Algebra 1

Contents

1. 1Translating and Evaluating Algebraic ExpressionsA.EO.1
   1. 1.1 The Language of Algebra
   2. 1.2 Expressions from Contextual Situations
   3. 1.3 Evaluating Expressions
   4. 1.4 Absolute Value, Square Roots, and Cube Roots in Evaluation

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2. 2Multistep and Literal Linear EquationsA.EI.1 (a, b, d, e, f)
   1. 2.1 Writing an Equation for a Situation
   2. 2.2 Solving Multistep Equations, One Named Property at a Time
   3. 2.3 The Variable on Both Sides, and Clearing Fractions and Decimals
   4. 2.4 One Solution, No Solution, Infinitely Many
   5. 2.5 Literal Equations and Formulas
   6. 2.6 Verifying Algebraically, Graphically, and with Technology

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3. 3Linear Inequalities in One VariableA.EI.1 (c, f)
   1. 3.1 Inequalities, Solution Sets, and the Number Line
   2. 3.2 The Reversal Rule and Why It Happens
   3. 3.3 Multistep Inequalities with Every Step Named
   4. 3.4 Verifying and Interpreting Solutions

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4. 4Functions, Domain, and RangeA.F.2 (a)
   1. 4.1 Relations and Their Four Representations
   2. 4.2 Deciding Whether a Relation Is a Function
   3. 4.3 Graphs and the Vertical Line Test
   4. 4.4 Domain and Range

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5. 5Linear Functions: Characteristics and FormsA.F.1 (a, b, c)
   1. 5.1 Domain and Range of a Linear Function
   2. 5.2 Slope and the Two Intercepts
   3. 5.3 The Zero of a Linear Function
   4. 5.4 The Parent Function $y = x$
   5. 5.5 Transformations of the Parent Function
   6. 5.6 Three Equivalent Forms

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6. 6Writing Equations of LinesA.F.1 (d, e)
   1. 6.1 From a Slope and a Point
   2. 6.2 From Two Points
   3. 6.3 From a Graph
   4. 6.4 Horizontal and Vertical Lines
   5. 6.5 Parallel and Perpendicular Lines

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7. 7Graphing and Evaluating Linear FunctionsA.F.1 (f, g, h)
   1. 7.1 Graphing by Hand from Slope-Intercept Form
   2. 7.2 Intercepts, Tables, and the Two Special Lines
   3. 7.3 Graphing with Technology
   4. 7.4 Determining $f(x)$, and Recovering $x$
   5. 7.5 Comparing the Four Representations

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8. 8Systems of Two Linear EquationsA.EI.2 (a, b, c, h)
   1. 8.1 What a System Is, and What a Solution Means
   2. 8.2 Solving a System by Graphing
   3. 8.3 Solving by Substitution
   4. 8.4 Solving by Elimination
   5. 8.5 One Solution, No Solution, or Infinitely Many
   6. 8.6 Modeling with Systems, and Verifying Three Ways

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9. 9Linear Inequalities in Two Variables and Their SystemsA.EI.2 (d, e, f, g, h)
   1. 9.1 From an Interval to a Region
   2. 9.2 Graphing a Linear Inequality in Two Variables
   3. 9.3 Writing an Inequality from a Situation
   4. 9.4 Systems of Two Linear Inequalities
   5. 9.5 Verifying and Interpreting Solutions

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10. 10The Laws of ExponentsA.EO.3 (a, b)
    1. 10.1 Powers and the Product Law
    2. 10.2 The Quotient Law
    3. 10.3 Zero and Negative Exponents
    4. 10.4 Powers of Bases
    5. 10.5 Multivariable Expressions and Ratios of Monomials

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11. 11Radical ExpressionsA.EO.4 (a, b, c, d)
    1. 11.1 Square Roots and Simplest Form
    2. 11.2 Estimating Square Roots
    3. 11.3 Cube Roots
    4. 11.4 Adding, Subtracting, and Multiplying Radicals
    5. 11.5 Rational Exponents

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12. 12Adding, Subtracting, and Multiplying PolynomialsA.EO.2 (a, b)
    1. 12.1 Polynomials, Terms, and Standard Form
    2. 12.2 Adding Polynomials
    3. 12.3 Subtracting Polynomials
    4. 12.4 Multiplying by a Monomial
    5. 12.5 Multiplying Two Polynomials

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13. 13Factoring PolynomialsA.EO.2 (c)
    1. 13.1 Factoring as Multiplication Run Backwards
    2. 13.2 The Greatest Common Factor
    3. 13.3 Trinomials with Leading Coefficient 1
    4. 13.4 Difference of Squares
    5. 13.5 Perfect Squares and Leading Coefficient Greater Than 1
    6. 13.6 Factoring Completely and Choosing a Method

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14. 14Dividing Polynomials and Equivalent Quadratic FormsA.EO.2 (d, e)
    1. 14.1 Dividing by a Monomial
    2. 14.2 Dividing by a Binomial
    3. 14.3 Completely Factored Divisors and Domain Restrictions
    4. 14.4 Equivalent Quadratic Forms

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15. 15Solving Quadratic EquationsA.EI.3 (a, b, c)
    1. 15.1 Standard Form and What a Solution Means
    2. 15.2 Solving by Square Roots
    3. 15.3 Solving by Factoring
    4. 15.4 Completing the Square
    5. 15.5 The Quadratic Formula and the Discriminant
    6. 15.6 Choosing a Method, Contexts, and Three-Way Verification

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16. 16Quadratic FunctionsA.F.2 (b, c, d, g)
    1. 16.1 Vertex, Axis, and Opening
    2. 16.2 Intercepts, Zeros, and the Vertex Formula
    3. 16.3 Domain and Range, Including Context
    4. 16.4 Transformations $f(x) + k$ and $kf(x)$
    5. 16.5 Standard Form, Factored Form, and the Graph
    6. 16.6 Evaluating $f(x)$ and Finding $x$

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17. 17Exponential FunctionsA.F.2 (e, f, g)
    1. 17.1 The Form $y = ab^x$
    2. 17.2 $y$-Intercept, Domain, and Range
    3. 17.3 Graphing and Transformations
    4. 17.4 Exponential Models in Context
    5. 17.5 Evaluating $f(x)$ for Exponential Functions

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18. 18Comparing Linear, Quadratic, and Exponential FunctionsA.F.2 (h)
    1. 18.1 Three Families on One Window
    2. 18.2 Growth Patterns in Tables
    3. 18.3 Rates of Change Compared
    4. 18.4 Choosing the Model That Fits

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19. 19The Data Cycle: Scatterplots and Curve of Best FitA.ST.1 (a–i)
    1. 19.1 The Data Cycle and Bivariate Questions
    2. 19.2 Choosing Variables and Sampling
    3. 19.3 Analyzing Relationships in a Scatterplot
    4. 19.4 Technology: Linear or Quadratic Fit
    5. 19.5 Regression Models and Predictions
    6. 19.6 Interpreting Parameters and Communicating Conclusions

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