Khan Academy

Algebra

Topics covered from very basic algebra all the way through algebra II. This is the best algebra playlist to start at if you’ve never seen algebra before. Once you get your feet wet, you may want to try some of the videos in the “Algebra I Worked Examples” playlist.

  1. Simple Equations
  2. Equations 2
  3. Equations 3
  4. Algebra: Linear Equations 4
  5. Algebra: Solving Inequalities
  6. Algebra: graphing lines 1
  7. Algebra: Slope and Y-intercept intuition
  8. Algebra: Slope
  9. Algebra: Slope 2
  10. Algebra: Slope 3
  11. Algebra: Equation of a line
  12. Slope and Y-intercept Intuition
  13. Averages
  14. Integer sums
  15. Taking percentages
  16. Growing by a percentage
  17. Another Percent Word Problem
  18. More percent problems
  19. systems of equations
  20. Introduction to Ratios (new HD version)
  21. Ratio problem with basic algebra (new HD)
  22. More advanced ratio problem–with Algebra (HD version)
  23. Alternate Solution to Ratio Problem (HD Version)
  24. Introduction to Ratios
  25. Advanced ratio problems
  26. Age word problems 1
  27. Age word problems 2
  28. Age word problems 3
  29. Level 1 multiplying expressions
  30. Solving a quadratic by factoring
  31. Introduction to i and Imaginary Numbers
  32. Calculating i Raised to Arbitrary Exponents
  33. i as the Principal Root of -1 (a little technical)
  34. Complex Numbers (part 1)
  35. Complex Numbers (part 2)
  36. Introduction to the quadratic equation
  37. Quadratic Equation part 2
  38. Completing the square
  39. Quadratic Formula (proof)
  40. Quadratic Inequalities
  41. Quadratic Inequalities (Visual Explanation)
  42. Introduction to functions
  43. Functions Part 2
  44. Functions (Part III)
  45. Functions (part 4)
  46. Domain of a function
  47. Proof: log a + log b = log ab
  48. Proof: A(log B) = log (B^A), log A – log B = log (A/B)
  49. Proof: log_a (B) = (log_x (B))/(log_x (A))
  50. Algebraic Long Division
  51. Introduction to Conic Sections
  52. Conic Sections: Intro to Circles
  53. Conic Sections: Intro to Ellipses
  54. Conic Sections: Intro to Hyperbolas
  55. Conic Sections: Hyperbolas 2
  56. Conic Sections: Hyperbolas 3
  57. Identifying Conics 1
  58. Identifying Conics 2
  59. Conic Identification 3
  60. Foci of an Ellipse
  61. Foci of a Hyperbola
  62. Proof: Hyperbola Foci
  63. Partial Fraction Expansion 1
  64. Partial Fraction Expansion 2
  65. Partial Fraction Expansion 3
  66. Parabola Focus and Directrix 1
  67. Focus and Directrix of a Parabola 2
  68. Two Passing Bicycles Word Problem
  69. Passed Bike Word Problem
  70. Passing Trains
  71. Overtaking Word Problem
  72. Early Train Word Problem
  73. Officer on Horseback
  74. Rational Inequalities
  75. Rational Inequalities 2
  76. Interesting Polynomial Coefficient Problem
  77. Geometric series sum to figure out mortgage payments
  78. Introduction to Function Inverses
  79. Function Inverse Example 1
  80. Function Inverses Example 2
  81. Function Inverses Example 3
  82. Direct and Inverse Variation
  83. Recognizing Direct and Inverse Variation
  84. Recognizing Odd and Even Functions
  85. Connection between even and odd numbers and functions
  86. New Operator Definitions
  87. Proof by Induction
  88. Alternate Proof to Induction for Integer Sum
  89. Writing Proportions
  90. Coverting Repeating Decimals to Fractions 1
  91. Coverting Repeating Decimals to Fractions 2

Algebra I Worked Examples

180 Worked Algebra I examples (problems written by the Monterey Institute of Technology and Education). You should look at the “Algebra” playlist if you’ve never seen algebra before or if you want instruction on topics in Algebra II. Use this playlist to see a ton of example problems in every topic in the California Algebra I Standards. If you can do all of these problems on your own, you should probably test out of Algebra I (seriously).

  1. Solving Equations 1
  2. Solving Equations 2
  3. Solving Equations with the Distributive Property
  4. Solving equations with the distributive property 2
  5. Algebraic Word Problem
  6. Sum of Consecutive Odd Integers
  7. Example of Solving for a Variable
  8. Solving for a Variable 2
  9. Absolute Value 1
  10. Absolute Value and Number Lines
  11. Absolute Value Equations 1
  12. Absolute Value Equation Example 2
  13. Patterns in Sequences 1
  14. Patterns in Sequences 2
  15. Equations of Sequence Patterns
  16. Finding the 100th Term in a Sequence
  17. Functional Relationships 1
  18. Testing if a relationship is a function
  19. Domain and Range 1
  20. Domain and Range 2
  21. Direct Variation 1
  22. Basic Rate Problem
  23. Basic Linear Function
  24. Exploring linear relationships
  25. Recognizing Linear Functions
  26. Exploring nonlinear relationships
  27. Slope of a line
  28. Slope Example
  29. X and Y intercepts
  30. X and Y intercepts 2
  31. Graphing a line in slope intercept form
  32. Equation of a line 2
  33. Converting to slope-intercept form
  34. Point-slope and standard form
  35. Parallel Lines
  36. Parallel Lines 2
  37. Parallel lines 3
  38. Perpendicular Lines
  39. Perpendicular lines 2
  40. Interpreting Inequalities
  41. Solving Inequalities
  42. Inequalities
  43. Absolute value inequalities Example 1
  44. Absolute Inequalities 2
  45. Absolute value inequalities example 3
  46. Writing and using inequalities
  47. Writing and using inequalities 2
  48. Writing and using inequalities 3
  49. Solving and graphing linear inequalities in two variables 1
  50. Graphing linear inequalities in two variables 2
  51. Graphing linear inequalities in two variables 3
  52. Solving systems by graphing
  53. Solving systems by graphing 2
  54. Solving systems by graphing 3
  55. Solving systems by substitution 1
  56. Solving systems by substitution 2
  57. Solving systems by substitution 3
  58. Solving systems by elimination
  59. Solving systems by elimination 2
  60. Solving systems by elimination 3
  61. Systems and rate problems
  62. Systems and rate problems 2
  63. Systems and rate problems 3
  64. Mixture problems 1
  65. Mixture problems 2
  66. Mixture problems 3
  67. Graphing systems of inequalities
  68. Graphing systems of inequalities 2
  69. Graphing systems of inequalities 3
  70. Exponent Rules 1
  71. Exponent Rules 2
  72. Exponent Rules 3
  73. Scientific notation 1
  74. Scientific notation 2
  75. Scientific notation 3
  76. Simplifying Expressions with Exponents
  77. Simplifying Expressions with Exponents 2
  78. Simplifying Expressions with Exponents 3
  79. Pythagorean Theorem 1
  80. Pythagorean Theorem 2
  81. Pythagorean Theorem 3
  82. Simplifying Radical Expressions1
  83. Simplifying Radical Expressions 2
  84. Simplifying Radical Expressions 3
  85. Solving Radical Equations 1
  86. Solving Radical Equations 2
  87. Solving Radical Equations 3
  88. Applying Radical Equations 1
  89. Applying Radical Equations 2
  90. Applying Radical Equations 3
  91. Fractional Exponent Expressions 1
  92. Fractional Exponent Expressions 2
  93. Fractional Exponent Expressions 3
  94. Multiplying and Dividing Monomials 1
  95. Multiplying and Dividing Monomials 2
  96. Multiplying and Dividing Monomials 3
  97. Polynomials1
  98. Polynomials 2
  99. Adding and Subtracting Polynomials 1
  100. Adding and Subtracting Polynomials 2
  101. Adding and Subtracting Polynomials 3
  102. Multiplying Polynomials1
  103. Multiplying Polynomials 2
  104. Multiplying Polynomials 3
  105. Special Products of Polynomials 1
  106. Special Products of Polynomials 2
  107. U08_L2_T4_we3 Special Products of Polynomials 3
  108. Bay Area CBS Station with Salman Khan
  109. Factoring and the Distributive Property
  110. Factoring and the Distributive Property 2
  111. Factoring and the Distributive Property 3
  112. Factoring Trinomials by Grouping 1
  113. Factoring Trinomials by Grouping 2
  114. U09_L1_T2_we3 Factoring Trinomials by Grouping 3
  115. Factoring Trinomials by Grouping 4
  116. Factoring Trinomials by Grouping 5
  117. Factoring Trinomials by Grouping 6
  118. U09_L2_T1_we1 Factoring Special Products 1
  119. Factoring Special Products 2
  120. U09_L2_T1_we3 Factoring Special Products 3
  121. Solving Quadratic Equations by Factoring.avi
  122. Solving Quadratic Equations by Factoring 2.avi
  123. Solving Quadratic Equations by Factoring 3.avi
  124. Quadratic Functions 1
  125. Quadratic Functions 2
  126. Quadratic Functions 3
  127. Completing the Square 1
  128. Completing the Square 2
  129. Completing the Square 3
  130. Completing the Square 4
  131. Quadratic Formula 1
  132. Quadratic Formula 2
  133. Quadratic Formula 3
  134. Applying Quadratic Functions 1
  135. Applying Quadratic Functions 2
  136. Applying Quadratic Functions 3
  137. Non-Linear Systems of Equations 1
  138. Non-Linear Systems of Equations 2
  139. Non-Linear Systems of Equations 3
  140. Simplifying Rational Expressions 1
  141. Simplifying Rational Expressions 2
  142. Simplifying Rational Expressions 3
  143. Multiplying and Dividing Rational Expressions 1
  144. Multiplying and Dividing Rational Expressions 2
  145. Multiplying and Dividing Rational Expressions 3
  146. Adding and Subtracting Rational Expressions 1
  147. Adding and Subtracting Rational Expressions 2
  148. Adding and Subtracting Rational Expressions 3
  149. Solving Rational Equations 1
  150. Solving Rational Equations 2
  151. Solving Rational Equations 3
  152. Applying Rational Equations 1
  153. Applying Rational Equations 2
  154. Applying Rational Equations 3
  155. Number Sets 1
  156. Number Sets 2
  157. Number Sets 3
  158. Understanding Logical Statements 1
  159. Understanding Logical Statements 2
  160. Understanding Logical Statements 3
  161. Understanding Logical Statements 4
  162. Understanding Logical Statements Commentary
  163. U12_L1_T3_we1 Inductive Reasoning 1
  164. Inductive Reasoning 2
  165. Inductive Reasoning 3
  166. Deductive Reasoning 1
  167. Deductive Reasoning 2
  168. Deductive Reasoning 3
  169. Events and Outcomes 1
  170. Events and Outcomes 2
  171. Events and Outcomes 3
  172. U12_L2_T2_we1 Independent Events 1
  173. Independent Events 2
  174. Independent Events 3
  175. Permutations and Combinations 1
  176. Permutations and Combinations 2
  177. Permutations and Combinations 3
  178. Permutations and Combinations 4
  179. Probability of Dependent Events
  180. Probability of Dependent Events 2
  181. U02_L2_T2_we1 Absolute Value Equations.avi
  182. U06_L3_T1_we3 Graphing Systems of Inequalities
  183. U06_L1_T1_we1 Solving Systems by Graphing
  184. Graphing Linear Inequalities in Two Variables Example 2
  185. U03_L2_T1_we2 Representing Functions as Graphs
  186. U03_L1_T1_we2 Inductive Patterns

Art History

Spontaneous conversations about works of art where the speakers are not afraid to disagree with each other or art history orthodoxy. Videos are made by Dr. Beth Harris and Dr. Steven Zucker along with other contributors.

