Advanced Mathematics: Geometry with Advanced Algebra 2nd Edition Buy a Subscription Course Content Lessons Status 1 Introduction: Prerequisites for the Course – How to Use the Math Book – Expectations of Students. 2 Algebra Review 3 Lesson 1: Review of Geometry Concepts. 4 Lesson 2: More Review on Areas of Cylinders & Prisms, Cones, Pyramids, and Spheres 5 Lesson 3: Review of the Pythagorean Theorem – Inequalities of Triangles, Similar Triangles, and Polygons 6 Lesson 4: Use of Construction Tools for Geometry 7 Lesson 5: Dealing with Exponents & Radicals, Complex Numbers, Areas of Geometric Figures, and Diagonals of Rectangular Solids 8 Lesson 6: Solving Fractional & Radical Equations and Systems of Three Linear Equations 9 Lesson 7: Working with Deductive and Inductive Reasoning & Logic – Considering the Contrapositive, Converse, and Inverse 10 Lesson 8: The Meaning of Similarity in Geometry – Working with Proportional Segments & Angle Bisectors – Ratios of Sides 11 Lesson 9: Defining the Term "Congruent" in Geometry – Describing What Proof Outlines Are 12 Lesson 10: Review of the Equation of a Line – Describing Rational Denominators – Solving Equations by Completing the Square 13 Lesson 11: Working with Circles – Properties Unique to Circles – Utilizing the Quadratic Formula 14 Lesson 12: Polygons and Their Angles & Diagonals – The Chord-Tangent Theorem and Its Proof 15 Lesson 13: The Products of Chord, Secant, and Tangent Segments– Working with Intersecting Secant and Tangent Chords 16 Lesson 14: Review of the Sine, Cosine, and Tangent Functions – Working with Angles of Elevation and Depression & Rectangular and Polar Coordinates and Their Conversions 17 Lesson 15: Reviewing the Differences Between Assumptions and Proof – Review of Two Column Proofs 18 Lesson 16: Complex and Abstract Fractions – Revisiting Division of Polynomials 19 Lesson 17: Working with Proofs of the Pythagorean Theorem and Geometric Proofs of Similarity 20 Lesson 18: Working with Advanced Word Problems 21 Lesson 19: Non-Linear Systems of Equations – Factoring Exponential Expressions & Factoring the Sum or Difference of Two Squares 22 Lesson 20: Using Trigonometry to Solve Two Special Triangles (45 – 45 – 90 and 30 – 60 – 90) 23 Lesson 21: Functions: Evaluating, Types of, and Tests for – Defining a Function by the Relationship Between its Domain and Range 24 Lesson 22: Defining Absolute Value – Describing How to Create a Valid Reciprocal Function 25 Lesson 23: Describing and Sketching the Exponential Function 26 Lesson 24: Working with Sums of Trigonometric Functions – Combining Algebraic Functions Using Sum, Difference, Product, etc. 27 Lesson 25: Working with Age and Rate Word Problems 28 Lesson 26: The Relationship Between Logarithms and Exponents of Their Base – Working with Logarithmic Equations 29 Lesson 27: Definition of Related Angles – Defining the Term “Signs of Trigonometric Functions” 30 Lesson 28: What “Factorial” Notation Means – Working with “Abstract” Word Problems 31 Lesson 29: Explaining the Relationship Between Sine & Cosine Using a Unit Circle – Working with Very Large and Very Small Fractions – Defining Quadrantal Angles 32 Lesson 30: Adding Vectors – Working with Overlapping Triangles 33 Lesson 31: Defining Symmetry, Reflections, and Translations when Used in Mathematics 34 Lesson 32: Working with Inverse Functions & Inverse Trigonometric Functions – Recalling the Four Signs of the Four Quadrants 35 Lesson 33: Defining Quadrilaterals – Properties, Types, and Conditions of Parallelograms – Defining Decomposing Functions 36 Lesson 34: Using Summation Notation – Defining a Linear Regression – Working with Decomposing Functions 37 Lesson 35: Effects of a Change in Coordinates – What is Meant by the Name of a Number? – Using the Distance Formula 38 Lesson 36: Angles Bigger than 360̊ – Adding Trigonometric Functions – Working with “Boat-in-the-River” Word Problems 39 Lesson 37: Definition of a Line – Using the Midpoint Formula 40 Lesson 38: Introducing the Fundamental Counting Principle and its Association with Permutations & Repetition – Defining Designated Roots and Overall Average Rates in Distance Word Problems 41 Lesson 39: Explaining Radian Measure of Angles and Five Different Forms of Linear Equations 42 Lesson 40: Defining the Argument of the Function in Mathematics – The Rules of Logarithms – Properties