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SAT Math Fundamentals

Math Academy official course import: SAT Math Fundamentals

627 节课

课程大纲

  1. 1.Preliminaries
    1. 1.1.1. Addition and Subtraction of Rational Numbers
      1. 1
        Subtracting a Positive Number From a Smaller Positive Number
      2. 2
        Subtracting a Positive Number From a Negative Number
      3. 3
        Subtracting a Positive Fraction From a Smaller Fraction
      4. 4
        Subtracting a Positive Decimal From a Smaller Decimal
      5. 5
        Adding a Positive Number to a Negative Number
      6. 6
        Adding a Negative Number
      7. 7
        Subtracting a Negative Number
      8. 8
        Additive Inverses of Numbers
      9. 9
        Solving Problems Using Addition and Subtraction of Rational Numbers
    2. 2.1.2. Multiplication and Division of Rational Numbers
      1. 1
        Multiplying Positive Numbers With Negative Numbers
      2. 2
        Multiplying Negative Numbers
      3. 3
        Dividing With Negative Numbers
      4. 4
        Equivalent Fractions With Negative Numbers
      5. 5
        Dividing With Negative Decimals and Fractions
      6. 6
        Reciprocals of Rational Numbers
      7. 7
        Multiplying and Dividing With Zero
      8. 8
        Fractions of Fractions
      9. 9
        Solving Problems Using the Four Operations on Rational Numbers
    3. 3.1.3. Exponents
      1. 1
        Squaring Rational Numbers
      2. 2
        Cubing Rational Numbers
      3. 3
        Exponents With Rational Bases
      4. 4
        The Zeroth Power
      5. 5
        Powers of Negative One
      6. 6
        Negative Exponents
      7. 7
        The Product Rule for Exponents
      8. 8
        The Quotient Rule for Exponents
      9. 9
        The Power Rule for Exponents
      10. 10
        The Power of Product Rule for Exponents
      11. 11
        The Power of Quotient Rule for Exponents
      12. 12
        Combining the Rules of Exponents
    4. 4.1.4. Radicals
      1. 1
        The Square Root of a Perfect Square
      2. 2
        Squaring a Square Root
      3. 3
        The Cube Root of a Perfect Cube
      4. 4
        Surds
      5. 5
        Simplifying Expressions With Surds
      6. 6
        Evaluating Numerical Expressions Containing Radicals
      7. 7
        Adding and Subtracting Radicals
      8. 8
        Rationalizing Denominators
      9. 9
        Rationalizing Denominators With Two Terms
      10. 10
        Radicals as Fractional Exponents
      11. 11
        The Product Rule for Radicals
      12. 12
        The Quotient Rule for Radicals
      13. 13
        Applying the Distributive Law to Radical Expressions
      14. 14
        Comparing Radicals
    5. 5.1.5. Order of Operations
      1. 1
        Natural Numbers, Integers, and Rational Numbers
      2. 2
        Evaluating Rational Number Expressions Without Exponents
      3. 3
        Evaluating Expressions With Positive Integer Exponents
      4. 4
        Evaluating Expressions With Integer Exponents
    6. 6.1.6. Algebraic Expressions
      1. 1
        Introduction to Algebraic Expressions
      2. 2
        Constructing Algebraic Expressions
      3. 3
        Evaluating Linear Expressions
      4. 4
        Evaluating Rational Expressions
      5. 5
        Identifying Terms in Linear Expressions
      6. 6
        Identifying Coefficients and Constants in Linear Expressions
      7. 7
        The Greatest Common Factor of Two Linear Expressions
    7. 7.1.7. Simplifying Linear Expressions
      1. 1
        Identifying Like Terms in a Linear Expression
      2. 2
        Collecting Like Terms in a Linear Expression
      3. 3
        Applying the Distributive Law With Linear Expressions
      4. 4
        The Distributive Law With Three Terms
      5. 5
        Distributing the Negative Sign in a Linear Expression
      6. 6
        Simplifying Linear Expressions Using the Distributive Law
      7. 7
        Simplifying Linear Expressions When a Group of Terms Is Subtracted
      8. 8
        Simplifying Linear Expressions Containing Fractions
      9. 9
        Factoring Numerical Expressions
      10. 10
        Factoring Linear Expressions
  2. 2.Algebra - Linear Equations in One Variable
    1. 1.2.1. Solving Linear Equations
      1. 1
