# Problem sets and exams

Almost every other Wednesday, starting on July 26, 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 Wednesday, but this page is not about that.) Unless otherwise specified, all problems in the problem sets are from the 10th Edition of Algebra & Trigonometry written by Sullivan and published by Prentice-Hall (Pearson).

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

1. Exam 1:
• Date taken: July 26 Wednesday.
• Review problems: from the Chapter 1 Review (pages 145&146): 2, 3, 5, 10, 28, 30, 36, 40, 41, 44, 46, 49.
• Problems from Section 2.1 (pages 154–157): 4, 15, 16, 19, 21, 23, 27, 31, 37, 41, 45, 46, 63, 71.
• Problems from Section 2.2 (pages 164–167): 1, 2, 7, 13, 17, 23, 29, 31, 34, 35, 41–48, 53–56, 61, 67, 71, 77, 85.
• Problems from Section 2.3 (pages 178–182): 2, 13–19 odd, 25, 26, 29–32, 39, 45, 47, 51, 57, 61, 68, 69, 74, 79, 85–88 (some of these are trick questions), 105, 107.
• Problems from Section 12.1 (pages 854–858): 1, 11, 19, 21, 27, 31, 45, 47, 65, 73, 88.
• Problems from Section 3.1 (pages 210–213): 1, 3, 4, 8, 31, 35, 36, 43, 49, 51, 53, 55, 59, 61, 67, 75, 77, 95.
• Problems from Section 3.2 (pages 218–223): 5, 11, 12, 14–17, 25, 27, 31, 41, 43, 44.
• Extra-credit essay question: Explain your background in mathematics and what you are going to use this course for.
2. Exam 2:
• Date taken: August 9 Wednesday.
• Problems from Section 3.3 (pages 232–236): 2, 3, 5, 13–24, 29–36, 37, 39, 43, 47, 65, 67, 71.
• Problems from Section 3.6 (pages 263–266): 1.a–c, 3.a, 5, 11.a&b, 13, 15, 19.a, 22.a–c, 24.
• Problems from Section 4.1 (pages 280–283): 2, 4, 8, 9, 13, 18, 19, 21–27 odd, 33, 34, 37, 47, 49.
• Problems from Section 3.4 (pages 244–247): 1, 2, 10, 11–26, 27, 29, 31–36, 43–46, 49.
• Problems from Section 6.1 (pages 408–410): 1, 2, 3, 9, 11, 15, 19, 25, 27, 29, 33, 55, 56.
• Problems from Section 6.2 (pages 419–423):
• 3, 4, 7, 8, 9, 12, 21–26, 37, 39, 43, 45–50;
• You may skip the graphs on these: 53, 55, 57, 63–69 odd;
• 77–82, 90.
• Additional extra-credit problems: 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. Where (if anywhere) is f increasing, where decreasing, and where constant?
5. Where (if anywhere) does have f local extrema, and what are their values?
[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.]
3. Exam 3:
• Date taken: August 23 Wednesday.
• Problems from Section 3.5 (pages 256–260):
• 3, 5–26, 27, 29, 31–36;
• Be sure to show all stages, including the untransformed original: 39, 43, 45, 47, 49, 55;
• 63, 64, 87, 88.
• Problems from Section 4.3 (pages 299–302): 1–4, 12–20, 21, 23, 25, 27, 33, 39, 43, 45, 51, 53, 57, 59, 97.
• Problems from Section 4.4 (pages 307–311): 1–9 odd, 11.a–c, 13, 15, 17, 31.
• Problems from Section 6.3 (pages 434–439):
• 1, 13, 14;
• Optional, to practise with your calculator: 19–25 odd;
• 27–33 odd, 35–42, 43, 45, 49, 51, 55, 57, 59, 63, 65, 69–77 odd, 81, 83, 89–92.
• Problems from Section 6.4 (pages 448–452):
• 1.a, 9, 11–26, 27–37 odd, 39, 43;
• Optional, to practise with your calculator: 51–57 odd;
• 65–72, 73, 79, 83, 86, 89–111 odd, 119, 129–132.
• Problems from Section 6.5 (pages 459&460):
• 7, 11, 13, 15, 17, 19–27 odd, 37–57 odd, 61–69 odd;
• Optional, to practise with your calculator: 71–77 odd;
• 87, 91, 97.
• Problems from Section 6.6 (pages 465–467): 1, 2, 5–9, 13–25 odd, 31, 35, 39, 41, 45, 53, 57.
• Additional extra-credit problem: Following Example 4.4.1 on pages 302–304, suppose that the cost of producing x calculators is C = 200 000 + 50x dollars.
1. Find the profit P = R − C as a function of either x or the price p.
2. 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.)
3. What is this maximum profit?
4. Exam 4:
• Date taken: September 13 Wednesday.
• Problems from Section 6.7 (pages 474–477): 1, 2, 7, 11, 13, 15, 21, 31, 32, 41, 43.
• Problems from Section 6.8 (pages 486–488): 1, 3, 5.b&c, 7.b, 9–21 odd, 23.a,c,d.
• Problems from Section 3.4 (pages 244–247): use a graphing calculator, or make a table of values using at least x = −2, −1, −1/2, 0, 1/2, 1, 2): 68, 69.
• Problems from Section 5.1 (pages 338–342):
• 1, 2, 3, 6, 12, 17–24, 29, 31, 35;
• Use 1 as the leading coefficient: 43, 45, 49;
• 51, 57–60, 67–72;
• Skip Step 4 (turning points): 81, 82, 87, 88.
• Problems from Section 5.5 (pages 386–389):
• 1–4, 11, 15, 19, 33–38, 45, 51, 53, 57, 59, 65, 67, 93, 99, 101.
• Problems from Section 5.6 (pages 394&395):
• 1, 2, 7–16;
• Use 1 as the leading coefficient: 17, 19, 21;
• 23, 27, 33, 37, 44–47.
• Problems from Section 5.2 (pages 350–353): 2, 3, 4, 15–19, 23, 27–32, 35, 45, 47, 49, 50.
• Problems from Section 5.3 (pages 365–368): 1, 5, 7–11, 17–23 odd, 31, 33, 35, 51–54.
• Problems from Section 5.4 (pages 372–375): 1, 5–8, 9, 13, 15, 19, 21, 23, 27, 29, 33, 37, 39, 41, 43.
• Additional extra-credit problem: Solve the inequality f(x) < 0, where f is the piecewise-defined function from Exercise 3.4.36 on page 245 of the textbook. (Show at least one intermediate step for each number in your final answer, or show a complete graph that matches your answer.)
That's it!
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