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Math All Grades K-12 Middle School & High School: Pre-Algebra, Algebra, Geometry, Algebra 2, Trigonometry, Pre-Calculus

 

LEARN THE MATH YOU WERE SUPPOSED TO LEARN BUT DIDNíT BECAUSE OF COVID19.

 

We all know the pandemic pretty much destroyed any learning the past 2 years. Students have fallen behind and they have a lot to catch up on. Remote learning simply doesnít work well for high school classes. HOWEVER, Private Tutoring is a totally different story. Students gain what they canít from school online classes. Iíve been doing online lessons since 2010, well before the pandemic came around, and I have this down to a science!

 

Teaching & tutoring goes far beyond just answering a studentís questions

 

- I analyze and determine what a student knows and doesn't know ( you would be surprised how many kids think they are "good" but actually don't know anything about the math building up to where they are at ) and find any gaps or deficiencies in knowledge that need to be learned.

 

- I provide far better teaching and explanations than other teachers / tutors so that a student truly understands what is going on. Students won't get any confusing explanations or answers that don't make sense.

 

- Learn the RIGHT Way to solve every question and problem. There are actually wrong methods to solve problems.

 

- Every lesson and explanation is adjusted in REAL-TIME just for that student: the speed & pacing, the complexity of explanation, and how far back we need to go to get to the root of what knowledge gap there is.

 

- Students do not learn just by listening / looking at answers. They learn by thinking and doing. Unlike other tutors who are just talking textbooks or talking webpages that tell you the answer to a question, what I provide is real teaching and learning

 

- I know when a student isn't getting it but thinks they do.Many students get the right answer by guessing or chance.

 

- I analyze and diagnose what is going wrong with the studentís thinking and problem solving process so it can be fixed.

 

- I will review the material you have done in class and make sure you understand the material that was covered in class, and teach you what your teacher did not

 

- I teach you new material if you want to get ahead

 

- Assess and check your understanding by giving you problems to work on. I also reinforce your understanding by giving you practice problems and drills. If needed, I can giveyou some reinforcement homework if needed

 

- What you learn goes beyond just math: real critical thinking, problem solving, analytical skills, organizational and proper study skills necessary to succeed in college and in life. These are lessons that you do not learn in school or from textbooks.

 

- I will challenge students to think so that they understand not only WHAT to do but also WHY they are doing it.

 

 

 

Math topics

 

Arithmetic

Pre-Algebra

Algebra

 

Whole numbers

 

1 Place Value

2 Comparing Numbers

3 Rounding Numbers

4 Addition

5 Subtraction

6 Estimating Sums and Differences

7 Addition and Subtraction Word Problems

8 Multiplication

9 Long Division

10 Estimating Products and Quotients

11 Multiplication and Division Word Problems

12 Addition Properties

13 Multiplication Properties

14 Patterns with Whole Numbers

Understanding fractions

 

15 Divisibility Rules

16 Factors and Primes

17 Multiples and Least Common Multiple

18 Greatest Common Factor

19 Introduction to Fractions

20 Equivalent Fractions (Part I)

21 Reducing Fractions to Lowest Terms

22 Equivalent Fractions (Part II)

23 Improper Fractions and Mixed Numbers

24 Comparing Proper Fractions

25 Comparing Mixed Numbers and Improper Fractions

26 Comparing Fractions Word Problems

Operations with fractions

 

27 Adding and Subtracting Like Fractions

28 Adding and Subtracting Unlike Fractions

29 Adding Mixed Numbers

30 Subtracting Mixed Numbers

31 Multiplying Fractions

32 Multiplying Mixed Numbers

33 Dividing Fractions

Adding and subtracting decimals

 

34 Understanding Decimals

35 Comparing Decimals

36 Rounding Decimals

37 Estimating Sums and Differences of Decimals

38 Adding Decimals

39 Subtracting Decimals

40 Adding and Subtracting Decimals Word Problems

Multiplying and dividing decimals

 

41 Multiplying Decimals by Whole Numbers

42 Multiplying Decimals by Decimals

43 Dividing Decimals by Whole Numbers

44 Dividing Decimals by Decimals

45 Multiplying and Dividing Decimals Word Problems

Geometry

 

46 Points, Lines, Segments, and Rays

47 Classifying Lines

48 Angles

49 Measuring Angles

50 Polygons

51 Quadrilaterals

52 Circles

53 Classifying 3-Dimensional Figures

Measurement

 

54 Customary Unit Conversions

55 Metric Unit Conversions

56 Perimeter

57 Area of Squares and Rectangles

Displaying data

 

58 Pictographs and Line Plots

59 Stem-and-Leaf Plots and Frequency Charts

 

6th grade

 

Whole numbers

 

1 Place Value

2 Comparing Numbers

3 Rounding Numbers

4 Addition

5 Subtraction

6 Estimating Sums and Differences

7 Addition and Subtraction Word Problems

8 Multiplication

9 Exponents

10 Long Division

11 Estimating Products and Quotients

12 Multiplication and Division Word Problems

13 Order of Operations

14 Grouping Symbols

15 Variables

16 Addition Properties

17 Multiplication Properties

Integers

 

18 Graphing and Writing Integers

19 Comparing Integers

20 Opposites and Absolute Value

21 Adding Integers

22 Subtracting Integers

23 Multiplying Integers

24 Dividing Integers

25 Integer Word Problems

Factors, multiples, and fractions

 

26 Divisibility Rules

27 Factors and Primes

28 Prime Factorization

29 Multiples and Least Common Multiple

30 Greatest Common Factor

31 Introduction to Fractions

32 Equivalent Fractions (Part I)

33 Reducing Fractions to Lowest Terms

34 Equivalent Fractions (Part II)

35 Improper Fractions and Mixed Numbers

36 Comparing Proper Fractions

37 Comparing Mixed Numbers and Improper Fractions

38 Comparing Fractions Word Problems

Operations with fractions

 

39 Adding and Subtracting Like Fractions

40 Adding and Subtracting Unlike Fractions

41 Adding Mixed Numbers

42 Subtracting Mixed Numbers

43 Multiplying Fractions

44 Multiplying Mixed Numbers

45 Dividing Fractions

46 Dividing Mixed Numbers

 

Decimal concepts

 

47 Understanding Decimals

48 Converting Decimals to Fractions

49 Converting Fractions to Decimals

50 Comparing Decimals

51 Rounding Decimals

52 Decimal Word Problems

 

Operations with decimals

 

53 Estimating Sums and Differences of Decimals

54 Adding Decimals

55 Subtracting Decimals

56 Adding and Subtracting Decimals Word Problems

57 Multiplying Decimals by Whole Numbers

58 Multiplying Decimals by Decimals

59 Dividing Decimals by Whole Numbers

60 Dividing Decimals by Decimals

61 Multiplying and Dividing Decimals Word Problems

62 Powers of 10

63 Terminating and Repeating Decimals

64 Determining if a Number is Rational or Irrational

Algebraic thinking

 

65 Evaluating Expressions

66 Combining Like Terms

67 Distributive Property

68 Modeling Expressions

69 Introduction to Equations

70 One-Step Addition Equations

71 One-Step Subtraction Equations

72 One-Step Multiplication Equations

73 One-Step Division Equations

74 Writing and Solving One-Step Equations

75 Introduction to Inequalities

76 One-Step Inequalities

77 The Coordinate Grid

78 Finding the nth Term in a Pattern

Ratios and percents

 

79 Introduction to Ratios

80 Equal Ratios

81 Unit Rate

82 Unit Price

83 Understanding Percents

84 Fractions and Percents

85 Decimals and Percents

86 Percent of a Number

87 Percent One Number is of Another

88 Using Percent to Find a Number

Geometry

 

89 Points, Lines, Segments, and Rays

90 Classifying Lines

91 Angles

92 Measuring Angles

93 Angles of a Triangle

94 Sides of a Triangle

95 Polygons

96 Quadrilaterals

97 Circles

98 Classifying 3-Dimensional Figures

99 Nets

100 Symmetry

101 Transformations

102 Reflections

Measurement

 

