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Algebra I

Math Academy official course import: Algebra I

223 节课

课程大纲

  1. 1.Equations & Inequalities
    1. 1.1.1. Linear Equations
      1. 1
        Solving Linear Equations With Unknown Coefficients
      2. 2
        Solving Linear Equations With Unknown Coefficients by Factoring
      3. 3
        Solving Linear Inequalities With Unknown Parameters
      4. 4
        Solving Many-Variable Equations
    2. 2.1.2. Modeling With Linear Equations
      1. 1
        Interpreting Linear Expressions
      2. 2
        Modeling With Linear Equations
      3. 3
        Consecutive Integer Problems
      4. 4
        Speed, Distance, Time Problems
      5. 5
        Further Speed, Distance, Time Problems
      6. 6
        Modeling Work Problems
      7. 7
        Modeling Mixture Problems
    3. 3.1.3. Linear Inequalities
      1. 1
        Solving Compound Inequalities
      2. 2
        Interval Notation
      3. 3
        Unbounded Intervals
      4. 4
        Unions of Intervals
      5. 5
        Intersections of Intervals
      6. 6
        Compound OR Inequalities
      7. 7
        Compound AND Inequalities
      8. 8
        Introduction to Modeling With Inequalities
      9. 9
        Modeling With One-Step Inequalities
      10. 10
        Modeling With Two-Step Inequalities
      11. 11
        Modeling With Compound Inequalities
    4. 4.1.4. Nonlinear Equations
      1. 1
        Solving Equations Using the Square Root Method
      2. 2
        Solving Equations With Odd Exponents Using the Nth Root Method
      3. 3
        Solving Equations With Even Exponents Using the Nth Root Method
  2. 2.Two-Variable Equations & Inequalities
    1. 1.2.1. Graphs of Linear Equations
      1. 1
        Equations of Lines in Slope-Intercept Form
      2. 2
        Properties of Lines Given in Slope-Intercept Form
      3. 3
        Equations of Lines in Point-Slope Form
      4. 4
        Equations of Lines in Standard Form
      5. 5
        Properties of Lines Given in Standard Form
      6. 6
        Parallel Lines in the Coordinate Plane
    2. 2.2.2. Modeling With Two-Variable Linear Equations
      1. 1
        Modeling With Linear Equations in Two Variables
      2. 2
        Modeling Totals Using Two-Variable Linear Equations
      3. 3
        Analyzing and Interpreting Graphs of Linear Equations
      4. 4
        Further Modeling With Linear Equations in Two Variables
      5. 5
        Distance-Time Graphs
      6. 6
        Calculating Acceleration From a Speed-Time Graph
      7. 7
        Calculating Distance From a Speed-Time Graph
    3. 3.2.3. Systems of Equations
      1. 1
        Introduction to the Elimination Method
      2. 2
        Solving Systems of Linear Equations Using Elimination: One Transformation
      3. 3
        Solving Systems of Linear Equations Using Elimination: Two Transformations
      4. 4
        Systems of Linear Equations With Fractional Coefficients
      5. 5
        Systems of Linear Equations With Decimal Coefficients
      6. 6
        Systems of Equations With No Solutions and Infinitely Many Solutions
      7. 7
        Consistency and Dependency in Linear Systems
      8. 8
        Calculating the Intersection of Two Lines
      9. 9
        Modeling Using Systems of Linear Equations
      10. 10
        Modeling Coin Problems Using Systems of Linear Equations
      11. 11
        Solving Systems of Nonlinear Equations Using Graphs
      12. 12
        Approximating Solutions to Systems of Linear Equations
      13. 13
        Approximating Solutions to Systems of Nonlinear Equations
    4. 4.2.4. Two-Variable Linear Inequalities
      1. 1
        Graphing Strict Two-Variable Linear Inequalities
      2. 2
        Graphing Non-Strict Two-Variable Linear Inequalities
      3. 3
        Further Graphing of Two-Variable Linear Inequalities
      4. 4
        Systems of Linear Inequalities
      5. 5
        Modeling With Two-Variable Linear Inequalities
      6. 6
        Modeling With Systems of Linear Inequalities
      7. 7
        Modeling and Solving Systems of Linear Inequalities Using Technology
  3. 3.Units
    1. 1.3.1. Working With Units
      1. 1
        Unit Conversions Using Base Units of Mass
      2. 2
        Two-Step Unit Conversions
      3. 3
        Unit Conversions Using Base Units of Length
      4. 4
        Unit Conversions Using Units of Time
      5. 5
        Converting Units of Area to Smaller Units
      6. 6
        Converting Units of Area to Larger Units
      7. 7
        Determining Units in Formulas
      8. 8
        Selecting Units for Rates of Change
      9. 9
        Converting Between Mixed Units
      10. 10
        Degrees of Accuracy
    2. 2.3.2. Direct and Inverse Variation
      1. 1
        Inverse Variation
      2. 2
        Modeling with Direct Variation
      3. 3
        Modeling With Inverse Variation
  4. 4.Radical Expressions
