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Integrated Math II (Honors)

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

329 节课

课程大纲

  1. 1.Number Systems
    1. 1.1.1. The Number System
      1. 1
        The Real Number System
      2. 2
        Writing Repeating Decimals as Fractions
      3. 3
        Sums and Products of Rational and Irrational Numbers
    2. 2.1.2. Introduction to Complex Numbers
      1. 1
        Imaginary Numbers
      2. 2
        Quadratic Equations with Purely Imaginary Solutions
      3. 3
        Complex Numbers
      4. 4
        Adding and Subtracting Complex Numbers
      5. 5
        Multiplying Complex Numbers
      6. 6
        Solving Quadratic Equations With Complex Roots
      7. 7
        The Cyclic Property of the Imaginary Unit
  2. 2.Polynomials
    1. 1.2.1. Polynomials
      1. 1
        The Least Common Multiple of Two Monomials
      2. 2
        The Least Common Multiple of Two Polynomials
      3. 3
        Describing Relationships Using Polynomial Identities
    2. 2.2.2. 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
    3. 3.2.3. Factoring Polynomials
      1. 1
        Further Factoring of Polynomials Using GCFs
      2. 2
        Factoring Higher-Order Polynomials as a Difference of Squares
      3. 3
        Factoring Cubic Expressions by Grouping
      4. 4
        Factoring Sums and Differences of Cubes
      5. 5
        Factoring Biquadratic Expressions
    4. 4.2.4. Polynomial Equations
      1. 1
        Determining the Roots of Polynomials
      2. 2
        Solving Polynomial Equations Using the GCF
      3. 3
        Solving Cubic Equations by Grouping
      4. 4
        Solving Biquadratic Equations
  3. 3.Quadratic Functions
    1. 1.3.1. 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
    2. 2.3.2. 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
  4. 4.Functions
    1. 1.4.1. Functions
      1. 1
        The Arithmetic of Functions
      2. 2
        Function Composition
      3. 3
        Describing Function Composition
      4. 4
        Local Extrema of Functions
      5. 5
        One-To-One Functions
      6. 6
        Introduction to Inverse Functions
      7. 7
        Calculating the Inverse of a Function
      8. 8
        Inverses of Quadratic Functions
      9. 9
        Graphs of Inverse Functions
      10. 10
        Domain and Range of Inverse Functions
      11. 11
        Invertible Functions
      12. 12
        Plotting X as a Function of Y
      13. 13
        Periodic Functions
      14. 14
        Even and Odd Functions
      15. 15
        Unbounded Behavior of Functions Near a Point
      16. 16
        The Average Rate of Change of a Function
    2. 2.4.2. Graph Transformations of Functions
      1. 1
        Vertical Translations of Functions
      2. 2
        Horizontal Translations of Functions
      3. 3
        Vertical Stretches of Functions
      4. 4
        Horizontal Stretches of Functions
      5. 5
        Vertical Reflections of Functions
      6. 6
        Horizontal Reflections of Functions
      7. 7
        Combining Graph Transformations: Two Operations
      8. 8
        Combining Graph Transformations: Three or More Operations
      9. 9
        Constructing Functions Using Transformations
      10. 10
        Combining Reflections With Other Graph Transformations
      11. 11
        Finding Points on Transformed Curves
      12. 12
        The Domain and Range of Transformed Functions
      13. 13
        Absolute Value Graph Transformations
  5. 5.Absolute Value Functions
    1. 1.5.1. 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
      7. 7
        Equations Connecting Absolute Value and Linear Functions
      8. 8
        Absolute Value Equations With Extraneous Solutions
  6. 6.Exponentials & Logarithms
    1. 1.6.1. Introduction to Logarithms
      1. 1
        Converting From Exponential to Logarithmic Form
      2. 2
        Converting From Logarithmic to Exponential Form
      3. 3
        Evaluating Logarithms
      4. 4
        The Natural Logarithm
      5. 5
        The Common Logarithm
      6. 6
        Simplifying Logarithmic Expressions
    2. 2.6.2. The Laws of Logarithms
      1. 1
        The Product Rule for Logarithms
      2. 2
        The Quotient Rule for Logarithms
      3. 3
        The Power Rule for Logarithms
      4. 4
        Combining the Laws of Logarithms
      5. 5
        The Change of Base Formula for Logarithms
    3. 3.6.3. Graphs of Exponential Functions
      1. 1
        Vertical Translations of Exponential Growth Functions
      2. 2
