# Problem sets and quizzes

Almost every Thursday and Wednesday, there will be a quiz at the end of class, taken from an associated problem set. (However, there is no quiz in the first week of the course, and the last quiz is on June 2 Thursday or June 3 Friday.) Unless otherwise specified, all problems are from the 10th Edition of Algebra & Trigonometry written by Sullivan and published by Prentice-Hall (Pearson). (The two class sections will always get different quizzes.)

Here are the quizzes and their associated problem sets:

1. Quiz 1:
• Date taken: April 7 or 6.
• Extra-credit essay question: Explain your background in mathematics and what you are going to use this course for.
• Problems from Section 2.1 (pages 154–157):
• No additional work needed: 4, 15, 16;
• Show what numerical calculation you make or what equation you solve: 19, 21, 23, 27, 31, 37, 41;
• No additional work needed: 45, 46;
• Show what numerical calculation you make or what equation you solve: 63, 71.
• Problems from Section 2.2 (pages 164–167):
• No additional work needed: 1, 2;
• Show what numerical calculations you make: 13, 17;
• Show your table of values: 23, 29;
• Label which point is which: 31, 34, 35;
• No additional work needed: 41–48, 53–56;
• Show at least one intermediate step for each result: 61, 67, 71;
• Show what equation you solve: 77;
• No additional work needed (but do everything that is asked, which is more than in the answer in the back): 85.
• Problems from Section 2.3 (pages 178–182):
• Show what numerical calculations you make or what equations you solve: 13–19 odd;
• No additional work needed: 25, 26, 29–32;
• Show the slope of each line: 39, 45;
• Show at least one intermediate step for each (unless the line is vertical): 47, 51, 57, 61, 68, 69;
• No additional work needed: 74;
• Show at least one intermediate step: 79;
• No additional work needed, but some of these are trick questions: 85–88;
• Give a reason for each answer: 105, 107.
2. Quiz 2:
• Date taken: April 14 or 13.
• Problems from Section 12.1 (pages 854–858):
• No additional work needed: 1;
• Show what numerical calculations you make: 11;
• Show enough work that I can tell which method you used: 19, 21, 27, 31, 45, 47;
• Show what equation or equations you solve: 65, 73;
• No additional work needed: 88.
• Problems from Section 3.1 (pages 210–213):
• No additional work needed: 1, 3, 4, 8, 31, 35, 36;
• Show what calculation you make for each part: 43, 49;
• Show what equations or inequalities you solve, if any: 51, 53, 55, 59, 61;
• Show what calculation you make for each part: 67, 75;
• Show what calculation you make or what equation you solve: 77, 95.
• Problems from Section 3.2 (pages 218–223):
• No additional work needed: 5, 11, 12, 14–17;
• Show what calculation you make or what equation you solve for each part: 25, 27;
• No additional work needed: 41;
• Extra credit: Give a reason for your answer to the first question: 42;
• No additional work needed: 43, 44.
3. Quiz 3:
• Date taken: April 21 or 20.
• Problems from Section 3.3 (pages 232–236):
• No additional work needed: 2, 3, 5, 13–24, 29–36;
• Show what calculations you make or what equations you check: 37, 39, 43, 47;
• Show what calculations you make or what equations you solve: 65, 67, 71.
• Problems from Section 3.6 (pages 263–266): Show at least one intermediate step for each part (except for 13.a): 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):
• No additional work needed: 2, 4, 8, 9, 13, 18, 19.
• Show what calculations you make to check: 21–27 odd;
• No additional work needed: 33, 34;
• Show what equations you solve or what numerical calculations you make: 37, 47, 49.
• Additional extra-credit problems: Consider a linear function f(x) = mx + b. Answer these questions about the function with generic answers that may vary with 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?
4. Quiz 4:
• Date taken: April 28 or 27.
• Problems from Section 3.4 (pages 244–247):
• No additional work needed: 1, 2, 11–26;
• Show what numerical calculations you make: 27, 29;
• Show at least what equations you solve for part B: 31–36;
• No additional work needed: 43–46;
• Show what numerical calculation you make: 49;
• Optional (using a graphing calculator, or by hand using at least x = −2, −1, −1/2, 0, 1/2, 1, 2): 68, 69.
• Problems from Section 6.1 (pages 408–410):
• No additional work needed: 1, 2, 3;
• Show one intermediate step for each part: 9, 11, 15, 19;
• Show what equations or inequalities you solve, if any, for each domain and show one other intermediate step for each part: 25, 27, 29, 33;
• Show what equation you solve: 55, 56.
• Problems from Section 6.2 (pages 419–423):
• No additional work needed: 3, 4, 7, 9, 21–26;
• Show at least one intermediate step in each direction: 37, 39, 43;
• No additional work needed: 45–50;
• The graphs are optional, but show what equation you solve: 53, 55, 57, 63–69 odd;
• No additional work needed: 77–82;
• Extra credit: Also explain why your restriction makes the function one-to-one: 90.
5. Quiz 5:
• Date taken: May 5 or 4.
• Problems from Section 3.5 (pages 256–260):
• No additional work needed: 3, 5–26;
• Show both intermediate formulas: 27, 29;
• No additional work needed: 31–36;