  1. Sculpture from the Parthenon’s East Pediment
  2. Head of Augustus
  3. Colosseum
  4. Law Code Stele of King Hammurabi
  5. Victory Stele of Naram-Sin
  6. After Praxiteles, Venus (Roman Copy)
  7. Mixing Vessel with Odysseus Escaping from the Cyclops’ Cave
  8. Arch of Titus
  9. Seated Scribe
  10. Great Lyre from the “King’s Grave” at Ur
  11. Ramesses II
  12. Rosetta Stone
  13. Parthenon Frieze
  14. New York Kouros
  15. Neo-Assyrian Art: Human Headed Winged Lion and Bull (Lamassu)
  16. The Parthenon: Metopes
  17. Erechtheion: Caryatid and Column
  18. Geometric Greek Krater
  19. Column of Trajan
  20. Nike of Samothrace
  21. Euphronios, Attic Calyx-Krater
  22. Classical Greek Sculpture
  23. Equestrian Sculpture of Marcus Aurelius
  24. Dying Gaul
  25. Arch of Constantine
  26. Hellenistic Art at the Metropolitan: Eros Sleeping and An Old Market Woman
  27. Temple of Portunus
  28. The Pantheon, Rome
  29. Bayeux Tapestry
  30. Sutton Hoo Ship Burial
  31. Virgin from Ger
  32. Wise and Foolish Virgins, Sant Quirze de Pedret
  33. Santa Pudenziana, Rome
  34. Sarcophagus of Junius Bassus
  35. Santa Sabina
  36. Basilica of Santa Prassede (Praxedes)
  37. Byzantine Art: Justinian and His Attendants
  38. Historiated Capitals, Church of Sant Miquel, Camarasa (Noguera)
  39. Early Christian Art before Constantine
  40. Ivory panel with Archangel
  41. Santa Maria Maggiore
  42. Berlinghieri’s St. Francis Altarpiece
  43. Cathedral of Notre Dame de Chartres
  44. Pre-Columbian Cup
  45. Duccio’s Rucellai Madonna
  46. Cimabue, Santa Trinita Madonna
  47. Duccio’s Madonna and Child
  48. Sienese Art: Duccio, Martini, and Lorenzetti
  49. Giotto’s Lamentation
  50. Nicola and Giovanni Pisano
  51. Giotto, St. Francis Receiving the Stigmata
  52. Duccio’s The Virgin and Child with Saints Dominic and Aurea
  53. Hebrew Astrolabe
  54. Simone Martini’s Annunciation
  55. Giotto, The Ognissanti Madonna
  56. Andrea Pisano’s Reliefs on the Campanile in Florence
  57. Icon of Saint George (the “Black George”)
  58. Holy Thorn Reliquary
  59. Follower of Bernardo Daddi, The Aldobrandini Triptych
  60. Giotto’s Epiphany
  61. Orsanmichele
  62. Campin’s Merode Altarpiece
  63. Representations of David in the Florentine Renaissance
  64. Fra Filippo Lippi’s Madonna and Child
  65. Hubert (?) and Jan van Eyck’s Ghent Altarpiece (closed) or The Adoration of the Mystic Lamb
  66. Linear Perspective: Brunelleschi’s Experiment
  67. Donatello’s David
  68. Mantegna’s Dead Christ
  69. Crivelli’s Madonna and Child Enthroned
  70. Bellini’s St. Francis
  71. Lippi’s Portrait of a Man and Woman at a Casement
  72. Hubert (?) and Jan van Eyck’s Ghent Altarpiece (open) or The Adoration of the Mystic Lamb
  73. Van Eyck’s Portrait of Giovanni Arnolfini and his Wife
  74. Masaccio’s The Tribute Money in the Brancacci Chapel
  75. Christus’s Portrait of a Carthusian
  76. Fra Angelico’s The Annunciation
  77. Fra Angelico’s The Annunciation (Prado)
  78. Van der Weyden’s The Last Judgment Polyptych
  79. Mantegna’s Saint Sebastian
  80. Van der Weyden’s Deposition
  81. Donatello, Saint Mark
  82. Piero della Francesca’s Portraits of Federico da Montefeltro & Battista Sforza
  83. Masaccio’s Holy Trinity
  84. Andrea Mantegna, Camera degli Sposi
  85. Botticelli’s Birth of Venus
  86. Piero della Francesca’s The Baptism of Christ
  87. Icon of the Triumph of Orthodoxy
  88. The Unicorn in Captivity
  89. Masaccio, Virgin and Child Enthroned
  90. Mantegna’s Dormition of the Virgin
  91. Veneziano’s St. Lucy Altarpiece
  92. Brunelleschi’s Dome
  93. Brunelleschi & Ghiberti The Sacrifice of Isaac
  94. Botticelli’s Primavera
  95. Raphael, Madonna of the Goldfinch
  96. Michelangelo’s Pietà
  97. Leonardo, Adoration of the Magi
  98. Bronzino and The Mannerist Portrait
  99. Raphael’s La belle jardinière
  100. Toward The High Renaissance
  101. Leonardo’s Virgin of the Rocks
  102. Leonardo da Vinci
  103. Dürer’s Prints
  104. Dürer’s Four Apostles
  105. Parmigianino’s Self-Portrait
  106. Raphael’s Alba Madonna
  107. Holbein’s The Ambassadors
  108. Cellini’s Perseus
  109. Leonardo’s Last Supper
  110. Bellini’s and Titian’s The Feast of the Gods
  111. Michelangelo’s Moses
  112. Michelangelo’s Slaves
  113. Parmigianino’s Madonna of the Long Neck
  114. Northern Renaissance
  115. Japan, Muromachi to Momoyama period Negoro ware ewer
  116. Raphael’s School of Athens
  117. Michelangelo’s Last Judgment (Sistine Chapel)
  118. Raphael’s Portrait of Pope Julius II
  119. Michelangelo’s Ceiling of the Sistine Chapel
  120. Cranach’s Adam and Eve
  121. Leonardo’s Virgin and Child with St Anne and St John the Baptist (Burlington House Cartoon)
  122. Saint Peter’s Basilica
  123. Hans Holbein the Younger’s Henry VIII
  124. Titian’s Bacchus and Ariadne
  125. Pontormo’s Entombment
  126. Dürer, Self-portrait
  127. Titian, Portrait of a Man
  128. El Greco’s Adoration of the Shepherds
  129. Michelangelo, Laurentian Library
  130. Bernini’s David
  131. Caravaggio’s Narcissus at the Source
  132. Bernini’s Pluto and Proserpina
  133. Borromini, San Carlo alle Quattro Fontane
  134. Caravaggio’s paintings in the Contarelli Chapel, San Luigi dei Francesi
  135. Rembrandt’s Self-Portrait
  136. Pierre Le Gros the Younger’s Stanislas Kostka on his Deathbed
  137. Baroque Art in Holland Vermeer’s Young Woman with a Water Pitcher
  138. Caravaggio’s Calling of Saint Matthew
  139. Poussin’s Landscape with St. John and Rape of the Sabines
  140. Guercino’s Saint Luke Displaying a Painting of the Virgin
  141. Caravaggio’s Crucifixion of Saint Peter
  142. Velázquez’s Las Meninas
  143. Il Gesù, Rome
  144. Rembrandt’s The Three Crosses
  145. Pozzo’s Saint Ignatius Chapel in the church Il Gesù, 1965 (Rome)
  146. Bernini’s Saint Peter’s Square
  147. Bernini’s Apollo and Daphne
  148. Velázquez’s Los Borrachos or The Triumph of Bacchus
  149. Rubens’s Arrival (or Disembarkation) of Marie de Medici at Marseilles, Medici Cycle
  150. Bernini’s Bust of Medusa
  151. Claude Lorraine’s The Judgment of Paris
  152. van Huysum, Vase with Flowers
  153. Velázquez’s Vulcan’s Forge
  154. Gentileschi’s Self-portrait as the Allegory of Painting
  155. Antoine or Louis Le Nain, Peasant Family in an Interior
  156. Rubens, The Consequences of War
  157. Bernini’s Ecstasy of Saint Theresa
  158. Rembrandt’s Self-Portraits
  159. Bernini’s Cathedra Petri (Chair of St. Peter)
  160. Rembrandt’s Bathsheba at her Bath
  161. Caravaggio’s Supper at Emmaus
  162. Carracci’s Crucifixion & Lamentation
  163. Carracci’s Ceiling of the Farnese Palace
  164. Caravaggio’s Death of the Virgin
  165. Rembrandt’s Girl at a Window
  166. Bernini’s Sant’Andrea al Quirinale
  167. Ribera’s Martyrdom of Saint Philip
  168. David’s Oath of the Horatii
  169. David’s Death of Socrates
  170. Fragonard’s The Swing
  171. Fragonard’s The Meeting
  172. Girodet’s The Sleep of Endymion
  173. Boucher’s Venus Consoling Love
  174. Vigée Le Brun’s Madame Perregaux
  175. Boucher’s Madame de Pompadour
  176. David’s The Lictors Returning to Brutus the Bodies of His Sons
  177. David’s The Intervention of the Sabine Women
  178. David’s The Emperor Napoleon In His Study at the Tuileries
  179. Reynolds’s Lady Cockburn and Her Three Eldest Sons
  180. Delacroix’s Scene of the massacre at Chios
  181. Romanticism in France Delacroix’s Liberty Leading the People
  182. Turner’s Rain, Steam, and Speed – The Great Western Railway
  183. Romanticism in Spain Goya’s Third of May, 1808
  184. Delacroix’s The Death of Sardanapalus
  185. Constable’s The Hay Wain
  186. Goya, The Family of Charles IV
  187. Friedrich’s A Walk at Dusk
  188. Gros’s Napoleon Bonaparte Visiting the Plague-Stricken in Jaffa
  189. Friedrich’s Monk by the Sea
  190. Ingres’ La Grand Odalisque
  191. Géricault’s Raft of the Medusa
  192. Ingres’ Raphael and the Fornarina
  193. Romanticism in the United States Cole’s The Oxbow
  194. Goya’s Saturn Devouring One of His Sons
  195. Redgrave’s The Sempstress
  196. Ingres’ Princesse de Broglie
  197. Erastus Salisbury Field’s Portrait of a Young Woman
  198. Academic Art: Gérôme’s Pygmalion and Galatea
  199. Courtbet, The Violoncellist (Self-Portrait)
  200. Courbet’s Burial at Ornans
  201. Bonheur’s Plowing in the Nivernais
  202. Édouard Manet’s Olympia
  203. Manet’s Émile Zola
  204. Courbet’s Young Women from the Village
  205. Seurat’s Bathers at Asnières
  206. Hunt’s Claudio and Isabella
  207. Millet’s L’Angelus
  208. Seurat’s Evening, Honfleur
  209. Édouard Manet’s The Railway
  210. Bonheur’s Sheep in the Highlands
  211. Millais’ The Vale of Rest
  212. Manet’s The Balcony
  213. Van Gogh’s Starry Night
  214. Gauguin’s Vision After the Sermon: Jacob Wrestling with the Angel
  215. Cézanne’s Still-Life with Plaster Cupid
  216. Van Gogh’s Portrait of the Joseph Roulin
  217. Cézanne’s Still Life with Apples
  218. Garnier’s Paris Opéra
  219. Dyce’s Pegwell Bay, Kent – a Recollection of October 5th 1858
  220. Édouard Manet’s Plum Brandy
  221. Manet’s Boating
  222. Courbet’s The Artist’s Studio, A real allegory summing up seven years of my artistic and moral life
  223. Caillebotte’s The Floor Scrapers
  224. Manet’s Corner of a Café-Concert
  225. Renoir’s La Loge
  226. Cassatt’s Breakfast in Bed
  227. Khnopff’s Jeanne Kéfer
  228. Cassatt’s The Loge
  229. Degas’ The Bellelli Family
  230. Gauguin’s The Red Cow
  231. Manet’s Le déjeuner sur l’herbe
  232. Édouard Manet’s A Bar at the Folies-Bergère
  233. Cassatt’s The Cup of Tea
  234. Degas’ The Dance Class
  235. Monet’s The Argenteuil Bridge
  236. Post-Impressionism Seurat’s A Sunday on La Grande Jatte – 1884
  237. Monet’s Gare St. Lazare
  238. Gauguin’s Nevermore
  239. Morisot’s The Mother and Sister of the Artist
  240. Young Woman Powdering Herself
  241. Burne-Jones’ King Cophetua and the Beggar Maid
  242. Millet’s The Gleaners
  243. Gaudí, Sagrada Família
  244. Carpeaux’s Dance
  245. Renoir’s Moulin de la Galette
  246. Caillebotte’s Man at his Bath
  247. Vincent van Gogh, Self-Portrait Dedicated to Paul Gauguin
  248. Monet’s Rouen Cathedral Series
  249. Symbolism: Munch’s The Storm
  250. Monet’s Water Lilies
  251. Rodin’s The Gates of Hell
  252. Degas’ Place de la Concorde or Viscount Lepic and his Daughters
  253. Degas’ Woman Bathing in a Shallow Tub
  254. Duchamp’s Boite-en-valise (the red box), series F
  255. Matisse’s Luxe, calme et volupté
  256. Expressionism & Kirchner’s Street, Dresden
  257. Giacometti’s The Palace at 4am
  258. Umbo’s The Roving Reporter
  259. Bellows’ Pennsylvania Station Excavation
  260. Kandinsky’s Composition VII
  261. Picasso’s Portrait of Gertrude Stein
  262. Cubism & Picasso’s Still Life with Chair Caning
  263. Matisse’s The Red Studio
  264. Giacometti’s City Square
  265. de Kooning’s Woman I
  266. Arp’s Untitled (Collage with Squares Arranged According to the Laws of Chance)
  267. Newman’s Onement I
  268. Picasso’s Les Demoiselles d’Avignon
  269. Matisse’s Piano Lesson
  270. Mark Rothko’s No. 3/No. 13
  271. Dada Duchamp and the Ready-Mades
  272. Italian Futurism
  273. Schwitters’s Merzbild 32A, The Cherry Picture
  274. Newman’s Vir Heroicus Sublimis
  275. Three Futurists Balla, Severini and Boccioni
  276. Gordon Bunshaft’s Lever House
  277. Magritte’s The Treachery of Images (Ceci n’est pas une pipe)
  278. Höch’s Cut with the Kitchen Knife Dada Through the Last Weimar Beer-Belly Cultural Epoch of Germany
  279. Suprematism: Malevich’s White on White
  280. August Sander’s Portraits
  281. Braque’s The Viaduct at L’Estaque
  282. Picasso’s The Reservoir, Horta de Ebro
  283. Feininger’s Cathedral for the Bauhaus
  284. Schad’s Self-Portrait
  285. Dali’s Metamorphosis of Narcissus
  286. Klee’s Twittering Machine
  287. De Stijl: Mondrian’s Composition No. II, with Red and Blue
  288. Cartier-Bresson’s Behind the Gare St. Lazare
  289. Frank Lloyd Wright, Solomon R. Guggenheim Museum
  290. Neue Sachlichkeit: Otto Dix’s Portrait of the Journalist Sylvia von Harden
  291. Picasso’s Guernica
  292. László Moholy-Nagy’s Composition A.XX
  293. O’Keeffe’s The Lawrence Tree
  294. Frida Kahlo’s Frieda and Diego Rivera
  295. Abstract Expressionism Pollock’s One: Number 31, 1950
  296. Johns’ Flag
  297. Brancusi’s Bird in Space
  298. Ludwig Mies van der Rohe’s Seagram Building
  299. Photography post 1960: Diane Arbus’ Boy with a Toy Hand Grenade
  300. Bacon’s Triptych – August 1972
  301. Claes Oldenburg’s Floor Cake
  302. Lucian Freud, Standing by the Rags, 1988-89
  303. Dan Flavin, Untitled (To Donna) II
  304. Warhol’s Gold Marilyn Monroe
  305. Sherman’s Untitled Film Still #21
  306. Hesse, Untitled (Rope Piece), 1970
  307. Joseph Beuys, Table with Accumulator
  308. William Eggleston’s Red Ceiling, or Greenwood, Mississippi, 1973
  309. Sherrie Levine’s Untitled (After Edward Weston, ca. 1925)
  310. Ed Kienholz and Nancy Reddin Kienholz Useful Art #5: The Western Hotel, 1992
  311. Bernd and Hilla Becher’s Cooling Towers
  312. Donald Judd’s Untitled
  313. Gerhard Richter, The Cage Paintings (1-6)
  314. Lichtenstein’s Rouen Cathedral Set V
  315. Eva Hesse’s Untitled
  316. Smithson, Spiral Jetty, 1970
  317. Jackie Winsor’s #1 Rope
  318. Judy Chicago’s Pasadena Lifesaver, Blue Series, No. 4 & Lynda Benglis’s Omega
  319. Gerhard Richter, September
  320. Robert Colescott’s Beauty is in the Eye of the Beholder

Biology

Covers topics seen in a first year college or high school biology course.

