6.A - Fractional Equations | Tutor Extraordinaire

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Saxon Advanced Mathematics (2nd edition)

Introduction to the Course

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Lesson 1

1.A - Points, Lines, and Rays (6:18)
1.B - Planes (2:38)
1.C - Angles (11:03)
1.D - Betweenness, Tick Marks, and Assumptions (8:38)
1.E - Triangles (6:05)
1.F - Transversals; Alternate and Corresponding Angles (11:06)
1.G - Area and Sectors of Circles (11:50)
1.H - Concept Review Problems (10:33)

Lesson 2

2.A - More on Area (6:43)
2.B - Cylinders and Prisms (12:29)
2.C - Cones and Pyramids (16:46)
2.D - Spheres (6:26)

Lesson 3

3.AB - Pythagorean Theorem and Triangle Inequalities (1) (4:29)
3.C - Similar polygons (10:04)
3.D - Similar triangles (21:05)

Lesson 4

4 - Construction (19:46)

Lesson 5

5.A - Exponents and Radicals (14:49)
5.B - Complex Numbers (9:43)
5.C - Areas of Similar Geometric Figures (7:15)
5.D - Diagonals of Rectangular Solids (9:16)

Lesson 6

6.A - Fractional Equations (7:50)
6.B - Radical Equations (5:26)
6.C - Systems of Three Linear Equations (7:41)

Lesson 7

7.AB - Inductive and Deductive Reasoning and Logic (12:04)
7.C - The Contrapositive (6:01)
7.D - Converse and Inverse (7:39)

Lesson 8

8.A - Statements of Similarity (8:37)
8.B - Proportional Segments (8:16)
8.C - Angle Bisectors and Side Ratios (8:39)

Lesson 9

9.A - Congruent Figures (13:17)
9.B - Proof Outlines (16:57)

Lesson 10

10.A - Equation of a Line (23:57)
10.B - Rational Denominators (14:05)
10.C - Completing the Square (5:33)

Lesson 11

11.AB - Circles and Properties of Circles (27:59)
11.C - The Quadratic Formula (7:50)

Lesson 12

12.A - Angles and Diagonals in Polygons (17:23)
12.B - Proof of the Chord-Tangent Theorem (13:10)

Lesson 13

13.A - Intersecting Secants (6:03)
13.B - Intersecting Secants and Tangents (15:32)
13.C - Products of Chord Segments (5:30)
13.D - Products of Secant and Tangent Segments (18:54)

Lesson 14

14.A - Sine, Cosine, and Tangent (10:30)
14.B - Angles of Elevation and Depression (9:22)
14.CD - Rectangular and Polar Coordinates; Coordinate Conversion (16:08)

Lesson 15

15.A - Assumptions (7:56)
15.B - Proofs (44:09)

Lesson 16

16.A - Complex Fractions (10:20)
16.B - Abstract Equations (5:42)
16.C - Division of Polynomials (5:03)

Lesson 17

17.A - Proofs of the Pythagorean Theorem (9:13)
17.B - Proofs of Similarity (15:02)

Lesson 18

18 - Advanced Word Problems (32:40)

Lesson 19

19.A - Nonlinear Systems (15:33)
19.B - Factoring Exponentials (7:56)
19.C - Sum and Difference of Two Cubes (9:01)

Lesson 20

20 - Two Special Triangles (11:05)

Lesson 21

21.A - Evaluating Functions (6:36)
21.B - Domain and Range (17:39)
21.C - Types of Functions (14:15)
21.D - Tests for Functions (8:02)

Lesson 22

22.A - Absolute Value (12:50)
22.B - Reciprocal Functions (8:02)

Lesson 23

23.AB - The Exponential Function and Sketching Exponentials (12:31)

Lesson 24

24.A - Sums of Trigonometric Functions (6:51)
24.B - Combining Functions (12:59)

Lesson 25

25.A - Age Problems (3:47)
25.B - Rate Problems (18:43)

Lesson 26

26.AB - The Logarithmic Form of the Exponential; Logarithmic Equations (14:58)

Lesson 27

27.AB - Related Angles and Signs of Trigonometric Functions (22:18)

Lesson 28

28.A - Factorial Notation (6:40)
28.B - Abstract Rate Problems (12:31)

Lesson 29

29.A - The Unit Circle (4:54)
29.B - Very Large and Very Small Fractions (5:38)
29.C - Quadrantal Angles (10:06)

Lesson 30

30.A - Addition of Vectors (19:36)
30.B - Overlapping Triangles (19:12)

Lesson 31

31.A - Symmetry (10:18)
31.B - Reflections (9:01)
31.C - Translations (15:15)

Lesson 32

32.A - Inverse Functions (10:14)
32.B - Four Quadrant Signs (4:24)
32.C - Inverse Trigonometric Functions (26:34)

Lesson 33

33.ABCD - Quadrilaterals; Parallelograms (29:13)
33.E - Trapezoids (11:59)