• Be sure to show all stages, including the untransformed original: 39, 43, 45, 47, 49, 55;
• No additional work needed: 63, 64, 87, 88.
• Problems from Section 4.3 (pages 299–302):
• No additional work needed: 1–4, 12–20;
• Show the intermediate steps in the graph by transformations: 21, 23;
• Show the form f(x) = a(x − h)2 + k, and show the intermediate steps in the graph by transformations: 25, 27;
• State the vertex and intercepts, and show what numerical calculations you make or what equations you solve to find them: 33, 39, 43, 45;
• Show at least one intermediate step: 51, 53;
• Show what numerical calculations you make: 57, 59;
• No additional work needed: 97.
• Problems from Section 4.4 (pages 307–311):
• No additional work needed: 1;
• Show what numerical calculations you make or what equations or inequalities you solve: 3–9 odd, 11.a–c, 13, 15, 17;
• No additional work needed: 31.
• Additional extra-credit problem: Following Example 4.4.1 on pages 302–304, suppose that the cost of producing x calculators is C = 200000 + 50x.
1. What is 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 will this maximum profit be?
6. Quiz 6:
• Date taken: May 12 or 11.
• Problems from Section 6.3 (pages 434–439):
• No additional work needed: 1, 13, 14;
• Optional, to practise with your calculator: 19–25 odd;
• Show what calculations you make to check: 27–33 odd;
• No additional work needed: 35–42;
• Show the graph before transforming as well: 43, 45, 49, 51, 55, 57, 59;
• No additional work needed: 63;
• Show at least one intermediate step for each: 65, 69–77 odd, 81, 83;
• No additional work needed: 89–92;
• Extra credit: 124.
• Problems from Section 6.4 (pages 448–452):
• No additional work needed: 1.a, 9, 11–26;
• Show at least one intermediate step: 27–37 odd;
• Show what equations or inequalities you solve: 39, 43;
• Optional, to practise with your calculator: 51–57 odd;
• No additional work needed: 65–72;
• Show what equations or inequalities you solve: 73, 79, 83, 86;
• Show at least one intermediate step for each: 89–111 odd;
• Show what numerical calculations you make: 119, 129–132.
• Problems from Section 6.5 (pages 459&460):
• No additional work needed: 7, 11, 13, 15, 17;
• Show at least one intermediate step for each: 19–27 odd, 37;
• No additional work needed: 39;
• Show at least one intermediate step for each: 41–57 odd, 61–69 odd;
• Optional, to practise with your calculator: 71–77 odd;
• Show an intermediate step for each: 87, 91, 97.
7. Quiz 7:
• Date taken: May 19 or 18.
• Problems from Section 6.6 (pages 465–467):
• No additional work needed: 1, 2;
• Show at least one intermediate step for each: 5–9, 13–25 odd, 31, 35;
• Extra credit: 40;
• Show at least one intermediate step for each: 41, 45, 53, 57.
• Problems from Section 6.7 (pages 474–477): Show what numerical calculations you make or what equations you solve: 1, 2, 7, 11, 13, 15, 21, 31, 32, 41, 43.
• Problems from Section 6.8 (pages 486–488): Show what numerical calculations you make or what equations you solve: 1, 3, 5.b&c, 7.b, 9–21 odd, 23.a,c,d.
8. Quiz 8:
• Date taken: May 26 or 25.
• Problems from Section 5.1 (pages 338–342):
• No additional work needed: 1, 2, 3, 6, 12, 17–24;
• Show the graph before transforming as well: 29, 31, 35;
• Use 1 as the leading coefficient and show the factored form as an intermediate step: 43, 45, 49;
• Show what numerical calculation you make or what equation you solve to find the leading coefficient: 51;
• No additional work needed, and skip part c: 57–60, 67, 68;
• No additional work needed: 69–72;
• Skip Step 4 (turning points), but be sure to write out your results for Steps 1 through 3: 81, 82, 87, 88.
• Problems from Section 5.5 (pages 386–389):
• No additional work necessary: 1–4;
• Show what numerical calculations you make: 11, 15, 19;
• No additional work necessary: 33–38;
• Show how you check each potential root/zero: 45, 51, 53;
• Show the polynomial in factored form: 57, 59, 65, 67, 93, 99, 101.
• Extra credit: Show each approximation along the way (m1, m2, m3, etc) and what numerical calculations you make to find and test them: 119.
• Problems from Section 5.6 (pages 394&395):
• No additional work needed: 1, 2, 7–16;
• Use 1 as the leading coefficient, and show the expression before and after expanding: 17, 19, 21;
• Show your factoring or division: 23, 27, 33, 37;
• No additional work needed: 44–47.
9. Quiz 9:
• Date taken: June 2 or 3.
• Problems from Section 5.2 (pages 350–353):
• No additional work needed: 2, 3, 4;
• Show at least one intermediate step: 15–19, 23;
• No additional work necessary: 27, 31;
• Show the graph before transforming as well: 35;
• Show what numerical calculations you make or what equations you solve: 45, 49, 50.
• Problems from Section 5.3 (pages 365–368):
• No additional work needed: 1, 5;
• Show what numerical calculations you make or what equations you solve: 7–11, 17–23 odd, 31, 33, 35;
• No additional work needed: 51–54.
• Problems from Section 5.4 (pages 372–375):
• No additional work needed: 3;
• Show the graph that you use: 9, 13, 15;
• Show what test calculations you make, what multiplicities you use, or otherwise enough work that I can tell what method you use: 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.)
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