  1. Introduction to Evolution and Natural Selection
  2. Ape Clarification
  3. Intelligent Design and Evolution
  4. Evolution Clarification
  5. Natural Selection and the Owl Butterfly
  6. DNA
  7. Variation in a Species
  8. Chromosomes, Chromatids, Chromatin, etc.
  9. Mitosis, Meiosis and Sexual Reproduction
  10. Phases of Mitosis
  11. Phases of Meiosis
  12. Embryonic Stem Cells
  13. Cancer
  14. Introduction to Heredity
  15. Punnett Square Fun
  16. Hardy-Weinberg Principle
  17. Sex-Linked Traits
  18. Bacteria
  19. Viruses
  20. ATP: Adenosine Triphosphate
  21. Introduction to Cellular Respiration
  22. Oxidation and Reduction Review From Biological Point-of-View
  23. Oxidation and Reduction in Cellular Respiration
  24. Glycolysis
  25. Krebs / Citric Acid Cycle
  26. Electron Transport Chain
  27. Oxidative Phosphorylation and Chemiosmosis
  28. Photosynthesis
  29. Photosynthesis: Light Reactions 1
  30. Photosynthesis: Light Reactions and Photophosphorylation
  31. Photosynthesis: Calvin Cycle
  32. Photorespiration
  33. C-4 Photosynthesis
  34. CAM Plants
  35. Parts of a cell
  36. Diffusion and Osmosis
  37. The Lungs and Pulmonary System
  38. Red blood cells
  39. Circulatory System and the Heart
  40. Hemoglobin
  41. Anatomy of a Neuron
  42. Sodium Potassium Pump
  43. Correction to Sodium and Potassium Pump Video
  44. Electrotonic and Action Potentials
  45. Saltatory Conduction in Neurons
  46. Neuronal Synapses (Chemical)
  47. Myosin and Actin
  48. Tropomyosin and troponin and their role in regulating muscle contraction
  49. Role of the Sarcoplasmic Reticulum in Muscle Cells
  50. Anatomy of a muscle cell
  51. Role of Phagocytes in Innate or Nonspecific Immunity
  52. Types of immune responses: Innate and Adaptive. Humoral vs. Cell-Mediated
  53. B Lymphocytes (B cells)
  54. Professional Antigen Presenting Cells (APC) and MHC II complexes
  55. Helper T Cells
  56. Cytotoxic T Cells
  57. Review of B cells, CD4+ T cells and CD8+ T cells
  58. Inflammatory Response
  59. The Kidney and Nephron
  60. Secondary Active Transport in the Nephron
  61. Species
  62. Taxonomy and the Tree of Life

CAHSEE Example Problems

Sal working through the 53 problems from the practice test available at http://www.cde.ca.gov/ta/tg/hs/documents/mathpractest.pdf for the CAHSEE (California High School Exit Examination). Clearly useful if you’re looking to take that exam. Probably still useful if you want to make sure you have a solid understanding of basic high school math.

  1. CAHSEE Practice: Problems 1-3
  2. CAHSEE Practice: Problems 4-9
  3. CAHSEE Practice: Problems 10-12
  4. CAHSEE Practice: Problems 13-14
  5. CAHSEE Practice: Problems 15-16
  6. CAHSEE Practice: Problems 17-19
  7. CAHSEE Practice: Problems 20-22
  8. CAHSEE Practice: Problems 23-27
  9. CAHSEE Practice: Problems 28-31
  10. CAHSEE Practice: Problems 32-34
  11. CAHSEE Practice: Problems 35-37
  12. CAHSEE Practice: Problems 38-42
  13. CAHSEE Practice: Problems 43-46
  14. CAHSEE Practice: Problems 47-51
  15. CAHSEE Practice: Problems 52-53

Calculus

Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)

  1. Introduction to Limits (HD)
  2. Introduction to Limits
  3. Limit Examples (part 1)
  4. Limit Examples (part 2)
  5. Limit Examples (part3)
  6. Limit Examples w/ brain malfunction on first prob (part 4)
  7. Squeeze Theorem
  8. Proof: lim (sin x)/x
  9. More Limits
  10. Epsilon Delta Limit Definition 1
  11. Epsilon Delta Limit Definition 2
  12. Calculus: Derivatives 1 (new HD version)
  13. Calculus: Derivatives 2 (new HD version)
  14. Calculus: Derivatives 2.5 (new HD version)
  15. Derivative Intuition Module
  16. Calculus: Derivatives 1
  17. Calculus: Derivatives 2
  18. Calculus: Derivatives 3
  19. The Chain Rule
  20. Chain Rule Examples
  21. Even More Chain Rule
  22. Product Rule
  23. Quotient Rule
  24. Derivatives (part 9)
  25. Proof: d/dx(x^n)
  26. Proof: d/dx(sqrt(x))
  27. Proof: d/dx(ln x) = 1/x
  28. Proof: d/dx(e^x) = e^x
  29. Proofs of Derivatives of Ln(x) and e^x
  30. Extreme Derivative Word Problem (advanced)
  31. Implicit Differentiation
  32. Implicit Differentiation (part 2)
  33. More implicit differentiation
  34. More chain rule and implicit differentiation intuition
  35. Trig Implicit Differentiation Example
  36. Calculus: Derivative of x^(x^x)
  37. Introduction to L’Hopital’s Rule
  38. L’Hopital’s Rule Example 1
  39. L’Hopital’s Rule Example 2
  40. L’Hopital’s Rule Example 3
  41. Maxima Minima Slope Intuition
  42. Inflection Points and Concavity Intuition
  43. Monotonicity Theorem
  44. Calculus: Maximum and minimum values on an interval
  45. Calculus: Graphing Using Derivatives
  46. Calculus Graphing with Derivatives Example
  47. Graphing with Calculus
  48. Optimization with Calculus 1
  49. Optimization with Calculus 2
  50. Optimization with Calculus 3
  51. Optimization Example 4
  52. Introduction to rate-of-change problems
  53. Equation of a tangent line
  54. Rates-of-change (part 2)
  55. Ladder rate-of-change problem
  56. Mean Value Theorem
  57. The Indefinite Integral or Anti-derivative
  58. Indefinite integrals (part II)
  59. Indefinite Integration (part III)
  60. Indefinite Integration (part IV)
  61. Indefinite Integration (part V)
  62. Integration by Parts (part 6 of Indefinite Integration)
  63. Indefinite Integration (part 7)
  64. Another u-subsitution example
  65. Introduction to definite integrals
  66. Definite integrals (part II)
  67. Definite Integrals (area under a curve) (part III)
  68. Definite Integrals (part 4)
  69. Definite Integrals (part 5)
  70. Definite integral with substitution
  71. Integrals: Trig Substitution 1
  72. Integrals: Trig Substitution 2
  73. Integrals: Trig Substitution 3 (long problem)
  74. Periodic Definite Integral
  75. Simple Differential Equations
  76. Solid of Revolution (part 1)
  77. Solid of Revolution (part 2)
  78. Solid of Revolution (part 3)
  79. Solid of Revolution (part 4)
  80. Solid of Revolution (part 5)
  81. Solid of Revolution (part 6)
  82. Solid of Revolution (part 7)
  83. Solid of Revolution (part 8)
  84. Sequences and Series (part 1)
  85. Sequences and series (part 2)
  86. Maclauren and Taylor Series Intuition
  87. Cosine Taylor Series at 0 (Maclaurin)
  88. Sine Taylor Series at 0 (Maclaurin)
  89. Taylor Series at 0 (Maclaurin) for e to the x
  90. Euler’s Formula and Euler’s Identity
  91. Visualizing Taylor Series Approximations
  92. Generalized Taylor Series Approximation
  93. Visualizing Taylor Series for e^x
  94. Polynomial approximation of functions (part 1)
  95. Polynomial approximation of functions (part 2)
  96. Approximating functions with polynomials (part 3)
  97. Polynomial approximation of functions (part 4)
  98. Polynomial approximations of functions (part 5)
  99. Polynomial approximation of functions (part 6)
  100. Polynomial approximation of functions (part 7)
  101. Taylor Polynomials
  102. Exponential Growth
  103. AP Calculus BC Exams: 2008 1 a
  104. AP Calculus BC Exams: 2008 1 b&c
  105. AP Calculus BC Exams: 2008 1 c&d
  106. AP Calculus BC Exams: 2008 1 d
  107. Calculus BC 2008 2 a
  108. Calculus BC 2008 2 b &c
  109. Calculus BC 2008 2d
  110. Partial Derivatives
  111. Partial Derivatives 2
  112. Gradient 1
  113. Gradient of a scalar field
  114. Divergence 1
  115. Divergence 2
  116. Divergence 3
  117. Curl 1
  118. Curl 2
  119. Curl 3
  120. Double Integral 1
  121. Double Integrals 2
  122. Double Integrals 3
  123. Double Integrals 4
  124. Double Integrals 5
  125. Double Integrals 6
  126. Triple Integrals 1
  127. Triple Integrals 2
  128. Triple Integrals 3
  129. (2^ln x)/x Antiderivative Example
  130. Introduction to the Line Integral
  131. Line Integral Example 1
  132. Line Integral Example 2 (part 1)
  133. Line Integral Example 2 (part 2)
  134. Position Vector Valued Functions
  135. Derivative of a position vector valued function
  136. Differential of a vector valued function
  137. Vector valued function derivative example
  138. Line Integrals and Vector Fields
  139. Using a line integral to find the work done by a vector field example
  140. Parametrization of a Reverse Path
  141. Scalar Field Line Integral Independent of Path Direction
  142. Vector Field Line Integrals Dependent on Path Direction
  143. Path Independence for Line Integrals
  144. Closed Curve Line Integrals of Conservative Vector Fields
  145. Example of Closed Line Integral of Conservative Field
  146. Second Example of Line Integral of Conservative Vector Field
  147. Green’s Theorem Proof Part 1
  148. Green’s Theorem Proof (part 2)
  149. Green’s Theorem Example 1
  150. Green’s Theorem Example 2
  151. Introduction to Parametrizing a Surface with Two Parameters
  152. Determining a Position Vector-Valued Function for a Parametrization of Two Parameters
  153. Partial Derivatives of Vector-Valued Functions
  154. Introduction to the Surface Integral
  155. Example of calculating a surface integral part 1
  156. Example of calculating a surface integral part 2
  157. Example of calculating a surface integral part 3
  158. 2011 Calculus AB Free Response #1a
  159. 2011 Calculus AB Free Response #1 parts b c d
  160. 2011 Calculus AB Free Response #2 (a & b)
  161. 2011 Calculus AB Free Response #2 (c & d)
  162. 2011 Calculus AB Free Response #3 (a & b)
  163. 2011 Calculus AB Free Response #3 (c)
  164. 2011 Calculus AB Free Response #4a
  165. 2011 Calculus AB Free Response #4b
  166. 2011 Calculus AB Free Response #4c
  167. 2011 Calculus AB Free Response #4d
  168. 2011 Calculus AB Free Response #5a
  169. 2011 Calculus AB Free Response #5b
  170. 2011 Calculus AB Free Response #5c.
  171. 2011 Calculus AB Free Response #6a
  172. 2011 Calculus AB Free Response #6b
  173. 2011 Calculus AB Free Response #6c
  174. 2011 Calculus BC Free Response #1a
  175. 2011 Calculus BC Free Response #1 (b & c)
  176. 2011 Calculus BC Free Response #1d
  177. 2011 Calculus BC Free Response #3a
  178. 2011 Calculus BC Free Response #3 (b & c)
  179. 2011 Calculus BC Free Response #6a
  180. 2011 Calculus BC Free Response #6b
  181. 2011 Calculus BC Free Response #6c
  182. Error or Remainder of a Taylor Polynomial Approximation
  183. Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation
  184. 2011 Calculus BC Free Response #6d

Chemistry

Videos on chemistry (roughly covering a first-year high school or college course).

  1. Elements and Atoms
  2. Introduction to the atom
  3. Orbitals
  4. More on orbitals and electron configuration
  5. Electron Configurations
  6. Electron Configurations 2
  7. Valence Electrons
  8. Groups of the Periodic Table
  9. Periodic Table Trends: Ionization Energy
  10. Other Periodic Table Trends
  11. Ionic, Covalent, and Metallic Bonds
  12. Molecular and Empirical Formulas
  13. The Mole and Avogadro’s Number
  14. Formula from Mass Composition
  15. Another mass composition problem
  16. Balancing Chemical Equations
  17. Stoichiometry
  18. Stoichiometry: Limiting Reagent
  19. Ideal Gas Equation: PV=nRT
  20. Ideal Gas Equation Example 1
  21. Ideal Gas Equation Example 2
  22. Ideal Gas Equation Example 3
  23. Ideal Gas Example 4
  24. Partial Pressure
  25. States of Matter
  26. States of Matter Follow-Up
  27. Specific Heat, Heat of Fusion and Vaporization
  28. Chilling Water Problem
  29. Phase Diagrams
  30. Van Der Waals Forces
  31. Covalent Networks, Metallic, and Ionic Crystals
  32. Vapor Pressure
  33. Suspensions, Colloids and Solutions
  34. Solubility
  35. Boiling Point Elevation and Freezing Point Supression
  36. Introduction to Kinetics
  37. Reactions in Equilibrium
  38. Mini-Video on Ion Size
  39. Keq Intuition (mathy and not necessary to progress)
  40. Keq derivation intuition (can skip; bit mathy)
  41. Heterogenous Equilibrium
  42. Le Chatelier’s Principle
  43. Introduction to pH, pOH, and pKw
  44. Acid Base Introduction
  45. pH, pOH of Strong Acids and Bases
  46. pH of a Weak Acid
  47. pH of a Weak Base
  48. Conjugate Acids and Bases
  49. pKa and pKb Relationship
  50. Buffers and Hendersen-Hasselbalch
  51. Strong Acid Titration
  52. Weak Acid Titration
  53. Half Equivalence Point
  54. Titration Roundup
  55. Introduction to Oxidation States
  56. More on Oxidation States
  57. Hydrogen Peroxide Correction
  58. Redox Reactions
  59. Galvanic Cells
  60. Types of Decay
  61. Half-Life
  62. Exponential Decay Formula Proof (can skip, involves Calculus)
  63. Introduction to Exponential Decay
  64. More Exponential Decay Examples
  65. Macrostates and Microstates
  66. Quasistatic and Reversible Processes
  67. First Law of Thermodynamics/ Internal Energy
  68. More on Internal Energy
  69. Work from Expansion
  70. PV-diagrams and Expansion Work
  71. Proof: U=(3/2)PV or U=(3/2)nRT
  72. Work Done by Isothermic Process
  73. Carnot Cycle and Carnot Engine
  74. Proof: Volume Ratios in a Carnot Cycle
  75. Proof: S (or Entropy) is a valid state variable
  76. Thermodynamic Entropy Definition Clarification
  77. Reconciling Thermodynamic and State Definitions of Entropy
  78. Entropy Intuition
  79. Maxwell’s Demon
  80. More on Entropy
  81. Efficiency of a Carnot Engine
  82. Carnot Efficiency 2: Reversing the Cycle
  83. Carnot Efficiency 3: Proving that it is the most efficient
  84. Enthalpy
  85. Heat of Formation
  86. Hess’s Law and Reaction Enthalpy Change
  87. Gibbs Free Energy and Spontaneity
  88. Gibbs Free Energy Example
  89. More rigorous Gibbs Free Energy/ Spontaneity Relationship
  90. A look at a seductive but wrong Gibbs/Spontaneity Proof
  91. Stoichiometry Example Problem 1
  92. Stoichiometry Example Problem 2
  93. Limiting Reactant Example Problem 1
  94. Empirical and Molecular Formulas from Stoichiometry
  95. Example of Finding Reactant Empirical Formula
  96. Stoichiometry of a Reaction in Solution
  97. Another Stoichiometry Example in a Solution
  98. Molecular and Empirical Forumlas from Percent Composition
  99. Acid Base Titration
  100. Spectrophotometry Introduction
  101. Spectrophotometry Example
  102. Hess’s Law Example
  103. Vapor Pressure Example
  104. Change of State Example

Cosmology and Astronomy

Videos attempting to grasp a little bit about our Universe (many of the topics associated with “Big History”)

