## Corrections

Early printings of the course guide did not include sample responses for each modeling prompt. To access these, visit the modeling prompt pages online (link).

Course Guide. In the Scope and Sequence, Unit 5 contains 13 days and no optional lessons. The total number of days in Algebra 2 is 124.

In the Course Guide, under Scope and Sequence, the Pacing Guide for Algebra 2 Unit 3 was edited to remove lesson 13 from the list of optional lessons.

Unit 1, Lesson 1, Practice Problem 1. The sample solution to the first question should use 20 instead of 25.

Unit 1, Lesson 5, Lesson Synthesis. The indexing for each of the explicit formulas are now corrected to use \(n-1\) instead of \(n\). For example, the first geometric sequence is now \(f(n) = 2 \boldcdot 3^{n-1}\) instead of \(f(n) = 2 \boldcdot 3^n\).

Unit 1, Lesson 6, Practice Problem 3. Choice 4 is updated to \(d(n) = d(n-1)+n\) because the lesson uses \(n=0\) to begin the sequence.

Unit 1, Lesson 9, Activity 3. In the solution for part 3 of the Are You Ready for More?, the fourth value is 1.61803406.

Unit 1, Lesson 10, Activity 2. The solution for the last equation of the second question is updated to apply for \(n \geq 0\).

Unit 1, Lesson 11, Practice Problem 5. Updated solution to use \(T(n)\).

Unit 1, End of Unit Assessment, Item 1. The solutions each gave a recursive formula for \(n \geq 1\), but should refer to \(n \geq 2\)

Unit 1, End of Unit Assessment, Item 2. The recursive definition for \(f\) in the statement should use \(n \ge 2\).

Unit 2, Lesson 2, Cool-down. The last question is corrected to begin, "After the 4th year, \$200 is added to the account."

Unit 2, Lesson 8, Activity 3 Synthesis. In the second list item, change "Only changing the exponent to something 6 or higher would. . ." to "Changing the exponent to 6 would . . ."

Unit 2, Lesson 8, Lesson Summary. The value in the table for the row labeled -10 and the column \(\text{-}20x^2\) should be negative.

Unit 2, Lesson 8, Practice Problem 5. In the solution for b, the constant term is 12.

Unit 2, Lesson 10, Activity 2. In the solution for 1, C is "...larger in the negative direction." and D is "...larger in the positive direction."

Unit 2, Lesson 13, Activity 4. For question 4, the cubic in standard form is \(\boxed{\phantom{30}}x^3 + 11x^2 - 17x + 6\)

Unit 2, Lesson 14, Practice Problem 6. Change the \(\text-15x\) inside the table to \(\text-5x\), and in the answer, change \(\text-3x\) to \(7x\).

Unit 2, Lesson 16, Activity 2. In the solution to 1, the height associated with radius 8 is 2.2.

Unit 2, Lesson 18, Practice Problem 2. The solution uses the line \(y = \text{-}3\).

Unit 2, Lesson 19. Change \(p(x)\) to \(q(x)\) throughout the lesson. Specifically:

- activity 2: narrative (2 places), task statement (2 places)
- activity 3: narrative (1 place), task statement (1 place), student response (3 places), synthesis (3 places)
- cool-down: task statement (1 place)

Unit 2, Lesson 19, Warm-up. The statement used the value 2772 instead of 2775.

Unit 2, Lesson 19, Practice Problem 4. Added to the problem statement: "(Note: Some of the answer choices are not used and some answer choices are used more than once.)"

Unit 2, Lesson 19, Practice Problem 5. The statement is updated to use \(f(\text{-}3)=0\) and \(f(1) = 0\). In the solution, the last term is \((x+3)\).

Unit 2, Lesson 19, Practice Problem 8. Updated one of the choices to "The value of the expression is 99." instead of getting closer and closer to the value.

Unit 2, Lesson 21, Activity 3. The solution to 3 is about 23 ohms.

Unit 2, Lesson 22, Warm-up. The statement incorrectly had a 1 in the numerator instead of a 3. The solution suggestions also mention \(x(x+2)\) instead of \(x(x-2)\). These have been corrected.

Unit 2, Lesson 23, Practice Problem 2. In the solution, change \(x^2+2x+1\) to \(2x^2+4x+2\).

Unit 2, Lesson 24, Practice Problem 6. Choice 4 is changed to \(2(3x^2 + 6x + 4)\).

Unit 3. Learning goals and learning targets updated from pilot versions.

Unit 3, Lesson 8, Activity 4. In the solution for question 2, \(m = 8\).

