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Prealgebra

Math Academy official course import: Prealgebra

199 节课

课程大纲

  1. 1.Ratios & Percentages
    1. 1.1.1. 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. 2.1.2. 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
    3. 3.1.3. Proportional Relationships
      1. 1
        Understanding Proportional Relationships Using Tables
      2. 2
        Understanding Proportional Relationships Using Graphs
      3. 3
        Understanding Proportional Relationships From Descriptions
    4. 4.1.4. 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
  2. 2.The Number System
    1. 1.2.1. 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. 2.2.2. 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. 3.2.3. Number Theory
      1. 1
        Divisibility of Integers by 2, 5, 10, 4, and 8
      2. 2
        Divisibility of Integers by 3, 9, 6, and 7
      3. 3
        Natural Numbers, Integers, and Rational Numbers
      4. 4
        Prime and Composite Numbers
      5. 5
        Prime Factors
      6. 6
        The Fundamental Theorem of Arithmetic
      7. 7
        Finding Greatest Common Factors Using Prime Factorization
      8. 8
        Finding Lowest Common Multiples Using Prime Factorization
  3. 3.Exponents & Radicals
    1. 1.3.1. 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
    2. 2.3.2. The Rules of Exponents
      1. 1
        The Product Rule for Exponents
      2. 2
        The Quotient Rule for Exponents
      3. 3
        The Power Rule for Exponents
      4. 4
        The Power of Product Rule for Exponents
      5. 5
        The Power of Quotient Rule for Exponents
      6. 6
        Combining the Rules of Exponents
    3. 3.3.3. Scientific Notation
      1. 1
        Writing Numbers in Scientific Notation
      2. 2
        Converting Scientific Notation to Standard Notation
      3. 3
        Comparing Numbers in Scientific Notation
      4. 4
        Addition and Subtraction in Scientific Notation
      5. 5
        Addition in Scientific Notation With Different Powers of Ten
      6. 6
        Subtraction in Scientific Notation With Different Powers of Ten
      7. 7
        Further Addition in Scientific Notation With Different Powers of Ten
      8. 8
        Multiplying Numbers in Scientific Notation
      9. 9
        Dividing Numbers in Scientific Notation
    4. 4.3.4. Order of Operations
      1. 1
        Evaluating Rational Number Expressions Without Exponents
      2. 2
        Evaluating Expressions With Positive Integer Exponents
      3. 3
        Evaluating Expressions With Integer Exponents
    5. 5.3.5. 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
    6. 6.3.6. The Rules of Radicals
      1. 1
        Radicals as Fractional Exponents
      2. 2
        The Product Rule for Radicals
      3. 3
        The Quotient Rule for Radicals
  4. 4.Algebraic Expressions
    1. 1.4.1. 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
    2. 2.4.2. 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
  5. 5.Equations & Inequalities
    1. 1.5.1. Solving One-Step 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
    2. 2.5.2. Solving Multi-Step Linear Equations
      1. 1
        Solving Two-Step Equations
      2. 2
        Solving Linear Equations With Fractional Coefficients
      3. 3
        Solving Linear Equations With Decimal Coefficients
      4. 4
        Solving Linear Equations With Variables on Both Sides
      5. 5
        Solving Linear Equations by Clearing a Rational Expression
      6. 6
        Solving Linear Equations Using Cross-Multiplication
      7. 7
        Solving Two-Variable Equations
      8. 8
        Linear Equations With Infinitely Many Solutions
      9. 9
        Linear Equations With No Solutions
    3. 3.5.3. Solving 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
    4. 4.5.4. 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
    5. 5.5.5. Systems of Equations
      1. 1
        Introduction to Systems of Linear Equations
      2. 2
        Solving Systems of Equations by Substitution
  6. 6.Geometry
    1. 1.6.1. 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. 2.6.2. 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. 3.6.3. 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. 4.6.4. 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 Triangle Inequality
      6. 6
        The Isosceles Triangle Theorem
      7. 7
        Heights of Triangles
    5. 5.6.5. 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
        The Perimeter of a Polygon
    6. 6.6.6. Quadrilaterals
      1. 1
        Classifying Quadrilaterals
      2. 2
        Properties of Rectangles and Squares
      3. 3
        Properties of Trapezoids
    7. 7.6.7. Area and Perimeter
      1. 1
        Areas of Rectangles and Squares
      2. 2
        Areas of Parallelograms
      3. 3
        Areas of Triangles
      4. 4
        Areas of Trapezoids
      5. 5
        Areas and Perimeters of Composite Shapes
      6. 6
        The Area Between Two Shapes
  7. 7.Statistics
    1. 1.7.1. 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
        Comparing Data Sets Using Measures of Centrality
      8. 8
        Comparing Data Sets Using Range and Quartiles
      9. 9
        Comparing Data Sets Using Standard Deviation and MAD
      10. 10
        Outliers
      11. 11
        Removing Outliers
    2. 2.7.2. Representing Data
      1. 1
        Frequency Tables
      2. 2
        Dot Plots
      3. 3
        Measuring Centrality From Dot Plots
      4. 4
        Measuring Range and MAD From Dot Plots
      5. 5
        Measuring Quartiles and IQR From Dot Plots
      6. 6
        Symmetry, Skew, and Outliers
      7. 7
        Box Plots
      8. 8
        Histograms
      9. 9
        Comparing Measures of Center
      10. 10
        Comparing Measures of Spread