Problem sets and exams

Almost every other Tuesday, starting on July 31, but on September 13 Thursday the last time, there will be an exam during the last hour of the class period, closely based on an associated problem set. (There is also a final exam on September 20 Thursday, but this page is not about that.) Unless otherwise specified, all problems in the problem sets are from Elementary Algebra written by Marecek & Anthony-Smith and published by OpenStax.

Here are the exam dates and the associated problem sets (Exam 1, Exam 2, Exam 3, Exam 4):

Arithmetic:
- Date taken: July 31 Tuesday.
- Exercises from Section 1.2 (pages 37–39): 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 107, 109, 111, 127, 129, 131, 133, 135, 149, 151, 153, 155, 157, 163, 165, 167, 169, 171, 173, 175, 177;
- Exercises from Section 6.2 (pages 697–700): 91, 93;
- Exercises from Section 6.5 (pages 744–747): 365, 367, 369;
- Exercises from Section 6.7 (pages 775–778): 501, 503.a, 509.a, 511.a, 513, 551, 553, 555, 557, 559, 561, 563, 565, 567, 569, 571, 573, 585;
- Exercises from Section 1.8 (pages 139–141): 659, 661, 663, 665, 667, 669;
- Exercises from the Chapter 1 review exercises (pages 183–195): 1041, 1043, 1045, 1047, 1049, 1127, 1129, 1131, 1133, 1135, 1137, 1251, 1253.
- Extra-credit exercise: One of the properties of exponents is that a^rs = (a^r)^s, whenever a is a real number and r and s are integers, as long as the operations are defined (so that 0 is never raised to the power of a negative number). But in this class, we also allow 1/2 as an exponent (where x^1/2 is the principal square root of x). Find a real number a, a number r that is either an integer or 1/2, and another number s that is either an integer or 1/2, such that a^rs does not equal (a^r)^s, even though the operations are defined in the real number system (so that 0 is never raised to the power of a negative number and a negative number is never raised to the power of 1/2).
Expressions and equations:
- Date taken: August 14 Tuesday.
- Exercises from Section 6.1 (pages 683–686): 1, 5, 9, 11, 13, 15, 17, 31, 33, 35, 37, 39, 41, 43, 45.
- Exercises from Section 6.2 (pages 697–700): 99, 101, 105, 107, 115, 119, 121, 123, 125, 127, 129, 131.
- Exercises from Section 6.3 (pages 713–716): 173, 175, 177, 179, 187, 189, 191, 199, 201, 203, 205, 237, 239, 267, 269.
- Exercises from Section 2.1 (pages 209–211): 1, 3, 5, 7, 13, 15, 21, 29, 51, 53, 55, 75.
- Exercises from Section 2.2 (pages 223–225): 77, 79, 81, 83, 87, 91, 93, 95, 97, 99, 113, 143, 147, 149, 173.
- Exercises from Section 2.3 (pages 234&235): 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 199, 201, 203, 205, 207, 209, 211.
- Exercises from Section 2.4 (pages 246–248): 233, 235, 237, 239, 241, 243, 245, 247, 249, 255, 257, 259, 261, 263, 265, 267, 269, 281, 293, 299, 301, 305, 307, 309.
- Exercises from Section 2.5 (pages 258&259): 319, 321, 323, 329, 331, 333, 339, 341, 343, 345, 355, 357, 359, 361, 363, 365, 367, 373.
- Exercises from Section 2.7 (pages 282–284): 435, 437, 439, 441, 447, 449, 451, 453, 467, 469, 471, 473, 475, 477, 479, 481, 493, 495, 497, 499, 501, 503, 505, 507, 509, 511.
- Extra-credit exercises: Read my online notes on absolute-value problems and then solve these equations and inequalites:
  1. |3x + 5| < 7.
  2. |2x − 9| ≥ 4.
  3. |4x + 6| = 12.
  (To show work for each exercise, include at least one intermediate step removing the absolute-value operator. But feel free to show more work than that!)
Word problems and graphing:
