College Algebra

263 shown

1. Alg 001 The Real Numbers A
2. Alg 002 Natural Numbers and Whole Numbers A
3. Alg 003 The Integers A
4. Alg 004 Rational Numbers A
5. Alg 005 Irrational Numbers A
6. Alg 007 Classifying a Real Number P
7. Alg 009 Exponential Notation A
8. Alg 010 The Order of Operations A
9. Alg 011 Exponents Before Negation A
10. Alg 012 The Invisible-Parentheses Error A
11. Alg 014 The Commutative Properties A
12. Alg 015 The Associative Properties A
13. Alg 016 The Distributive Property A
14. Alg 017 The Identity Properties A
15. Alg 018 The Inverse Properties A
16. Alg 022 The Product Rule of Exponents A
17. Alg 023 The Quotient Rule of Exponents A
18. Alg 025 The Power Rule of Exponents A
19. Alg 026 The Power-Product Confusion A
20. Alg 028 The Zero Exponent Rule of Exponents A
21. Alg 029 The Zero-Power Error A
22. Alg 031 The Negative Rule of Exponents A
23. Alg 032 The Negative-Exponent Sign Error A
24. Alg 034 The Power of a Product Rule of Exponents A
25. Alg 035 The Power of a Quotient Rule of Exponents A
26. Alg 037 Simplifying with the Exponent Rules P
27. Alg 039 Scientific Notation A
28. Alg 040 Absolute Value A
29. Alg 041 The Principal Square Root A
30. Alg 042 The Square Root of a Square A
31. Alg 043 The Dropped-Absolute-Value Error A
32. Alg 045 The Product Rule for Simplifying Square Roots A
33. Alg 046 The Split-Sum Error A
34. Alg 048 The Quotient Rule for Simplifying Square Roots A
35. Alg 050 Simplifying a Square Root P
36. Alg 052 Like Radicals A
37. Alg 054 Rationalizing a Denominator P
38. Alg 056 The Principal nth Root A
39. Alg 057 Rational Exponents: the 1/n Power A
40. Alg 058 Rational Exponents: the m/n Power A
41. Alg 060 From Counting to Rational Exponents C
42. Alg 061 Polynomials A
43. Alg 062 Degree and Leading Coefficient A
44. Alg 063 Monomials, Binomials, Trinomials A
45. Alg 065 Adding and Subtracting Polynomials A
46. Alg 067 Multiplying Polynomials A
47. Alg 068 FOIL A
48. Alg 070 Squaring a Binomial A
49. Alg 071 The Missing-Middle Error A
50. Alg 073 The Difference of Squares A
51. Alg 081 Factoring A
52. Alg 082 The Greatest Common Factor A
53. Alg 083 Factoring Out the GCF P
54. Alg 085 Factoring x² + bx + c A
55. Alg 086 Factoring ax² + bx + c by Grouping P
56. Alg 088 Factoring a Perfect Square Trinomial A
57. Alg 090 Factoring a Difference of Squares A
58. Alg 091 The Sum of Squares A
59. Alg 093 The Sum and Difference of Cubes A
60. Alg 095 Choosing a Factoring Strategy P
61. Alg 101 Rational Expressions A
62. Alg 103 Only Factors Cancel A
63. Alg 104 The Canceled-Term Error A
64. Alg 106 Simplifying a Rational Expression P
65. Alg 108 Multiplying Rational Expressions A
66. Alg 109 Dividing Rational Expressions A
67. Alg 111 The Least Common Denominator A
68. Alg 112 Adding and Subtracting Rational Expressions P
69. Alg 114 Splitting a Fraction over Its Numerator A
70. Alg 115 The Denominator-Split Error A
71. Alg 117 Simplifying a Complex Rational Expression P
72. Alg 120 The Arithmetic of Polynomials C
73. Alg 121 The Cartesian Coordinate System A
74. Alg 122 Graphing by Plotting Points A
75. Alg 124 Intercepts A
76. Alg 126 The Distance Formula A
77. Alg 127 The Midpoint Formula A
78. Alg 131 Linear Equations in One Variable A
79. Alg 132 The Solution of an Equation A
80. Alg 133 Solving a Linear Equation P
81. Alg 135 Identity, Conditional, and Inconsistent Equations A
82. Alg 137 Rational Equations A
83. Alg 138 Checking in the Original Equation A
84. Alg 140 Solving a Rational Equation P
85. Alg 142 The Slope of a Line A
86. Alg 143 The Slope Formula A
87. Alg 145 Slope-Intercept Form A