Unit 3, Lesson 3, Activity 3. The image in the launch is updated to show +1.

Unit 3, Lesson 13, Activity 3. The solutions to parts 2 and 3 of Are You Ready for More? are updated to \(\text-6+i-9j+8k\) and \(\text-6+7i+9j+4k\), respectively.

Unit 3, Lesson 14, Activity 2. The Are You Ready for More? solution to 1f is updated to \(\text{-}4 + \text{-}4i\)

Unit 3, Lesson 18, Activity 3. Row 3 for partner B is updated to \(2z^2+6z=\text{-}19\) so that the solutions match.

Unit 3, Lesson 19, Activity 1. For the first function, \(f(x)=0\) when \(x = 0, \text{-}2\)

Unit 3, Lesson 19, Practice Problem 2. Updated the image to label the axes correctly.

Unit 4, Lesson 2, Cool down. The sample response for question 2 is corrected to correctly calculate the value as 182.25.

Unit 4, Lesson 3, Practice Problem 1. C and D are included as correct answers.

Unit 4, Lesson 6, Activity 2. Data Card 1 is updated to "The rate of increase from 0 to 1.5 is 337.5%."

Unit 4, Lesson 8, Practice Problem 3. Corrected the solution from -5 to -4 as the first entry in the top row.

Unit 4, Lesson 8, Practice Problem 7. The solution to the second question should refer to 0.09375 picograms instead of 0.9375 picograms.

Unit 4, Lesson 10, Activity 1. For the explanation in the student response, the second bullet point had the 1 and 0 reversed. This is fixed.

Unit 4, Lesson 14, Practice Problem 2. The solution is \(d = \text{-}2\) instead of \(d = 0\).

Unit 4, Lesson 18, Practice Problem 4. The horizontal line \(y = 1,\!000\) should be used instead of \(y = 100\).

Unit 4, Mid-Unit Assessment, Item 7. The solution for the last part of the question used the incorrect initial value for the equation. This has been corrected.

Unit 4, End-of-Unit Assessment, Item 7. The equation should be \(A(d) = 100 \boldcdot e^{0.25d}\). The question and solutions are corrected.

Unit 5, Lesson 1, Lesson Summary. Corrected 32 to 36 in the sentence, "What did multiplying by 45 and adding 36 do to the graph?"

Unit 5, Lesson 2, Practice Problem 2. Updated solutions for parts b and c to \(B(30)= 375\) and \(B(t) = P(t)+25\) respectively.

Unit 5, Lesson 2, Practice Problem 3. Updated solution for part b to indicate that the graph of \(h\) is shifted to the left.

Unit 5, Lesson 2, Practice Problem 5. Updated the problem statements to better indicate which line is being translated (from given line to the line containing the points). Updated solution to part a to reflect this change (left instead of right).

Unit 5, Lesson 3, Practice Problem 3. The correct point for Han is \((1,85)\).

Unit 5, Lesson 5, Activity 3. The blackline master is updated so that card N has 2 in the \(y\) column to match the graph.

Unit 5, Lesson 5, Practice Problem 7. Adjusted the graph back an hour to begin at \((0.5, 80)\) so that the translation fits on the given axes.

Unit 5, Lesson 7, Activity 1. The statement (and solution) had the last part of the table listed in the wrong order. This has been corrected to ask for translations first, then reflections.

Unit 5, Lesson 7, Lesson Synthesis. The order of the transformations for the third function has been corrected to do translations before reflection.

Unit 5, Lesson 7, Practice Problem 2. The first question should have \(g(x) = -e^x + 2.7\)

Unit 5, Lesson 7, Practice Problem 3. Correct answers should open down with a negative leading coefficient. A possible response is \(y = \text{-}(x-2)^2 - 3\).

Unit 5, Lesson 8, Practice Problem 5. Changed \(f(0)\) to 0 in the table.

Unit 5, Lesson 9, Practice Problem 1. The solution to b should be \(k = 0.625\) and the solution to d should be \(k = \text-\frac{1}{2}\).

Unit 5, Lesson 10, Practice Problem 2. The solution is corrected to \(x = 0\) and \(x = \text{-}2\).

Unit 5, Lesson 10, Practice Problem 10. The solution is corrected so that \(r(t)\) starts at 212.

Unit 5, Lesson 11, Practice Problem 6. The graph is shifted right first, then compressed. The graph is compressed horizontally by a factor of \(\frac{1}{3}\).

Unit 6, Lesson 1, Practice Problem 5. Option d is updated to \(k(x) = \frac{3x^2 - 16x + 12}{x-6}\) and choice 6 is updated to, "The graph approaches \(y = 3x+2\)."