Unique to Inverse Functions 43 Lesson 41: Names for Reciprocal Trig Functions – General Notation for Permutations & Its Relationship to the Concept of Factorials 44 Lesson 42: Working with Conic Sections and Circles – Working with Constants in Exponential Functions 45 Lesson 43: Defining Periodic Functions – Graphing the Sine and Cosine Functions of an Angle 46 Lesson 44: Working with Abstract Rate Word Problems 47 Lesson 45: More on Permutations: Conditional Permutations – Doing Two-Variable Analysis Without a Graphing Calculator 48 Lesson 46: Working with Complex Roots – Factoring Quadratic Polynomials Over the Set of Complex Numbers 49 Lesson 47: Working with Vertical Sinusoid Translations and the Inverse Trigonometric Function, Arctan 50 Lesson 48: Evaluating the Powers of Trigonometric Functions – Finding Perpendicular Bisectors of Line Segments 51 Lesson 49: Logarithm Functions – Developing Three Rules for Logarithms 52 Lesson 50: Working with Trigonometric Functions 53 Lesson 51: The Difference Between “Common” and “ Natural” Logarithms 54 Lesson 52: Working with the Inviolable Argument and Working with Arguments in Trigonometric Equations 55 Lesson 53: Reviewing Unit Multipliers – Working with Angular Velocity vs Linear Velocity 56 Lesson 54: How a Parabola is Formed 57 Lesson 55: Circular and Distinguishable Permutations 58 Lesson 56: Reviewing Areas of Triangles, Areas of Segments, Systems of Inequalities 59 Lesson 57: Phase Shifts in Sinusoids – Sinusoids as Periodic Functions 60 Lesson 58: Calculating the Distance from a Point to a Line – Explaining What Creates “Narrow” and “Wide Parabolas” 61 Lesson 59: Working with Advanced Logarithms – What Does the Author Mean by “The Color of the White House?” 62 Lesson 60: Factoring Trig Functions – Creating a Defective Trig Equation by Erroneous Division 63 Lesson 61: Analyzing Single-Variable Data – What is a Normal Distribution – Returning to “Box & Whisker” Plots 64 Lesson 62: Solving Abstract Equations – Defining Linear vs Direct Variation 65 Lesson 63: Using “Completing the Square” to Graph a Circle 66 Lesson 64: Graphing “Complex Numbers” in the Argand Plane, the Polar Form, and Sums & Products of Complex Numbers 67 Lesson 65: Working with Radicals in Trigonometric Functions and Sketching Graphs of Logarithm Functions 68 Lesson 66: Working with Formulas for Systems of Equations – Phase Shifts and Period Changes in Trigonometric Functions 69 Lesson 67: Defining What an “Antilogarithm” Is 70 Lesson 68: Defining the “Locus” of All Points in a Parabola – Equation of a Translated Parabola, Applications, & Derivations 71 Lesson 69: Defining a “Matrix” – Finding the Determinant in a Square Matrix 72 Lesson 70: Calculating Percentiles and “Z” Scores in Statistics 73 Lesson 71: First Circles, then Parabolas, now Ellipses (Part I) 74 Lesson 72: Solving Right Triangles – Using the “Law of Sines” to Solve for Unknown Parts of Triangles 75 Lesson 73: Solving Problems Involving Regular Polygons of Any Number of Sides, Inscribed in a Circle 76 Lesson 74: Using “Cramer’s Rule” to Solve a System of Linear Equations 77 Lesson 75: Combinations are Processed Differently Than We Processed Permutations Earlier in the Textbook 78 Lesson 76: Graphing Functions of (- x) – Finding functions of the “Other Angle” – Trig Identities (Part I) – Making “Rules to Follow” 79 Lesson 77: Defining Binomial Expansion (Part I) 80 Lesson 78: Graphing the “Hyperbola” 81 Lesson 79: Using “De Moivre’s Theorem” – Finding Roots of Complex Numbers 82 Lesson 80: Trig Identities (Part II) 83 Lesson 81: Working with and Understanding the “Law of Cosines” 84 Lesson 82: Explaining How to “Take the Logarithm of a Number or an Expression” – Defining an “Exponential Equation” 85 Lesson 83: Defining “Simple Probability” – “Independent Events” and the Effects of “Replacement” in Probability 86 Lesson 84: Factoring “Factorable” Trig Expressions – Successfully Sketching Sinusoids 87 Lesson 85: Solving Advanced Trigonometric Equations – Solving “Clock” Word Problems 88 Lesson 86: Defining “Arithmetic Progressions” and the “Arithmetic Mean” 89 Lesson 87: Introducing “Sum & Difference” Trig Identities and “Tangent” Identities 90 Lesson 88: Working with “Growth & Decay” of Exponential Functions 91 Lesson 89: More on Ellipses (Part II) 92 Lesson 90: Introducing “Double-Angle” and “Half-Angle” Trig Identities