88. Alg 146 The Point-Slope Formula A
89. Alg 148 Writing a Line from Two Points P
90. Alg 150 Parallel Lines A
91. Alg 151 Perpendicular Lines A
92. Alg 153 Horizontal and Vertical Lines A
93. Alg 156 Interval Notation A
94. Alg 158 Solutions of Linear Inequalities A
95. Alg 159 The Addition Property of Inequality A
96. Alg 160 The Multiplication Property of Inequality A
97. Alg 161 The Kept-Sign Error A
98. Alg 163 Solving a Linear Inequality P
99. Alg 165 Compound Inequalities A
100. Alg 167 Absolute Value as Distance A
101. Alg 168 Absolute Value Inequalities: Less Than A
102. Alg 169 Absolute Value Inequalities: Greater Than A
103. Alg 170 The Swapped-Cases Error A
104. Alg 172 Solving an Absolute Value Inequality P
105. Alg 180 The Line and the Balance C
106. Alg 181 The Imaginary Unit A
107. Alg 182 Complex Numbers in Standard Form A
108. Alg 184 Adding and Subtracting Complex Numbers A
109. Alg 185 Multiplying Complex Numbers A
110. Alg 187 The Complex Conjugate A
111. Alg 188 Dividing Complex Numbers P
112. Alg 190 Square Roots of Negative Numbers A
113. Alg 191 The Powers of i A
114. Alg 196 Quadratic Equations A
115. Alg 197 The Zero-Product Property A
116. Alg 198 Solving a Quadratic by Factoring P
117. Alg 200 Keeping Every Factor A
118. Alg 201 The Divided-Away Solution A
119. Alg 203 The Square Root Property A
120. Alg 204 The Lost-Root Error A
121. Alg 206 Completing the Square P
122. Alg 208 The Quadratic Formula A
123. Alg 209 The Discriminant A
124. Alg 211 Solving with the Quadratic Formula P
125. Alg 213 Complex Solutions of Quadratics A
126. Alg 216 Radical Equations A
127. Alg 217 Checking After Raising to a Power A
128. Alg 218 The Unchecked-Squaring Error A
129. Alg 220 Solving a Radical Equation P
130. Alg 222 Equations Quadratic in Form A
131. Alg 224 Equations with Rational Exponents A
132. Alg 226 Absolute Value Equations A
133. Alg 230 Every Quadratic Surrenders C
134. Alg 231 Relations A
135. Alg 232 Functions A
136. Alg 234 Function Notation A
137. Alg 235 Evaluating a Function A
138. Alg 236 Evaluating at a Sum A
139. Alg 237 The Assumed-Linearity Error A
140. Alg 239 Evaluating versus Solving A
141. Alg 241 One-to-One Functions A
142. Alg 242 The Vertical Line Test A
143. Alg 243 The Horizontal Line Test A
144. Alg 245 Determining Whether a Relation Is a Function P
145. Alg 249 The Domain of a Function A
146. Alg 250 The Range A
147. Alg 252 Finding a Domain from an Equation P
148. Alg 254 Piecewise-Defined Functions A
149. Alg 256 The Absolute Value Function A
150. Alg 263 The Average Rate of Change A
151. Alg 265 Increasing and Decreasing Functions A
152. Alg 266 Local Maxima and Minima A
153. Alg 273 The Algebra of Functions A
154. Alg 275 Function Composition A
155. Alg 276 Evaluating a Composite Function P
156. Alg 278 Composition Order Matters A
157. Alg 281 Vertical Shifts A
158. Alg 282 Horizontal Shifts A
159. Alg 284 Reflections A
160. Alg 285 Even and Odd Functions A
161. Alg 287 Vertical Stretches and Compressions A
162. Alg 288 Horizontal Stretches and Compressions A
163. Alg 290 Graphing by Transformations P
164. Alg 293 Inverse Functions A
165. Alg 294 The Reciprocal-Inverse Error A
166. Alg 296 The Composition Test for Inverses A
167. Alg 297 Finding an Inverse Algebraically P
168. Alg 299 Graphs of Inverse Functions A
169. Alg 300 The Function Machine C
170. Alg 301 Linear Functions A
171. Alg 302 Direction from the Slope A
172. Alg 304 Slope as a Rate A
173. Alg 306 Building a Linear Model P
174. Alg 308 A Linear Model from Two Data Points P
175. Alg 310 Where Two Lines Meet A
