homepage: Dr. Carol JVF Burns
Updated to MathJax 2.2
I started updating my website to MathJax 2.2 on November 7, 2013.
The files shown here have been updated.
Algebra I updates are complete (1165); 24 of these exercises use JSXGraph
Geometry updates are complete (166193); 4 of these exercises use JSXGraph
Algebra II updates are complete (194237); 1 of these exercises uses JSXGraph
Precalculus updates are complete (238309); 11 of these exercises use JSXGraph
Calculus updates are complete (310316); 3 of these exercises use JSXGraph
| # | UPDATED WEB PAGE | ✓ IF USES JSXGRAPH |
| | ALGEBRA I: | |
| 1. | Expressions versus Sentences | |
| 2. | Basic Addition Practice | |
| 3. | Multiplication | |
| 4. | Divisibility | |
| 5. | Basic Properties of Zero and One | |
| 6. | Mixed Basic Add/Subtract Multiply/Divide Practice | |
| 7. | Deciding if a Number is a Whole Number, Integer, etc. | |
| 8. | Addition of Signed Numbers | |
| 9. | Subtraction of Signed Numbers | |
| 10. | Mixed Addition and Subtraction of Signed Numbers | |
| 11. | Writing Fractions with a Denominator of 2 in Decimal Form | |
| 12. | Average of Two Signed Numbers | |
| 13. | Average of Signed Numbers | |
| 14. | Identifying Place Values | |
| 15. | Multiplying by Powers of Ten | |
| 16. | Changing Decimals to Fractions | |
| 17. | Multiplying and Dividing Decimals by Powers of Ten | |
| 18. | Changing Decimals to Percents | |
| 19. | Changing Percents to Decimals | |
| 20. | Introduction to Sets | |
| 21. | Interval and List Notation | |
| 22. | Introduction to Variables | |
| 23. | Reading Set Notation | |
| 24. | Going From a Sequence of Operations to an Expression | |
| 25. | Going From an Expression to a Sequence of Operations | |
| 26. | Solving Simple Sentences By Inspection | |
| 27. | Using Mathematical Conventions | |
| 28. | ‘Undoing’ a Sequence of Operations | |
| 29. | Solving for a Particular Variable | |
| 30. | Direct and Inverse Variation | |
| 31. | Scientific Notation | |
| 32. | Significant Figures | ✓ |
| 33. | Rewriting Fractions as a Whole Number plus a Fraction | |
| 34. | Locating Fractions on a Number Line | |
| 35. | Fractions Involving Zero | |
| 36. | Finding Reciprocals | |
| 37. | Determining if a Product is Positive or Negative | |
| 38. | Multiplying and Dividing Fractions | |
| 39. | Practice with the form a(b/c) | |
| 40. | More Practice with the Form a(b/c) | |
| 41. | Renaming Fractional Expressions | |
| 42. | Practice with Multiples | |
| 43. | Finding Least Common Multiples | |
| 44. | Renaming Fractions with a Specified Denominator | |
| 45. | Practice with Factors | |
| 46. | Adding and Subtracting Fractions | |
| 47. | Adding and Subtracting Simple Fractions With Variables | |
| 48. | Divisibility Equivalences | |
| 49. | Identifying Inequalities as True or False | |
| 50. | Bigger, Smaller, Greater, Lesser | |
| 51. | Practice with the phrases "at least" and "at most" | |
| 52. | Identifying Inequalities with Variables as True or False | |
| 53. | Solving Equations of the form $\,xy = 0\,$ | ✓ |
| 54. | Recognizing Zero and One | |
| 55. | Writing Fractions in Simplest Form | |
| 56. | Deciding if a Fraction is a Finite or Infinite Repeating Decimal | |
| 57. | Deciding if Numbers are Equal or Approximately Equal | |
| 58. | Rounding Decimals to a Specified Number of Places | |
| 59. | Tables of Unit Conversion Information (no MathJax) | |