  1. Scale of Earth and Sun
  2. Scale of Solar System
  3. Scale of Distance to Closest Stars
  4. Scale of the Galaxy
  5. Intergalactic Scale
  6. Hubble Image of Galaxies
  7. Big Bang Introduction
  8. Radius of Observable Universe
  9. (Correction) Radius of Observable Universe
  10. Red Shift
  11. Cosmic Background Radiation
  12. Cosmic Background Radiation 2
  13. Cosmological Time Scale 1
  14. Cosmological Time Scale 2
  15. Four Fundamental Forces
  16. Birth of Stars
  17. Becoming a Red Giant
  18. White and Black Dwarfs
  19. A Universe Smaller than the Observable
  20. Star Field and Nebula Images
  21. Parallax in Observing Stars
  22. Stellar Parallax
  23. Stellar Distance Using Parallax
  24. Stellar Parallax Clarification
  25. Parsec Definition
  26. Hubble’s Law
  27. Lifecycle of Massive Stars
  28. Supernova (Supernovae)
  29. Supernova clarification
  30. Black Holes
  31. Cepheid Variables 1
  32. Why Cepheids Pulsate
  33. Why Gravity Gets So Strong Near Dense Objects
  34. Supermassive Black Holes
  35. Quasars
  36. Quasar Correction
  37. Galactic Collisions
  38. Earth Formation
  39. Beginnings of Life
  40. Ozone Layer and Eukaryotes Show Up in the Proterozoic Eon
  41. Biodiversity Flourishes in Phanerozoic Eon
  42. First living things on land clarification
  43. Plate Tectonics– Difference between crust and lithosphere
  44. Structure of the Earth
  45. Plate Tectonics — Evidence of plate movement
  46. Plate Tectonics — Geological Features of Divergent Plate Boundaries
  47. Plate Tectonics– Geological features of Convergent Plate Boundaries
  48. Plates Moving Due to Convection in Mantle
  49. Hawaiian Islands Formation
  50. Compositional and Mechanical Layers of the Earth
  51. Seismic Waves
  52. Why S-Waves Only Travel in Solids
  53. Refraction of Seismic Waves
  54. The Mohorovicic Seismic Discontinuity
  55. How we know about the Earth’s core
  56. Pangaea
  57. Scale of the Large
  58. Scale of the Small
  59. Detectable Civilizations in our Galaxy 1
  60. Detectable Civilizations in our Galaxy 2
  61. Detectable Civilizations in our Galaxy 3
  62. Detectable Civilizations in our Galaxy 4
  63. Detectable Civilizations in our Galaxy 5
  64. Human Evolution Overview
  65. Understanding Calendar Notation
  66. Correction Calendar Notation
  67. Development of Agriculture and Writing
  68. Introduction to Light
  69. Seasons Aren’t Dictated by Closeness to Sun
  70. How Earth’s Tilt Causes Seasons
  71. Milankovitch Cycles Precession and Obliquity
  72. Are Southern Hemisphere Seasons More Severe?
  73. Precession Causing Perihelion to Happen Later
  74. What Causes Precession and Other Orbital Changes
  75. Apsidal Precession (Perihelion Precession) and Milankovitch Cycles
  76. Firestick Farming
  77. Carbon 14 Dating 1
  78. Carbon 14 Dating 2
  79. Potassium-Argon (K-Ar) Dating
  80. K-Ar Dating Calculation
  81. Chronometric Revolution
  82. Collective Learning
  83. Land Productivity Limiting Human Population
  84. Energy Inputs for Tilling a Hectare of Land
  85. Random Predictions for 2060

Developmental Math

Worked developmental math examples from the Monterey Institute. These start pretty basic and would prepare a student for the Algebra I worked examples

  1. Place Value 1
  2. Place Value 2
  3. Place Value 3
  4. Rounding Whole Numbers 1
  5. Rounding Whole Numbers 2
  6. Rounding Whole Numbers 3
  7. Comparing Whole Numbers
  8. Comparing Whole Numbers 2
  9. Comparing Whole Numbers 3
  10. Adding Whole Numbers and Applications 1
  11. Adding Whole Numbers and Applications 2
  12. Adding Whole Numbers and Applications 3
  13. Adding Whole Numbers and Applications 4
  14. Subtracting Whole Numbers
  15. Subtraction with Borrowing or Regrouping
  16. Subtraction Word Problem
  17. Rounding to Estimate Differences
  18. Rounding to Estimate Sums
  19. Rounding to Estimate Sums 2
  20. Multiplying Whole Numbers and Applications 1
  21. Multiplying Whole Numbers and Applications 2
  22. Multiplying Whole Numbers and Applications 3
  23. Multiplying Whole Numbers and Applications 4
  24. Multiplying Whole Numbers and Applications 5
  25. Multiplying Whole Numbers and Applications 6
  26. Dividing Whole Numbers and Applications 1
  27. Dividing Whole Numbers and Applications 2
  28. Dividing Whole Numbers and Applications 3
  29. Dividing Whole Numbers and Applications 4
  30. Dividing Whole Numbers and Applications 5
  31. Dividing Whole Numbers and Applications 6
  32. Properties of Whole Numbers
  33. Identity Property of 1
  34. Commutative Law of Addition
  35. Commutative Law of Multiplication
  36. Associative Law of Addition
  37. Associative Law of Multiplication
  38. The Distributive Property
  39. The Distributive Property 2
  40. Understanding Exponents
  41. Understanding Exponents 2
  42. Understanding Square Roots
  43. Order of Operations
  44. Order of Operations 2
  45. Numerator and Denominator of a Fraction
  46. Identifying Fraction Parts
  47. Proper and Improper Fractions
  48. Converting Mixed Numbers to Improper Fractions
  49. Changing an Improper Fraction to a Mixed Number
  50. Recognizing Divisibility
  51. Finding Factors of a Number
  52. Prime Factorization
  53. Recognizing Prime Numbers
  54. Equivalent Fractions Example
  55. Fractions in lowest terms
  56. Comparing Fractions
  57. Comparing Fractions 2
  58. Multiplying Fractions
  59. Multiplying Mixed Numbers
  60. Multiplying Fractions and Mixed Numbers
  61. Multiplying Fractions Word Problem
  62. Reciprocal of a Mixed Number
  63. Dividing Fractions Example
  64. Dividing Mixed Numbers
  65. Dividing Mixed Numbers and Fractions
  66. Dividing Fractions Word Problem
  67. Adding Fractions with Like Denominators
  68. Least Common Multiple (LCM)
  69. Finding Common Denominators
  70. Adding Fractions with Unlike Denominators
  71. Adding Mixed Numbers
  72. Adding Mixed Numbers with Unlike Denominators
  73. Adding Mixed Numbers Word Problem
  74. Subtracting Fractions
  75. Subtracting Mixed Numbers
  76. Subtracting Mixed Numbers 2
  77. Subtracting Mixed Numbers Word Problem
  78. Decimal Place Value
  79. Decimal Place Value 2
  80. Decimals and Fractions
  81. Converting Fractions to Decimals Example
  82. Comparing Decimals
  83. Rounding Decimals
  84. Decimals on a Number Line
  85. Comparing Decimals 4
  86. Adding Decimals
  87. Subtracting Decimals
  88. Subtracting Decimals Word Problem
  89. Multiplying Decimals
  90. Multiplying a Decimal by a Power of 10
  91. Dividing Decimals
  92. Dividing a Decimal by a Power of 10
  93. Dividing Decimals 2.1
  94. Mulitplyling Decimals 3
  95. Estimation with Decimals
  96. Ratios as Fractions in Simplest Form
  97. Simplifying Rates and Ratios
  98. Finding Unit Rates
  99. Finding Unit Prices
  100. Understanding Proportions
  101. Find an Unknown in a Proportion
  102. Find an Unknown in a Proportion 2
  103. Describing the Meaning of Percent
  104. Describing the Meaning of Percent 2
  105. Representing a number as a decimal, percent, and fraction
  106. Representing a number as a decimal, percent, and fraction 2
  107. Identifying Percent Amount and Base
  108. Solving Percent Problems 2
  109. Solving Percent Problems 3
  110. Unit Conversion with Fractions
  111. Adding different units of length
  112. Converting units of length
  113. Converting pounds to ounces
  114. Adding different units for weight
  115. Application problems involving units of weight
  116. Converting Gallons to quarts pints and cups
  117. Performing arithmetic calculations on units of volume
  118. Solving application problems involving units of volume
  119. U.S. Customary and Metric units
  120. Conversion between metric units
  121. Converting within the metric system
  122. Perimeter and Unit Conversion
  123. Comparing Celsius and Farenheit temperature scales
  124. Converting Farenheit to Celsius
  125. Congruent and Similar Triangles
  126. Similar Triangles Corresponding Sides and Angles
  127. Missing Measurements for Similar Triangles
  128. Application of Similar Triangles
  129. Using the Pythagorean Theorem
  130. Pythagorean Theorem Application
  131. Quadrilateral Properties
  132. Parts of a Circle
  133. Circumference of a Circle
  134. Area of a Circle
  135. Area and Perimeter of Composite Figures
  136. Identifying Geometric Solids
  137. Volume of a Composite Shape
  138. Identifying Rays
  139. Acute Obtuse and Right Angles
  140. Identifying Parallel and Perpendicular Lines
  141. Identifying Complementary and Supplementary Angles
  142. Finding Missing Angles
  143. Perimeter of a Polygon
  144. Area of a Trapezoid
  145. Perimeter and Area of a Non-Standard Polygon
  146. Volume of a Sphere

Developmental Math 2

Worked developmental math examples from the Monterey Institute (part 2). These start at Algebra I and would prepare a student for basic college mathematics.

  1. Reading Pictographs
  2. Reading Bar Graphs
  3. Reading Pie Graphs (Circle Graphs)
  4. u08_l1_t2_we2 Reading Line Graphs
  5. u08_l1_t2_we3 Stem-and-leaf Plots
  6. Mean Median and Mode
  7. Range and Mid-range
  8. Measures of Center
  9. Reading Box-and-Whisker Plots
  10. Box-and-Whisker Plots
  11. Misleading Line Graphs
  12. Simple Probability
  13. Probability of More Complex Outcome
  14. Coin Flipping Example
  15. Variables and Expressions 1
  16. Evaluating Expressions with Two Variables
  17. Locate integers on a number line
  18. Absolute Value of Integers
  19. Opposite of a given number
  20. u09 l1 t2 we4 Adding Real Numbers Application
  21. Points on a number line
  22. Number Sets
  23. Comparing Rational Numbers
  24. Identifying Rational Numbers
  25. Adding Negative Numbers
  26. Adding integers with different signs
  27. Adding real numbers with different signs
  28. Adding fractions with different signs
  29. Identity property of 0
  30. Application of addition of real numbers
  31. Subtracting Real Numbers
  32. Adding and subtracting real numbers
  33. Adding and subtracting real numbers application
  34. Multiplying negative real numbers
  35. Dividing real numbers with different signs
  36. Identity property of 1 (second example)
  37. Multiplying real number application
  38. Commutative Property for Addition
  39. Associative property for multiplication
  40. Distributive property 3
  41. Order of Operations 1
  42. Order of Operations 2 (old)
  43. Solving One-Step Equations
  44. Solving One-Step Equations 2
  45. Multi-step equations 1
  46. One-Step Equation Involving Fractions
  47. Multi-step equations 2
  48. More Involved Multi-Step Equation
  49. Equation Special Cases
  50. Application problems with equation in one variable
  51. Evaluate a formula using substitution
  52. Rearrange formulas to isolate specific variables
  53. Inequalities on a number line
  54. One-Step Inequalities
  55. One-Step Inequalities 2
  56. Multi-Step Inequalities
  57. Multi-Step Inequalities 2
  58. Compund Inequalities
  59. Compund Inequalities 2
  60. Compound Inequalities 3
  61. Compound Inequalities 4
  62. Absolute Value Equations Example 1
  63. Absolute Value Inequalities Example 2
  64. Absolute Value Equations 2
  65. Evaluating exponential expressions
  66. Evaluating exponential expressions 2
  67. Negative and Positive Exponents
  68. Exponent Properties 1
  69. Exponent Properties 2
  70. Exponent Properties 3
  71. Exponent Properties 4
  72. Exponent Properties 5
  73. Exponent Properties 6
  74. Exponent Properties 7
  75. Scientific Notation I
  76. Scientific Notation Example 2
  77. Scientific Notation 3 (new)
  78. Multiplying in Scientific Notation
  79. Terms coefficients and exponents in a polynomial
  80. Evaluating a polynomial at a given value
  81. Simply a polynomial
  82. Adding Polynomials
  83. Opposite of a Polynomial
  84. Subtracting Polynomials
  85. Multiplying Monomials
  86. Multiplying Monomials by Polynomials
  87. Multiplying Binomials
  88. Multiplying Polynomials
  89. Special Polynomials Products 1
  90. Square a Binomial
  91. Polynomial divided by monomial
  92. Dividing Monomials
  93. Dividing polynomials 1
  94. Dividing polynomials with remainders
  95. Evaluating an expression with multiple variables
  96. Simplifying an expression with multiple variables
  97. Simplifying Multivariable Polynomial
  98. Subtracting polynomials with multiple variables
  99. More multiplying polynomials
  100. Dividing multivariable polynomial with monomial
  101. Monomial Greatest Common Factor
  102. GCF to Factor a Polynomial
  103. Factor expressions by grouping
  104. Factoring trinomials with a leading 1 coefficient
  105. Factoring trinomials with a common factor
  106. Factoring trinomials with a non-1 leading coefficient by grouping
  107. Factoring perfect square trinomials
  108. Factoring difference of squares
  109. Factoring Sum of Cubes
  110. Difference of Cubes Factoring
  111. Solving factored equations
  112. Solving quadratics by factoring
  113. Applications Problem Factoring Quadratics
  114. Plotting (x,y) relationships
  115. Quadrants of Coordinate Plane
  116. Graphing using X and Y intercepts
  117. Ordered Pair Solutions of Equations
  118. Application problem with graph
  119. Graphical Slope of a Line
  120. Slope of a Line 2
  121. Slope of a Line 3
  122. Hairier Slope of Line
  123. Equation of a line 1
  124. Equation of a line 2
  125. Equation of a line 3
  126. Perpendicular Line Slope
  127. Equation of a Line hairier example
  128. Parallel Line Equation
  129. Graphing Inequalities 1
  130. Graphing Inequalities 2
  131. Plot ordered pairs