176. Alg 312 The Zero of a Linear Function A
177. Alg 321 Quadratic Functions and Parabolas A
178. Alg 322 The Vertex and Axis of Symmetry A
179. Alg 324 General Form and Standard Form A
180. Alg 325 Reading the Vertex from Standard Form A
181. Alg 326 The Vertex-Sign Error A
182. Alg 327 The Vertex Formula A
183. Alg 329 Converting General to Standard Form P
184. Alg 331 Maximum and Minimum Values A
185. Alg 333 Zeros, x-Intercepts, Solutions A
186. Alg 335 The Full Quadratic Workup P
187. Alg 337 Optimizing with a Quadratic P
188. Alg 350 The Parabola Dossier C
189. Alg 351 Power Functions A
190. Alg 352 End Behavior A
191. Alg 354 End Behavior from the Leading Term A
192. Alg 356 Zeros and Multiplicity A
193. Alg 358 Turning Points A
194. Alg 360 Sketching a Polynomial P
195. Alg 364 Polynomial Long Division P
196. Alg 366 Synthetic Division P
197. Alg 368 The Remainder Theorem A
198. Alg 369 The Factor Theorem A
199. Alg 371 Finding Zeros with the Factor Theorem P
200. Alg 376 Rational Functions A
201. Alg 377 Vertical Asymptotes A
202. Alg 378 Removable Discontinuities A
203. Alg 379 The Erased-Hole Error A
204. Alg 381 Horizontal Asymptotes A
205. Alg 383 Analyzing a Rational Function P
206. Alg 386 Radical Functions and Their Domains A
207. Alg 388 Restricting a Domain for an Inverse A
208. Alg 391 Direct Variation A
209. Alg 392 Inverse Variation A
210. Alg 393 Joint Variation A
211. Alg 395 Solving a Variation Problem P
212. Alg 410 The Anatomy of Higher Functions C
213. Alg 411 Exponential Functions A
214. Alg 412 Growth and Decay A
215. Alg 414 Linear versus Exponential Change A
216. Alg 416 Evaluating Exponential Functions A
217. Alg 418 Compound Interest P
218. Alg 420 The Number e A
219. Alg 421 Continuous Growth and Decay A
220. Alg 423 Graphs of Exponential Functions A
221. Alg 426 The Logarithm A
222. Alg 427 Logarithms and Exponentials Are Inverses A
223. Alg 429 Common and Natural Logarithms A
224. Alg 431 Converting Between Forms P
225. Alg 433 Evaluating Logarithms Mentally A
226. Alg 435 Graphs of Logarithmic Functions A
227. Alg 446 The Product Rule for Logarithms A
228. Alg 447 The Split-Sum Log Error A
229. Alg 448 The Multiplied-Logs Error A
230. Alg 450 The Quotient Rule for Logarithms A
231. Alg 451 The Divided-Logs Error A
232. Alg 453 The Power Rule for Logarithms A
233. Alg 455 Expanding and Condensing Logarithms P
234. Alg 457 The Change-of-Base Formula A
235. Alg 463 The One-to-One Property of Exponential Functions A
236. Alg 465 Solving Exponential Equations with Logarithms P
237. Alg 467 The One-to-One Property of Logarithms A
238. Alg 468 Solving Logarithmic Equations P
239. Alg 473 Doubling Time P
240. Alg 480 The Inverse Kingdom C
241. Alg 481 Systems of Linear Equations A
242. Alg 482 The Substitution Method A
243. Alg 484 Solving by Substitution P
244. Alg 486 The Addition Method A
245. Alg 488 Solving by Addition P
246. Alg 490 Independent, Dependent, Inconsistent A
247. Alg 492 A System from a Story P
248. Alg 496 Systems in Three Variables A
249. Alg 498 Solving a Three-Variable System P
250. Alg 501 Nonlinear Systems A
251. Alg 503 Solving a Nonlinear System P
252. Alg 511 The Multiplication Principle A
253. Alg 513 Factorials A
254. Alg 515 Permutations A
255. Alg 516 Combinations A
256. Alg 518 Binomial Coefficients A
257. Alg 520 The Binomial Theorem A
258. Alg 522 Expanding with the Binomial Theorem P
259. Alg 524 A Single Term of an Expansion A
260. Alg 530 Many Unknowns, Counted Ways C
261. Alg 536 The Error Families C
262. Alg 538 The Course, One Thread C
263. Alg 540 Where the Numbers End C