103 Customary Unit Conversions

104 Metric Unit Conversions

105 Perimeter

106 Area of Squares and Rectangles

107 Area of Triangles

108 Area of Parallelograms and Trapezoids

109 Surface Area

Displaying and describing data

 

110 Pictographs and Line Plots

111 Bar Graphs

112 Line Graphs

113 Stem-and-Leaf Plots and Frequency Charts

114 Histograms

115 Scatterplots and Trends

116 Dependency and Correlational Relationships

117 Misleading Graphs

118 Range, Median, and Mode

119 Box-and-Whisker Plots

120 Mean

121 Central Tendency Word Problems

 

 

Whole numbers

 

1 Place Value

2 Comparing Numbers

3 Rounding Numbers

4 Addition

5 Subtraction

6 Estimating Sums and Differences

7 Addition and Subtraction Word Problems

8 Multiplication

9 Exponents

10 Long Division

11 Estimating Products and Quotients

12 Multiplication and Division Word Problems

13 Order of Operations

14 Grouping Symbols

15 Variables

16 Addition Properties

17 Multiplication Properties

 

Integers

 

18 Graphing and Writing Integers

19 Comparing Integers

20 Opposites and Absolute Value

21 Adding Integers

22 Subtracting Integers

23 Multiplying Integers

24 Dividing Integers

25 Order of Operations with Integers

26 Integer Word Problems

27 Absolute Value with Addition and Subtraction

28 Absolute Value with Multiplication and Division

 

Fractions

 

29 Divisibility Rules

30 Factors and Primes

31 Prime Factorization

32 Multiples and Least Common Multiple

33 Greatest Common Factor

34 Introduction to Fractions

35 Equivalent Fractions (Part I)

36 Reducing Fractions to Lowest Terms

37 Equivalent Fractions (Part II)

38 Improper Fractions and Mixed Numbers

39 Comparing Proper Fractions

40 Comparing Mixed Numbers and Improper Fractions

41 Comparing Fractions Word Problems

42 Adding and Subtracting Like Fractions

43 Adding and Subtracting Unlike Fractions

44 Adding Mixed Numbers

45 Subtracting Mixed Numbers

46 Multiplying Fractions

47 Multiplying Mixed Numbers

48 Dividing Fractions

49 Dividing Mixed Numbers

Decimals

 

50 Understanding Decimals

51 Converting Decimals to Fractions

52 Converting Fractions to Decimals

53 Comparing Decimals

54 Rounding Decimals

55 Decimal Word Problems

56 Estimating Sums and Differences of Decimals

57 Adding Decimals

58 Subtracting Decimals

59 Adding and Subtracting Decimals Word Problems

60 Multiplying Decimals by Whole Numbers

61 Multiplying Decimals by Decimals

62 Dividing Decimals by Whole Numbers

63 Dividing Decimals by Decimals

64 Multiplying and Dividing Decimals Word Problems

65 Powers of 10

66 Converting from Scientific to Standard Notation

67 Converting from Standard to Scientific Notation

68 Terminating and Repeating Decimals

69 Determining if a Number is Rational or Irrational

Algebraic thinking

 

70 Patterns with Whole Numbers

71 Patterns with Fractions, Decimals, and Integers

72 Advanced Patterns

73 Pattern Word Problems

74 Evaluating Expressions

75 Combining Like Terms

76 Distributive Property

77 Modeling Expressions

78 Introduction to Equations

79 One-Step Addition Equations

80 One-Step Subtraction Equations

81 One-Step Multiplication Equations

82 One-Step Division Equations

83 Writing and Solving One-Step Equations

84 Two-Step Equations

85 Equations with Variable on Both Sides

86 Equations with the Distributive Property

87 Writing and Solving Multi-Step Equations

88 Introduction to Inequalities

89 One-Step Inequalities

Ratio, proportion, & percent

 

90 Introduction to Ratios

91 Equal Ratios

92 Unit Rate

93 Unit Price

94 Introduction to Proportion

95 Solving Proportions

96 Proportion Word Problems

97 Understanding Percents

98 Fractions and Percents

99 Decimals and Percents

100 Percent of a Number

101 Percent One Number is of Another

102 Using Percent to Find a Number

103 Percent Increase or Decrease

104 Discount

105 Sales Tax

106 Interest

 

Geometry

 

107 Points, Lines, Segments, and Rays

108 Classifying Lines

109 Angles

110 Measuring Angles

111 Complementary and Supplementary Angles

112 Angles of a Triangle

113 Sides of a Triangle

114 Polygons

115 Quadrilaterals

116 Circles

117 Classifying 3-Dimensional Figures

118 Nets

119 Perspective Drawings

120 Congruent Figures

121 Similar Figures

122 Problem Solving with Similar Figures

123 Symmetry

124 The Coordinate Grid

125 Relations and Functions

126 Evaluating and Graphing Functions

127 Transformations

128 Reflections

129 Translations

130 Rotations

131 Dilations

 

Measurement

 

132 Customary Unit Conversions

133 Metric Unit Conversions

134 Units of Measurement

135 Perimeter

136 Circumference

137 Perimeter and Circumference Word Problems

138 Area of Squares and Rectangles

139 Area of Triangles

140 Area of Parallelograms and Trapezoids

141 Area of a Circle

142 Changing Dimensions

143 Area Word Problems

144 Surface Area

145 Volume of Prisms and Pyramids

146 Volume of Cylinders, Spheres, and Cones

147 Surface Area and Volume Word Problems

148 Square Roots

149 Using Square Roots to Solve Equations

150 Pythagorean Theorem

151 Pythagorean Triples

 

Probability & statistics

 

152 Pictographs and Line Plots

153 Bar Graphs

154 Line Graphs

155 Circle Graphs

156 Stem-and-Leaf Plots and Frequency Charts

157 Histograms

158 Scatterplots and Trends

159 Misleading Graphs

160 Range, Median, and Mode

161 Box-and-Whisker Plots

162 Mean

163 Central Tendency Word Problems

164 Simple Probability

165 Experimental Probability

166 Probability of Independent Events

167 Probability of Dependent Events

168 Simulations

169 Tree Diagrams and the Counting Principle

170 Permutations

171 Combinations

 

Simplifying

 

1 Adding and Subtracting Integers

2 Multiplying and Dividing Integers

3 Order of Operations

4 Evaluation

5 Least Common Multiple

6 Adding and Subtracting Fractions

7 Multiplying and Dividing Fractions

8 Order of Operations with Fractions

9 Evaluation with Fractions

10 Absolute Value

11 Absolute Value with Fractions

12 Combining Like Terms

13 Distributive Property

14 Distributive Property and Combining Like Terms

 

Equations

 

15 One-Step Equations

16 Two-Step Equations

17 Equations with Fractions

18 Equations Involving Distributive

19 Equations with Variable on Both Sides

20 Equations with Variable on Both Sides and Fractions

21 Equations with Variable on Both Sides and Distributive

22 Equations with Decimals

23 Equations with Decimals and Decimal Solutions

24 Equations with Fraction Solutions

25 Literal Equations

 

Word problems

 

26 Number Word Problems

27 Consecutive Integer Word Problems

28 Geometry Word Problems

29 Percent Word Problems

30 Age Word Problems

31 Value Word Problems

32 Interest Word Problems

33 Motion Word Problems

 

Inequalities, absolute value, functions, graphing

 

34 Solving and Graphing Inequalities

35 Combined Inequalities

36 The Coordinate System

37 Domain and Range

38 Definition of a Function

39 Function and Arrow Notation

40 Graphing within a Given Domain

41 Graphing Lines

42 The Intercept Method

43 Graphing Inequalities in Two Variables

 

Linear equations

 