        Solving Linear Equations by Trial and Error
      2. 2
        Solving One-Step Addition and Subtraction Equations
      3. 3
        Solving One-Step Multiplication and Division Equations
      4. 4
        Solving Two-Step Equations
      5. 5
        Solving Linear Equations With Fractional Coefficients
      6. 6
        Solving Linear Equations With Decimal Coefficients
      7. 7
        Solving Linear Equations With Variables on Both Sides
      8. 8
        Solving Linear Equations Containing Binomials
      9. 9
        Solving Linear Equations Containing Binomials by Factoring
      10. 10
        Solving Linear Equations by Clearing a Rational Expression
      11. 11
        Solving Linear Equations Using Cross-Multiplication
      12. 12
        Manipulating Expressions and Equations
      13. 13
        Solving Two-Variable Equations
      14. 14
        Linear Equations With Infinitely Many Solutions
      15. 15
        Linear Equations With No Solutions
      16. 16
        Solving Linear Equations With Unknown Coefficients
      17. 17
        Solving Linear Equations With Unknown Coefficients by Factoring
      18. 18
        Solving Linear Inequalities With Unknown Parameters
      19. 19
        Solving Many-Variable Equations
    2. 2.2.2. 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.Algebra - Linear Equations in Two Variables
    1. 1.3.1. Graphs of Linear Equations
      1. 1
        The Cartesian Coordinate System
      2. 2
        Distances Between Points in the Coordinate Plane
      3. 3
        Two-Variable Linear Equations and Their Solutions
      4. 4
        Graphing Linear Equations
      5. 5
        Horizontal and Vertical Lines
      6. 6
        Calculating Slopes of Straight Lines
      7. 7
        Equations of Lines in Slope-Intercept Form
      8. 8
        Properties of Lines Given in Slope-Intercept Form
      9. 9
        Working With Lines in Slope-Intercept Form
      10. 10
        Equations of Lines in Point-Slope Form
      11. 11
        Equations of Lines in Standard Form
      12. 12
        Properties of Lines Given in Standard Form
      13. 13
        Parallel Lines in the Coordinate Plane
      14. 14
        Finding Equations of Parallel Lines
      15. 15
        Perpendicular Lines in the Coordinate Plane
      16. 16
        Finding Equations of Perpendicular Lines
    2. 2.3.2. 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
        Interpreting Coefficients of Two-Variable Equations
      4. 4
        Analyzing and Interpreting Graphs of Linear Equations
      5. 5
        Further Modeling With Linear Equations in Two Variables
      6. 6
        Distance-Time Graphs
      7. 7
        Calculating Acceleration From a Speed-Time Graph
      8. 8
        Calculating Distance From a Speed-Time Graph
    3. 3.3.3. Systems of Equations
      1. 1
        Introduction to Systems of Linear Equations
      2. 2
        Solving Systems of Equations by Substitution
      3. 3
        Introduction to the Elimination Method
      4. 4
        Solving Systems of Linear Equations Using Elimination: One Transformation
      5. 5
        Solving Systems of Linear Equations Using Elimination: Two Transformations
      6. 6
        Systems of Linear Equations With Fractional Coefficients
      7. 7
        Systems of Linear Equations With Decimal Coefficients
      8. 8
        Systems of Equations With No Solutions and Infinitely Many Solutions
      9. 9
        Parametrizing Systems With Infinitely Many Solutions
      10. 10
        Determining Unknown Parameters in Systems of Linear Equations
      11. 11
        Calculating the Intersection of Two Lines
      12. 12
        Solving Systems of Linear Equations by Identifying Structure
      13. 13
        Larger Systems of Equations
      14. 14
        Modeling Using Systems of Linear Equations
      15. 15
        Modeling Coin Problems Using Systems of Linear Equations
  4. 4.Algebra - Linear Inequalities
    1. 1.4.1. Linear Inequalities
      1. 1
        Inequalities
      2. 2
        Compound Inequalities
      3. 3
        Verifying Solutions of Linear Inequalities
      4. 4
        Solving One-Step Linear Inequalities
      5. 5
        Solving Two-Step Inequalities
      6. 6
        Representing Solutions to Inequalities on Number Lines