- Date taken: August 28 Tuesday.
- Exercises from Section 3.1 (pages 309–311): 3, 5, 7, 9, 11, 13, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61.
- Exercises from Section 3.6 (pages 388–390): 309, 311, 313, 315, 333, 335.
- Exercises from Section 3.2 (pages 326–329): 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159.
- Exercises from Section 3.3 (pages 343–345): 161, 163, 165, 179, 181, 183, 193, 195, 205.
- Exercises from Section 3.5 (pages 379–381): 283, 285, 287, 305.
- Exercises from Section 2.6 (pages 267–269): 377, 379, 389, 393, 397, 399, 405, 407, 409, 411, 413, 415, 417, 419, 427, 429.
- Exercises from Section 4.1 (pages 419–423): 1, 3, 9, 11, 13, 15, 21, 23, 29, 31, 33, 35, 37, 39, 49, 53.
- Exercises from Section 4.2 (pages 441–443): 55, 59, 61, 63, 65, 67, 69, 79, 81, 83, 85, 87, 89, 103, 105, 107, 109, 115.
- Exercises from Section 4.3 (pages 455–458): 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 179, 181, 183, 185, 205, 209.
- Exercises from Section 4.4 (pages 480–485): 227, 229, 231, 233, 243, 245, 247, 249, 251, 253, 255, 257, 263, 265, 267, 269, 271, 273, 279, 281, 283, 285, 287.
- Exercises from Section 4.5 (pages 507–511): 289, 291, 293, 295, 297, 299, 301, 305, 307, 309, 311, 313, 315, 317, 319, 345, 353, 357, 363, 371, 375.
- Exercises from Section 4.6 (pages 525–529): 387, 389, 403, 405, 411, 413, 415, 417, 419, 429, 431, 433, 435, 437, 455, 457, 471.
- Extra-credit exercise: Draw a graph of the inequality 2x + 3y > 4. Show enough work that I can see how you graphed the boundary line and include a brief explanation of why your boundary line is solid or dashed and why you shaded the region that you did. (Hint: Look at §4.7 of the textbook, pages 530–543)
Dividing and factoring polynomials:
- Date taken: September 13 Thursday.
- Exercises from Section 6.5 (pages 744–747): 357, 359, 361, 363, 375, 377, 411, 413, 415, 417, 439.
- Exercises from Section 6.7 (pages 775–778): 521, 523, 525, 527, 529, 531, 535, 537, 539, 543, 545, 547, 549.
- Exercises from Section 6.6 (pages 758&759): 443, 445, 447, 449, 451, 453, 455, 457, 475, 477, 479, 481, 495.
- Exercises from Section 7.1 (pages 801&802): 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 37, 39, 45, 47, 49, 51.
- Exercises from Section 7.2 (pages 814&815): 63, 65, 67, 75, 77, 79, 81, 83, 85, 87, 97, 99, 101, 131.
- Exercises from Section 7.3 (pages 831–833): 189, 191, 193, 195, 197, 199, 203, 205, 207.
- Exercises from Section 6.4 (pages 727–729): 303, 307, 309, 315, 323, 329, 331, 335, 339, 355.
- Exercises from Section 7.4 (pages 848&849): 215, 217, 219, 229, 231, 233, 235, 237, 245, 247, 249, 251, 255, 257.
- Exercises from Section 7.5 (pages 859&860): 279, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299, 301, 303, 305, 307, 309, 313, 314.
- Exercises from Section 7.6 (pages 874&875): 315, 317, 319, 321, 323, 325, 327, 329, 331, 333, 335, 337, 339, 341.
- Exercises from Section 8.1 (pages 897–900): 1, 3, 5, 7, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 57, 59, 61, 71.
- Exercises from Section 8.2 (pages 911–913): 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 117, 119, 121, 123, 127.
- Extra-credit exercise: Factor x⁶ − y⁶ in two ways: first by treating it as a difference of squares (and then factoring further) and second by treating it as a difference of cubes (and then factoring further). Did you get the same result both times? Which way is easier? Explain briefly.

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