Advanced Mathematics: Trigonometry and Pre-Calculus

2nd Edition

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Course Content

Lessons Status

Introduction: Prerequisites for the Course – How to Use the Math Book – Expectations of Students

Lesson 61: Analyzing Single-Variable Data – What Is a Normal Distribution – Returning to “Box & Whisker” Plots

Lesson 62: Solving Abstract Equations – Defining Linear vs Direct Variation

Lesson 63: Using “Completing the Square” to Graph a Circle

Lesson 64: Graphing “Complex Numbers” in the Argand Plane, the Polar Form, and Sums & Products of Complex Numbers

Lesson 65: Working with Radicals in Trigonometric Functions and Sketching Graphs of Logarithm Functions

Lesson 66: Working with Formulas for Systems of Equations – Phase Shifts and Period Changes in Trigonometric Functions

Lesson 67: Defining What an “Antilogarithm” Is

Lesson 68: Defining the “Locus” of All Points in a Parabola – Equation of a Translated Parabola, Applications, & Derivations

Lesson 69: Defining a “Matrix” – Finding the Determinant in a Square Matrix

Lesson 70: Calculating Percentiles and “Z” Scores in Statistics

Lesson 71: First Circles, then Parabolas, now Ellipses (Part I)

Lesson 72: Solving Right Triangles – Using the “Law of Sines” to Solve for Unknown Parts of Triangles

Lesson 73: Solving Problems Involving Regular Polygons of Any Number of Sides, Inscribed in a Circle

Lesson 74: Using “Cramer’s Rule” to Solve a System of Linear Equations

Lesson 75: Combinations are Processed Differently than We Processed Permutations Earlier in the Textbook

Lesson 76: Graphing Functions of (- x) – Finding functions of the “Other Angle” – Trig Identities (Part I) – Making “Rules to Follow”

Lesson 77: Defining Binomial Expansion (Part I)

Lesson 78: Graphing the “Hyperbola”

Lesson 79: Using “De Moivre’s Theorem” – Finding Roots of Complex Numbers

Lesson 80: Trig Identities (Part II)

Lesson 81: Working with and Understanding the “Law of Cosines”

Lesson 82: Explaining How to “Take the Logarithm of a Number or an Expression” – Defining an “Exponential Equation”

Lesson 83: Defining “Simple Probability” – “Independent Events” and the Effects of “Replacement” in Probability

Lesson 84: Factoring “Factorable” Trig Expressions – Successfully Sketching Sinusoids

Lesson 85: Solving Advanced Trigonometric Equations – Solving “Clock” Word Problems

Lesson 86: Defining “Arithmetic Progressions” and the “Arithmetic Mean”

Lesson 87: Introducing “Sum & Difference” Trig Identities and “Tangent” Identities

Lesson 88: Working with “Growth & Decay” of Exponential Functions

Lesson 89: More on Ellipses (Part II)

Lesson 90: Introducing “Double-Angle” and “Half-Angle” Trig Identities

Lesson 91: Defining Geometric Expressions

Lesson 92: The Probability of “Mutually Exclusive Events” – Using Notations for Permutations or Combinations

Lesson 93: Working with Advanced Trigonometry Identities and Several Triangle Inequalities

Lesson 94: Graphing the Secant & Cosecant and then Graphing the Tangent & Cotangent

Lesson 95: Working with More Advanced Complex Roots

Lesson 96: More Work with Double-Angle Identities – Triangle Area Formulas Using the Sine Function – Working with a Proof of the “Law of Sines” – Equal Angles in Similar Triangles Implies Proportional Sides Among Them

Lesson 97: What is Meant by the “Ambiguous Case”?

Lesson 98: Finding a Logarithm to a Base Other Than “10” or “e” – Working with “Contrived Logarithm Problems”

Lesson 99: Using Different Notations for Different Sequences – Solving Advanced Sequence Problems – Finding the Arithmetic and Geometric Means

Lesson 100: Working with the Product of, and the Sum & Difference of, Trigonometric Identities

Lesson 101: More on Determinants – Evaluating Systems with and Without Determinants – Describing the Effects of Independent Equations in a Linear System

Lesson 102: More on Binomial Expansions (Part II)

Lesson 103: Doing Calculations Using Logarithms and Using Them to Calculate the pH (Relative Acidity) or H⁺ (Concentration of Hydrogen ions)

Lesson 104: Defining the Difference Between the Arithmetic and Geometric Series

Lesson 105: Defining “Cofactors” & Using Them to Evaluate Determinants

Lesson 106: Translation of a Conic Section – Recognizing the Difference Between the Equations of an Ellipse and a Hyperbola

Lesson 107: Describing a Convergent Geometric Series

Lesson 108: Learning How to Add and Multiply Matrices

Lesson 109: More Work with Rational Numbers

Lesson 110: Graphing the Arcsine & Arccosine, Arcsecant & Arccosecant, and the Arctangent & Arccotangent