Unit 6, Lesson 2, Practice Problem 1. Updated choices C and D. C: \(\sin(C) = \frac{6}{10}\) and D: \(\cos(C) = \frac{8}{10}\).

Unit 6, Lesson 3, Practice Problem 7. Exchanged the names of side lengths \(d\) and \(e\) so that \(d\) is across from angle \(D\) and \(e\) is across from angle \(E\).

Unit 6, Lesson 4, Practice Problem 5. Added "\(BC\) is shorter than \(AC\)" to the prompt.

Unit 6, Lesson 7, Practice Problem 2. The solutions should use \(100+85\sin(\theta)\) for the height. This also updates the estimates.

Unit 6, Lesson 9, Cool-down. The \(x\)-axis is corrected to show \(\frac{5\pi}{6}\).

Unit 6, Lesson 11, Practice Problem 5. The solution to part d now correctly has a 2 in the denominator instead of a 4.

Unit 6, Lesson 12, Practice Problem 6. The second and third questions are updated to 12 and 24 hours respectively.

Unit 6, Lesson 12, Practice Problem 7. The solution to c is corrected to, "...translated 6 units to the left."

Unit 6, Lesson 17, Activity 1. In the activity synthesis, corrected the first question to, "...and then translate it left 1 and down 3..."

Unit 6, Lesson 19, Practice Problem 2. Added D as a correct response.

Unit 6, Lesson 19, Practice Problem 5. The solution points are S and T instead of U and V.

Unit 7, Lesson 1, Practice Problem 6. Added D as a correct response.

Unit 7, Lesson 3, Activity 3. The sample solutions are updated. 2a is 14.6 square meters and 2d is 8.2 square meters.

Unit 7, Lesson 6, Lesson Synthesis. The 3rd bullet should say that 4.5 is the mean.

Unit 7, Lesson 10, Learning Target. Corrected to "I know that a smaller margin of error means less variability, ..."

Unit 7, Lesson 13, Practice Problem 4. Removed the instructions to round from the question.

Unit 7, Lesson 14, Practice Problem 3. Question b corrected to ask about more extreme than 2.5. Solution to b updated to 0.0139 and solution to c updated to match these changes.

Unit 7, Lesson 14, Practice Problem 4. Updated part b to read, "...difference at least as great as the difference in means between the control and treatment groups?" Added additional tick marks on the \(y\)-axis of the image. Updated solution to part b to \(\frac{46}{100}\).

Unit 7, Lesson 14, Practice Problem 6. Corrected mention of "mean lengths" to "mean weights."

Unit 7, Lesson 14, Activity 3. Solutions are updated to use the correct area of 0.0084 for questions 2 through 4.

Unit 7, Lesson 15, Practice Problem 3. The solution to part e is updated to 0.005.

Unit 7, End of Unit Assessment, Problem 6. Corrected the Tier 1 response to show the correct decimal places in the multiplication.

## Lesson Numbering for Learning Targets

In some printed copies of the student workbooks, we erroneously printed a lesson number instead of the unit and lesson number. This table provides a key to match the printed lesson number with the unit and lesson number.