44 Patterns and Table Building

45 Word Problems and Table Building

46 Slope as a Rate of Change

47 Slope of a Line

48 Using Slope to Graph a Line

49 Using Coordinates to Find Slope (Graphs and Tables)

50 Slope Formula

51 Using Slope Formula to Find Missing Coordinates

52 Slope-Intercept Form

53 Converting to Slope-Intercept Form and Graphing

54 Linear Parent Graph and Transformations

55 Writing Equations of Lines

56 Writing Equations of Lines Using Tables

57 Direct Variation

58 Applications of Direct Variation and Linear Functions

 

Systems of equations

 

59 Solving Systems by Graphing

60 Solving Systems by Addition

61 Solving Systems by Substitution

62 Number and Value Word Problems

63 Wind and Current Word Problems

64 Digit Word Problems

Exponents & polynomials

 

65 The Product Rule

66 The Power Rule

67 The Quotient Rule

68 Numerical Bases and Exponents of Zero

69 Combining Exponent Rules

70 Multiplying Polynomials

71 F.O.I.L.

 

Factoring

 

72 Greatest Common Factor

73 Factoring out the Greatest Common Factor

74 Factoring Trinomials with Positive Constants

75 Factoring Trinomials with Negative Constants

76 Difference of Two Squares

77 Factoring Trinomials with Lead Coefficients and Positive Constants

78 Factoring Trinomials with Lead Coefficients and Negative Constants

79 Factoring Completely

80 Beginning Polynomial Equations

81 Intermediate Polynomial Equations

 

Rational expressions & equations

 

82 Simplifying Rational Expressions

83 Multiplying and Dividing Rational Expressions

84 Adding Rational Expressions

85 Subtracting Rational Expressions

86 Rational Equations

 

Radicals

 

87 Simplifying Radicals

88 Multiplying Radicals

89 Dividing Radicals

90 Adding Radicals and FOILing with Radicals

91 Radical Equations

 

Quadratics

 

92 Linear or Quadratic Functions

93 Graphs of Quadratic Functions and Beginning Transformations

94 Graphs of Quadratic Functions and Advanced Transformations

95 Solving Quadratic Equations by Graphing

96 Taking the Square Root of Both Sides

97 Completing The Square

98 Quadratic Formula

 

 

99 Variables, Expressions, and Equations

100 Translating English to Algebra

101 Using Manipulatives to Model Algebraic Equations

102 Using Algebra Tiles to Model Algebraic Equations

103 Field Properties

104 Recognizing Patterns

105 Finding the nth Term in a Pattern

106 Finite Differences to Generalize a Rule

107 Dependency and Correlational Relationships

108 Recognizing and Evaluating Functions

109 Functions in Problem Situations

110 Domain and Range

111 Linear and Quadratic Relationships

112 Parent Graphs and Transformations

113 Slope and Intercept

114 Interpreting Graphs

115 Direct Variation

116 Inverse Variation

 

 

Geometry

Introduction

 

1 Adding and Subtracting Integers

2 Multiplying and Dividing Integers

3 Equations Involving the Distributive Property

4 Equations with the Variable on Both Sides

5 Points, Lines, Planes, and Space

6 Segments, Rays, and Length

7 Segment Addition Postulate and Midpoint

8 Angles and Measure

9 Angle Addition Postulate and Angle Bisector

10 Inductive vs. Deductive Reasoning

11 Conditional Statements

12 Properties

13 Algebra Proofs with Properties

14 Geometry Proofs with Midpoints and Angle Bisectors

 

Angle pairs & perpendicular lines

 

15 Solving Systems by Addition

16 Solving Systems by Substitution and Method of Choice

17 Factoring Trinomials

18 Factoring Trinomials and Difference of Two Squares

19 Polynomial Equations

20 Complementary and Supplementary Angles

21 Advanced Complementary and Supplementary Angles

22 Vertical Angles

23 Problems Involving Perpendicular Lines

24 Theorems Involving Perpendicular Lines

 

Parallel lines and polygons

 

25 Parallel Lines Vocabulary

26 Given Lines are Parallel

27 Proving Lines are Parallel

28 Triangle Vocabulary and Triangle Sum Theorem

29 Advanced Triangle Sum Theorem

30 Triangle Word Problems and Exterior Angle Theorem

31 Polygon Vocabulary

32 Sum of Interior and Exterior Angles of a Polygon

33 Regular Polygons

 

Triangles

 

34 Congruent Figures

35 Proving Triangles are Congruent by SSS, SAS, and ASA

36 Isosceles Triangle Theorems

37 Proving Triangles are Congruent by AAS and HL

38 Medians, Altitudes, and Perpendicular Bisectors

 

Quadrilaterals

 

39 Properties of Parallelograms

40 Proving a Quadrilateral is a Parallelogram

41 More Parallel Line Theorems

42 Rectangles, Rhombuses, and Squares

43 Trapezoids

 

Similarity

 

44 Ratio

45 Proportion

46 Properties of Similar Polygons

47 Angle-Angle Similarity Postulate

48 Similarity Word Problems

49 SSS and SAS Similarity Theorems

50 Triangle Proportionality and Triangle Angle-Bisector Theorems

 

Right triangles

 

51 Simplifying Square Roots

52 Multiplying Square Roots

53 Dividing Square Roots

54 Adding and Subtracting Square Roots

55 Pythagorean Theorem

56 Pythagorean Theorem Word Problems

57 Converse of the Pythagorean Theorem

58 30-60-90 and 45-45-90 Degree Triangles

59 Advanced 30-60-90 and 45-45-90 Degree Triangles

60 Sine, Cosine, and Tangent

61 Sine, Cosine, and Tangent with a Calculator

62 Trigonometry Word Problems

 

Circles

 

63 Circle Vocabulary

64 Tangents

65 Arcs and Central Angles

66 Arcs and Chords

67 Advanced Arcs and Chords

68 Inscribed Angles

69 Angles Formed by Chords, Secants, and Tangents

70 Circle Segment Lengths

71 Advanced Circle Segment Lengths

 

Area

 

72 Area of Rectangles and Squares

73 Advanced Area of Rectangles and Squares

74 Area of Parallelograms

75 Area of Triangles

76 Area of Rhombuses

77 Area of Trapezoids

78 Area of Regular Polygons

79 Area and Circumference of Circles

 

Volume

 

80 Area and Volume of Prisms

81 Advanced Area and Volume of Prisms

82 Area and Volume of Pyramids

83 Advanced Area and Volume of Pyramids

84 Area and Volume of Cylinders and Cones

85 Area and Volume of Spheres

 

Algebra 2

 

Simplifying

 

1 Adding and Subtracting Integers

2 Multiplying and Dividing Integers

3 Order of Operations

4 Evaluation

5 Absolute Value

6 Distributive Property and Combining Like Terms

 

Equations

 

7 Two-Step Equations

8 Equations with Fractions

9 Equations with Variable on Both Sides

10 Equations with Variable on Both Sides and Distributive

11 Literal Equations

12 Advanced Literal Equations

 

Word problems

 

13 Number Word Problems

14 Geometry Word Problems

15 Mixture Word Problems

16 Motion Word Problems

17 Advanced Motion Word Problems

 

Inequalities, absolute value, functions, graphing

 

18 Solving and Graphing Inequalities

19 Combined Inequalities

20 Advanced Inequalities

21 Absolute Value Equations

22 Absolute Value Inequalities

23 The Coordinate System

24 Domain and Range

25 Definition of a Function

26 Function and Arrow Notation

27 Graphing Lines

28 The Intercept Method

 

Linear equations

 

29 Slope of a Line

30 Using Slope to Graph a Line

31 Slope Formula

32 Using Slope Formula to Find Missing Coordinates

33 Slope-Intercept Form

34 Converting to Slope-Intercept Form and Graphing

35 Writing Equations of Lines in Standard Form

36 Writing Equations of Lines Using the Point-Slope Formula

37 Writing Equations of Lines Given Two Points

38 Writing Equations of Parallel and Perpendicular Lines

 

Systems of equations

 

39 Solving Systems by Graphing

40 Solving Systems by Addition

41 Solving Systems by Substitution

42 Systems of Equations with Fractions and Method of Choice

43 Number and Value Word Problems

44 Wind and Current Word Problems

 