Lesson 34

34.A - Summation Notation (6:44)
34.B - Linear Regression (9:26)
34.C - Decomposing Functions (3:44)

Lesson 35

35.A - Change in Coordinates (7:13)
35.B - The Name of a Number (9:58)
35.C - The Distance Formula (8:43)

Lesson 36

36.AB - Angles Greater Than 360°; Sums of Trigonometric Functions (12:36)
36.C - Boat-in-the-River Problems (6:43)

Lesson 37

37.A - The Line as a Locus (14:27)
37.B - The Midpoint Formula (4:37)

Lesson 38

38.A - Fundamental Counting Principle and Permutations (9:20)
38.B - Designated Roots (6:40)
38.C - Overall Average Rate (8:46)

Lesson 39

39.A - Radian Measure (25:28)
39.B - Forms of Linear Equations (10:30)

Lesson 40

40.A - The Argument in Mathematics (3:39)
40.B - The Laws of Logarithms (12:17)
40.C - Properties of Inverse Functions (5:56)

Lesson 41

41.A - Reciprocal Trigonometric Functions (17:02)
41.B - Permutation Notation (6:44)

Lesson 42

42.AB - Conic Sections and Circles (13:06)
42.C - Constants in Exponential Functions (7:49)

Lesson 43

43.AB - Periodic Functions; Graphs of Sin ø and Cos ø (15:16)

Lesson 44

44 - Abstract Rate Problems (15:57)

Lesson 45

45.A - Conditional Permutations (12:21)
45.B - Two-Variable Analysis Using a Graphing Calculator (4:44)

Lesson 46

46.AB - Complex Roots and Factoring Over the Complex Numbers (12:31)

Lesson 47

47.A - Vertical Sinusoid Translations (6:27)
47.B - Arctan (2:40)

Lesson 48

48.A - Powers of Trigonometric Functions (5:18)
48.B - Perpendicular Bisectors (9:14)

Lesson 49

49.A - The Logarithmic Function (3:28)
49.B - Development for the Rules of Logarithms (9:10)

Lesson 50

50 - Trigonometric Equations (8:47)

Lesson 51

51 - Common Logarithms and Natural Logarithms (10:26)

Lesson 52

52.AB - The Inviolable Argument and Arguments in Trigonometric Equations (7:33)

Lesson 53

53.A - Review of Unit Multipliers (4:51)
53.B - Angular Velocity (15:27)

Lesson 54

54 - Parabolas (14:49)

Lesson 55

55.A - Circular Permutations (5:21)
55.B - Distinguishable Permutations (8:04)

Lesson 56

56.A - Triangular Areas (6:18)
56.B - Areas of Segments (7:33)
56.C - Systems of Inequalities (8:28)

Lesson 57

57.A - Phase Shifts in Sinusoids (10:46)
57.B - Period of a Sinusoid (7:40)

Lesson 58

58.A - Distance From a Point to a Line (13:39)
58.B - "Narrow" and "Wide" Parabolas (15:29)

Lesson 59

59.A - Advanced Logarithm Problems (8:50)
59.B - The Color of the White House (9:19)

Lesson 60

60.AB - Factorable Trigonometric Equations; Loss of Solutions Caused by Division (14:45)

Lesson 61

61.A - Single-Variable Analysis (8:45)
61.B - The Normal Distribution (15:44)
61.C - Box-and-Whisker Plots (22:02)

Lesson 62

62.A - Abstract Coefficients (6:48)
62.B - Linear Variation (7:52)

Lesson 63

63 - Circles and Completing the Square (9:48)

Lesson 64

64.A - The Complex Plane (2:35)
64.B - Polar Form of a Complex Number (3:42)
64.C - Sums and Products of Complex Numbers (9:49)

Lesson 65

65.A - Radicals in Trigonometric Equations (12:28)
65.B - Graphs of Logarithmic Functions (4:20)

Lesson 66

66.A - Formulas for Systems of Equations (9:34)
66.B - Phase Shifts and Period Changes (9:03)

Lesson 67

67 - Antilogarithms (10:18)

Lesson 68

68.A - Locus Definition of a Parabola (14:10)
68.B - Translated Parabolas (7:07)
68.CD - Applications and Derivation (8:06)

Lesson 69

69.AB - Matrices and Determinants (11:32)

Lesson 70

70 - Percentiles and z Scores (19:06)

Lesson 71

71 - The Ellipse (1) (11:08)

Lesson 72

72.AB - One Side Plus Two Other Parts; Law of Sines (14:52)

Lesson 73

73 - Regular Polygons (9:24)

Lesson 74

74 - Cramer's Rule (14:17)

Lesson 75

75 - Combinations (20:52)

Lesson 76

76.A - Functions of (-x) (19:02)
76.B - Functions of the Other Angle (4:12)
76.CD - Trigonometric Identities (1); Rules of the Game (14:38)

Lesson 77

77 - Binomial Expansions (1) (12:09)

Lesson 78

78 - The Hyperbola (18:21)