Developmental Math 3

More Developmental math videos

  1. Graphings Systems of Equations
  2. Testing a solution for a system of equations
  3. Consistent and Inconsistent Systems
  4. Independent and Dependent Systems
  5. Graphical Systems Application Problem
  6. u14 l1 t1 we INT Consistent System of Independent Equations t2
  7. Graphical System of Inequalities
  8. Testing Solutions for a System of Inequalities
  9. System of Inequalities Application
  10. Substitution Method
  11. Substitution Method 2
  12. Substitution Method 3
  13. Addition Elimination Method 1
  14. Addition Elimination Method 2
  15. Addition Elimination Method 3
  16. Addition Elimination Method 4
  17. Systems of Three Variables
  18. Systems of Three Variables 2
  19. Three Equation Application Problem
  20. Solutions to Three Variable System
  21. Domain of a Rational Expression 1
  22. Simplifying Rational Expressions Example 2
  23. Multiplying and Simplifying Rational Expressions
  24. Dividing and Simplifying Rational Expressions
  25. Algebraic Expression Least Common Multiple
  26. Adding Rational Expressions
  27. Subtracting Rational Expressions
  28. Simplifying First for Subtracting Rational Expressions
  29. Adding and Subtracting Rational Expressions
  30. Complicated Rational Expressions
  31. Rational Equations
  32. Extraneous Solutions to Rational Equations
  33. Rate Problem Involving Rational Equations
  34. Another Take on the Rate Problem
  35. Solving for a Variable
  36. Direct Inverse and Joint Variation
  37. Proportionality Constant for Direct Variation
  38. Direct Variation Application
  39. Inverse Variation Application
  40. Joint Variation Application
  41. Approximating Square Roots
  42. Simplifying Square Roots
  43. Simplifying Square Roots Comment Response
  44. Finding Cube Roots
  45. Simplifying Cube Roots
  46. Radical Equivalent to Rational Exponents
  47. Radical Equivalent to Rational Exponents 2
  48. Rational Exponents and Exponent Laws
  49. More Rational Exponents and Exponent Laws
  50. Multiply and Simplify a Radical Expression 1
  51. Multiply and Simplify a Radical Expression 2
  52. Adding and Simplifying Radicals
  53. Subtracting and Simplifying Radicals
  54. Multiplying Binomials with Radicals
  55. Rationalizing Denominators of Expressions
  56. Rationalizing Denominators with Conjugates
  57. Solving Radical Equations
  58. Extraneous Solutions for Radical Equations
  59. Radical Equation Application Problem
  60. Complex Numbers
  61. Imaginary Roots of Negative Numbers
  62. Adding Complex Numbers
  63. Subtracting Complex Numbers
  64. Multiplying Complex Numbers
  65. Complex Conjugates Example
  66. Dividing Complex Numbers
  67. Simple Quadratic Equation
  68. Completing Perfect Square Trinomials
  69. Completing the Square to Solve Quadratic Equations
  70. Quadratic Equations in Standard Form
  71. Applying the Quadratic Formula
  72. Complex Roots from the Quadratic Formula
  73. Discriminant for Types of Solutions for a Quadratic
  74. Application Problem with Quadratic Formula
  75. Domain and Range of a Relation
  76. Relations and Functions
  77. Graphical Relations and Functions
  78. Evaluating Functions
  79. Graphing a Basic Function
  80. Graphing a Quadratic Function
  81. Graphing Radical Functions
  82. Domain and Range of a Function Given a Formula
  83. Domain of a Radical Function
  84. Sum of Functions
  85. Difference of Functions
  86. Product of Functions
  87. Quotient of Functions
  88. Graphing Exponential Functions
  89. Exponential Application
  90. Logarithmic Equations
  91. Logarithmic Equations 2
  92. Graphing Logarithmic Functions
  93. Solving Logarithmic Equations
  94. Sum of Logarithms with Same Base
  95. Difference of Logarithms with Same Base
  96. Logarithm of a Power
  97. Using Multiple Logarithm Properties to Simplify
  98. Natural Logarithm with a Calculator
  99. Graphing Natural Logarithm Function
  100. u18_l3_t1_we4 Calculator for Powers of e
  101. Calculator for Powers of 10
  102. Calculator for Natural Logarithms
  103. Calculator for Logarithms
  104. Solving Exponential Equations
  105. Solving Logarithmic Equations
  106. Applying Logarithms
  107. Applying Logarithms 2

Differential Equations

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus playlist before starting here.

  1. What is a differential equation
  2. Separable Differential Equations
  3. Separable differential equations 2
  4. Exact Equations Intuition 1 (proofy)
  5. Exact Equations Intuition 2 (proofy)
  6. Exact Equations Example 1
  7. Exact Equations Example 2
  8. Exact Equations Example 3
  9. Integrating factors 1
  10. Integrating factors 2
  11. First order homegenous equations
  12. First order homogenous equations 2
  13. 2nd Order Linear Homogeneous Differential Equations 1
  14. 2nd Order Linear Homogeneous Differential Equations 2
  15. 2nd Order Linear Homogeneous Differential Equations 3
  16. 2nd Order Linear Homogeneous Differential Equations 4
  17. Complex roots of the characteristic equations 1
  18. Complex roots of the characteristic equations 2
  19. Complex roots of the characteristic equations 3
  20. Repeated roots of the characteristic equation
  21. Repeated roots of the characterisitic equations part 2
  22. Undetermined Coefficients 1
  23. Undetermined Coefficients 2
  24. Undetermined Coefficients 3
  25. Undetermined Coefficients 4
  26. Laplace Transform 1
  27. Laplace Transform 2
  28. Laplace Transform 3 (L{sin(at)})
  29. Laplace Transform 4
  30. Laplace Transform 5
  31. Laplace Transform 6
  32. Laplace Transform to solve an equation
  33. Laplace Transform solves an equation 2
  34. More Laplace Transform tools
  35. Using the Laplace Transform to solve a nonhomogenous eq
  36. Laplace Transform of : L{t}
  37. Laplace Transform of t^n: L{t^n}
  38. Laplace Transform of the Unit Step Function
  39. Inverse Laplace Examples
  40. Laplace/Step Function Differential Equation
  41. Dirac Delta Function
  42. Laplace Transform of the Dirac Delta Function
  43. Introduction to the Convolution
  44. The Convolution and the Laplace Transform
  45. Using the Convolution Theorem to Solve an Initial Value Prob

Finance

Videos on finance and macroeconomics

  1. Introduction to interest
  2. Interest (part 2)
  3. Introduction to Present Value
  4. Present Value 2
  5. Present Value 3
  6. Present Value 4 (and discounted cash flow)
  7. Introduction to Balance Sheets
  8. More on balance sheets and equity
  9. Home equity loans
  10. Renting vs. Buying a home
  11. Renting vs. buying a home (part 2)
  12. Renting vs. Buying (detailed analysis)
  13. The housing price conundrum
  14. Housing price conundrum (part 2)
  15. Housing Price Conundrum (part 3)
  16. Housing Conundrum (part 4)
  17. What it means to buy a company’s stock
  18. Bonds vs. Stocks
  19. Shorting Stock
  20. Shorting Stock 2
  21. Is short selling bad?
  22. Chapter 7:Bankruptcy Liquidation
  23. Chapter 11: Bankruptcy Restructuring
  24. Return on capital
  25. Credit Default Swaps (CDS) Intro
  26. Mortgage Back Security Overview
  27. Collateralized Debt Obligation Overview
  28. Mortgage-Backed Securities I
  29. Mortgage-backed securities II
  30. Mortgage-backed securities III
  31. Collateralized Debt Obligation (CDO)
  32. Introduction to the yield curve
  33. Introduction to compound interest and e
  34. Compound Interest and e (part 2)
  35. Compound Interest and e (part 3)
  36. Compound Interest and e (part 4)
  37. Bailout 1: Liquidity vs. Solvency
  38. Bailout 2: Book Value
  39. Bailout 3: Book value vs. market value
  40. Bailout 4: Mark-to-model vs. mark-to-market
  41. Bailout 5: Paying off the debt
  42. Bailout 6: Getting an equity infusion
  43. Bailout 7: Bank goes into bankruptcy
  44. Bailout 8: Systemic Risk
  45. Bailout 9: Paulson’s Plan
  46. Bailout 10: Moral Hazard
  47. Credit Default Swaps
  48. Credit Default Swaps 2
  49. Investment vs. Consumption 1
  50. Investment vs. Comsumption 2
  51. Bailout 11: Why these CDOs could be worth nothing
  52. Bailout 12: Lone Star Transaction
  53. Bailout 13: Does the bailout have a chance of working?
  54. Wealth Destruction 1
  55. Wealth Destruction 2
  56. Bailout 14: Possible Solution
  57. Bailout 15: More on the solution
  58. Banking 1
  59. Banking 2: A bank’s income statement
  60. Banking 3: Fractional Reserve Banking
  61. Banking 4: Multiplier effect and the money supply
  62. Personal Bankruptcy: Chapters 7 and 13
  63. Introduction to Compound Interest
  64. The Rule of 72 for Compound Interest
  65. Annual Percentage Rate (APR) and Effective APR
  66. Introduction to Bonds
  67. Relationship between bond prices and interest rates
  68. Introduction to Mortgage Loans
  69. Traditional IRAs
  70. Roth IRAs
  71. 401(k)s
  72. Payday Loans
  73. Institutional Roles in Issuing and Processing Credit Cards
  74. Ponzi Schemes
  75. Currency Exchange Introduction
  76. Currency Effect on Trade
  77. Currency Effect on Trade Review
  78. Pegging the Yuan
  79. Chinese Central Bank Buying Treasuries
  80. American-Chinese Debt Loop
  81. Debt Loops Rationale and Effects
  82. American Call Options
  83. Basic Shorting
  84. American Put Options
  85. Call Option as Leverage
  86. Put vs. Short and Leverage
  87. Call Payoff Diagram
  88. Put Payoff Diagram
  89. Long Straddle
  90. Put as Insurance
  91. Put-Call Parity
  92. Put Writer Payoff Diagrams
  93. Call Writer Payoff Diagram
  94. Arbitrage Basics
  95. Put-Call Parity Arbitrage I
  96. Put-Call Parity Arbitrage II
  97. Put-Call Parity Clarification
  98. Actual Option Quotes
  99. Option Expiration and Price
  100. Forward Contract Introduction
  101. Futures Introduction
  102. Motivation for the Futures Exchange
  103. Futures Margin Mechanics
  104. Verifying Hedge with Futures Margin Mechanics
  105. Futures and Forward Curves
  106. Contango from Trader Perspective
  107. Severe Contango Generally Bearish
  108. Backwardation Bullish or Bearish
  109. Futures Curves II
  110. Contango
  111. Backwardation
  112. Contango and Backwardation Review
  113. Upper Bound on Forward Settlement Price
  114. Lower Bound on Forward Settlement Price
  115. Arbitraging Futures Contract
  116. Arbitraging Futures Contracts II
  117. Cash Accounting
  118. Accrual Basis of Accounting
  119. Comparing Accrual and Cash Accounting
  120. Balance Sheet and Income Statement Relationship
  121. Basic Cash Flow Statement
  122. Doing the example with Accounts Payable growing
  123. Expensing a Truck leads to inconsistent performance
  124. Depreciating the truck
  125. Depreciation in Cash Flow
  126. Amortization and Depreciation
  127. Basic Capital Structure Differences
  128. Market Capitalization
  129. Market Value of Assets
  130. LIBOR
  131. Fair Value Accounting
  132. Tax Deductions Introduction
  133. Alternative Minimum Tax
  134. Term Life Insurance and Death Probability
  135. Back of Envelope Office Space Conundrum
  136. Corporations and Limited Liability
  137. Is Limited Liability or Double Taxation Fair
  138. Open-Ended Mutual Fund (Part 1)
  139. Open-End Mutual Fund Redemptions
  140. Closed-End Mutual Funds
  141. Exchange Traded Funds (ETFs)
  142. Hedge Funds Intro
  143. Hedge Fund Structure and Fees
  144. Are Hedge Funds Bad?
  145. Hedge Funds, Venture Capital, and Private Equity
  146. Treasury Bond Prices and Yields
  147. Annual Interest Varying with Debt Maturity
  148. The Yield Curve
  149. Fed Open Market Operations
  150. Quantitative Easing
  151. More on Quantitative Easing (and Credit Easing)
  152. Hedge Fund Strategies – Long Short 1
  153. Hedge Fund Strategies – Long Short 2
  154. Hedge Fund Strategies – Merger Arbitrage 1
  155. Stock Dilution
  156. Acquisitions with Shares
  157. Price Behavior After Announced Acquisition
  158. Simple Merger Arb with Share Acquisition
  159. Basic Leveraged Buyout (LBO)
  160. Corporate Debt versus Traditional Mortgages
  161. AMT Overview
  162. Open market operations and Quantitative Easing Overview
  163. Another Quantitative Easing Video
  164. US and Japanese Quantitative Easing
  165. Term and Whole Life Insurance Policies 2
  166. Term and Whole Life Insurance Policies
  167. Estate Tax Introduction
  168. Human Capital
  169. Risk and Reward Introduction
  170. Futures Fair Value in the Pre-Market
  171. What is Inflation
  172. Inflation Data
  173. Moderate Inflation in a Good Economy
  174. Stagflation
  175. Real and Nominal Return
  176. Calculating Real Return in Last Year Dollars
  177. Relation Between Nominal and Real Returns and Inflation
  178. Use Cases for Credit Default Swaps
  179. Financial Weapons of Mass Destruction
  180. Deflation
  181. Velocity of Money Rather than Quantity Driving Prices
  182. Deflation Despite Increases in Money Supply
  183. Deflationary Spiral
  184. Hyperinflation
  185. Estate Tax Basics
  186. Term and Whole Life
  187. Open-Ended Mutual Funds
  188. Unemployment Rate Primer (v2)
  189. Time Value of Money
  190. Mortgage Interest Rates
  191. Inflation Overview
  192. Basics of US Income Tax Rate Schedule
  193. Carry Trade Basics
  194. Interpretting Futures Fair Value in the PreMarket
  195. Interest Rate Swap 1
  196. Interest Rate Swap 2

Geithner Plan

Geometry

Videos on geometry. Basic understanding of Algebra I necessary. After this, you’ll be ready for Trigonometry.