Lesson 111: Working with Logarithmic Inequalities when the Base is “Less Than” or “Greater Than” 1

Lesson 112: Introduction to an Identity Called the “Binomial Theorem”

Lesson 113: Applying Synthetic Division Using a “Long Division Algorithm” – The Difference Between “Zeroes” and “Roots”

Lesson 114: Graphing Factored Polynomial Functions

Lesson 115: Applying the “Remainder Theorem”

Lesson 116: Defining the “Region of Interest” in a “Normalized Polynomial Equation”

Lesson 117: The Difference Between a “Prime Number” and “Relatively Prime Number” – Explanation and Application of the “Rational Roots Theorem”

Lesson 118: Finding the Roots of Polynomial Equations

Lesson 119: Using Descartes’ “Rule of Signs” – Applying the “Upper & Lower Bound” Theorem – Problems with Irrational Roots

Lesson 120: More About Matrices – Finding Inverse Matrices

Lesson 121: Writing the Equation of a “Piecewise” Function – Graphing the “Greatest Integer” Function

Lesson 122: Graphing Rational Functions – How Do You Graph a Function Whose Equation Has a Zero in the Denominator?

Lesson 123: Knowing of a General Equation to Describe All Conic sections

Lesson 124: Accurately Calculating the Coordinate Change when Using a “Point of Division” Formula

Lesson 125: Using the Texas Instrument Graphing Calculator (TI -82) to Graph – Solve Systems of Equations & Find Roots

Lesson 1: Working with “Real Numbers” and Review of Some Fundamental Algebraic Concepts

Lesson 2: More Review of Fundamental Algebraic Concepts – Using a Texas Instrument (TI-83) Graphing Calculator

Lesson 3: The Alternate Statement – The “Contrapositive” – Working with the “Converse,” Inverse,” and “If” Statements

Lesson 4: Measuring Angles in Radians – Using Trig Ratios – Signs of the “Four Quadrants” – Simplifying Trig Expressions

Lesson 5: A Review of Solving Various Word Problems

Lesson 6: Equations and Graphs of Functions – Using Functional Notation and Defining the Domain and Range of a Function

Lesson 7: Describing the “Unit Circle” – Defining of the “Centerline,” “Amplitude,” and “Phase Angle”of a Sinusoid – Describing What Is Meant by the “Period of a Trig Function” – Important Numbers in Mathematics – Working with Exponential Functions”

Lesson 8: Using the “Pythagorean Theorem” to Create “Pythagorean Trig Identities” – Negative Trig Identities & Even and Odd Trig Functions – Creating and Working with Trigonometric Identities – Trig Co-functions – Working with Similar Triangles

Lesson 9: Using the Absolute Value as the Distance – Working with “Special” Functions – A Review of Logarithms – Common vs Natural Logarithms – Solving Simple Logarithm Problems

Lesson 10: Working with Quadratic Polynomials and Their Equations & Functions – Applying the “Remainder Theorem” – A Review of Synthetic Division – Applying the “Rational Root Theorem”

Lesson 11: Continuity in Functions. – Identifying Left-Hand and Right-Hand Limits of Functions

Lesson 12: Working with Sum & Difference, Double-Angle & Half-Angle Trig Identities – More on Graphing Logarithm Functions

Lesson 13: Graphing Inverse Trig Functions – Solving Trigonometric Equations

Lesson 14: Introduction to Limits of Functions

Lesson 15: Introduction to “Interval Notation” & Products of Linear Factors – Tangent Lines – Describing “Increasing & Decreasing Functions”

Lesson 16: Finding Logarithms of Products & Quotients – Finding Logarithms of Powers – Solving Exponential Equations

Lesson 17: Describing Infinity as a Limit – Working with “Undefined Limits”

Lesson 18: Finding the Sums & Differences and Products & Quotients of Functions – Composing Functions

Lesson 19: Introduction to the “First Derivative” and its Notations – Finding Slopes of Curves

Lesson 20: Finding a Logarithm of a Base Other than “10” or “e” – Graphing Conics on a Graphing Calculator – or Not!

Lesson 21: Translations of Functions on Graphs – Graphing Rational Functions (Part I)

Lesson 22: Using the Binomial Theorem to Locate Specific Terms of a Binomial Expansion – Review of the Equations of the Five Types of Conic Sections

Lesson 23: Review of Trig Functions of nƟ – More Graphing of Conics Using a Graphing Calculator – or Not!

Lesson 24: Different Notations for Defining a First Derivative – Finding the First Derivative of x^n (x Raised to the nth Power)

Lesson 25: The Effects of the Constant-Multiple Rule for Derivatives – Defining the Derivatives of Sums & Differences – Working with the Proof of the Derivative of a Sum