| 60. | Classifying Units as Length, Time, Volume, Weight/Mass | |
| 61. | Practice with Unit Abbreviations | |
| 62. | Practice with Unit Names | |
| 63. | Practice with Unit Conversion Information | |
| 64. | One-Step Conversions | |
| 65. | Multi-Step Conversions | |
| 66. | Rate Problems | |
| 67. | Work Problems (MathJax not loaded via Javascript) | |
| 68. | Practice with Exponents | |
| 69. | Practice with Order of Operations | |
| 70. | Basic Exponent Practice with Fractions | |
| 71. | Practice with "Same Base, Things Multiplied, Add the Exponents" | |
| 72. | Practice with "Something to a Power to a Power, Multiply the Exponents" | |
| 73. | Practice with "Same Power, Divided, Subtract the Exponents" | |
| 74. | Practice with "Negative Power, Gives a Flip" | |
| 75. | One-Step Exponent Law Practice | |
| 76. | Multi-step Exponent Law Practice | |
| 77. | Practice With Radicals | |
| 78. | Approximating Radicals | |
| 79. | Writing Radicals in Rational Exponent Form | |
| 80. | Writing Rational Exponents as Radicals | |
| 81. | Practice with Rational Exponents | |
| 82. | Practice with $\,x\,$ and $\,-x\,$ | |
| 83. | Practice with Products of Signed Variables | |
| 84. | Practice with the Distributive Law | |
| 85. | Mental Math: Addition | |
| 86. | Don't Mix Up $\,3x\,$ versus $\,x^3\,$! | |
| 87. | Equal or Opposites? | |
| 88. | Recognizing the patterns $\,x^n\,$ and $\,(-x)^n\,$ | |
| 89. | Writing Expressions in the Form $\,kx^n\,$ | |
| 90. | Writing More Complicated Expressions in the Form $\,kx^n\,$ | |
| 91. | Writing Quite Complicated Expressions in the Form $\,kx^n\,$ | |
| 92. | Identifying Variable Parts and Coefficients of Terms | |
| 93. | Combining Like Terms | |
| 95. | Simplifying Expressions like $\,-a(3b - 2c - d)\,$ | |
| 96. | Basic FOIL | |
| 97. | More Complicated FOIL | |
| 98. | Simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$ | |
| 99. | Simplifying Expressions like $\,(a - b)(c + d - e)\,$ | |
| 100. | Practice With the Mathematical Words "and", "or", "is equivalent to" | |
| 101. | Recognizing Products and Sums; Identifying Factors and Terms | |
| 102. | Identifying Common Factors | |
| 103. | Factoring Simple Expressions | |
| 104. | Listing All the Factors of a Whole Number | |
| 105. | Finding the Greatest Common Factor of 2 or 3 Numbers | |
| 106. | Finding the Greatest Common Factor of Variable Expressions | |
| 107. | Factoring out the Greatest Common Factor | |
| 108. | The Addition Property of Equality | |
| 109. | The Multiplication Property of Equality | |
| 110. | Solving Simple Linear Equations with Integer Coefficients | ✓ |
| 111. | Solving More Complicated Linear Equations with Integer Coefficients | ✓ |
| 112. | Solving Linear Equations Involving Fractions | ✓ |
| 113. | Solving Linear Equations, all mixed up | ✓ |
| 114. | Simple Word Problems resulting in Linear Equations | |
| 115. | Solving Simple Linear Inequalities with Integer Coefficients | ✓ |
| 116. | Solving Linear Inequalities with Integer Coefficients | ✓ |
| 117. | Solving Linear Inequalities Involving Fractions | ✓ |
| 118. | Solving Linear Inequalities, all mixed up | ✓ |
| 119. | Simplifying Basic Absolute Value Expressions | |
| 120. | Determining the Sign (positive or negative) of Absolute Value Expressions | |
| 121. | Solving Simple Absolute Value Sentences | ✓ |