  1. Basic Language and Notation of Geometry
  2. Lines, Line Segments, and Rays
  3. Language and Notation of the Circle
  4. Angle Basics
  5. Measuring Angles in Degrees
  6. Using a Protractor
  7. Measuring Angles
  8. Complementary and Supplementary Angles
  9. Angles at the intersection of two lines
  10. Proof-Vertical Angles are Equal
  11. Angles Formed by Parallel Lines and Transversals
  12. Proof – Sum of Measures of Angles in a Triangle are 180
  13. Triangle Angle Example 1
  14. Triangle Angle Example 2
  15. Triangle Angle Example 3
  16. Challenging Triangle Angle Problem
  17. Proof – Corresponding Angle Equivalence Implies Parallel Lines
  18. Finding more angles
  19. Sum of Interior Angles of a Polygon
  20. Congruent Triangles and SSS
  21. SSS to Show a Radius is Perpendicular to a Chord that it Bisects
  22. Other Triangle Congruence Postulates
  23. Two column proof showing segments are perpendicular
  24. Sum of the exterior angles of convex polygon
  25. Finding Congruent Triangles
  26. More on why SSA is not a postulate
  27. Congruent Triangle Proof Example
  28. Congruent Triangle Example 2
  29. Congruent legs and base angles of Isosceles Triangles
  30. Equilateral Triangle Sides and Angles Congruent
  31. Equilateral and Isosceles Example Problems
  32. Another Isosceles Example Problem
  33. Example involving an isosceles triangle and parallel lines
  34. Figuring out all the angles for congruent triangles example
  35. Perimeter and Area Basics
  36. Triangle Area Proofs
  37. Interesting Perimeter and Area Problems
  38. Koch Snowflake Fractal
  39. Area of an Equilateral Triangle
  40. Area of Koch Snowflake (part 1) – Advanced
  41. Area of Koch Snowflake (part 2) – Advanced
  42. Challenging Perimeter Problem
  43. Similar Triangle Basics
  44. Similarity Postulates
  45. Similar Triangle Example Problems
  46. Similarity Example Problems
  47. Challenging Similarity Problem
  48. Similarity example where same side plays different roles
  49. Finding Area Using Similarity and Congruence
  50. Pythagorean Theorem Proof Using Similarity
  51. 30-60-90 Triangle Side Ratios Proof
  52. 45-45-90 Triangle Side Ratios
  53. 30-60-90 Triangle Example Problem
  54. The Golden Ratio
  55. Introduction to angles (old)
  56. Angles (part 2)
  57. Angles (part 3)
  58. Angles formed between transversals and parallel lines
  59. Angles of parallel lines 2
  60. The Angle Game
  61. Similar triangles
  62. Similar triangles (part 2)
  63. Angle Game (part 2)
  64. Acute Right and Obtuse Angles
  65. Area and Perimeter
  66. Circles: Radius, Diameter and Circumference
  67. Area of a circle
  68. The Pythagorean Theorem
  69. Pythagorean Theorem II
  70. 45-45-90 Triangles
  71. Intro to 30-60-90 Triangles
  72. 30-60-90 Triangles II
  73. Solid Geometry Volume
  74. Cylinder Volume and Surface Area
  75. Heron’s Formula
  76. Part 1 of Proof of Heron’s Formula
  77. Part 2 of the Proof of Heron’s Formula
  78. Inscribed and Central Angles
  79. Area of Inscribed Equilateral Triangle (some basic trig used)
  80. Right Triangles Inscribed in Circles (Proof)
  81. Area of Diagonal Generated Triangles of Rectangle are Equal
  82. Triangle Medians and Centroids
  83. Triangle Medians and Centroids (2D Proof)
  84. Rhombus Diagonals
  85. 2003 AIME II Problem 7
  86. Perpendicular Radius Bisects Chord
  87. Circumcenter of a Triangle
  88. Circumcenter of a Right Triangle
  89. Three Points Defining a Circle
  90. Point Line Distance and Angle Bisectors
  91. Incenter and incircles of a triangle
  92. Angle Bisector Theorem Proof
  93. Inradius Perimeter and Area
  94. Angle Bisector Theorem Examples
  95. Medians divide into smaller triangles of equal area
  96. Exploring Medial Triangles
  97. Proving that the Centroid is 2-3rds along the Median
  98. Median Centroid Right Triangle Example
  99. Proof – Triangle Altitudes are Concurrent (Orthocenter)
  100. Review of Triangle Properties
  101. Euler Line
  102. Euler’s Line Proof
  103. Common Orthocenter and Centroid
  104. Quadrilateral Overview
  105. Proof – Opposite Sides of Parallelogram Congruent
  106. Proof – Diagonals of a Parallelogram Bisect Each Other
  107. Proof – Opposite Angles of Parallelogram Congruent
  108. Proof – Rhombus Diagonals are Perpendicular Bisectors
  109. Proof – Rhombus Area Half Product of Diagonal Length
  110. Area of a Parallelogram
  111. Problem involving angle derived from square and circle
  112. Area of a Regular Hexagon

Khan Academy-Related Talks and Interviews

Collection of interviews with and presentations by Salman Khan. Also a few other mentions of Khan Academy at other talks.

  1. PBS NewsHour on the Khan Academy
  2. Salman Khan on CNN
  3. Salman Khan Speaks at GEL (Good Experience Live) Conference
  4. Salman Khan Talk at the MIT Club of Northern California
  5. Salman Khan talk at Castilleja School on January 5th, 2010
  6. Sal Khan Interview with IT Conversations – January 31,2010
  7. Salman Khan interview with NPR’s All Things Considered on 12/28/2009
  8. Khan Academy on PBS NewsHour (Edited)
  9. Sal Khan (with a severe cold!) on Future Talk
  10. Brian Lehrer Interview with Salman Khan
  11. Salman Khan Interview with Mixergy.com
  12. Bill Gates talks about the Khan Academy at Aspen Ideas Festival 2010
  13. Khan Academy Vision and Social Return
  14. Bay Area CBS Station with Salman Khan
  15. CNN: Google award to Khan Academy
  16. Fareed Zakaria talks about Khan Academy on CNN GPS
  17. Khan Academy on the Gates Notes
  18. Sal on ABC News
  19. Forbes Names You Need To Know: Khan Academy
  20. Salman Khan on KQED MindShift
  21. Khan Academy Exercise Software
  22. Salman Khan talk at TED 2011 (from ted.com)
  23. Khan Academy on Nightly News
  24. Sal on Dylan Ratigan show
  25. Authors@Google: Salman Khan
  26. LinkedIn Speaker Series Salman Khan
  27. TEDxSanJoseCA – Salman Khan – (Sequel to talk at TED)
  28. Salman Khan on Charlie Rose
  29. Salman Khan on Big Think
  30. Salman Khan on Marketplace (NPR) on 5-24-2011
  31. May 29th, 2011 CNN Piece
  32. Salman Khan at TiEcon 2011
  33. Khan Academy on Perry’s Principles (6/2/2011)
  34. Khan Academy on California Report (June 2011)
  35. Ideal Math and Science Class Time
  36. NPR Story on KA Los Altos Pilots (June 2011)
  37. Salman Khan interviewed on NPR’s On Point
  38. 21st Century Challenges (Royal Geographic Society)
  39. Answers for Malibu Magazine
  40. NCSU Answers
  41. Questions from Superinteressante (8-22-2011)
  42. Answers to Questions from the Independent
  43. The Gates Notes: Sal on Khan Academy
  44. The Gates Notes: Students in Los Altos
  45. The Gates Notes: Teachers in Los Altos
  46. The Gates Notes: Administrators in Los Altos
  47. The Gates Notes: Insights into students’ progress
  48. Early Show
  49. Brainwave Sep 2011
  50. School Leadership Briefing Questions (Sep 12 2011) 2
  51. School Leadership Briefing (Sep 12 2011)
  52. Center for Future of Museums
  53. Sal during Education Week (Sep 2011) 1
  54. Khan Academy on 20 20 (Sep 2011)
  55. KA on John Stossel Documentary
  56. Tom Brokaw interviews Sal at Education Nation 2011
  57. Financial Times October 2011
  58. 2011 Roundtable at Stanford: Education Nation 2.0
  59. Year 2060: Education Predictions
  60. Verbal Answers to “Ask Me Anything” on Reddit

Linear Algebra

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn’t a prereq) so don’t confuse this with regular high school algebra.

  1. Introduction to matrices
  2. Matrix multiplication (part 1)
  3. Matrix multiplication (part 2)
  4. Inverse Matrix (part 1)
  5. Inverting matrices (part 2)
  6. Inverting Matrices (part 3)
  7. Matrices to solve a system of equations
  8. Matrices to solve a vector combination problem
  9. Singular Matrices
  10. 3-variable linear equations (part 1)
  11. Solving 3 Equations with 3 Unknowns
  12. Linear Algebra: Introduction to Vectors
  13. Linear Algebra: Vector Examples
  14. Linear Algebra: Parametric Representations of Lines
  15. Linear Combinations and Span
  16. Linear Algebra: Introduction to Linear Independence
  17. More on linear independence
  18. Span and Linear Independence Example
  19. Linear Subspaces
  20. Linear Algebra: Basis of a Subspace
  21. Vector Dot Product and Vector Length
  22. Proving Vector Dot Product Properties
  23. Proof of the Cauchy-Schwarz Inequality
  24. Linear Algebra: Vector Triangle Inequality
  25. Defining the angle between vectors
  26. Defining a plane in R3 with a point and normal vector
  27. Linear Algebra: Cross Product Introduction
  28. Proof: Relationship between cross product and sin of angle
  29. Dot and Cross Product Comparison/Intuition
  30. Matrices: Reduced Row Echelon Form 1
  31. Matrices: Reduced Row Echelon Form 2
  32. Matrices: Reduced Row Echelon Form 3
  33. Matrix Vector Products
  34. Introduction to the Null Space of a Matrix
  35. Null Space 2: Calculating the null space of a matrix
  36. Null Space 3: Relation to Linear Independence
  37. Column Space of a Matrix
  38. Null Space and Column Space Basis
  39. Visualizing a Column Space as a Plane in R3
  40. Proof: Any subspace basis has same number of elements
  41. Dimension of the Null Space or Nullity
  42. Dimension of the Column Space or Rank
  43. Showing relation between basis cols and pivot cols
  44. Showing that the candidate basis does span C(A)
  45. A more formal understanding of functions
  46. Vector Transformations
  47. Linear Transformations
  48. Matrix Vector Products as Linear Transformations
  49. Linear Transformations as Matrix Vector Products
  50. Image of a subset under a transformation
  51. im(T): Image of a Transformation
  52. Preimage of a set
  53. Preimage and Kernel Example
  54. Sums and Scalar Multiples of Linear Transformations
  55. More on Matrix Addition and Scalar Multiplication
  56. Linear Transformation Examples: Scaling and Reflections
  57. Linear Transformation Examples: Rotations in R2
  58. Rotation in R3 around the X-axis
  59. Unit Vectors
  60. Introduction to Projections
  61. Expressing a Projection on to a line as a Matrix Vector prod
  62. Compositions of Linear Transformations 1
  63. Compositions of Linear Transformations 2
  64. Linear Algebra: Matrix Product Examples
  65. Matrix Product Associativity
  66. Distributive Property of Matrix Products
  67. Linear Algebra: Introduction to the inverse of a function
  68. Proof: Invertibility implies a unique solution to f(x)=y
  69. Surjective (onto) and Injective (one-to-one) functions
  70. Relating invertibility to being onto and one-to-one
  71. Determining whether a transformation is onto
  72. Linear Algebra: Exploring the solution set of Ax=b
  73. Linear Algebra: Matrix condition for one-to-one trans
  74. Linear Algebra: Simplifying conditions for invertibility
  75. Linear Algebra: Showing that Inverses are Linear
  76. Linear Algebra: Deriving a method for determining inverses
  77. Linear Algebra: Example of Finding Matrix Inverse
  78. Linear Algebra: Formula for 2×2 inverse
  79. Linear Algebra: 3×3 Determinant
  80. Linear Algebra: nxn Determinant
  81. Linear Algebra: Determinants along other rows/cols
  82. Linear Algebra: Rule of Sarrus of Determinants
  83. Linear Algebra: Determinant when row multiplied by scalar
  84. Linear Algebra: (correction) scalar muliplication of row
  85. Linear Algebra: Determinant when row is added
  86. Linear Algebra: Duplicate Row Determinant
  87. Linear Algebra: Determinant after row operations
  88. Linear Algebra: Upper Triangular Determinant
  89. Linear Algebra: Simpler 4×4 determinant
  90. Linear Algebra: Determinant and area of a parallelogram
  91. Linear Algebra: Determinant as Scaling Factor
  92. Linear Algebra: Transpose of a Matrix
  93. Linear Algebra: Determinant of Transpose
  94. Linear Algebra: Transpose of a Matrix Product
  95. Linear Algebra: Transposes of sums and inverses
  96. Linear Algebra: Transpose of a Vector
  97. Linear Algebra: Rowspace and Left Nullspace
  98. Lin Alg: Visualizations of Left Nullspace and Rowspace
  99. Linear Algebra: Orthogonal Complements
  100. Linear Algebra: Rank(A) = Rank(transpose of A)
  101. Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n
  102. Lin Alg: Representing vectors in Rn using subspace members
  103. Lin Alg: Orthogonal Complement of the Orthogonal Complement
  104. Lin Alg: Orthogonal Complement of the Nullspace
  105. Lin Alg: Unique rowspace solution to Ax=b
  106. Linear Alg: Rowspace Solution to Ax=b example
  107. Lin Alg: Showing that A-transpose x A is invertible
  108. Linear Algebra: Projections onto Subspaces
  109. Linear Alg: Visualizing a projection onto a plane
  110. Lin Alg: A Projection onto a Subspace is a Linear Transforma
  111. Linear Algebra: Subspace Projection Matrix Example
  112. Lin Alg: Another Example of a Projection Matrix
  113. Linear Alg: Projection is closest vector in subspace
  114. Linear Algebra: Least Squares Approximation
  115. Linear Algebra: Least Squares Examples
  116. Linear Algebra: Another Least Squares Example
  117. Linear Algebra: Coordinates with Respect to a Basis
  118. Linear Algebra: Change of Basis Matrix
  119. Lin Alg: Invertible Change of Basis Matrix
  120. Lin Alg: Transformation Matrix with Respect to a Basis
  121. Lin Alg: Alternate Basis Tranformation Matrix Example
  122. Lin Alg: Alternate Basis Tranformation Matrix Example Part 2
  123. Lin Alg: Changing coordinate systems to help find a transformation matrix
  124. Linear Algebra: Introduction to Orthonormal Bases
  125. Linear Algebra: Coordinates with respect to orthonormal bases
  126. Lin Alg: Projections onto subspaces with orthonormal bases
  127. Lin Alg: Finding projection onto subspace with orthonormal basis example
  128. Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix
  129. Lin Alg: Orthogonal matrices preserve angles and lengths
  130. Linear Algebra: The Gram-Schmidt Process
  131. Linear Algebra: Gram-Schmidt Process Example
  132. Linear Algebra: Gram-Schmidt example with 3 basis vectors
  133. Linear Algebra: Introduction to Eigenvalues and Eigenvectors
  134. Linear Algebra: Proof of formula for determining Eigenvalues
  135. Linear Algebra: Example solving for the eigenvalues of a 2×2 matrix
  136. Linear Algebra: Finding Eigenvectors and Eigenspaces example
  137. Linear Algebra: Eigenvalues of a 3×3 matrix
  138. Linear Algebra: Eigenvectors and Eigenspaces for a 3×3 matrix
  139. Linear Algebra: Showing that an eigenbasis makes for good coordinate systems
  140. Vector Triple Product Expansion (very optional)
  141. Normal vector from plane equation
  142. Point distance to plane
  143. Distance Between Planes

MA Tests for Education Licensure (MTEL) -Pre-Alg

Microeconomics

Topics covered in an traditional college level introductory microeconomics course