    1. 1.4.1. Radical Expressions
      1. 1
        The Square Root of a Perfect Square With Algebraic Expressions
      2. 2
        The Square Root of a Perfect Square With Domain Restrictions
      3. 3
        The Cube Root of a Perfect Cube With Algebraic Expressions
      4. 4
        Simplifying Square Root Expressions Using the Product Rule
      5. 5
        Combining Radical Expressions Using the Product Rule
      6. 6
        Simplifying Square Root Expressions Using the Quotient Rule
      7. 7
        Evaluating Algebraic Radical Expressions
      8. 8
        Adding and Subtracting Radical Expressions
      9. 9
        Rationalizing Denominators of Algebraic Expressions
      10. 10
        Rationalizing Denominators With Two Terms
      11. 11
        Further Rationalizing Denominators of Algebraic Expressions
      12. 12
        Solving Radical Equations
  5. 5.Rational Expressions & Equations
    1. 1.5.1. Rational Expressions
      1. 1
        Equivalent Expressions With Fractions
      2. 2
        Simplifying Rational Expressions
      3. 3
        Simplifying Rational Expressions by Factoring
    2. 2.5.2. Rational Equations
      1. 1
        Solving Rational Equations Containing One Fractional Term
      2. 2
        Solving Rational Equations Using Cross-Multiplication
      3. 3
        Solving Rational Equations Containing Binomials Using Cross-Multiplication
      4. 4
        Solving Rational Equations Using the Flip Method
  6. 6.Functions
    1. 1.6.1. Functions
      1. 1
        Introduction to Functions
      2. 2
        Visual Representations of Functions
      3. 3
        Graphs of Functions
      4. 4
        The Domain of a Function
      5. 5
        The Vertical Line Test
      6. 6
        Global Extrema of Functions
      7. 7
        End Behavior of Functions
      8. 8
        The Range of a Function
      9. 9
        The Range of a Function: Advanced Cases
      10. 10
        The Roots of a Function
      11. 11
        Increasing and Decreasing Functions
      12. 12
        Piecewise Functions
      13. 13
        Modeling With Linear Functions
      14. 14
        Constructing Linear Functions
      15. 15
        The Arithmetic of Functions
      16. 16
        Function Composition
      17. 17
        Describing Function Composition
      18. 18
        Introduction to Inverse Functions
  7. 7.Absolute Value
    1. 1.7.1. Absolute Value Expressions, Equations & Inequalities
      1. 1
        Absolute Value Expressions
      2. 2
        Rules of Absolute Value
      3. 3
        Further Rules of Absolute Value
      4. 4
        Absolute Value Equations
      5. 5
        Further Absolute Value Equations
      6. 6
        Equations Connecting Absolute Value and Linear Functions
      7. 7
        Absolute Value Equations With Extraneous Solutions
      8. 8
        Absolute Value Inequalities
    2. 2.7.2. Absolute Value Functions
      1. 1
        Absolute Value Graphs
      2. 2
        Vertical Reflections of Absolute Value Graphs
      3. 3
        Stretches of Absolute Value Graphs
      4. 4
        Combining Transformations of Absolute Value Graphs
      5. 5
        Domain and Range of Absolute Value Functions
      6. 6
        Roots of Absolute Value Functions
  8. 8.Exponential Functions
    1. 1.8.1. Rules of Exponents
      1. 1
        Writing Radical Expressions Using Fractional Exponents
      2. 2
        The Product Rule for Exponents With Algebraic Expressions
      3. 3
        The Quotient Rule for Exponents With Algebraic Expressions
      4. 4
        The Power Rule for Exponents With Algebraic Expressions
      5. 5
        The Power of Product Rule With Algebraic Expressions
      6. 6
        The Power of Quotient Rule With Algebraic Expressions
      7. 7
        Combining the Rules of Exponents With Algebraic Expressions
    2. 2.8.2. Exponential Expressions & Equations
      1. 1
        Solving Exponential Equations
      2. 2
        Solving Exponential Equations with Fractional Solutions
      3. 3
        Creating Exponential Growth Expressions
      4. 4
        Creating Exponential Decay Expressions
    3. 3.8.3. Exponential Functions
      1. 1
        Exponential Functions
      2. 2
        Modeling Exponential Growth With Functions
      3. 3
        Interpreting Exponential Growth
      4. 4
        Solving Exponential Growth Problems
      5. 5
        Modeling Exponential Decay With Functions
      6. 6
        Interpreting Exponential Decay
      7. 7
        Solving Exponential Decay Problems
      8. 8
        Linear vs. Exponential Growth and Decay
      9. 9
        Linear vs. Exponential Growth and Decay Models
      10. 10
        Graphing Exponential Growth Functions
      11. 11
        Graphing Exponential Decay Functions
  9. 9.Polynomials
    1. 1.9.1. Polynomials
      1. 1
        Introduction to Polynomials
      2. 2
        The Degree of a Polynomial
      3. 3
