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Integrated Math I (Honors)

Math Academy official course import: Integrated Math I (Honors)

226 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
    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
        Unit Conversions Using Base Units of Length
      3. 3
        Unit Conversions Using Units of Time
      4. 4
        Two-Step Unit Conversions
      5. 5
        Converting Units of Area to Smaller Units
      6. 6
        Converting Units of Area to Larger Units
      7. 7
        Converting Between Mixed Units
      8. 8
        Determining Units in Formulas
      9. 9
        Selecting Units for Rates of Change
      10. 10
        Degrees of Accuracy
    2. 2.3.2. Direct and Inverse Variation
      1. 1
        Modeling with Direct Variation
      2. 2
        Inverse Variation
      3. 3
        Modeling With Inverse Variation
  4. 4.Radicals and Rationals
    1. 1.4.1. Radical Expressions
      1. 1
        Writing Radical Expressions Using Fractional Exponents
      2. 2
        The Square Root of a Perfect Square With Algebraic Expressions
      3. 3
        The Square Root of a Perfect Square With Domain Restrictions
      4. 4
        The Cube Root of a Perfect Cube With Algebraic Expressions
      5. 5
        Simplifying Square Root Expressions Using the Product Rule
      6. 6
        Combining Radical Expressions Using the Product Rule
      7. 7
        Simplifying Square Root Expressions Using the Quotient Rule
      8. 8
        Evaluating Algebraic Radical Expressions
      9. 9
        Adding and Subtracting Radical Expressions
    2. 2.4.2. Rational Expressions
      1. 1
        Equivalent Expressions With Fractions
      2. 2
        Simplifying Rational Expressions
      3. 3
        Simplifying Rational Expressions by Factoring
      4. 4
        Splitting Rational Expressions Into Separate Terms
    3. 3.4.3. 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
  5. 5.Functions
    1. 1.5.1. 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
  6. 6.Absolute Value
    1. 1.6.1. 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
        Absolute Value Inequalities
  7. 7.Exponents
    1. 1.7.1. Rules of Exponents
      1. 1
        The Product Rule for Exponents With Algebraic Expressions
      2. 2
        The Quotient Rule for Exponents With Algebraic Expressions
      3. 3
        The Power Rule for Exponents With Algebraic Expressions
      4. 4
        The Power of Product Rule With Algebraic Expressions
      5. 5
        The Power of Quotient Rule With Algebraic Expressions
      6. 6
        Combining the Rules of Exponents With Algebraic Expressions
    2. 2.7.2. Exponential Expressions and 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. 3.7.3. 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
  8. 8.Polynomials
    1. 1.8.1. 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. 2.8.2. 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
  9. 9.Sequences
    1. 1.9.1. Introduction to Sequences
      1. 1
        Introduction to Sequences
      2. 2
        Recursive Sequences
      3. 3
        Fibonacci Sequences
    2. 2.9.2. 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
  10. 10.Geometry
    1. 1.10.1. Geometric Proofs
      1. 1
        Identifying Angle Postulates
      2. 2
        Identifying Angle Theorems
      3. 3
        Proving Alternate Angle Theorems
      4. 4
        Further Proving Alternate Angle Theorems
      5. 5
        Proving Consecutive Angle Theorems
      6. 6
        Further Proving Consecutive Angle Theorems
      7. 7
        Proving Perpendicular Line Theorems
      8. 8
        Further Proving Perpendicular Line Theorems
    2. 2.10.2. Geometric Transformations
      1. 1
        Translations of Geometric Figures
      2. 2
        Rotations of Geometric Figures
      3. 3
        Rotating Objects in the Coordinate Plane Using Functions
      4. 4
        Reflections of Geometric Figures in the Cartesian Plane
      5. 5
        Reflections of Figures Across Arbitrary Lines
      6. 6
        Dilations of Geometric Figures
      7. 7
        Dilations of Figures in the Coordinate Plane
      8. 8
        Stretches of Geometric Figures
      9. 9
        Combining Stretches of Geometric Figures
      10. 10
        Combining Geometric Transformations
      11. 11
        Reflective Symmetry
      12. 12
        Rotational Symmetry
    3. 3.10.3. Congruence
      1. 1
        The ASA Congruence Criterion
      2. 2
        The AAS Congruence Criterion
      3. 3
        The SAS Congruence Criterion
      4. 4
        The SSS Congruence Criterion
      5. 5
        The HL Congruence Criterion
      6. 6
        Combining Congruence Criteria for Triangles
      7. 7
        Rigid Motions and Congruence
      8. 8
        Properties of Congruence
      9. 9
        Proving Congruence Statements
    4. 4.10.4. Triangles
      1. 1
        The Pythagorean Theorem
      2. 2
        The 45-45-90 Triangle
      3. 3
        30-60-90 Triangles
      4. 4
        The Area of a 45-45-90 Triangle
      5. 5
        The Area of a 30-60-90 Triangle
      6. 6
        The Area of an Equilateral Triangle
      7. 7
        Diagonals of Squares
      8. 8
        Medians and Centroids of Triangles
      9. 9
        The Exterior Angle Theorem
    5. 5.10.5. Circles
      1. 1
        Circles
      2. 2
        Arcs, Segments, and Sectors of Circles
      3. 3
        The Circumference of a Circle
      4. 4
        Areas of Circles
      5. 5
        Central Angles and Arcs
      6. 6
        Calculating Arc Lengths of Circular Sectors
      7. 7
        Calculating Areas of Circular Sectors
      8. 8
        Further Calculating Areas of Sectors
      9. 9
        Problem Solving With Circles
      10. 10
        Circles Inscribed in Squares
      11. 11
        Squares Inscribed in Circles
    6. 6.10.6. Coordinate Geometry
      1. 1
        Parallel Lines in the Coordinate Plane
      2. 2
        Finding Equations of Parallel Lines
      3. 3
        Perpendicular Lines in the Coordinate Plane
      4. 4
        Finding Equations of Perpendicular Lines
      5. 5
        Midpoints in the Coordinate Plane
      6. 6
        Partitioning Line Segments
      7. 7
        The Distance Formula
      8. 8
        The Shortest Distance Between a Point and a Line
      9. 9
        Calculating Perimeters in the Plane
      10. 10
        Calculating Areas of Rectangles in the Plane
      11. 11
        Calculating Areas of Triangles and Quadrilaterals in the Plane
  11. 11.Statistics
    1. 1.11.1. Correlation
      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
        Correlation vs. Causation