  1. Production Possibilities Frontier
  2. Opportunity Cost
  3. Increasing Opportunity Cost
  4. Allocative Efficiency and Marginal Benefit
  5. Economic Growth through Investment
  6. Comparative Advantage Specialization and Gains from Trade
  7. Comparative Advantage and Absolute Advantage
  8. Law of Demand
  9. Price of Related Products and Demand
  10. Changes in Income, Population, or Preferences
  11. Normal and Inferior Goods
  12. Inferior Goods Clarification
  13. Law of Supply
  14. Factors Affecting Supply
  15. Market Equilibrium
  16. Changes in Market Equilibrium
  17. Price Elasticity of Demand
  18. More on Elasticity of Demand
  19. Perfect Inelasticity and Perfect Elasticity of Demand
  20. Constant Unit Elasticity
  21. Total Revenue and Elasticity
  22. More on Total Revenue and Elasticity
  23. Cross Elasticity of Demand
  24. Elasticity of Supply
  25. Elasticity and Strange Percent Changes
  26. Demand Curve as Marginal Benefit Curve
  27. Consumer Surplus Introduction
  28. Total Consumer Surplus as Area
  29. Producer Surplus
  30. Rent Control and Deadweight Loss
  31. Minimum Wage and Price Floors
  32. Taxation and Dead Weight Loss
  33. Percentage Tax on Hamburgers
  34. Taxes and Perfectly Inelastic Demand
  35. Taxes and Perfectly Elastic Demand
  36. Marginal Utility
  37. Equalizing Marginal Utility per Dollar Spent
  38. Deriving Demand Curve from Tweaking Marginal Utility per Dollar
  39. Budget Line
  40. Optimal Point on Budget Line
  41. Types of Indifference Curves
  42. Economic Profit vs Accounting Profit
  43. Depreciation and Opportunity Cost of Capital
  44. Fixed, Variable, and Marginal Cost.
  45. Visualizing Average Costs and Marginal Costs as Slope
  46. Marginal Cost and Average Total Cost
  47. Marginal Revenue and Marginal Cost
  48. Marginal Revenue Below Average Total Cost
  49. Long Term Supply Curve and Economic Profit
  50. Perfect Competition
  51. Monopoly Basics
  52. Monopolist Optimizing Price (part 1)- Total Revenue.
  53. Monopolist Optimizing Price (part 2)- Marginal Revenue
  54. Monopolist Optimizing Price (part 3)- Dead Weight Loss.avi
  55. Optional Calculus Proof to Show that MR has Twice Slope of Demand
  56. Review of Revenue and Cost Graphs for a Monopoly
  57. Oligopolies and Monopolisitc Competition

New and Noteworthy

  1. SOPA and PIPA
  2. Thank You Khan Academy!
  3. Vitamin C and the Limeys
  4. Salman Khan talk at TED 2011 (from ted.com)
  5. Visualizing Taylor Series Approximations
  6. Correlation and Causality
  7. The Golden Ratio
  8. Carry Trade Basics
  9. Heart Disease and Heart Attacks
  10. Koch Snowflake Fractal
  11. Galactic Collisions
  12. Systemic Thinking About Cancer
  13. Elements and Atoms
  14. Scale of the Small
  15. How Earth’s Tilt Causes Seasons
  16. Gravity for Astronauts in Orbit
  17. Primaries and Caucuses
  18. Deficit and Debt Ceiling
  19. Social Security Intro
  20. FICA Tax
  21. Carbon 14 Dating 1
  22. Scale of Earth and Sun
  23. Introduction to Light
  24. US and Japanese Quantitative Easing
  25. Newton’s First Law of Motion
  26. Clearing the Green Monster at Fenway
  27. Addition Rule for Probability
  28. Basic Trigonometry
  29. Khan Academy Exercise Software
  30. Richter Scale
  31. Logarithmic Scale
  32. Firestick Farming
  33. Proof by Induction
  34. Human Evolution Overview
  35. Hubble’s Law
  36. The Kidney and Nephron
  37. Electoral College
  38. French Invasion of Russia
  39. Black Holes
  40. Glucose Insulin and Diabetes
  41. Diffusion and Osmosis
  42. Why Gravity Gets So Strong Near Dense Objects
  43. Earth Formation
  44. Appomattox Court House and Lincoln’s Assassination
  45. Plate Tectonics — Evidence of plate movement
  46. Hawaiian Islands Formation
  47. Ponzi Schemes
  48. Vi and Sal Explore How We Think About Scale
  49. Pangaea
  50. Introduction to Programs Data Types and Variables
  51. Stock Dilution
  52. Fair Value Accounting
  53. American Call Options
  54. Calculus: Derivatives 1 (new HD version)
  55. Challenging Perimeter Problem
  56. The Gates Notes: Teachers in Los Altos
  57. Vi and Sal Talk About the Mysteries of Benford’s Law
  58. Probability with Playing Cards and Venn Diagrams
  59. Are Southern Hemisphere Seasons More Severe?
  60. Introduction to i and Imaginary Numbers
  61. Tau versus Pi
  62. Ideal Math and Science Class Time
  63. Development of Agriculture and Writing
  64. Economic Profit vs Accounting Profit
  65. Inferior Goods Clarification
  66. Thomas Malthus and Population Growth

Organic Chemistry

Topics covered in college organic chemistry course. Basic understanding of basic high school or college chemistry assumed

  1. Representing Structures of Organic Molecules
  2. Naming Simple Alkanes
  3. Naming Alkanes with Alkyl Groups
  4. Correction – 2-Propylheptane should never be the name!
  5. Common and Systematic Naming-Iso, Sec and Tert Prefixes
  6. More Organic Chemistry Naming Examples 1
  7. Organic Chemistry Naming Examples 2
  8. Organic Chemistry Naming Examples 3
  9. Organic Chemistry Naming Examples 4
  10. Organic Chemistry Naming Examples 5
  11. Naming Alkenes Examples
  12. Naming Alkyl Halides
  13. sp3 Hybridized Orbitals and Sigma Bonds
  14. Pi bonds and sp2 Hybridized Orbitals
  15. Newman Projections
  16. Newman Projections 2
  17. Chair and Boat Shapes for Cyclohexane
  18. Double Newman Diagram for Methcyclohexane
  19. Introduction to Chirality
  20. Chiral Examples 1
  21. Chiral Examples 2
  22. Cahn-Ingold-Prelog System for Naming Enantiomers
  23. R,S (Cahn-Ingold-Prelog) Naming System Example 2
  24. Stereoisomers, Enantiomers, Diastereomers, Constitutional Isomers and Meso Compounds
  25. Cis-Trans and E-Z Naming Scheme for Alkenes
  26. Entgegen-Zusammen Naming Scheme for Alkenes Examples
  27. Introduction to Reaction Mechanisms
  28. Markovnikov’s Rule and Carbocations
  29. Addition of Water (Acid-Catalyzed) Mechanism
  30. Polymerization of Alkenes with Acid
  31. Sn2 Reactions
  32. Sn1 Reactions
  33. Steric Hindrance
  34. Sn2 Stereochemistry
  35. Solvent Effects on Sn1 and Sn2 Reactions
  36. Nucleophilicity (Nucleophile Strength)
  37. Nucleophilicity vs. Basicity
  38. E2 Reactions
  39. E1 Reactions
  40. Zaitsev’s Rule
  41. Comparing E2 E1 Sn2 Sn1 Reactions
  42. E2 E1 Sn2 Sn1 Reactions Example 2
  43. E2 E1 Sn2 Sn1 Reactions Example 3
  44. Free Radical Reactions
  45. Alcohols
  46. Alcohol Properties
  47. Resonance
  48. Ether Naming and Introduction
  49. Cyclic ethers and epoxide naming
  50. Ring-opening Sn2 reaction of expoxides
  51. Sn1 and Sn2 epoxide opening discussion
  52. Aromatic Compounds and Huckel’s Rule
  53. Naming Benzene Derivatives Introduction
  54. Electrophilic Aromatic Substitution
  55. Bromination of Benzene
  56. Amine Naming Introduction
  57. Amine Naming 2
  58. Amine as Nucleophile in Sn2 Reaction
  59. Amine in Sn2 part 2
  60. Sn1 Amine Reaction
  61. Aldehyde Introduction
  62. Ketone Naming
  63. Friedel Crafts Acylation
  64. Friedel Crafts Acylation Addendum
  65. Keto Enol Tautomerization
  66. Carboxlic Acid Introduction
  67. Carboxylic Acid Naming
  68. Fisher Esterification
  69. Acid Chloride Formation
  70. Amides, Anhydrides, Esters and Acyl Chlorides
  71. Relative Stability of Amides Esters Anhydrides and Acyl Chlorides
  72. Amide Formation from Acyl Chloride
  73. Aldol Reaction

Physics

Projectile motion, mechanics and electricity and magnetism. Solid understanding of algebra and a basic understanding of trigonometry necessary.

  1. Introduction to Vectors and Scalars
  2. Calculating Average Velocity or Speed
  3. Solving for Time
  4. Displacement from Time and Velocity Example
  5. Acceleration
  6. Newton’s First Law of Motion
  7. Newton’s Second Law of Motion
  8. Newton’s Third Law of Motion
  9. Airbus A380 Take-off Time
  10. Airbus A380 Take-off Distance
  11. Why Distance is Area under Velocity-Time Line
  12. Average Velocity for Constant Acceleration
  13. Acceleration of Aircraft Carrier Takeoff
  14. Race Cars with Constant Speed Around Curve
  15. Introduction to Gravity
  16. Mass and Weight Clarification
  17. Gravity for Astronauts in Orbit
  18. Would a Brick or Feather Fall Faster
  19. Deriving Displacement as a Function of Time, Acceleration and Initial Velocity
  20. Plotting Projectile Displacement, Acceleration, and Velocity
  21. Projectile Height Given Time
  22. Deriving Max Projectile Displacement Given Time
  23. Impact Velocity From Given Height
  24. Visualizing Vectors in 2 Dimensions
  25. Projectile at an Angle
  26. Different Way to Determine Time in Air
  27. Launching and Landing on Different Elevations
  28. Total Displacement for Projectile
  29. Total Final Velocity for Projectile
  30. Correction to Total Final Velocity for Projectile
  31. Projectile on an Incline
  32. Unit Vectors and Engineering Notation
  33. Clearing the Green Monster at Fenway
  34. Green Monster at Fenway Part 2
  35. Optimal angle for a projectile part 1
  36. Optimal angle for a projectile part 2 – Hangtime
  37. Optimal angle for a projectile part 3 – Horizontal distance as a function of angle (and speed)
  38. Optimal angle for a projectile part 4 Finding the optimal angle and distance with a bit of calculus
  39. Normal Force and Contact Force
  40. Normal Force in an Elevator
  41. Inclined Plane Force Components
  42. Ice Accelerating Down an Incline
  43. Force of Friction Keeping the Block Stationary
  44. Correction to Force of Friction Keeping the Block Stationary
  45. Force of Friction Keeping Velocity Constant
  46. Intuition on Static and Kinetic Friction Comparisons
  47. Static and Kinetic Friction Example
  48. Introduction to Tension
  49. Tension (part 2)
  50. Tension in an accelerating system and pie in the face
  51. Moving pulley problem (part 1)
  52. Moving pulley problem (part 2)
  53. Introduction to Momentum
  54. Momentum: Ice skater throws a ball
  55. 2-dimensional momentum problem
  56. 2-dimensional momentum problem (part 2)
  57. Introduction to work and energy
  58. Work and Energy (part 2)
  59. Conservation of Energy
  60. Work/Energy problem with Friction
  61. Introduction to mechanical advantage
  62. Mechanical Advantage (part 2)
  63. Mechanical Advantage (part 3)
  64. Center of Mass
  65. Introduction to Torque
  66. Moments
  67. Moments (part 2)
  68. Unit Vector Notation
  69. Unit Vector Notation (part 2)
  70. Projectile Motion with Unit Vectors
  71. Projectile Motion with Unit Vectors (part 2)
  72. Projectile Motion with Ordered Set Notation
  73. Centripetal Force and Acceleration Intuition
  74. Visual Understanding of Centripetal Acceleration Formula
  75. Relationship between angular velocity and speed
  76. Calculus proof of centripetal acceleration formula
  77. Loop De Loop Question
  78. Loop De Loop Answer part 1
  79. Loop De Loop Answer part 2
  80. Acceleration Due to Gravity at the Space Station
  81. Space Station Speed in Orbit
  82. Conservation of angular momemtum
  83. Introduction to Newton’s Law of Gravitation
  84. Gravitation (part 2)
  85. Intro to springs and Hooke’s Law
  86. Potential energy stored in a spring
  87. Spring potential energy example (mistake in math)
  88. Introduction to Harmonic Motion
  89. Harmonic Motion Part 2 (calculus)
  90. Harmonic Motion Part 3 (no calculus)
  91. Fluids (part 1)
  92. Fluids (part 2)
  93. Fluids (part 3)
  94. Fluids (part 4)
  95. Fluids (part 5)
  96. Fluids (part 6)
  97. Fluids (part 7)
  98. Fluids (part 8)
  99. Fluids (part 9)
  100. Fluids (part 10)
  101. Fluids (part 11)
  102. Fluids (part 12)
  103. Thermodynamics (part 1)
  104. Thermodynamics (part 2)
  105. Thermodynamics (part 3)
  106. Thermodynamics (part 4)
  107. Thermodynamics (part 5)
  108. Electrostatics (part 1): Introduction to Charge and Coulomb’s Law
  109. Electrostatics (part 2)
  110. Proof (Advanced): Field from infinite plate (part 1)
  111. Proof (Advanced): Field from infinite plate (part 2)
  112. Electric Potential Energy
  113. Electric Potential Energy (part 2– involves calculus)
  114. Voltage
  115. Capacitance
  116. Circuits (part 1)
  117. Circuits (part 2)
  118. Circuits (part 3)
  119. Circuits (part 4)
  120. Cross product 1
  121. Cross Product 2
  122. Cross Product and Torque
  123. Introduction to Magnetism
  124. Magnetism 2
  125. Magnetism 3
  126. Magnetism 4
  127. Magnetism 5
  128. Magnetism 6: Magnetic field due to current
  129. Magnetism 7
  130. Magnetism 8
  131. Magnetism 9: Electric Motors
  132. Magnetism 10: Electric Motors
  133. Magnetism 11: Electric Motors
  134. Magnetism 12: Induced Current in a Wire
  135. The dot product
  136. Dot vs. Cross Product
  137. Calculating dot and cross products with unit vector notation
  138. Introduction to Waves
  139. Amplitude, Period, Frequency and Wavelength of Periodic Waves
  140. Introduction to the Doppler Effect
  141. Doppler effect formula for observed frequency
  142. Doppler effect formula when source is moving away
  143. When the source and the wave move at the same velocity
  144. Mach Numbers
  145. Specular and Diffuse Reflection
  146. Specular and Diffuse Reflection 2
  147. Refraction and Snell’s Law
  148. Refraction in Water
  149. Snell’s Law Examples 1
  150. Snell’s Law Example 2
  151. Total Internal Reflection
  152. Virtual Image
  153. Parabolic Mirrors and Real Images
  154. Parabolic Mirrors 2
  155. Convex Parabolic Mirrors
  156. Convex Lenses
  157. Convex Lens Examples
  158. Concave Lenses
  159. Object Image and Focal Distance Relationship (Proof of Formula)
  160. Object Image Height and Distance Relationship
  161. Viewing g as the value of Earth’s Gravitational Field Near the Surface

SAT Preparation

I am going to work through every problem in the College Board “Official SAT Study Guide.” You should take the practice tests on your own, grade them and then use these videos to understand the problems you didn’t get or review. Have fun!