        Simplifying Polynomials
      4. 4
        The Distributive Law for Polynomials
      5. 5
        Adding and Subtracting Polynomials
      6. 6
        Monomials, Binomials and Trinomials
      7. 7
        Multiplying Binomials
      8. 8
        Multiplying Polynomials
      9. 9
        Squaring Binomials
      10. 10
        Expanding Binomials Using Pascal's Triangle
      11. 11
        The Difference of Squares Formula
    2. 2.9.2. Factoring Polynomials
      1. 1
        The Greatest Common Factor of Two Monomials
      2. 2
        Factoring Polynomials Using GCFs
      3. 3
        Factoring Perfect Square Trinomials
      4. 4
        Factoring Perfect Square Trinomials With Leading Coefficients
      5. 5
        Factoring Differences of Squares
      6. 6
        Factoring Trinomials
      7. 7
        Factoring Trinomials Using Common Factors
      8. 8
        Factoring Trinomials With Leading Coefficients
      9. 9
        Further Factoring Trinomials With Leading Coefficients
  10. 10.Quadratic Equations & Functions
    1. 1.10.1. Quadratic Equations
      1. 1
        Introduction to Quadratic Equations
      2. 2
        Solving Perfect Square Quadratic Equations
      3. 3
        Perfect Square Quadratic Equations with One or No Solutions
      4. 4
        The Zero Product Rule for Solving Quadratic Equations
      5. 5
        Solving Quadratic Equations Using a Difference of Squares
      6. 6
        Solving Quadratic Equations with No Constant Term
      7. 7
        Solving Quadratic Equations by Factoring
      8. 8
        Solving Quadratic Equations with Leading Coefficients by Factoring
      9. 9
        Completing the Square
      10. 10
        Completing the Square With Odd Linear Terms
      11. 11
        Completing the Square With Leading Coefficients
      12. 12
        Solving Quadratic Equations by Completing the Square
      13. 13
        Solving Quadratic Equations With Leading Coefficients by Completing the Square
      14. 14
        The Quadratic Formula
      15. 15
        The Discriminant of a Quadratic Equation
      16. 16
        Determining Unknown Parameters in Quadratic Equations With One Real Solution
      17. 17
        Modeling With Quadratic Equations
    2. 2.10.2. Quadratic Functions
      1. 1
        Graphing Elementary Quadratic Functions
      2. 2
        Vertical Reflections of Quadratic Functions
      3. 3
        Graphs of General Quadratic Functions
      4. 4
        Roots of Quadratic Functions
      5. 5
        The Discriminant of a Quadratic Function
      6. 6
        The Axis of Symmetry of a Parabola
      7. 7
        The Average of the Roots Formula
      8. 8
        The Vertex Form of a Parabola
      9. 9
        Writing the Equation of a Parabola in Vertex Form
      10. 10
        Domain and Range of Quadratic Functions
      11. 11
        Solving Systems of Nonlinear Equations
      12. 12
        Finding Intersections of Lines and Quadratic Functions
    3. 3.10.3. Modeling With Quadratic Functions
      1. 1
        Modeling Downwards Vertical Motion
      2. 2
        Modeling Upwards Vertical Motion
      3. 3
        Vertical Motion
      4. 4
        Revenue, Cost, and Profit Functions
      5. 5
        Constructing Revenue, Cost, and Profit Functions
      6. 6
        Maximizing Profit and Break-Even Points
  11. 11.Sequences
    1. 1.11.1. Introduction to Sequences
      1. 1
        Introduction to Sequences
      2. 2
        Recursive Sequences
      3. 3
        Fibonacci Sequences
    2. 2.11.2. Arithmetic Sequences
      1. 1
        Arithmetic Sequences
      2. 2
        Recursive Formulas for Arithmetic Sequences
      3. 3
        The Nth Term of an Arithmetic Sequence
      4. 4
        Translating Between Explicit and Recursive Formulas for Arithmetic Sequences
      5. 5
        Finding the Common Difference of an Arithmetic Sequence
      6. 6
        Finding the Nth Term of an Arithmetic Sequence Given Two Terms
      7. 7
        Determining Indexes of Terms in Arithmetic Sequences
      8. 8
        Solving for Variables in Arithmetic Sequences
      9. 9
        Modeling With Arithmetic Sequences
    3. 3.11.3. Geometric Sequences
      1. 1
        Introduction to Geometric Sequences
      2. 2
        The Recursive Formula for a Geometric Sequence
      3. 3
        The Nth Term of a Geometric Sequence
      4. 4
        Translating Between Explicit and Recursive Formulas for Geometric Sequences
      5. 5
        Finding the Common Ratio of a Geometric Sequence Given Two Terms
      6. 6
        Determining Indexes of Terms in Geometric Sequences
  12. 12.Bivariate Statistics
    1. 1.12.1. Correlation & Regression
      1. 1
        Scatter Plots
      2. 2
        Trend Lines
      3. 3
        Making Predictions Using Trend Lines
      4. 4
        Interpreting Trend Line Coefficients
      5. 5
        Linear Correlation
      6. 6
        Selecting a Regression Model