      7. 7
        Further Solving Linear Inequalities
      8. 8
        Solving Compound Inequalities
      9. 9
        Interval Notation
      10. 10
        Unbounded Intervals
      11. 11
        Unions of Intervals
      12. 12
        Intersections of Intervals
      13. 13
        Compound OR Inequalities
      14. 14
        Optimizing Sums, Differences, Products, and Quotients
    2. 2.4.2. 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
    3. 3.4.3. Modeling With Inequalities
      1. 1
        Introduction to Modeling With Inequalities
      2. 2
        Modeling With One-Step Inequalities
      3. 3
        Modeling With Two-Step Inequalities
      4. 4
        Modeling With Compound 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
  5. 5.Geometry - Points, Lines, & Angles
    1. 1.5.1. Introduction to Geometry
      1. 1
        Units of Area and Volume
      2. 2
        Points, Lines, Rays, and Segments
      3. 3
        Parallel and Perpendicular Lines
      4. 4
        Measures of Segments
      5. 5
        Congruent Segments
      6. 6
        Midpoints
      7. 7
        Collinear Points
      8. 8
        The Segment Addition Postulate
    2. 2.5.2. Angles
      1. 1
        Angles and Measures of Angles
      2. 2
        Connecting Angles and Circles
      3. 3
        Measuring Angles Using a Protractor
      4. 4
        Sums of Angles
      5. 5
        Right, Straight, Full, and Null Angles
      6. 6
        Acute, Obtuse, and Reflex Angles
      7. 7
        Congruent Angles
      8. 8
        Vertical Angles
      9. 9
        Solving Problems With Angles
    3. 3.5.3. Advanced Angles
      1. 1
        Complementary Angles
      2. 2
        Supplementary Angles
      3. 3
        Corresponding Angles
      4. 4
        Alternate Angles
      5. 5
        Consecutive Angles
      6. 6
        Angle Criteria for Parallel Lines
      7. 7
        Angle Bisectors
      8. 8
        Segment Bisectors and the Perpendicular Bisector Theorem
    4. 4.5.4. Geometric Transformations
      1. 1
        Translations of Geometric Figures
      2. 2
        Rotations of Geometric Figures
      3. 3
        Reflections of Geometric Figures in the Cartesian Plane
      4. 4
        Reflections of Figures Across Arbitrary Lines
      5. 5
        Reflective Symmetry
      6. 6
        Rotational Symmetry
  6. 6.Geometry - Polygons & Solids
    1. 1.6.1. Triangles
      1. 1
        Interior Angles of Triangles
      2. 2
        Exterior Angles of Triangles
      3. 3
        Problem Solving With Angles of Triangles
      4. 4
        Classifying Triangles
      5. 5
        The Isosceles Triangle Theorem
      6. 6
        Heights of Triangles
      7. 7
        Medians and Centroids of Triangles
    2. 2.6.2. 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
        Recognizing 30-60-90 Triangles
      9. 9
        Solving Geometry Problems by Manipulating Radicals
    3. 3.6.3. Polygons
      1. 1
        Polygons
      2. 2
        Interior Angles of Polygons
      3. 3
        Exterior Angles of Polygons
      4. 4
        Congruent Polygons
      5. 5
        Regular Polygons
      6. 6
        Properties of Rectangles and Squares
    4. 4.6.4. 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
  7. 7.Geometry - Congruence & Similarity
    1. 1.7.1. 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
        Solving Problems Describing Congruent Triangles
    2. 2.7.2. 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
        Working With Descriptions of Similar Shapes
      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
        Solving Problems Describing Similar Triangles
      11. 11
        Solving Parallel Line Problems From Descriptions
      12. 12
        The Midpoint Theorem
      13. 13
        The Triangle Proportionality Theorem
      14. 14
        Surface Areas and Volumes of Similar Solids
      15. 15
        Working With Descriptions of Similar Solids
  8. 8.Geometry - Length, Area & Volume
    1. 1.8.1. Perimeter & Area of Plane Figures
      1. 1
        The Perimeter of a Polygon
      2. 2
        Areas of Rectangles and Squares
      3. 3
        Areas of Parallelograms
      4. 4
        Areas of Triangles
      5. 5
        Areas of Trapezoids
      6. 6
