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 | |