| 122. | Solving Sentences Involving "Plus or Minus" | ✓ |
| 123. | Solving Absolute Value Equations | ✓ |
| 124. | Solving Absolute Value Inequalities Involving "Less Than" | ✓ |
| 125. | Solving Absolute Value Inequalities Involving "Greater Than" | ✓ |
| 126. | Solving Absolute Value Sentences, All Types | ✓ |
| 127. | Identifying Perfect Squares | |
| 128. | Writing Expressions in the form $\,A^2\,$ | |
| 129. | Factoring a Difference of Squares | |
| 130. | Solving Simple Equations Involving Perfect Squares | ✓ |
| 131. | Solving More Complicated Equations Involving Perfect Squares | ✓ |
| 132. | Translating Simple Mathematical Phrases | |
| 133. | Word Problems Involving Perfect Squares | |
| 134. | Basic Concepts Involved in Factoring Trinomials | |
| 135. | Factoring Trinomials (coefficient of x^2 term is 1, constant term is positive) | |
| 136. | Factoring Trinomials (coefficient of x^2 term is 1, constant term is negative) | |
| 137. | Factoring Trinomials, All Mixed Up | ✓ |
| 138. | Identifying Quadratic Equations | |
| 139. | Writing Quadratic Equations in Standard Form | |
| 140. | Solving Simple Quadratic Equations by Factoring | ✓ |
| 141. | Factoring Trinomials (coefficient of squared term is not 1) | ✓ |
| 142. | Solving More Complicated Quadratic Equations by Factoring | ✓ |
| 143. | Multiplying and Dividing Fractions with Variables | ✓ |
| 144. | Adding and Subtracting Fractions With Variables | |
| 145. | Writing expressions involving percent increase and decrease | |
| 146. | Calculating Percent Increase and Decrease | |
| 147. | Problems involving percent increase and decrease | |
| 148. | More Problems Involving Percent Increase and Decrease | |
| 149. | Locating Points in Quadrants and on Axes | |
| 150. | Practice With Points | |
| 151. | the Pythagorean Theorem | ✓ |
| 152. | the Distance Formula | |
| 153. | the Midpoint Formula | |
| 154. | Introduction to Equations and Inequalities in Two Variables | |
| 155. | Introduction to the Slope of a Line | |
| 156. | Practice With Slope | |
| 157. | Graphing Lines | |
| 158. | Finding Equations of Lines | |
| 159. | Point-Slope Form | |
| 160. | Horizontal and Vertical Lines | |
| 161. | Parallel and Perpendicular lines | |
| 162. | Introduction to Functions | |
| 163. | Introduction to Function Notation | |
| 164. | More Practice with Function Notation | |
| 165. | Domain and Range of a Function | |
| | GEOMETRY: | |
| 166. | Introduction to Geometry: Points, Lines, and Planes | |
| 167. | Segments, Rays, Angles | |
| 168. | Introduction to Polygons | |
| 169. | Interior and Exterior Angles in Polygons | |
| 170. | Quadrilaterals | ✓ |
| 171. | "If ... Then ..." Sentences | |
| 172. | Contrapositive and Converse | |
| 173. | Proof Techniques | |
| 174. | Logical Equivalences and Practice with Truth Tables | |
| 175. | Applying Logical Equivalences to Algebraic and Geometric Statements | |
| 176. | Constructions | |
| 177. | Introduction to the Two-Column Proof | |
| 178. | the Pythagorean Theorem | ✓ |
| 179. | More Terminology for Segments and Angles | |
| 180. | Angles: Complementary, Supplementary, Vertical, and Linear Pairs | |
| 181. | Equivalence Relations | |
| 182. | Triangle Congruence | |
| 183. | Relationships Between Angles and Sides in Triangles | |
| 184. | Practice with Two-Column Proofs | |
| 185. | Is there an "SSA" Congruence Theorem? NO! | |