        Areas and Perimeters of Composite Shapes
      7. 7
        The Area Between Two Shapes
      8. 8
        Border Problems
      9. 9
        Constructing Functions Representing Properties of 2D Shapes
    2. 2.8.2. Coordinate Geometry
      1. 1
        Midpoints in the Coordinate Plane
      2. 2
        The Distance Formula
      3. 3
        Calculating Perimeters in the Plane
      4. 4
        Calculating Areas of Rectangles in the Plane
      5. 5
        Calculating Areas of Triangles and Quadrilaterals in the Plane
      6. 6
        Equations of Tangent Lines to Circles
    3. 3.8.3. Inscribed Shapes in Two Dimensions
      1. 1
        Circles Inscribed in Squares
      2. 2
        Squares Inscribed in Circles
      3. 3
        Equilateral Triangles Inscribed in Circles
      4. 4
        Circles Inscribed in Equilateral Triangles
      5. 5
        Areas of Inscribed Triangles
    4. 4.8.4. Surface Area and Volume
      1. 1
        Volumes of Cubes
      2. 2
        Surface Areas of Cubes
      3. 3
        Face Diagonals of Cubes
      4. 4
        Surface Areas of Rectangular Solids
      5. 5
        Volumes of Rectangular Solids
      6. 6
        Volumes of Cylinders
      7. 7
        Surface Areas of Cylinders
      8. 8
        Volumes of Spheres
      9. 9
        Slant Heights of Right Cones
      10. 10
        Volumes of Right Cones
      11. 11
        Volumes of Pyramids
      12. 12
        Constructing Functions Representing Properties of Rectangular Solids
      13. 13
        Constructing Functions Representing Volumes of Cylinders, Cones, and Pyramids
      14. 14
        Composite Solids
      15. 15
        Surface Areas of Combined Prisms
  9. 9.Geometry - Circles
    1. 1.9.1. 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
        Tangent Lines to Circles
      11. 11
        Isosceles Triangles in Circles
      12. 12
        Perpendicular Bisectors of Chords
    2. 2.9.2. Circles in the Coordinate Plane
      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
        Transforming Circles
    3. 3.9.3. 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
  10. 10.Trigonometry
    1. 1.10.1. 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
        Calculating Trigonometric Ratios From Descriptions
      11. 11
        Special Trigonometric Ratios
      12. 12
        Calculating the Area of a Right Triangle Using Trigonometry
      13. 13
        Solving Multiple Right Triangles Using Trigonometry
    2. 2.10.2. 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
    3. 3.10.3. 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
      6. 6
        Trigonometric Ratios of Large Angles in Degrees
      7. 7
        Trigonometric Ratios of Large Angles in Radians
  11. 11.Advanced Algebra - Functions
    1. 1.11.1. 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
        Local Extrema of Functions
      8. 8
        End Behavior of Functions
      9. 9
        The Range of a Function
      10. 10
        The Range of a Function: Advanced Cases
      11. 11
        The Roots of a Function
      12. 12
        Increasing and Decreasing Functions
      13. 13
        Piecewise Functions
      14. 14
        The Arithmetic of Functions
      15. 15
        Function Composition
      16. 16
        Describing Function Composition
      17. 17
        Introduction to Inverse Functions
      18. 18
        Even and Odd Functions
      19. 19
        Introduction to Sequences
    2. 2.11.2. Linear Functions
      1. 1
        Modeling With Linear Functions
      2. 2
        Constructing Linear Functions
      3. 3
        Linear Functions in Tabular Form
      4. 4
        Analyzing Linear Functions in Tabular Form
      5. 5
        Transformations of Linear Functions in Tabular Form
      6. 6
        Linear Functions in Tabular Form Containing Unknown Parameters
    3. 3.11.3. Graph Transformations of Functions
      1. 1
        Vertical Translations of Functions
      2. 2
        Horizontal Translations of Functions
      3. 3
        Vertical Reflections of Functions
      4. 4
        Finding Equations of Translated Functions
      5. 5
        Transforming Polynomial Functions
  12. 12.Advanced Algebra - Absolute Value
    1. 1.12.1. Absolute Value Expressions and Equations
      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