        Vertical Translations of Exponential Decay Functions
      3. 3
        Interpreting Graphs of Exponential Functions
      4. 4
        Vertical Reflections of Exponential Functions
      5. 5
        Combining Graph Transformations of Exponential Functions
      6. 6
        Properties of Transformed Exponential Functions
    4. 4.6.4. Graphs of Logarithmic Functions
      1. 1
        Graphing Logarithmic Functions
      2. 2
        Combining Graph Transformations of Logarithmic Functions
      3. 3
        Properties of Transformed Logarithmic Functions
      4. 4
        Inverses of Exponential and Logarithmic Functions
    5. 5.6.5. Exponential Equations
      1. 1
        Solving Exponential Equations Using Logarithms
      2. 2
        Solving Equations Containing the Exponential Function
      3. 3
        Solving Exponential Equations With Different Bases
      4. 4
        Solving Exponential Equations With Different Bases Using Logarithms
      5. 5
        Solving Exponential Equations Using the Zero-Product Property
    6. 6.6.6. Logarithmic Equations
      1. 1
        Solving Logarithmic Equations
      2. 2
        Solving Logarithmic Equations Containing the Natural Logarithm
      3. 3
        Solving Logarithmic Equations Using the Laws of Logarithms
      4. 4
        Solving Logarithmic Equations by Combining the Laws of Logarithms
      5. 5
        Solving Logarithmic Equations With Logarithms on Both Sides
      6. 6
        Solving Logarithmic Equations Using the Zero-Product Property
    7. 7.6.7. Modeling with Exponential Functions
      1. 1
        Modeling With Compound Interest
      2. 2
        Continuously Compounded Interest
      3. 3
        Converting Between Exponents
  7. 7.Sequences & Series
    1. 1.7.1. 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
    2. 2.7.2. Arithmetic Series
      1. 1
        Sigma Notation
      2. 2
        Properties of Finite Series
      3. 3
        Expressing an Arithmetic Series in Sigma Notation
      4. 4
        Finding the Sum of an Arithmetic Series
      5. 5
        Finding the First Term of an Arithmetic Series
      6. 6
        Calculating the Number of Terms in an Arithmetic Series
      7. 7
        Modeling With Arithmetic Series
    3. 3.7.3. The Binomial Theorem
      1. 1
        Pascal's Triangle and the Binomial Coefficients
      2. 2
        Expanding a Binomial Using Binomial Coefficients
      3. 3
        The Special Case of the Binomial Theorem
      4. 4
        Approximating Values Using the Binomial Theorem
  8. 8.Rationals & Radicals
    1. 1.8.1. Rational Expressions
      1. 1
        Simplifying Rational Expressions Using Polynomial Factorization
      2. 2
        Adding and Subtracting Rational Expressions
      3. 3
        Adding Rational Expressions With No Common Factors in the Denominator
      4. 4
        Multiplying Rational Expressions
      5. 5
        Dividing Rational Expressions
    2. 2.8.2. Radical Equations
      1. 1
        Solving Radical Equations
      2. 2
        Solving Advanced Radical Equations
  9. 9.Geometry
    1. 1.9.1. Similarity
      1. 1
        Similarity and Similar Polygons
      2. 2
        Side Lengths and Angle Measures of Similar Polygons
      3. 3
        Areas of Similar Polygons
      4. 4
        Working With Areas of Similar Polygons
      5. 5
        Similarity Transformations
      6. 6
        The AA Similarity Criterion
      7. 7
        The SSS Similarity Criterion
      8. 8
        The SAS Similarity Criterion
      9. 9
        Combining Similarity Criteria for Triangles
      10. 10
        Proving Similarity Statements
      11. 11
        The Midpoint Theorem
      12. 12
        Proving the Midpoint Theorem
      13. 13
        The Triangle Proportionality Theorem
    2. 2.9.2. Circles
      1. 1
        Inscribed Angles
      2. 2
        Problem-Solving With Inscribed Angles
      3. 3
        Thales' Theorem
      4. 4
        Angles in Inscribed Right Triangles
      5. 5
        Further Angles in Inscribed Right Triangles
      6. 6
        Inscribed Quadrilaterals
      7. 7
        Tangent Lines to Circles
      8. 8
        Tangent-Tangent Lines to Circles
      9. 9
        Secant-Secant Angles to Circles
      10. 10
        Secant-Tangent Angles to Circles
      11. 11
        The Tangent-Chord Theorem
      12. 12
        Circle Similarity
      13. 13
        Proving Circle Similarity
    3. 3.9.3. Polygons
      1. 1
        Proving Triangle Theorems
      2. 2
        Proofs Involving Isosceles Triangles
      3. 3
        Proofs Involving Medians and Centroids