| 186. | More on Exterior Angles in Triangles | |
| 187. | Parallel Lines | |
| 188. | Parallelograms and Negating Sentences | |
| 189. | Introduction to Area and Perimeter | |
| 190. | Area Formulas: Triangle, Parallelogram, Trapezoid | ✓ |
| 191. | Similarity, Ratios, and Proportions | |
| 192. | Perimeters and Areas of Similar Polygons | |
| 193. | Two Special Triangles | ✓ |
| | ALGEBRA II: | |
| 194. | Introduction to Recursion and Sequences | |
| 195. | Arithmetic and Geometric Sequences | |
| 196. | Loans and Investments | |
| 197. | Compound Interest Formula | |
| 198. | Graphs of Functions | |
| 199. | Basic Models You Must Know | |
| 200. | Graphical Interpretation of Sentences like $\,f(x)=0\,$ and $\,f(x)>0\,$ | |
| 201. | Graphical Interpretation of Sentences like $\,f(x)=g(x)\,$ and $\,f(x)>g(x)\,$ | |
| 202. | Composition of Functions | |
| 203. | Advanced Set Concepts | |
| 204. | Basic Probability Concepts | |
| 205. | More Probability Concepts | |
| 206. | Probability Tree Diagrams | ✓ |
| 207. | Choosing Things: Does Order Matter? | |
| 208. | Factorial Notation | |
| 209. | Combinations and Permutations | |
| 210. | Summation Notation | |
| 211. | Mean, Median, and Mode | |
| 212. | Measures of Spread | |
| 213. | Introduction to Systems of Equations | |
| 214. | Solving Systems Using Substitution | |
| 215. | Solving Systems Using Elimination | |
| 216. | Simple Word Problems resulting in a System of Equations | |
| 217. | Introduction to Matrices | |
| 218. | Basic Arithmetic With Matrices | |
| 219. | Multiplying Matrices | |
| 220. | Graphing Tools: Vertical and Horizontal Translations | |
| 221. | Graphing Tools: Vertical and Horizontal Scaling | |
| 222. | Graphing Tools: Reflections and the Absolute Value Transformation | |
| 223. | Graphical Transformations: All Mixed Up | |
| 224. | Parabolas | |
| 225. | Equations of Simple Parabolas | |
| 226. | Quadratic Functions and the Completing the Square Technique | |
| 227. | Algebraic Definition of Absolute Value | |
| 228. | The Quadratic Formula | |
| 229. | Complex Numbers | |
| 230. | Arithmetic with Complex Numbers | |
| 231. | Equations of Circles | |
| 232. | Introduction to Logarithms | |
| 233. | Properties of Logarithms | |
| 234. | Change of Base Formula for Logarithms | |
| 235. | Introduction to Logarithmic Functions | |
| 236. | Introduction to Exponential Functions | |
| 237. | Introduction to Polynomials | |
| | PRECALCULUS: | |
| 238. | Prerequisites: Language of Mathematics Essentials | |
| 239. | Prerequisites: Function Review; Difference Quotients | |
| 240. | Solving Linear Inequalities in One Variable | ✓ |
| 241. | Solving Nonlinear Inequalities in One Variable (introduction) | |
| 242. | The Test Point Method for Sentences Like: $\,f(x) > 0\,$ | ✓ |
| 243. | The Test Point Method for Sentences Like: $\,f(x) > g(x)\,$ | ✓ |
| 244. | he Test Point Method in a Nutshell, and Additional Practice | |
| 245. | Absolute Value as Distance From Zero | ✓ |
| 246. | Absolute Value as Distance Between Two Numbers | ✓ |
| 247. | Circles and the Completing the Square Technique | ✓ |
| 248. | Review of Lines and Slopes of Lines | |
| 249. | Review of Coordinate Geometry: the Distance Formula, the Midpoint Formula | |
| 250. | Sketching Regions in the Coordinate Plane | ✓ |
| 251. | Testing Equations for Symmetry | ✓ |
| 252. | More on Difference Quotients | |