    2. 2.12.2. 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
        Roots of Absolute Value Functions
  13. 13.Advanced Algebra - Polynomials
    1. 1.13.1. 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
        The Difference of Squares Formula
    2. 2.13.2. Factoring Polynomials
      1. 1
        The Greatest Common Factor of Two Monomials
      2. 2
        The Least Common Multiple of Two Monomials
      3. 3
        The Least Common Multiple of Two Polynomials
      4. 4
        Factoring Polynomials Using GCFs
      5. 5
        Factoring Perfect Square Trinomials
      6. 6
        Factoring Perfect Square Trinomials With Leading Coefficients
      7. 7
        Factoring Differences of Squares
      8. 8
        Factoring Differences of Squares Using Surds
      9. 9
        Factoring Trinomials
      10. 10
        Factoring Trinomials Using Common Factors
      11. 11
        Factoring Trinomials With Leading Coefficients
      12. 12
        Further Factoring Trinomials With Leading Coefficients
      13. 13
        Factoring Biquadratic Expressions
      14. 14
        Factoring Expressions Containing Binomials
      15. 15
        Factoring Expressions Containing Hidden Factors
      16. 16
        Equating Polynomial Coefficients
    3. 3.13.3. Quadratic Equations
      1. 1
        Introduction to Quadratic Equations
      2. 2
        Solving Equations Using the Square Root Method
      3. 3
        Solving Equations With Odd Exponents Using the Nth Root Method
      4. 4
        Solving Equations With Even Exponents Using the Nth Root Method
      5. 5
        Solving Perfect Square Quadratic Equations
      6. 6
        Perfect Square Quadratic Equations with One or No Solutions
      7. 7
        The Zero Product Rule for Solving Quadratic Equations
      8. 8
        The Zero Product Rule for Solving Polynomial Equations
      9. 9
        Solving Quadratic Equations Using a Difference of Squares
      10. 10
        Solving Quadratic Equations with No Constant Term
      11. 11
        Solving Quadratic Equations by Factoring
      12. 12
        Solving Quadratic Equations with Leading Coefficients by Factoring
      13. 13
        Completing the Square
      14. 14
        Completing the Square With Odd Linear Terms
      15. 15
        Completing the Square With Leading Coefficients
      16. 16
        Solving Quadratic Equations by Completing the Square
      17. 17
        Solving Quadratic Equations With Leading Coefficients by Completing the Square
      18. 18
        The Quadratic Formula
      19. 19
        The Discriminant of a Quadratic Equation
      20. 20
        Vieta's Formulas
      21. 21
        Solving Biquadratic Equations
      22. 22
        Solving Quadratic Equations Containing Unknown Parameters
      23. 23
        Determining Unknown Parameters in Quadratic Equations With One Real Solution
      24. 24
        Solving Elementary Quadratic Inequalities
      25. 25
        Determining Unknown Parameters in Quadratic Equations With Real Solutions
      26. 26
        Determining Unknown Parameters in Quadratic Equations With No Real Solutions
      27. 27
        Reasoning About Coefficients of Quadratics Using Standard and Factored Forms
    4. 4.13.4. 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
        Fitting Quadratic Functions to Data Using Vertex Form
      11. 11
        Reasoning About Coefficients of Quadratics Using Symmetry
    5. 5.13.5. Systems of Equations
      1. 1
        Solving Systems of Nonlinear Equations Using Graphs
      2. 2
        Solving Systems of Nonlinear Equations by Identifying Structure
      3. 3
        Solving Systems of Nonlinear Equations
      4. 4
        Finding Intersections of Lines and Quadratic Functions
      5. 5
        Determining Unknown Parameters in Quadratic Systems With One Intersection Point
      6. 6
        Determining Unknown Parameters in Quadratic Systems With Zero or Two Intersection Points
    6. 6.13.6. 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
        Modeling Using Systems of Non-Linear Equations
    7. 7.13.7. Polynomial Expressions & Equations
      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
        Determining the Roots of Polynomials
      5. 5
        Solving Polynomial Equations Using the GCF