Lesson 79

79.A - De Moivre's Theorem (7:14)
79.B - Roots of Complex Numbers (19:11)

Lesson 80

80 - Trigonometric Identities (2) (24:04)

Lesson 81

81 - Law of Cosines (28:23)

Lesson 82

82.AB - Taking the Logarithm of; Exponential Equations (15:01)

Lesson 83

83.A - Simple Probability (6:46)
83.B - Independent Events (4:12)
83.C - Replacement (5:34)

Lesson 84

84.A - Factorable Expressions (14:54)
84.B - Sketching Sinusoids (12:19)

Lesson 85

85.A - Advanced Trigonometric Equations (20:41)
85.B - Clock Problems (13:38)

Lesson 86

86 - Arithmetic Progressions and Arithmetic Means (21:40)

Lesson 87

87.A - Sum and Difference Identities (9:52)
87.B - Tangent Identities (11:45)

Lesson 88

88 - Exponential Functions (Growth and Decay) (23:22)

Lesson 89

89 - The Ellipse (2) (13:37)

Lesson 90

90.A - Double-Angle Identities (7:28)
90.B - Half-Angle Identities (6:43)

Lesson 91

91 - Geometric Progressions (14:47)

Lesson 92

92.A - Probability of Either (14:14)
92.B - Notations for Permutations and Combinations (4:01)

Lesson 93

93.A - Advanced Trigonometric Identities (13:12)
93.B - Triangle Inequalities (2) (8:30)

Lesson 94

94.A - Graphs of Secant and Cosecant (5:26)
94.B - Graphs of Tangent and Cotangent (9:04)

Lesson 95

95 - Advanced Complex Roots (7:48)

Lesson 96

96.A - More Double-Angle Identities (8:25)
96.B - Triangle Area Formula (4:05)
96.C - Proof of the Law of Sines (3:26)
96.D - Equal Sides Imply Proportional Sides (4:19)

Lesson 97

97 - The Ambiguous Case (11:20)

Lesson 98

98.A - Change of Base (5:19)
98.B - Contrived Logarithm Problems (16:31)

Lesson 99

99.AB - Sequence Notations and Advanced Sequence Problems (13:40)
99.C - The Arithmetic and Geometric Means (8:18)

Lesson 100

100.A - Product Identities (9:24)
100.B - More Sum and Difference Identities (8:35)

Lesson 101

101.A - Zero Determinants (4:24)
101.B - 3x3 Determinants (3:26)
101.C - Determinant Solutions of 3x3 Systems (15:02)
101.D - Independent Equations (9:16)

Lesson 102

102 - Binomial Expansions (2) (11:35)

Lesson 103

103.A - Calculations with Logarithms (11:08)
103.B - Power of the Hydrogen (6:08)

Lesson 104

104.A - Arithmetic Series (8:24)
104.B - Geometric Series (10:52)

Lesson 105

105.A - Cofactors (8:46)
105.B - Expansion by Cofactors (11:17)

Lesson 106

106.A - Translations of Conic Sections (3:01)
106.B - Equations of the Ellipse (13:47)
106.C - Equations of the Hyperbola (11:59)

Lesson 107

107 - Convergent Geometric Series (16:35)

Lesson 108

108 - Matrix Addition and Multiplication (26:03)

Lesson 109

109 - Rational Numbers (10:39)

Lesson 110

110.A - Graphs of Arcsine and Arccosine (7:24)
110.B - Graphs of Arcsecant and Arccosecant (5:39)
110.C - Graphs of Arctangent and Arccotangent (10:40)

Lesson 111

111.A - Logarithmic Inequalities: Base Greater Than 1 (3:03)
111.B - Logarithmic Inequalities: Base Less Than 1 (2:21)

Lesson 112

112 - Binomial Theorem (11:11)

Lesson 115

115 - The Remainder Theorem (14:32)

Lesson 116

116 - The Region of Interest (20:27)

Lesson 117

117.A - Prime and Relatively Prime (4:22)
117.B - Rational Roots Theorem (14:43)

Lesson 118

118 - Roots of Polynomial Equations (16:48)

Lesson 119

119.A - Descartes' Rule of Signs (7:33)
119.B - Upper and Lower Bound Theorem (13:17)
119.C - Irrational Roots (13:17)

Lesson 120

120.A - Matrix Algebra (6:37)
120.B - Finding Inverse Matrices (11:39)

Lesson 121

121.A - Piecewise Functions (7:52)
121.B - Greatest Integer Function (3:51)

Lesson 122

122.A - Graphs of Rational Functions (9:26)
122.B - Graphs That Contain Holes (9:19)

Lesson 123

123 - The General Conic Equation (15:48)

Lesson 124

124 - Point of Division Problems (12:45)

Lesson 125

125.A - Using the Graphing Calculator to Graph (3:37)
125.B - Solutions to Systems of Equations Using the Graphing Calculator (2:58)
125.C - Roots (4:39)

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6.A - Fractional Equations

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