Exponents & polynomials

 

45 The Product Rule

46 The Power Rule

47 The Quotient Rule

48 Numerical Bases and Exponents of Zero

49 Combining Exponent Rules

50 F.O.I.L.

51 Advanced Multiplying Polynomials

 

Factoring

 

52 Greatest Common Factor

53 Factoring out the Greatest Common Factor

54 Factoring Trinomials with Positive Constants

55 Factoring Trinomials with Negative Constants

56 Difference of Two Squares

57 Factoring Trinomials with Lead Coefficients and Positive Constants

58 Factoring Trinomials with Lead Coefficients and Negative Constants

59 Factoring by Grouping

60 Advanced Factoring by Grouping

61 Factoring Completely

62 Advanced Factoring Completely

63 Beginning Polynomial Equations

64 Intermediate Polynomial Equations

65 Advanced Polynomial Equations

 

Rational expressions & equations

 

66 Simplifying Rational Expressions

67 Multiplying and Dividing Rational Expressions

68 Adding Rational Expressions

69 Subtracting Rational Expressions

70 Complex Fractions

71 Rational Equations

72 Advanced Rational Equations

 

Radicals

 

73 Simplifying Radicals

74 Multiplying Radicals

75 Dividing Radicals

76 Adding Radicals and FOILing with Radicals

77 Dividing Radicals Using Conjugates

78 Radical Equations

79 Advanced Radical Equations

 

Quadratics

 

80 Taking the Square Root of Both Sides

81 Completing The Square

82 Advanced Completing The Square

83 Quadratic Formula

84 Advanced Quadratic Formula

85 Solving Quadratic Equations Using Method of Choice

 

Imaginary & complex numbers

 

86 Imaginary Numbers

87 Advanced Imaginary Numbers

88 Complex Numbers

89 Advanced Complex Numbers

 

Quadratic equations & functions

 

90 Understanding y - k = a(x - h)2 Form

91 Graphing Quadratic Equations in y - k = a(x - h)2 Form

92 Writing Quadratic Equations in y - k = a(x - h)2 Form

93 Graphing Quadratic Functions

94 Sum and Product of Roots Formula

95 Writing Quadratic Functions

 

Coordinate geometry

 

96 Distance Formula

97 Midpoint Formula

98 Equation of a Circle

 

Negative & rational exponents

 

99 Negative Exponents

100 Numerical Bases with Negative Exponents

101 Multiplying and Dividing with Negative Exponents

102 Multiplying and Dividing with Scientific Notation

103 Rational Exponents

104 Numerical Bases with Rational Exponents

105 Writing Radicals in Exponential Form

106 Solving Equations with Rational Exponents

107 Radical Exponents

 

Composite & inverse functions

 

108 Composite Functions: f(g(x)) and g(f(x))

109 Inverse Relations

110 Inverse Functions

 

Logarithms

 

111 Evaluating Logarithms and Logarithmic vs. Exponential Form

112 Solving Logarithmic Equations

113 Logarithm Rules and Properties

114 Evaluating Logarithms by Condensing or Expanding

115 Solving Advanced Logarithmic Equations

116 Logarithm Calculator Problems

117 Exponential Equations and Change of Base Formula

118 Exponential Growth and Decay

119 Half Life and Doubling Time Formulas

120 Natural Logarithms

121 Solving Natural Logarithm Equations with ln and e

 

Advanced concepts

 

122 Systems of Inequalities

123 Systems of Three Equations

124 Sum and Difference of Two Cubes

125 Quadratic Word Problems

126 Polynomial Inequalities

127 Work Word Problems

128 Adding and Subtracting Polynomials

129 Polynomial Long Division

130 Synthetic Division

 

Factors and multiples

Factors and multiples: Factors and multiples

Prime and composite numbers: Factors and multiples

Prime factorization: Factors and multiples

 

Patterns

Math patterns: Patterns

Writing expressions: Patterns

Number patterns: Patterns

 

Ratios and rates

Intro to ratios: Ratios and rates

Equivalent ratios: Ratios and rates

Visualize ratios: Ratios and rates

Ratio application: Ratios and rates

Intro to rates: Ratios and rates

 

Percentages

Intro to percents: Percentages

Percent, decimal, fraction conversions: Percentages

Percent problems: Percentages

Percent word problems: Percentages

 

Exponents intro and order of operations

Exponents: Exponents intro and order of operations

Order of operations: Exponents intro and order of operations

 

Variables & expressions

Parts of algebraic expressions: Variables & expressions

Substitution & evaluating expressions: Variables & expressions

Expression value intuition: Variables & expressions

Evaluating expressions word problems: Variables & expressions

Writing algebraic expressions introduction: Variables & expressions

Writing basic algebraic expressions word problems: Variables & expressions

Distributive property with variables: Variables & expressions

Combining like terms: Variables & expressions

Equivalent expressions: Variables & expressions

 

Equations & inequalities introduction

Algebraic equations basics: Equations & inequalities introduction

One-step equations intuition: Equations & inequalities introduction

One-step addition & subtraction equations: Equations & inequalities introduction

One-step multiplication and division equations: Equations & inequalities introduction

Finding mistakes in one-step equations: Equations & inequalities introduction

One-step equation word problems: Equations & inequalities introduction

Intro to inequalities with variables: Equations & inequalities introduction

Dependent and independent variables: Equations & inequalities introduction

 

Percent & rational number word problems

Percent word problems: Percent & rational number word problems

Rational number word problems: Percent & rational number word problems

 

Proportional relationships

Rate problems with fractions: Proportional relationships

Constant of proportionality: Proportional relationships

Compare and interpret constants of proportionality: Proportional relationships

Identifying proportional relationships: Proportional relationships

Graphs of proportional relationships: Proportional relationships

Writing & solving proportions: Proportional relationships

Equations of proportional relationships: Proportional relationships

 

One-step and two-step equations & inequalities

Combining like terms: One-step and two-step equations & inequalities

The distributive property & equivalent expressions: One-step and two-step equations & inequalities

Interpreting linear expressions: One-step and two-step equations & inequalities

Two-step equations intro: One-step and two-step equations & inequalities

Two-step equations with decimals and fractions: One-step and two-step equations & inequalities

Two-step equation word problems: One-step and two-step equations & inequalities

One-step inequalities: One-step and two-step equations & inequalities

Two-step inequalities: One-step and two-step equations & inequalities

 

Roots, exponents, & scientific notation

Square roots & cube roots: Roots, exponents, & scientific notation

Exponent properties intro: Roots, exponents, & scientific notation

Negative exponents: Roots, exponents, & scientific notation

Exponent properties (integer exponents): Roots, exponents, & scientific notation

Working with powers of 10: Roots, exponents, & scientific notation

Scientific notation intro: Roots, exponents, & scientific notation

Arithmetic with numbers in scientific notation: Roots, exponents, & scientific notation

Scientific notation word problems: Roots, exponents, & scientific notation

 

Multi-step equations

Equations with variables on both sides: Multi-step equations

Equations with parentheses: Multi-step equations

Number of solutions to equations: Multi-step equations

Equations word problems: Multi-step equations

 

Two-variable equations

Graphing proportional relationships: Two-variable equations

Solutions to linear equations: Two-variable equations

Intercepts: Two-variable equations

Slope: Two-variable equations

Intro to slope-intercept form: Two-variable equations

Graphing slope-intercept form: Two-variable equations

Writing slope-intercept equations: Two-variable equations

 

Functions and linear models

Functions: Functions and linear models

Linear models: Functions and linear models

Comparing linear functions: Functions and linear models

Constructing linear models for real-world relationships: Functions and linear models

Recognizing functions: Functions and linear models

Linear and nonlinear functions: Functions and linear models

 

Systems of equations

Intro to systems of equations: Systems of equations

Systems of equations with graphing: Systems of equations

Solving systems with substitution

 