    8. 8.13.8. Polynomial Theorems
      1. 1
        The Factor Theorem
      2. 2
        Reasoning About Coefficients in Quadratic Equations Using the Factor Theorem
      3. 3
        Factoring Cubic Polynomials Using the Factor Theorem
      4. 4
        Multiplicities of the Roots of Polynomials
      5. 5
        Dividing Polynomials Using Synthetic Division
      6. 6
        The Remainder Theorem
    9. 9.13.9. Graphs of Polynomials
      1. 1
        Graphing Elementary Cubic Functions
      2. 2
        Graphing Cubic Curves Containing Three Distinct Real Roots
      3. 3
        Graphing Cubic Curves Containing a Double Root
      4. 4
        Graphing Cubic Curves Containing One Distinct Real Root
      5. 5
        End Behavior of Polynomials
      6. 6
        Graphing General Polynomials
      7. 7
        Identifying Valid Outputs of Factored Polynomials
  14. 14.Advanced Algebra - Exponential Equations & Functions
    1. 1.14.1. Exponential Expressions & Equations
      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
      8. 8
        Rewriting Radical Expressions Using the Laws of Exponents
      9. 9
        Applying the Distributive Law to Exponential Expressions
      10. 10
        Combining Exponential Expressions
      11. 11
        Solving Exponential Equations
      12. 12
        Solving Exponential Equations with Fractional Solutions
      13. 13
        Creating Exponential Growth Expressions
      14. 14
        Creating Exponential Decay Expressions
    2. 2.14.2. 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
        Time-Shifting Exponential Models
      11. 11
        Working With Equivalent Forms of Exponential Functions
    3. 3.14.3. Graphs of Exponential Functions
      1. 1
        Graphing Exponential Growth Functions
      2. 2
        Graphing Exponential Decay Functions
      3. 3
        Vertical Translations of Exponential Growth Functions
      4. 4
        Vertical Translations of Exponential Decay Functions
      5. 5
        Vertical Reflections of Exponential Functions
      6. 6
        Extrema of Exponential Functions
      7. 7
        Interpreting Graphs of Exponential Functions
      8. 8
        Determining Unknown Parameters in Exponential Functions
  15. 15.Advanced Algebra - Rational and Radical Equations
    1. 1.15.1. Rational Expressions
      1. 1
        Equivalent Expressions With Fractions
      2. 2
        Simplifying Rational Expressions
      3. 3
        Simplifying Rational Expressions by Factoring
      4. 4
        Simplifying Rational Expressions Using Polynomial Factorization
      5. 5
        Splitting Rational Expressions Into Separate Terms
      6. 6
        Adding and Subtracting Rational Expressions
      7. 7
        Adding Rational Expressions With No Common Factors in the Denominator
      8. 8
        Adding Rational Expressions Using Polynomial Factorization
      9. 9
        Multiplying Rational Expressions
      10. 10
        Dividing Rational Expressions
      11. 11
        Fractions of Fractions With Algebraic Expressions
    2. 2.15.2. 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
      5. 5
        Rational Equations With Three Terms
      6. 6
        Advanced Rational Equations
      7. 7
        Solving Many-Variable Rational Equations
    3. 3.15.3. 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
        Solving Radical Equations
      10. 10
        Solving Many-Variable Nonlinear Equations
  16. 16.Problem Solving - Ratios & Percentages
    1. 1.16.1. Ratios
      1. 1
        Introduction to Ratios
      2. 2
        Equivalent Ratios
      3. 3
        Writing Ratios Using Fractions
      4. 4
        Working With Equivalent Ratios
      5. 5
        More on Equivalent Ratios
      6. 6
        Ratio Tables
      7. 7
        Graphing Ratios
    2. 2.16.2. Unit Rates
      1. 1
        Unit Rates
      2. 2
        Solving Problems Using Unit Rates
      3. 3
        Speed as a Unit Rate
      4. 4
        Calculating Unit Rates Associated With Ratios of Fractions
      5. 5
        Solving Unit Rate Problems Using Ratios of Fractions
      6. 6
        Manipulating Ratios in Various Contexts
    3. 3.16.3. Proportional Relationships
      1. 1
        Understanding Proportional Relationships Using Tables