      4. 4
        Diagonals of Squares
      5. 5
        Properties of Parallelograms
      6. 6
        Proving Properties of Parallelograms
      7. 7
        Proving Criteria for Parallelograms and Rectangles
    4. 4.9.4. Circles
      1. 1
        Circles in the Coordinate Plane
      2. 2
        Equations of Circles Centered at the Origin
      3. 3
        Equations of Circles
      4. 4
        Determining Circle Properties by Completing the Square
      5. 5
        Calculating Circle Intercepts
      6. 6
        Intersections of Circles with Lines
      7. 7
        Equations of Tangent Lines to Circles
      8. 8
        Perpendicular Bisectors of Diameters in the Coordinate Plane
      9. 9
        Perpendicular Bisectors of Chords
      10. 10
        Perpendicular Bisectors of Chords in the Coordinate Plane
      11. 11
        Thales' Theorem in the Coordinate Plane
    5. 5.9.5. Parabolas
      1. 1
        Upward and Downward Opening Parabolas
      2. 2
        Left and Right Opening Parabolas
      3. 3
        The Vertex of a Parabola
      4. 4
        Calculating the Vertex of a Parabola by Completing the Square
      5. 5
        The Focus-Directrix Property of a Parabola
      6. 6
        Calculating the Focus of a Parabola
      7. 7
        Calculating the Directrix of a Parabola
      8. 8
        Calculating Intercepts of Parabolas
      9. 9
        Intersections of Parabolas With Lines
  10. 10.Solid Geometry
    1. 1.10.1. Introduction to Solid Geometry
      1. 1
        Identifying Three-Dimensional Shapes
      2. 2
        Faces, Vertices, and Edges of Polyhedrons
      3. 3
        Nets of Polyhedrons
      4. 4
        Finding Surface Areas Using Nets
      5. 5
        The Distance Formula in Three Dimensions
      6. 6
        Euler's Formula for Polyhedra
      7. 7
        The Five Platonic Solids
      8. 8
        Surface Areas and Volumes of Similar Solids
    2. 2.10.2. Rectangular Solids and Pyramids
      1. 1
        Volumes of Cubes
      2. 2
        Surface Areas of Cubes
      3. 3
        Face Diagonals of Cubes
      4. 4
        Diagonals of Cubes
      5. 5
        Volumes of Rectangular Solids
      6. 6
        Surface Areas of Rectangular Solids
      7. 7
        Diagonals of Rectangular Solids
      8. 8
        Volumes of Pyramids
      9. 9
        Surface Areas of Pyramids
    3. 3.10.3. Non-Polyhedrons
      1. 1
        Volumes of Cylinders
      2. 2
        Surface Areas of Cylinders
      3. 3
        Volumes of Right Cones
      4. 4
        Slant Heights of Right Cones
      5. 5
        Surface Areas of Right Cones
      6. 6
        Volumes of Spheres
      7. 7
        Surface Areas of Spheres
      8. 8
        Conical Frustums
      9. 9
        Volumes of Revolution
  11. 11.Trigonometry
    1. 1.11.1. Introduction to Trigonometry
      1. 1
        Angles and Sides in Right Triangles
      2. 2
        The Trigonometric Ratios
      3. 3
        Calculating Trigonometric Ratios Using the Pythagorean Theorem
      4. 4
        Calculating Side Lengths of Right Triangles Using Trigonometry
      5. 5
        Calculating Angles in Right Triangles Using Trigonometry
      6. 6
        Modeling With Trigonometry
      7. 7
        The Reciprocal Trigonometric Ratios
      8. 8
        Trigonometric Ratios in Similar Right Triangles
      9. 9
        Trigonometric Functions of Complementary Angles
      10. 10
        Special Trigonometric Ratios
      11. 11
        Calculating the Area of a Right Triangle Using Trigonometry
      12. 12
        Solving Multiple Right Triangles Using Trigonometry
    2. 2.11.2. Radians
      1. 1
        Introduction to Radians
      2. 2
        Calculating Arc Length Using Radians
      3. 3
        Calculating Areas of Sectors Using Radians
      4. 4
        Trigonometric Ratios With Radians
    3. 3.11.3. The Unit Circle
      1. 1
        Angles in the Coordinate Plane
      2. 2
        Negative Angles in the Coordinate Plane
      3. 3
        Coterminal Angles
      4. 4
        Calculating Reference Angles
      5. 5
        Properties of the Unit Circle in the First Quadrant
      6. 6
        Extending the Trigonometric Ratios Using the Unit Circle
      7. 7
        Extending the Trigonometric Ratios Using Angles in Radians
      8. 8
        Extending the Trigonometric Ratios to Negative Angles
      9. 9
        Extending the Trigonometric Ratios to Large Angles
      10. 10
        Using the Pythagorean Identity in the First Quadrant
      11. 11
        Extending the Pythagorean Identity to All Quadrants