| 253. | Finding the Domain and Range of a Function | |
| 254. | Working with Linear Functions: Finding a New Point, Given a Point and a Slope | |
| 255. | Reading Information from the Graph of a Function | ✓ |
| 256. | Increasing and Decreasing Functions | |
| 257. | Basic Function Models You Must Know | ✓ |
| 258. | Piecewise-Defined Functions | |
| 259. | Direct and Inverse Variation | |
| 260. | Proportionality Problems | |
| 261. | What is the Graph of $\,y = f(x)\,$? | |
| 262. | Shifting Graphs Up/Down/Left/Right | |
| 263. | Horizontal and Vertical Stretching/Shrinking | |
| 264. | Reflecting About Axes, and the Absolute Value Transformation | |
| 265. | Multi-Step Practice with all the Graphical Transformations | |
| 266. | Even and Odd Functions | |
| 267. | Extreme Values of Functions (Max/Min) | ✓ |
| 268. | Review of Quadratic Functions: Vertex Form, Max/Min, Intercepts, More | |
| 269. | Max/Min Problems Resulting in Quadratic Functions | |
| 270. | Combining Functions to get New Functions | |
| 271. | Composition of Functions | |
| 272. | Writing a Function as a Composition | |
| 273. | Using a Function Box Backwards | |
| 274. | One-to-One Functions | |
| 275. | Undoing a One-to-One Function; Inverse Functions | |
| 276. | Properties of Inverse Functions | |
| 277. | Finding Inverse Functions (when there's only one x in the formula) | |
| 278. | Finding Inverse Functions (switch input/output names method) | |
| 279. | The Graph of an Inverse Function | |
| 280. | Introduction to Polynomials | |
| 281. | Relationship Between the Zeros (Roots) and Factors of Polynomials | |
| 282. | End Behavior of Polynomials | |
| 283. | Turning Points of Polynomials | |
| 284. | Long Division of Polynomials | |
| 285. | the Division Algorithm | |
| 286. | Synthetic Division | |
| 287. | the Remainder Theorem | |
| 288. | Trapping the Roots of a Polynomial | |
| 289. | Introduction to Complex Numbers | |
| 290. | Arithmetic with Complex Numbers | |
| 291. | The Square Root of a Negative Number | |
| 292. | The Complex Conjugate | |
| 293. | The Quadratic Formula Revisited; the Discriminant | |
| 294. | Multiplicity of Zeros and Graphical Consequences | |
| 295. | Discussion: Graphing Polynomials with Technology | |
| 296. | Solve an Equation? Find a Zero? Your Choice! | |
| 297. | the Fundamental Theorem of Algebra | |
| 298. | Polynomials with Real Number Coefficients | |
| 299. | Solving Polynomial Equations | |
| 300. | Introduction to Rational Functions | |
| 301. | Introduction to Asymptotes | |
| 302. | Introduction to Puncture Points (holes) | |
| 303. | Finding Vertical Asymptotes | |
| 304. | Puncture Points (holes) | |
| 305. | Finding Horizontal Asymptotes | |
| 306. | Finding Slant Asymptotes | |
| 307. | Exponential Functions: Review and Additional Properties | |
| 308. | Linear versus Exponential Functions | |
| 309. | Recognizing Linear and Exponential Behavior from Tables of Data | |
| | CALCULUS: | |
| 310. | Average Rate of Change | ✓ |
| 311. | Introduction to Limits | ✓ |
| 312. | Basic Differentiation Shortcuts (differentiating constants and linear functions; the Simple Power Rule) | ✓ |
| 313. | Differentiation Formula Practice | |
| 314. | Mixed Differentiation Practice | |
| 315. | Mixed Differentiation Practice (strict parentheses version) | |
| 316. | Mixed Integration Practice | |