Foundations

Negative numbers: Foundations

Absolute value: Foundations

Exponents: Foundations

Square roots: Foundations

Order of operations: Foundations

Fractions: Foundations

Decimals, fractions and percentages: Foundations

Operations with decimals: Foundations

Area of triangles: Foundations

Circumference and area of circles: Foundations

 

Algebraic expressions

Introduction to variables: Algebraic expressions

Substitution & evaluating expressions: Algebraic expressions

Writing algebraic expressions: Algebraic expressions

Combining like terms: Algebraic expressions

Distributive property: Algebraic expressions

Equivalent algebraic expressions: Algebraic expressions

Nested fractions: Algebraic expressions

 

Linear equations and inequalities

One-step equations: Linear equations and inequalities

Two-steps equations: Linear equations and inequalities

Multi-step equations: Linear equations and inequalities

One-step inequalities: Linear equations and inequalities

Two-step inequalities: Linear equations and inequalities

Multi-step inequalities: Linear equations and inequalities

Writing & solving proportions: Linear equations and inequalities

 

Graphing lines and slope

Coordinate plane: Graphing lines and slope

Solutions to two-variable linear equations: Graphing lines and slope

x-intercepts and y-intercepts: Graphing lines and slope

Slope: Graphing lines and slope

Horizontal & vertical lines: Graphing lines and slope

Slope-intercept form intro: Graphing lines and slope

Writing slope-intercept equations: Graphing lines and slope

Graphing two-variable inequalities: Graphing lines and slope

 

Systems of equations

Systems of equations intro: Systems of equations

Elimination method for systems of equations: Systems of equations

Substitution method for systems of equations: Systems of equations

Number of solutions to systems of equations: Systems of equations

 

Expressions with exponents

Exponent properties intro: Expressions with exponents

Negative exponents: Expressions with exponents

Exponent properties (integer exponents): Expressions with exponents

Scientific notation intro: Expressions with exponents

Scientific notation word problems: Expressions with exponents

 

Quadratics and polynomials

Adding & subtracting polynomials: Quadratics and polynomials

Multiplying binomials: Quadratics and polynomials

Special products of binomials: Quadratics and polynomials

Factoring polynomials by taking common factors: Quadratics and polynomials

Factoring quadratics 1: Quadratics and polynomials

Factoring quadratics 2: Quadratics and polynomials

Factoring quadratics: Difference of squares: Quadratics and polynomials

Factoring quadratics: Perfect squares: Quadratics and polynomials

Solving quadratic equations by factoring: Quadratics and polynomials

 

Equations and geometry

Equations & geometry: Equations and geometry

Triangle angles: Equations and geometry

Pythagorean theorem: Equations and geometry

Triangle similarity intro: Equations and geometry

Solving similar triangles

 

 

Algebra foundations

Overview and history of algebra: Algebra foundations

Introduction to variables: Algebra foundations

Substitution and evaluating expressions: Algebra foundations

Combining like terms: Algebra foundations

Introduction to equivalent expressions: Algebra foundations

Division by zero: Algebra foundations

 

Solving equations & inequalities

Linear equations with variables on both sides: Solving equations & inequalities

Linear equations with parentheses: Solving equations & inequalities

Analyzing the number of solutions to linear equations: Solving equations & inequalities

Linear equations with unknown coefficients: Solving equations & inequalities

Multi-step inequalities: Solving equations & inequalities

Compound inequalities: Solving equations & inequalities

 

Working with units

Rate conversion: Working with units

Appropriate units: Working with units

Word problems with multiple units: Working with units

 

Linear equations & graphs

Two-variable linear equations intro: Linear equations & graphs

Slope: Linear equations & graphs

Horizontal & vertical lines: Linear equations & graphs

x-intercepts and y-intercepts: Linear equations & graphs

Applying intercepts and slope: Linear equations & graphs

 

Forms of linear equations

Intro to slope-intercept form: Forms of linear equations

Graphing slope-intercept equations: Forms of linear equations

Writing slope-intercept equations: Forms of linear equations

Point-slope form: Forms of linear equations

Standard form: Forms of linear equations

Summary: Forms of two-variable linear equations: Forms of linear equations

 

Systems of equations

Introduction to systems of equations: Systems of equations

Solving systems of equations with substitution: Systems of equations

Solving systems of equations with elimination: Systems of equations

Equivalent systems of equations: Systems of equations

Number of solutions to systems of equations: Systems of equations

Systems of equations word problems: Systems of equations

 

Inequalities (systems & graphs)

Checking solutions of two-variable inequalities: Inequalities (systems & graphs)

Graphing two-variable inequalities: Inequalities (systems & graphs)

Modeling with linear inequalities: Inequalities (systems & graphs)

 

Functions

Evaluating functions: Functions

Inputs and outputs of a function: Functions

Functions and equations: Functions

Interpreting function notation: Functions

Introduction to the domain and range of a function: Functions

Determining the domain of a function: Functions

Recognizing functions: Functions

Maximum and minimum points: Functions

Intervals where a function is positive, negative, increasing, or decreasing: Functions

Interpreting features of graphs: Functions

Average rate of change: Functions

Average rate of change word problems: Functions

Intro to inverse functions: Functions

 

Sequences

Introduction to arithmetic sequences: Sequences

Constructing arithmetic sequences: Sequences

Introduction to geometric sequences: Sequences

Constructing geometric sequences: Sequences

Modeling with sequences: Sequences

General sequences: Sequences

 

Absolute value & piecewise functions

Graphs of absolute value functions: Absolute value & piecewise functions

Piecewise functions: Absolute value & piecewise functions

 

Exponents & radicals

Exponent properties review: Exponents & radicals

Radicals: Exponents & radicals

Simplifying square roots: Exponents & radicals

 

Exponential growth & decay

Exponential vs. linear growth: Exponential growth & decay

Exponential expressions: Exponential growth & decay

Graphs of exponential growth: Exponential growth & decay

Exponential vs. linear growth over time: Exponential growth & decay

Exponential growth & decay: Exponential growth & decay

Exponential functions from tables & graphs: Exponential growth & decay

Exponential vs. linear models: Exponential growth & decay

 

Quadratics: Multiplying & factoring

Multiplying monomials by polynomials: Quadratics: Multiplying & factoring

Multiplying binomials: Quadratics: Multiplying & factoring

Special products of binomials: Quadratics: Multiplying & factoring

Introduction to factoring: Quadratics: Multiplying & factoring

Factoring quadratics intro: Quadratics: Multiplying & factoring

Factoring quadratics by grouping: Quadratics: Multiplying & factoring

Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring

Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring

Strategy in factoring quadratics: Quadratics: Multiplying & factoring

 

Quadratic functions & equations

Intro to parabolas: Quadratic functions & equations

Solving and graphing with factored form: Quadratic functions & equations

Solving by taking the square root: Quadratic functions & equations

Vertex form: Quadratic functions & equations

Solving quadratics by factoring: Quadratic functions & equations

The quadratic formula: Quadratic functions & equations

Completing the square intro: Quadratic functions & equations

More on completing the square: Quadratic functions & equations

Strategizing to solve quadratic equations: Quadratic functions & equations

Quadratic standard form: Quadratic functions & equations

Features & forms of quadratic functions: Quadratic functions & equations

Comparing quadratic functions: Quadratic functions & equations

Transforming quadratic functions: Quadratic functions & equations

 

Irrational numbers

Mastery unavailable

Irrational numbers: Irrational numbers

Sums and products of rational and irrational numbers: Irrational numbers

Proofs concerning irrational numbers

 

Intro to area and perimeter

Count unit squares to find area: Intro to area and perimeter

Area formula intuition: Intro to area and perimeter

Multiply to find area: Intro to area and perimeter

Area and the distributive property: Intro to area and perimeter

Decompose figures to find area: Intro to area and perimeter

Perimeter intro: Intro to area and perimeter

Perimeters of polygons with missing side lengths: Intro to area and perimeter

Perimeter word problems: Intro to area and perimeter

Comparing area and perimeter: Intro to area and perimeter

Area versus perimeter: Intro to area and perimeter

 