      2. 2
        Understanding Proportional Relationships Using Graphs
      3. 3
        Understanding Proportional Relationships From Descriptions
      4. 4
        Modeling with Direct Variation
    4. 4.16.4. Percentages
      1. 1
        Understanding Percentages Using Models
      2. 2
        Converting Between Percentages and Fractions
      3. 3
        Converting Between Percentages and Decimals
      4. 4
        Finding Part of a Number Given a Whole and a Percentage
      5. 5
        Finding Part of a Number Given a Whole and a Percentage: Word Problems
      6. 6
        Finding a Percentage Given Two Numbers
      7. 7
        Finding a Percentage Given Two Numbers: Word Problems
      8. 8
        Finding a Total Given a Part and a Percentage
      9. 9
        Percentage Increase, Decrease, and Error
      10. 10
        Percentages in Commerce and Finance
      11. 11
        Further Percentages in Commerce and Finance
      12. 12
        Solving Multipart Commerce and Finance Percentage Problems
    5. 5.16.5. 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
        Converting Between Mixed Units Containing Squares
      11. 11
        Degrees of Accuracy
      12. 12
        Density
      13. 13
        Interpreting Descriptions of Physical Phenomena
      14. 14
        Interpreting Rates of Change of Physical Phenomena
  17. 17.Data Analysis - Statistics & Probability
    1. 1.17.1. Sampling
      1. 1
        Sampling
      2. 2
        Estimation From Samples
      3. 3
        Biased and Unbiased Samples
      4. 4
        Interpreting Sample Results
      5. 5
        Sampling and Margin of Error
    2. 2.17.2. Summarizing Data
      1. 1
        Introduction to Statistics
      2. 2
        The Mean of a Data Set
      3. 3
        The Median of a Data Set
      4. 4
        The Mode of a Data Set
      5. 5
        Range, Quartiles, and IQR
      6. 6
        Mean Absolute Deviation
      7. 7
        Outliers
      8. 8
        Removing Outliers
      9. 9
        Combining Means
      10. 10
        Determining Unknown Observations Given Statistical Metrics
    3. 3.17.3. Frequency Tables
      1. 1
        Frequency Tables
      2. 2
        Joint Frequency Tables
      3. 3
        Cumulative Frequency
      4. 4
        Calculating Means From Frequency Tables
      5. 5
        Calculating Medians From Frequency Tables
      6. 6
        Calculating Modes From Frequency Tables
    4. 4.17.4. Representing Data
      1. 1
        Dot Plots
      2. 2
        Box Plots
      3. 3
        Histograms
      4. 4
        Measuring Centrality From Dot Plots
      5. 5
        Measuring Range and MAD From Dot Plots
      6. 6
        Measuring Quartiles and IQR From Dot Plots
      7. 7
        Calculating Modes and Medians From Histograms
      8. 8
        Calculating Means From Histograms
      9. 9
        Symmetry, Skew, and Outliers
    5. 5.17.5. Comparing Data
      1. 1
        Comparing Means
      2. 2
        Comparing Medians
      3. 3
        Comparing Modes
      4. 4
        Comparing Data Sets Using Range and Quartiles
      5. 5
        Comparing Data Sets Using Standard Deviation and MAD
      6. 6
        Comparing Measures of Center
      7. 7
        Comparing Measures of Spread
      8. 8
        Bounding Statistics for Grouped Data
      9. 9
        The Effects of Data Change on the Mean
      10. 10
        Statistical Effects of Data Transformations
    6. 6.17.6. Correlation
      1. 1
        Scatter Plots
      2. 2
        Trend Lines
      3. 3
        Making Predictions Using Trend Lines
      4. 4
        Comparing Data Points to Lines of Best Fit
      5. 5
        Interpreting Trend Line Coefficients
      6. 6
        Linear Correlation
      7. 7
        Residuals and Residual Plots
      8. 8
        Quadratic Regression
      9. 9
        Selecting a Regression Model
    7. 7.17.7. 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
    8. 8.17.8. 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
        Conditional Probabilities From Venn Diagrams
      7. 7
        Conditional Probabilities From Tables
      8. 8
        The Multiplication Law for Conditional Probability
      9. 9
        Finding Conditional Probabilities From Frequency Tables
      10. 10
        Independent Events