    4. 4.11.4. Special Trigonometric Ratios
      1. 1
        Finding Trigonometric Ratios of Quadrantal Angles
      2. 2
        Trigonometric Ratios of Quadrantal Angles Outside the Standard Range
      3. 3
        Finding Trigonometric Ratios of Special Angles Using the Unit Circle
      4. 4
        Evaluating Trigonometric Expressions
      5. 5
        Further Extensions of the Special Trigonometric Ratios
    5. 5.11.5. Graphing Trigonometric Functions
      1. 1
        Graphing Sine and Cosine
      2. 2
        Graphing Tangent and Cotangent
      3. 3
        Graphing Secant and Cosecant
    6. 6.11.6. Properties of Trigonometric Functions
      1. 1
        Describing Properties of the Sine Function
      2. 2
        Describing Properties of the Cosine Function
      3. 3
        Describing Properties of the Tangent Function
      4. 4
        Describing Properties of the Secant Function
      5. 5
        Describing Properties of the Cosecant Function
      6. 6
        Describing Properties of the Cotangent Function
    7. 7.11.7. Graph Transformations of Trigonometric Functions
      1. 1
        Vertical Translations of Trigonometric Functions
      2. 2
        Vertical Stretches of Trigonometric Functions
      3. 3
        Horizontal Translations of Trigonometric Functions
      4. 4
        Horizontal Stretches of Trigonometric Functions
      5. 5
        Combining Graph Transformations of Sine and Cosine
      6. 6
        Graph Transformations of Tangent and Cotangent
      7. 7
        Combining Graph Transformations of Tangent and Cotangent
      8. 8
        Combining Graph Transformations of Secant and Cosecant
      9. 9
        Graphing Reflections of Trigonometric Functions
      10. 10
        Graphing Reflections of Trigonometric Functions: Three or More Transformations
    8. 8.11.8. Properties of Transformed Trigonometric Functions
      1. 1
        Properties of Transformed Sine and Cosine Functions
      2. 2
        Finding Zeros and Extrema of Transformed Sine and Cosine Functions
      3. 3
        Properties of Transformed Tangent and Cotangent Functions
      4. 4
        Properties of Transformed Secant and Cosecant Functions
      5. 5
        Interpreting Trigonometric Models
      6. 6
        Modeling With Trigonometric Functions
  12. 12.Probability & Statistics
    1. 1.12.1. Introduction to Probability
      1. 1
        Sets
      2. 2
        Probability From Experimental Data
      3. 3
        Sample Spaces and Events in Probability
      4. 4
        Single Events in Probability
      5. 5
        The Complement of an Event
      6. 6
        Venn Diagrams in Probability
      7. 7
        Geometric Probability
    2. 2.12.2. Compound Events in Probability
      1. 1
        The Union of Sets
      2. 2
        The Intersection of Sets
      3. 3
        Compound Events in Probability From Experimental Data
      4. 4
        Computing Probabilities for Compound Events Using Venn Diagrams
      5. 5
        Computing Probabilities of Events Containing Complements Using Venn Diagrams
      6. 6
        Computing Probabilities for Three Events Using Venn Diagrams
    3. 3.12.3. Conditional Probability
      1. 1
        Conditional Probabilities From Venn Diagrams
      2. 2
        Conditional Probabilities From Tables
      3. 3
        The Multiplication Law for Conditional Probability
      4. 4
        The Law of Total Probability
      5. 5
        Tree Diagrams for Dependent Events
      6. 6
        Tree Diagrams for Dependent Events: Applications
      7. 7
        Independent Events
      8. 8
        Tree Diagrams for Independent Events
      9. 9
        The Addition Law of Probability
      10. 10
        Applying the Addition Law With Event Complements
      11. 11
        Mutually Exclusive Events
    4. 4.12.4. Combinatorics
      1. 1
        The Rules of Sum and Product
      2. 2
        Factorials
      3. 3
        Factorials in Variable Expressions
      4. 4
        Ordering Objects
      5. 5
        Permutations
      6. 6
        Combinations
      7. 7
        Computing Probabilities Using Combinatorics
    5. 5.12.5. Analyzing Data
      1. 1
        Sampling
      2. 2
        The Mean of a Data Set
      3. 3
        Variance and Standard Deviation
      4. 4
        Estimating Means and Variances For Grouped Data
      5. 5
        Covariance
      6. 6
        Sums of Squares
    6. 6.12.6. Correlation and Regression
      1. 1
        The Linear Correlation Coefficient
      2. 2
        Residuals and Residual Plots
      3. 3
        Selecting a Regression Model