Intro to mass and volume

Mass: Intro to mass and volume

Volume: Intro to mass and volume

 

Measuring angles

Parts of plane figures: Measuring angles

Angle introduction: Measuring angles

Angle types: Measuring angles

Understanding angle measurement: Measuring angles

Measuring angles: Measuring angles

Decomposing angles: Measuring angles

 

Plane figures

Quadrilaterals introduction: Plane figures

Classifying triangles: Plane figures

Parallel and perpendicular: Plane figures

Classifying geometric shapes: Plane figures

Lines of symmetry: Plane figures

More on quadrilaterals: Plane figures

Properties of shapes: Plane figures

 

Units of measurement

Estimating length: Units of measurement

Converting units of mass: Units of measurement

Converting units of volume: Units of measurement

Converting units of length: Units of measurement

Conversion word problems (larger to smaller): Units of measurement

Converting to larger or smaller: Units of measurement

Converting metric units word problems: Units of measurement

 

Volume

Volume with unit cubes: Volume

Volume of rectangular prisms: Volume

Decompose figures to find volumes: Volume

Volume word problems: Volume

 

Coordinate plane

Intro to the coordinate plane: Coordinate plane

Coordinate plane word problems: Coordinate plane

Points in all four quadrants: Coordinate plane

Problem solving in all quadrants: Coordinate plane

 

Decomposing to find area

Area of parallelograms: Decomposing to find area

Area of triangles: Decomposing to find area

Area and perimeter on the coordinate plane: Decomposing to find area

Area of composite figures: Decomposing to find area

 

3D figures

Rectangular prism volume with fractions: 3D figures

Surface area with nets: 3D figures

Finding surface area: 3D figures

Slicing geometric shapes: 3D figures

Volume and surface area word problems: 3D figures

 

Circles, cylinders, cones, and spheres

Area and circumference of circles: Circles, cylinders, cones, and spheres

Area and circumference of fractions of circles: Circles, cylinders, cones, and spheres

Volume of cylinders, spheres, and cones: Circles, cylinders, cones, and spheres

 

Angle relationships

Vertical, complementary, and supplementary angles: Angle relationships

Missing angles problems: Angle relationships

Parallel lines and transversals: Angle relationships

Triangle angles: Angle relationships

 

Scale

Scale copies: Scale

Scale drawings: Scale

 

Triangle side lengths

Constructing triangles: Triangle side lengths

Pythagorean theorem: Triangle side lengths

Pythagorean theorem application: Triangle side lengths

Pythagorean theorem and distance between points: Triangle side lengths

 

Geometric transformations

Transformations intro: Geometric transformations

Translations: Geometric transformations

Rotations: Geometric transformations

Reflections: Geometric transformations

Properties & definitions of transformations: Geometric transformations

Dilations: Geometric transformations

Congruence and similarity

 

Performing transformations

Intro to Euclidean geometry: Performing transformations

Introduction to rigid transformations: Performing transformations

Translations: Performing transformations

Rotations: Performing transformations

Reflections: Performing transformations

Dilations: Performing transformations

 

Transformation properties and proofs

Rigid transformations overview: Transformation properties and proofs

Dilation preserved properties: Transformation properties and proofs

Properties & definitions of transformations: Transformation properties and proofs

Symmetry: Transformation properties and proofs

Proofs with transformations: Transformation properties and proofs

 

Congruence

Transformations & congruence: Congruence

Triangle congruence from transformations: Congruence

Congruent triangles: Congruence

Theorems concerning triangle properties: Congruence

Working with triangles: Congruence

Theorems concerning quadrilateral properties: Congruence

Proofs of general theorems: Congruence

Constructing lines & angles: Congruence

 

Similarity

Definitions of similarity: Similarity

Introduction to triangle similarity: Similarity

Solving similar triangles: Similarity

Angle bisector theorem: Similarity

Solving problems with similar & congruent triangles: Similarity

Proving relationships using similarity: Similarity

Solving modeling problems with similar & congruent triangles: Similarity

 

Right triangles & trigonometry

Pythagorean theorem: Right triangles & trigonometry

Pythagorean theorem proofs: Right triangles & trigonometry

Special right triangles: Right triangles & trigonometry

Ratios in right triangles: Right triangles & trigonometry

Introduction to the trigonometric ratios: Right triangles & trigonometry

Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry

Solving for an angle in a right triangle using the trigonometric ratios: Right triangles & trigonometry

Sine & cosine of complementary angles: Right triangles & trigonometry

Modeling with right triangles: Right triangles & trigonometry

 

Analytic geometry

Distance and midpoints: Analytic geometry

Dividing line segments: Analytic geometry

Problem solving with distance on the coordinate plane: Analytic geometry

Parallel & perpendicular lines on the coordinate plane: Analytic geometry

Equations of parallel & perpendicular lines: Analytic geometry

 

Conic sections

Graphs of circles intro: Conic sections

Standard equation of a circle: Conic sections

Expanded equation of a circle: Conic sections

Focus and directrix of a parabola: Conic sections

 

Circles

Circle basics: Circles

Arc measure: Circles

Arc length (from degrees): Circles

Introduction to radians: Circles

Arc length (from radians): Circles

Sectors: Circles

Inscribed angles: Circles

Inscribed shapes problem solving: Circles

Proofs with inscribed shapes: Circles

Properties of tangents: Circles

Constructing regular polygons inscribed in circles: Circles

Constructing circumcircles & incircles: Circles

Constructing a line tangent to a circle: Circles

 

Solid geometry

2D vs. 3D objects: Solid geometry

Cavalieri's principle and dissection methods: Solid geometry

Volume and surface area: Solid geometry

Density

 

 

Polynomial arithmetic

Intro to polynomials: Polynomial arithmetic

Average rate of change of polynomials: Polynomial arithmetic

Adding and subtracting polynomials: Polynomial arithmetic

Multiplying monomials by polynomials: Polynomial arithmetic

Multiplying binomials by polynomials: Polynomial arithmetic

Special products of polynomials: Polynomial arithmetic

 

Complex numbers

The imaginary unit i: Complex numbers

Complex numbers introduction: Complex numbers

The complex plane: Complex numbers

Adding and subtracting complex numbers: Complex numbers

Multiplying complex numbers: Complex numbers

Quadratic equations with complex solutions: Complex numbers

 

Polynomial factorization

Factoring monomials: Polynomial factorization

Greatest common factor: Polynomial factorization

Taking common factors: Polynomial factorization

Factoring higher degree polynomials: Polynomial factorization

Factoring using structure: Polynomial factorization

Polynomial identities: Polynomial factorization

Geometric series: Polynomial factorization

 

Polynomial division

Dividing polynomials by x: Polynomial division

Dividing quadratics by linear factors: Polynomial division

Dividing polynomials by linear factors: Polynomial division

Polynomial Remainder Theorem: Polynomial division

 

Polynomial graphs

Zeros of polynomials: Polynomial graphs

Positive and negative intervals of polynomials: Polynomial graphs

End behavior of polynomials: Polynomial graphs

Putting it all together: Polynomial graphs

 

Rational exponents and radicals

Rational exponents: Rational exponents and radicals

Properties of exponents (rational exponents): Rational exponents and radicals

Evaluating exponents & radicals: Rational exponents and radicals

Equivalent forms of exponential expressions: Rational exponents and radicals

Solving exponential equations using properties of exponents: Rational exponents and radicals

 

Exponential models

Interpreting the rate of change of exponential models: Exponential models

Constructing exponential models according to rate of change: Exponential models

Advanced interpretation of exponential models: Exponential models

 

Logarithms

Introduction to logarithms: Logarithms

The constant e and the natural logarithm: Logarithms

Properties of logarithms: Logarithms

The change of base formula for logarithms: Logarithms

Solving exponential equations with logarithms: Logarithms

Solving exponential models: Logarithms

 

