Problem sets and exams

Almost every other Wednesday or Thursday, starting on April 17 or 18 (but on June 3 or 4 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 June 10 or 11, but this page is not about that.) Unless otherwise specified, all exercises in the problem sets are from Algebra & Trigonometry written by Abramson and published by OpenStax.

Here are the exam dates and the associated problem sets (Exam 1, Exam 2, Exam 3, Exam 4): but anything whose assigned date is in the future is subject to change!

Exam 1:
- Date taken: April 17 or 18.
- From the Chapter 2 Review Exercises (pages 155–157): 13, 16, 23, 24, 27, 34, 41, 51, 61, 66.
- Exercises from Section 2.1 (pages 84–86): 1, 5, 7, 17, 19, 23, 25, 31, 33, 39, 54, 63.
- Exercises from Section 2.2 (pages 100&101): 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 55.
- Exercises from Section 11.1 (pages 889–891): 7, 9, 11, 13, 21, 23.
- Exercises from Section 11.2 (pages 899–902): 7, 11, 17, 55.
- Exercises from Section 11.3 (pages 911&912): 7, 9, 11, 17.
- Exercises from Section 3.1 (pages 176–179): 9, 11, 13, 15, 17, 19, 27, 29, 35, 37, 39, 41, 43, 45, 47, 53, 55, 57, 66, 67, 75, 89, 91.
- Additional extra-credit exercise: Can the graph of a function consist of a single point in the coordinate plane? Explain why or why not, giving an example if possible.
Exam 2:
- Date taken: May 1 or 2.
- Exercises from Section 3.2 (pages 193–195): 7, 9, 11, 13, 15, 17, 19, 21, 27, 29, 31, 33, 39, 41, 43, 45, 49.
- Exercises from Section 3.5 (pages 243–246): 5, 47, 49, 51.
- Exercises from Section 3.3 (pages 206–208): 2, 5, 7, 17, 19, 21, 23, 25, 27, 29, 31, 43, 45.
- Exercises from Section 3.4 (pages 218–221): 1, 4, 5, 11, 19, 23, 43, 45, 47, 49, 59, 61, 63, 65, 81, 91.
- Exercises from Section 3.7 (pages 264–266): 5, 7, 9, 11, 13, 17, 25, 27, 29, 33, 35, 37, 39, 41, 45.
- Exercises from Section 4.1 (pages 304–308): 1, 3, 7, 9, 11, 13, 29, 64–69, 77, 79, 81, 83, 89, 91, 93, 95, 117.
- Exercises from Section 4.2 (pages 317–321): 9, 13, 15, 39, 45.
- Additional extra-credit exercises: Consider a linear function f(x) = mx + b. Answer these questions about the function with generic answers that may refer to m and b:
  1. What are the domain and range of f?
  2. Is f even or odd (or both or neither)?
  3. What (if any) are the zeroes/roots of f?
  4. What (if anything) is the initial value of f?
  5. Where (if anywhere) is f increasing, where decreasing, and where constant?
  [To clarify what I'm looking for, here is my answer to (1):
  1. The domain of f is the set of all real numbers. The range of f is also the set of all real numbers, if m ≠ 0; however, if m = 0, then the range of f is {b}.
  Now you should answer (2)–(5) in a similar way.]
Exam 3:
- Date taken: May 15 or 16.
- Exercises from Section 3.5 (pages 243–246): 1, 3, 7, 9, 11, 13, 15, 17, 19, 27, 29, 33, 35, 37, 39, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 79, 81.
- Exercises from Section 3.6 (pages 252&253): 17, 19, 21, 23.
- Exercises from Section 5.1 (pages 357–359): 1, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 35, 37, 41, 43, 67, 69, 71, 73, 75.
- Exercises from Section 6.1 (pages 476–478): 23, 25, 27.
- Exercises from Section 6.2 (pages 488–490): 11, 19, 21, 27, 39, 41, 43.
- Exercises from Section 6.3 (pages 497&498):
  - 3, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53;
  - Optional, to practise with your calculator: 55, 57.
- Exercises from Section 6.4 (pages 513–515): 1, 7, 9, 11, 13, 15, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45.
- Exercises from Section 6.5 (page 525):
  - 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 31;
  - Optional, to practise with your calculator: 33, 35, 37.
- Exercises from Section 6.6 (pages 535–536): 2, 5, 7, 9, 11, 13, 15, 17, 19, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49.
- Additional extra-credit exercise: Following Example 5.1.6 on page 352 of the textbook, suppose that the cost of printing and delivering a newspaper for a quarter year is 20 dollars.
  1. Express the cost C (in dollars) of printing and delivering Q papers for a quarter as a function of either Q or the quarterly subscription price of p dollars. (Remember that Q = 159 000 − 2500p in this example.)
  2. Find the profit P = R − C (where R is the revenue pQ) as a function of either Q or p.
  3. What price will produce the maximum profit, and what quantity will be produced and sold at that price? (Show what numerical calculations you make or what equations you solve.)
Exam 4:
- Date taken: June 3 or 4.
- Exercises from Section 6.1 (pages 476–478): 15, 17, 31, 37, 39, 41, 59, 61, 65.
- Exercises from Section 6.7 (page 549–551): 29, 31, 33, 37, 39, 41, 43, 45.
- Exercises from Section 5.2 (pages 372–374): 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41.
- Exercises from Section 5.3 (pages 390–392): 7, 9, 11, 13, 15, 17, 19, 25, 27, 31, 33, 35, 37, 39, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61.
- Exercises from Section 5.4 (pages 400&401): 1, 15, 17, 19, 21, 23, 37, 39, 41, 43.
- Exercises from Section 5.5 (pages 412&413): 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 57, 59, 67, 69.
- Exercises from Section 5.6 (pages 431–434): 7, 9, 11, 13, 15, 17, 19, 21, 23, 31, 33, 39, 41, 43, 45, 47, 75, 77, 79.
- Exercises from the OpenStax textbook for Intermediate Algebra (Section ES33 only):
  - Exercises from Section 9.8 (page 977, PDF, DjVu): 363, 365, 367, 369, 371, 373, 375, 377.
  - Exercises from Section 7.6 (pages 730&731, PDF, DjVu): 339, 341, 343, 345, 355, 357, 363, 365, 367, 369.
- Extra credit: Notice that the polynomial x³ + x + 1 cannot be factored. Nevertheless, the equation x³ + x + 1 = 0 has a solution. Read about the cubic formula and use it to give an exact real solution to that equation, expressed using radicals.

That's it!

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