive, PDF)

Unit 2-13: Composition of Functions (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
(OPTIONAL)

Video Lessons: (p1, p2)

Sample Quiz: (Interactive, PDF)

Unit 2-14: Even Odd Functions (Doc, PDF, Key)

Sketchpad Animation (Odd Fold, Even Fold)

Georgia Standards of Excellence (Click to Expand)
MGSE9-12:Identify the effect on the graph of replacing f(x) by f(x)+k, kf(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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Video Lessons: (p1, p2)

Sample Quiz: (Interactive, PDF)

Unit 2-15: Sequences (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.F.BF.1a:Determine an explicit expression and the recursive process (steps for calculation) from context.

MGSE9-12.F.BF.2:Write arithmetic & geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.

MGSE9-12.F.IF.3:Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

MGSE9-12.F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

Video Lessons: (p1, p2, p3, p4, p5)

Sample Quiz: (Interactive, PDF)

TEST : Testing Item Banks for Exam View

(396 available questions for Unit 2)