Transformations of functions

Shifting functions: Transformations of functions

Reflecting functions: Transformations of functions

Symmetry of functions: Transformations of functions

Scaling functions: Transformations of functions

Putting it all together: Transformations of functions

Graphs of square and cube root functions: Transformations of functions

Graphs of exponential functions: Transformations of functions

Graphs of logarithmic functions: Transformations of functions

 

Equations

Rational equations: Equations

Square-root equations: Equations

Extraneous solutions: Equations

Cube-root equations: Equations

Quadratic systems: Equations

Solving equations by graphing: Equations

 

Trigonometry

Unit circle introduction: Trigonometry

Radians: Trigonometry

The Pythagorean identity: Trigonometry

Trigonometric values of special angles: Trigonometry

Graphs of sin(x), cos(x), and tan(x): Trigonometry

Amplitude, midline and period: Trigonometry

Transforming sinusoidal graphs: Trigonometry

Graphing sinusoidal functions: Trigonometry

Sinusoidal models: Trigonometry

 

Modeling

Modeling with function combination: Modeling

Interpreting features of functions: Modeling

Manipulating formulas: Modeling

Modeling with two variables: Modeling

Modeling with multiple variables

 

 

Right triangles & trigonometry

Ratios in right triangles: Right triangles & trigonometry

Introduction to the trigonometric ratios: Right triangles & trigonometry

Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry

Solving for an angle in a right triangle using the trigonometric ratios: Right triangles & trigonometry

Sine and cosine of complementary angles: Right triangles & trigonometry

Modeling with right triangles: Right triangles & trigonometry

The reciprocal trigonometric ratios: Right triangles & trigonometry

 

Trigonometric functions

Unit circle introduction: Trigonometric functions

Radians: Trigonometric functions

The Pythagorean identity: Trigonometric functions

Special trigonometric values in the first quadrant: Trigonometric functions

Trigonometric values on the unit circle: Trigonometric functions

Graphs of sin(x), cos(x), and tan(x): Trigonometric functions

Amplitude, midline, and period: Trigonometric functions

Transforming sinusoidal graphs: Trigonometric functions

Graphing sinusoidal functions: Trigonometric functions

Sinusoidal models: Trigonometric functions

Long live Tau: Trigonometric functions

 

Non-right triangles & trigonometry

Law of sines: Non-right triangles & trigonometry

Law of cosines: Non-right triangles & trigonometry

Solving general triangles: Non-right triangles & trigonometry

 

Trigonometric equations and identities

Inverse trigonometric functions: Trigonometric equations and identities

Sinusoidal equations: Trigonometric equations and identities

Sinusoidal models: Trigonometric equations and identities

Angle addition identities: Trigonometric equations and identities

Using trigonometric identities: Trigonometric equations and identities

Challenging trigonometry problems

 

Analyzing categorical data

Analyzing one categorical variable: Analyzing categorical data

Two-way tables: Analyzing categorical data

Distributions in two-way tables: Analyzing categorical data

 

Displaying and comparing quantitative data

Displaying quantitative data with graphs: Displaying and comparing quantitative data

Describing and comparing distributions: Displaying and comparing quantitative data

More on data displays: Displaying and comparing quantitative data

 

Summarizing quantitative data

Measuring center in quantitative data: Summarizing quantitative data

More on mean and median: Summarizing quantitative data

Interquartile range (IQR): Summarizing quantitative data

Variance and standard deviation of a population: Summarizing quantitative data

Variance and standard deviation of a sample: Summarizing quantitative data

More on standard deviation: Summarizing quantitative data

Box and whisker plots: Summarizing quantitative data

Other measures of spread: Summarizing quantitative data

 

Modeling data distributions

Percentiles: Modeling data distributions

Z-scores: Modeling data distributions

Effects of linear transformations: Modeling data distributions

Density curves: Modeling data distributions

Normal distributions and the empirical rule: Modeling data distributions

Normal distribution calculations: Modeling data distributions

More on normal distributions: Modeling data distributions

 

Exploring bivariate numerical data

Introduction to scatterplots: Exploring bivariate numerical data

Correlation coefficients: Exploring bivariate numerical data

Introduction to trend lines: Exploring bivariate numerical data

Least-squares regression equations: Exploring bivariate numerical data

Assessing the fit in least-squares regression: Exploring bivariate numerical data

More on regression: Exploring bivariate numerical data

 

Study design

Statistical questions: Study design

Sampling and observational studies: Study design

Sampling methods: Study design

Types of studies (experimental vs. observational): Study design

Experiments: Study design

 

Probability

Basic theoretical probability: Probability

Probability using sample spaces: Probability

Basic set operations: Probability

Experimental probability: Probability

Randomness, probability, and simulation: Probability

Addition rule: Probability

Multiplication rule for independent events: Probability

Multiplication rule for dependent events: Probability

Conditional probability and independence: Probability

 

Counting, permutations, and combinations

Counting principle and factorial: Counting, permutations, and combinations

Permutations: Counting, permutations, and combinations

Combinations: Counting, permutations, and combinations

Combinatorics and probability: Counting, permutations, and combinations

 

Random variables

Discrete random variables: Random variables

Continuous random variables: Random variables

Transforming random variables: Random variables

Combining random variables: Random variables

Binomial random variables: Random variables

Binomial mean and standard deviation formulas: Random variables

Geometric random variables: Random variables

More on expected value: Random variables

Poisson distribution: Random variables

 

Sampling distributions

What is a sampling distribution?: Sampling distributions

Sampling distribution of a sample proportion: Sampling distributions

Sampling distribution of a sample mean: Sampling distributions

 

Confidence intervals

Introduction to confidence intervals: Confidence intervals

Estimating a population proportion: Confidence intervals

Estimating a population mean: Confidence intervals

More confidence interval videos: Confidence intervals

 

Significance tests (hypothesis testing)

The idea of significance tests: Significance tests (hypothesis testing)

Error probabilities and power: Significance tests (hypothesis testing)

Tests about a population proportion: Significance tests (hypothesis testing)

Tests about a population mean: Significance tests (hypothesis testing)

More significance testing videos: Significance tests (hypothesis testing)

 

Two-sample inference for the difference between groups

Mastery unavailable

Comparing two proportions: Two-sample inference for the difference between groups

Comparing two means: Two-sample inference for the difference between groups

 

Inference for categorical data (chi-square tests)

Chi-square goodness-of-fit tests: Inference for categorical data (chi-square tests)

Chi-square tests for relationships: Inference for categorical data (chi-square tests)

 

Advanced regression (inference and transforming)

Mastery unavailable

Inference about slope: Advanced regression (inference and transforming)

Nonlinear regression: Advanced regression (inference and transforming)

 

Composite and inverse functions

Composing functions: Composite and inverse functions

Modeling with composite functions: Composite and inverse functions

Invertible functions: Composite and inverse functions

Inverse functions in graphs and tables: Composite and inverse functions

Verifying inverse functions by composition: Composite and inverse functions

 

Trigonometry

Special trigonometric values in the first quadrant: Trigonometry

Trigonometric identities on the unit circle: Trigonometry

Inverse trigonometric functions: Trigonometry

Law of sines: Trigonometry

Law of cosines: Trigonometry

Solving general triangles: Trigonometry

Sinusoidal equations: Trigonometry

Sinusoidal models: Trigonometry

Angle addition identities: Trigonometry

Using trigonometric identities: Trigonometry

 

Complex numbers

The complex plane: Complex numbers

Distance and midpoint of complex numbers: Complex numbers

Complex conjugates and dividing complex numbers: Complex numbers

Identities with complex numbers: Complex numbers

Modulus (absolute value) and argument (angle) of complex numbers: Complex numbers

Polar form of complex numbers: Complex numbers

Graphically multiplying complex numbers: Complex numbers

Multiplying and dividing complex numbers in polar form: Complex numbers

The fundamental theorem of algebra: Complex numbers

 