  1. SAT prep: test 1 section3 part 1
  2. SAT Prep: Test 1 Section 3 Part 2
  3. SAT Prep: Test 1 Section 3 Part 3
  4. SAT Prep: Test 1 Section 3 Part 4
  5. SAT Prep: Test 1 Section 3 Part 5
  6. SAT Prep: Test 1 Section 3 Part 6
  7. SAT Prep: Test 1 Section 3 Part 7
  8. SAT Prep: Test 1 Section 3 Part 8
  9. SAT Prep: Test 1 Section 6 Part 1
  10. SAT Prep: Test 1 Section 6 Part 2
  11. SAT Prep: Test 1 Section 6 Part 3
  12. SAT Prep: Test 1 Section 6 Part 4
  13. SAT Prep: Test 1 Section 6 Part 5
  14. SAT Prep: Test 1 Section 6 Part 6
  15. SAT Prep: Test 1 Section 9 Part 1
  16. SAT Prep: Test 1 Section 9 Part 2
  17. SAT Prep: Test 1 Section 9 Part 3
  18. SAT Prep: Test 1 Section 9 Part 4
  19. SAT Prep: Test 1 Section 9 Part 5
  20. SAT Prep: Test 2 Section 3 part 1
  21. SAT Prep: Test 2 Section 3 Part 2
  22. SAT Prep: Test 2 Section 3 Part 3
  23. SAT Prep: Test 2 Section 3 Part 4
  24. SAT Prep: Test 2 Section 3 Part 5
  25. SAT Prep: Test 2 Section 3 Part 6
  26. SAT Prep: Test 2 Section 6 Part 1
  27. SAT Prep: Test 2 Section 6 Part 2
  28. SAT Prep: Test 2 Section 6 Part 3
  29. SAT Prep: Test 2 Section 6 Part 4
  30. SAT Prep: Test 2 Section 6 Part 5
  31. SAT Prep: Test 2 Section 6 Part 6
  32. SAT Prep: Test 2 Section 9 Part 1
  33. SAT Prep: Test 2 Section 9 Part 2
  34. SAT Prep: Test 2 Section 9 Part 3
  35. SAT Prep: Test 2 Section 9 Part 4
  36. SAT Prep: Test 3 Section 2 Part 1
  37. SAT Prep: Test 3 Section 2 Part 2
  38. SAT Prep: Test 3 Section 2 Part 3
  39. SAT Prep: Test 3 Section 2 Part 4
  40. Test 3 Section 2 Part 5
  41. SAT Prep: Test 3 Section 4 Part 1
  42. SAT Prep: Test 3 Section 4 Part 2
  43. SAT Prep: Test 3 Section 4 Part 3
  44. SAT Prep: Test 3 Section 4 Part 4
  45. SAT Prep: Test 3 Section 4 Part 5
  46. SAT Prep: Test 3 Section 8 Part 1
  47. SAT Prep: Test 3 Section 8 Part 2
  48. SAT Prep: Test 3 Section 8 Part 3
  49. SAT Prep: Test 3 Section 8 Part 4
  50. SAT Prep: Test 4 Section 2 Part 1
  51. SAT Prep: Test 4 Section 2 Part 2
  52. SAT Prep: Test 4 Section 2 Part 3
  53. SAT Prep: Test 4 Section 2 Part 4
  54. SAT Prep: Test 4 Section 2 Part 5
  55. SAT Prep: Test 4 Section 2 Part 6
  56. SAT Prep: Test 4 Section 4 Part 1
  57. SAT Prep: Test 4 Section 4 Part 2
  58. SAT Prep: Test 4 Section 4 Part 3
  59. SAT Prep: Test 4 Section 4 Part 4
  60. SAT Prep: Test 4 Section 8 Part 1
  61. SAT Prep: Test 4 Section 8 Part 2
  62. SAT Prep: Test 4 Section 8 Part 3
  63. SAT Prep: Test 4 Section 8 Part 4
  64. SAT Prep: Test 5 Section 3 Part 1
  65. SAT Prep: Test 5 Section 3 Part 2
  66. SAT Prep: Test 5 Section 3 Part 3
  67. SAT Prep: Test 5 Section 3 Part 4
  68. SAT Prep: Test 5 Section 3 Part 5
  69. SAT Prep: Test 5 Section 3 Part 6
  70. SAT Prep: Test 5 Section 7 Part 1
  71. SAT Prep: Test 5 Section 7 Part 2
  72. SAT Prep: Test 5 Section 7 Part 3
  73. SAT Prep: Test 5 Section 7 Part 4
  74. SAT Prep: Test 5 Section 7 Part 5
  75. SAT Prep: Test 5 Section 7 Part 6
  76. SAT Prep: Test 5 Section 9 Part 1
  77. SAT Prep: Test 5 Section 9 Part 2
  78. SAT Prep: Test 5 Section 9 Part 3
  79. SAT Prep: Test 5 Section 9 Part 4
  80. SAT Prep: Test 6 Section 3 Part 1
  81. SAT Prep: Test 6 Section 3 Part 2
  82. SAT Prep: Test 6 Section 3 Part 3
  83. SAT Prep: Test 6 Section 3 Part 4
  84. SAT Prep: Test 6 Section 3 Part 5
  85. SAT Prep: Test 6 Section 7 Part 1
  86. SAT Prep: Test 6 Section 7 Part 2
  87. SAT Prep: Test 6 Section 7 Part 3
  88. SAT Prep: Test 6 Section 7 Part 4
  89. SAT Prep: Test 6 Section 7 Part 5
  90. SAT Prep: Test 6 Section 7 Part 6
  91. SAT Prep: Test 6 Section 9 Part 1
  92. SAT Prep: Test 6 Section 9 Part 2
  93. SAT Prep: Test 6 Section 9 Part 3
  94. SAT Prep: Test 6 Section 9 Part 4
  95. SAT Prep: Test 7 Section 2 Part 1
  96. SAT Prep: Test 7 Section 2 Part 2
  97. SAT Prep: Test 7 Section 2 Part 3
  98. SAT Prep: Test 7 Section 2 Part 4
  99. SAT Prep: Test 7 Section 5 Part 1
  100. SAT Prep: Test 7 Section 5 Part 2
  101. SAT Prep: Test 7 Section 5 Part 3
  102. SAT Prep: Test 7 Section 5 Part 4
  103. SAT Prep: Test 7 Section 5 Part 5
  104. SAT Prep: Test 7 Section 8 Part 1
  105. SAT Prep: Test 7 Section 8 Part 2
  106. SAT Prep: Test 7 Section 8 Part 3
  107. SAT Prep: Test 7 Section 8 Part 4
  108. SAT Prep: Test 8 Section 2 Part 1
  109. SAT Prep: Test 8 Section 2 Part 2
  110. SAT Prep: Test 8 Section 2 Part 3
  111. SAT Prep: Test 8 Section 2 Part 4
  112. SAT Prep: Test 8 Section 5 Part 1
  113. SAT Prep: Test 8 Section 5 Part 2
  114. SAT Prep: Test 8 Section 5 Part 3
  115. SAT Prep: Test 8 Section 5 Part 4
  116. SAT Prep: Test 8 Section 8 Part 1
  117. SAT Prep: Test 8 Section 8 Part 2
  118. SAT Prep: Test 8 Section 8 Part 3

Statistics

Introduction to statistics. Will eventually cover all of the major topics in a first-year statistics course (not there yet!)

  1. Statistics: The Average
  2. Statistics: Sample vs. Population Mean
  3. Statistics: Variance of a Population
  4. Statistics: Sample Variance
  5. Statistics: Standard Deviation
  6. Statistics: Alternate Variance Formulas
  7. Introduction to Random Variables
  8. Probability Density Functions
  9. Binomial Distribution 1
  10. Binomial Distribution 2
  11. Binomial Distribution 3
  12. Binomial Distribution 4
  13. Expected Value: E(X)
  14. Expected Value of Binomial Distribution
  15. Poisson Process 1
  16. Poisson Process 2
  17. Law of Large Numbers
  18. Normal Distribution Excel Exercise
  19. Introduction to the Normal Distribution
  20. ck12.org Normal Distribution Problems: Qualitative sense of normal distributions
  21. ck12.org Normal Distribution Problems: z-score
  22. ck12.org Normal Distribution Problems: Empirical Rule
  23. ck12.org Exercise: Standard Normal Distribution and the Empirical Rule
  24. ck12.org: More Empirical Rule and Z-score practice
  25. Central Limit Theorem
  26. Sampling Distribution of the Sample Mean
  27. Sampling Distribution of the Sample Mean 2
  28. Standard Error of the Mean
  29. Sampling Distribution Example Problem
  30. Confidence Interval 1
  31. Mean and Variance of Bernoulli Distribution Example
  32. Bernoulli Distribution Mean and Variance Formulas
  33. Margin of Error 1
  34. Margin of Error 2
  35. Confidence Interval Example
  36. Small Sample Size Confidence Intervals
  37. Hypothesis Testing and P-values
  38. One-Tailed and Two-Tailed Tests
  39. Z-statistics vs. T-statistics
  40. Type 1 Errors
  41. Small Sample Hypothesis Test
  42. T-Statistic Confidence Interval
  43. Large Sample Proportion Hypothesis Testing
  44. Variance of Differences of Random Variables
  45. Difference of Sample Means Distribution
  46. Confidence Interval of Difference of Means
  47. Clarification of Confidence Interval of Difference of Means
  48. Hypothesis Test for Difference of Means
  49. Comparing Population Proportions 1
  50. Comparing Population Proportions 2
  51. Hypothesis Test Comparing Population Proportions
  52. Squared Error of Regression Line
  53. Proof (Part 1) Minimizing Squared Error to Regression Line
  54. Proof (Part 3) Minimizing Squared Error to Regression Line
  55. Proof (Part 4) Minimizing Squared Error to Regression Line
  56. Regression Line Example
  57. Proof Part 2 Minimizing Squared Error to Line
  58. R-Squared or Coefficient of Determination
  59. Second Regression Example
  60. Calculating R-Squared
  61. Covariance and the Regression Line
  62. Chi-Square Distribution Introduction
  63. Pearson’s Chi Square Test (Goodness of Fit)
  64. Contingency Table Chi-Square Test
  65. ANOVA 1 – Calculating SST (Total Sum of Squares)
  66. ANOVA 2 – Calculating SSW and SSB (Total Sum of Squares Within and Between).avi
  67. ANOVA 3 -Hypothesis Test with F-Statistic
  68. Correlation and Causality

ck12.org Algebra 1 Examples

Select problems from ck12.org’s Algebra 1 FlexBook (Open Source Textbook). This is a good playlist to review if you want to make sure you have a good understanding of all of the major topics in Algebra I.

  1. Variable Expressions
  2. Order of Operations Example
  3. Patterns and Equations
  4. Equations and Inequalities
  5. Domain and Range of a Function
  6. Functions as Graphs
  7. Word Problem Solving Plan 1
  8. Word Problem Solving Strategies
  9. Integers and Rational Numbers
  10. Addition of Rational Numbers
  11. Subraction of Rational Numbers
  12. Multiplication of Rational Numbers
  13. Distributive Property Example 1
  14. Division of Rational Numbers
  15. Square Roots and Real Numbers
  16. Problem Solving Word Problems 2
  17. One Step Equations
  18. Two-Step Equations
  19. Multi-Step Equations
  20. Equations with Variables on Both Sides
  21. Ratio and Proportion
  22. Scale and Indirect Measurement
  23. Percent Problems
  24. Word Problem Solving 3
  25. The Coordinate Plane
  26. Graphing Using Intercepts
  27. Graphs of Linear Equations
  28. Slope and Rate of Change
  29. Graphs Using Slope-Intercept Form
  30. Direct Variation Models
  31. Linear Function Graphs
  32. Word Problem Solving 4
  33. Linear Equations in Slope Intercept Form
  34. Linear Equations in Point Slope Form
  35. Linear Equations in Standard Form
  36. Equations of Parallel and Perpendicular Lines
  37. Fitting a Line to Data
  38. Predicting with Linear Models
  39. Using a Linear Model
  40. Inequalities Using Addition and Subtraction
  41. Inequalities Using Multiplication and Division
  42. Multi-Step Inequalities
  43. Compound Inequalities
  44. Absolute Value Equations
  45. Absolute Value Inequalities
  46. Graphing Inequalities
  47. Solving Linear Systems by Graphing
  48. Solving Linear Systems by Substitution
  49. Solving Systems of Equations by Elimination
  50. Solving Systems of Equations by Multiplication
  51. Special Types of Linear Systems
  52. Systems of Linear Inequalities
  53. Exponent Properties Involving Products
  54. Exponent Properties Involving Quotients
  55. Zero, Negative, and Fractional Exponents
  56. Scientific Notation
  57. Exponential Growth Functions
  58. Exponential Decay Functions
  59. Geometric Sequences (Introduction)
  60. Word Problem Solving- Exponential Growth and Decay
  61. Addition and Subtraction of Polynomials
  62. Multiplication of Polynomials
  63. Special Products of Binomials
  64. Polynomial Equations in Factored Form
  65. Factoring Quadratic Expressions
  66. Factoring Special Products
  67. Factor by Grouping and Factoring Completely
  68. Graphs of Quadratic Functions
  69. Solving Quadratic Equations by Graphing
  70. Solving Quadratic Equations by Square Roots
  71. Solving Quadratic Equations by Completing the Square
  72. Using the Quadratic Formula
  73. Proof of Quadratic Formula
  74. Discriminant of Quadratic Equations
  75. Linear, Quadratic, and Exponential Models
  76. Identifying Quadratic Models
  77. Identifying Exponential Models
  78. Quadratic Regression
  79. Graphs of Square Root Functions
  80. Radical Expressions with Higher Roots
  81. More Simplifying Radical Expressions
  82. How to Rationalize a Denominator
  83. Extraneous Solutions to Radical Equations
  84. Radical Equation Examples
  85. More Involved Radical Equation Example
  86. Pythagorean Theorem
  87. Distance Formula
  88. Midpoint Formula
  89. Visual Pythagorean Theorem Proof
  90. Average or Central Tendency: Arithmetic Mean, Median, and Mode
  91. Range, Variance and Standard Deviation as Measures of Dispersion
  92. Stem and Leaf Plots
  93. Histograms
  94. Box-and-whisker Plot
  95. Proportionality
  96. Asymptotes of Rational Functions
  97. Another Rational Function Graph Example
  98. A Third Example of Graphing a Rational Function
  99. Polynomial Division
  100. Simplifying Rational Expressions Introduction
  101. Multiplying and Dividing Rational Expressions
  102. Adding Rational Expressions Example 1
  103. Adding Rational Expressions Example 2
  104. Adding Rational Expressions Example 3
  105. Solving Rational Equations
  106. Two more examples of solving rational equations
  107. Surveys and Samples

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