Rational functions

Reducing rational expressions to lowest terms: Rational functions

End behavior of rational functions: Rational functions

Discontinuities of rational functions: Rational functions

Graphs of rational functions: Rational functions

Modeling with rational functions: Rational functions

Multiplying and dividing rational expressions: Rational functions

Adding and subtracting rational expressions: Rational functions

 

Conic sections

Introduction to conic sections: Conic sections

Center and radii of an ellipse: Conic sections

Foci of an ellipse: Conic sections

Introduction to hyperbolas: Conic sections

Foci of a hyperbola: Conic sections

Hyperbolas not centered at the origin: Conic sections

 

Vectors

Vectors introduction: Vectors

Vector components: Vectors

Magnitude of vectors: Vectors

Scalar multiplication: Vectors

Vector addition and subtraction: Vectors

Direction of vectors: Vectors

Vector components from magnitude and direction: Vectors

Adding vectors in magnitude and direction form: Vectors

Vectors word problems: Vectors

 

Matrices

Introduction to matrices: Matrices

Using matrices to represent data: Matrices

Multiplying matrices by scalars: Matrices

Adding and subtracting matrices: Matrices

Properties of matrix addition & scalar multiplication: Matrices

Using matrices to manipulate data: Matrices

Matrices as transformations of the plane: Matrices

Using matrices to transform the plane: Matrices

Transforming 3D and 4D vectors with matrices: Matrices

Multiplying matrices by matrices: Matrices

Properties of matrix multiplication: Matrices

Representing systems of equations with matrices: Matrices

Introduction to matrix inverses: Matrices

Finding inverses of 2x2 matrices: Matrices

Solving linear systems with matrices: Matrices

 

Probability and combinatorics

Venn diagrams and the addition rule: Probability and combinatorics

Multiplication rule for probabilities: Probability and combinatorics

Permutations: Probability and combinatorics

Combinations: Probability and combinatorics

Probability using combinatorics: Probability and combinatorics

Probability distributions introduction: Probability and combinatorics

Theoretical & empirical probability distributions: Probability and combinatorics

Decisions with probability: Probability and combinatorics

Expected value: Probability and combinatorics

 

Series

Mastery unavailable

Geometric series: Series

Geometric series (with summation notation): Series

The binomial theorem: Series

Arithmetic series: Series

 

Limits and continuity

Mastery unavailable

Defining limits and using limit notation: Limits and continuity

Estimating limit values from graphs: Limits and continuity

Estimating limit values from tables: Limits and continuity

Determining limits using algebraic properties of limits: limit properties: Limits and continuity

Determining limits using algebraic properties of limits: direct substitution: Limits and continuity

Determining limits using algebraic manipulation: Limits and continuity

Selecting procedures for determining limits: Limits and continuity

Determining limits using the squeeze theorem: Limits and continuity

Exploring types of discontinuities: Limits and continuity

Defining continuity at a point: Limits and continuity

Confirming continuity over an interval: Limits and continuity

Removing discontinuities: Limits and continuity

Connecting infinite limits and vertical asymptotes: Limits and continuity

Connecting limits at infinity and horizontal asymptotes: Limits and continuity

Working with the intermediate value theorem

 

Displaying a single quantitative variable

Frequency tables and dot plots: Displaying a single quantitative variable

Histograms: Displaying a single quantitative variable

Mean and median in data displays: Displaying a single quantitative variable

Interquartile range: Displaying a single quantitative variable

Box and whisker plots: Displaying a single quantitative variable

 

Analyzing a single quantitative variable

Standard deviation: Analyzing a single quantitative variable

Comparing distributions: Analyzing a single quantitative variable

Percentiles and z-scores: Analyzing a single quantitative variable

Normal distributions and the empirical rule: Analyzing a single quantitative variable

Normal distribution calculations: Analyzing a single quantitative variable

 

Two-way tables

Two-way tables introduction: Two-way tables

Distributions in two-way tables: Two-way tables

 

Scatterplots

Fitting trend lines to scatterplots: Scatterplots

Analyzing trend lines in scatterplots: Scatterplots

Residuals: Scatterplots

 

Study design

Introduction to planning a study: Study design

Potential problems with sampling: Study design

Sampling methods: Study design

Introduction to experimental design: Study design

Inference and experiments: Study design

 

Probability

Venn diagrams and the addition rule: Probability

Multiplication rule for probabilities: Probability

Conditional probability: Probability

Probability from simulations: Probability

Permutations: Probability

Combinations: Probability

Probability using combinatorics: Probability

 

Probability distributions & expected value

Probability distributions introduction: Probability distributions & expected value

Theoretical & empirical probability distributions: Probability distributions & expected value

Decisions with probability: Probability distributions & expected value

Expected value

 

Polynomial arithmetic

Intro to polynomials: Polynomial arithmetic

Average rate of change of polynomials: Polynomial arithmetic

Adding and subtracting polynomials: Polynomial arithmetic

Multiplying monomials by polynomials: Polynomial arithmetic

Multiplying binomials by polynomials: Polynomial arithmetic

Special products of polynomials: Polynomial arithmetic

 

Complex numbers

The imaginary unit i: Complex numbers

Complex numbers introduction: Complex numbers

The complex plane: Complex numbers

Adding and subtracting complex numbers: Complex numbers

Multiplying complex numbers: Complex numbers

Quadratic equations with complex solutions: Complex numbers

 

Polynomial factorization

Factoring monomials: Polynomial factorization

Greatest common factor: Polynomial factorization

Taking common factors: Polynomial factorization

Factoring higher degree polynomials: Polynomial factorization

Factoring using structure: Polynomial factorization

Polynomial identities: Polynomial factorization

Geometric series: Polynomial factorization

 

Polynomial division

Dividing polynomials by x: Polynomial division

Dividing quadratics by linear factors: Polynomial division

Dividing polynomials by linear factors: Polynomial division

Polynomial Remainder Theorem: Polynomial division

 

Polynomial graphs

Zeros of polynomials: Polynomial graphs

Positive and negative intervals of polynomials: Polynomial graphs

End behavior of polynomials: Polynomial graphs

Putting it all together: Polynomial graphs

 

Rational exponents and radicals

Rational exponents: Rational exponents and radicals

Properties of exponents (rational exponents): Rational exponents and radicals

Evaluating exponents & radicals: Rational exponents and radicals

Equivalent forms of exponential expressions: Rational exponents and radicals

Solving exponential equations using properties of exponents: Rational exponents and radicals

 

Exponential models

Interpreting the rate of change of exponential models: Exponential models

Constructing exponential models according to rate of change: Exponential models

Advanced interpretation of exponential models: Exponential models

 

Logarithms

Introduction to logarithms: Logarithms

The constant e and the natural logarithm: Logarithms

Properties of logarithms: Logarithms

The change of base formula for logarithms: Logarithms

Solving exponential equations with logarithms: Logarithms

Solving exponential models: Logarithms

 

Transformations of functions

Shifting functions: Transformations of functions

Reflecting functions: Transformations of functions

Symmetry of functions: Transformations of functions

Scaling functions: Transformations of functions

Putting it all together: Transformations of functions

Graphs of square and cube root functions: Transformations of functions

Graphs of exponential functions: Transformations of functions

Graphs of logarithmic functions: Transformations of functions

 

Equations

Rational equations: Equations

Square-root equations: Equations

Extraneous solutions: Equations

Cube-root equations: Equations

Quadratic systems: Equations

Solving equations by graphing: Equations

 

Trigonometry

Unit circle introduction: Trigonometry

Radians: Trigonometry

The Pythagorean identity: Trigonometry

Trigonometric values of special angles: Trigonometry

Graphs of sin(x), cos(x), and tan(x): Trigonometry

Amplitude, midline and period: Trigonometry

Transforming sinusoidal graphs: Trigonometry

Graphing sinusoidal functions: Trigonometry

Sinusoidal models: Trigonometry

 

Modeling

Modeling with function combination: Modeling

Interpreting features of functions: Modeling

Manipulating formulas: Modeling

Modeling with two variables: Modeling

Modeling with multiple variables

 

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