Lesson Number | Unit and Lesson | Lesson Title |
---|---|---|

1 | 1.1 | A Towering Sequence |

2 | 1.2 | Introducing Geometric Sequences |

3 | 1.3 | Different Types of Sequences |

4 | 1.4 | Using Technology to Work with Sequences |

5 | 1.5 | Sequences are Functions |

6 | 1.6 | Representing Sequences |

7 | 1.7 | Representing More Sequences |

8 | 1.8 | The $n^{\text{th}}$ Term |

9 | 1.9 | What’s the Equation? |

10 | 1.10 | Situations and Sequence Types |

11 | 1.11 | Adding Up |

12 | 2.1 | Let’s Make a Box |

13 | 2.2 | Funding the Future |

14 | 2.3 | Introducing Polynomials |

15 | 2.4 | Combining Polynomials |

16 | 2.5 | Connecting Factors and Zeros |

17 | 2.6 | Different Forms |

18 | 2.7 | Using Factors and Zeros |

19 | 2.8 | End Behavior (Part 1) |

20 | 2.9 | End Behavior (Part 2) |

21 | 2.10 | Multiplicity |

22 | 2.11 | Finding Intersections |

23 | 2.12 | Polynomial Division (Part 1) |

24 | 2.13 | Polynomial Division (Part 2) |

25 | 2.14 | What Do You Know About Polynomials? |

26 | 2.15 | The Remainder Theorem |

27 | 2.16 | Minimizing Surface Area |

28 | 2.17 | Graphs of Rational Functions (Part 1) |

29 | 2.18 | Graphs of Rational Functions (Part 2) |

30 | 2.19 | End Behavior of Rational Functions |

31 | 2.20 | Rational Equations (Part 1) |

32 | 2.21 | Rational Equations (Part 2) |

33 | 2.22 | Solving Rational Equations |

34 | 2.23 | Polynomial Identities (Part 1) |

35 | 2.24 | Polynomial Identities (Part 2) |

36 | 2.25 | Summing Up |

37 | 2.26 | Using the Sum |

38 | 3.1 | Properties of Exponents |

39 | 3.2 | Square Roots and Cube Roots |

40 | 3.3 | Exponents That Are Unit Fractions |

41 | 3.4 | Positive Rational Exponents |

42 | 3.5 | Negative Rational Exponents |

43 | 3.6 | Squares and Square Roots |

44 | 3.7 | Inequivalent Equations |

45 | 3.8 | Cubes and Cube Roots |

46 | 3.9 | Solving Radical Equations |

47 | 3.10 | A New Kind of Number |

48 | 3.11 | Introducing the Number $i$ |

49 | 3.12 | Arithmetic with Complex Numbers |

50 | 3.13 | Multiplying Complex Numbers |

51 | 3.14 | More Arithmetic with Complex Numbers |

52 | 3.15 | Working Backwards |

53 | 3.16 | Solving Quadratics |

54 | 3.17 | Completing the Square and Complex Solutions |

55 | 3.18 | The Quadratic Formula and Complex Solutions |

56 | 3.19 | Real and Non-Real Solutions |

57 | 4.1 | Growing and Shrinking |

58 | 4.2 | Representations of Growth and Decay |

59 | 4.3 | Understanding Rational Inputs |

60 | 4.4 | Representing Functions at Rational Inputs |

61 | 4.5 | Changes Over Rational Intervals |

62 | 4.6 | Writing Equations for Exponential Functions |

63 | 4.7 | Interpreting and Using Exponential Functions |

64 | 4.8 | Unknown Exponents |

65 | 4.9 | What is a Logarithm? |

66 | 4.10 | Interpreting and Writing Logarithmic Equations |

67 | 4.11 | Evaluating Logarithmic Expressions |

68 | 4.12 | The Number $e$ |

69 | 4.13 | Exponential Functions with Base $e$ |

70 | 4.14 | Solving Exponential Equations |

71 | 4.15 | Using Graphs and Logarithms to Solve Problems (Part 1) |

72 | 4.16 | Using Graphs and Logarithms to Solve Problems (Part 2) |

73 | 4.17 | Logarithmic Functions |

74 | 4.18 | Applications of Logarithmic Functions |

75 | 5.1 | Matching up to Data |

76 | 5.2 | Moving Functions |

77 | 5.3 | More Movement |

78 | 5.4 | Reflecting Functions |

79 | 5.5 | Some Functions Have Symmetry |

80 | 5.6 | Symmetry in Equations |

81 | 5.7 | Expressing Transformations of Functions Algebraically |

82 | 5.8 | Scaling the Outputs |

83 | 5.9 | Scaling the Inputs |

84 | 5.10 | Combining Functions |

85 | 5.11 | Making a Model for Data |

86 | 6.1 | Moving in Circles |

87 | 6.2 | Revisiting Right Triangles |

88 | 6.3 | The Unit Circle (Part 1) |

89 | 6.4 | The Unit Circle (Part 2) |

90 | 6.5 | The Pythagorean Identity (Part 1) |

91 | 6.6 | The Pythagorean Identity (Part 2) |

92 | 6.7 | Finding Unknown Coordinates on a Circle |

93 | 6.8 | Rising and Falling |

94 | 6.9 | Introduction to Trigonometric Functions |

95 | 6.10 | Beyond $2\pi$ |

96 | 6.11 | Extending the Domain of Trigonometric Functions |

97 | 6.12 | Tangent |

98 | 6.13 | Amplitude and Midline |

99 | 6.14 | Transforming Trigonometric Functions |

100 | 6.15 | Features of Trigonometric Graphs (Part 1) |

101 | 6.16 | Features of Trigonometric Graphs (Part 2) |

102 | 6.17 | Comparing Transformations |

103 | 6.18 | Modeling Circular Motion |

104 | 6.19 | Beyond Circles |

105 | 7.1 | Being Skeptical |

106 | 7.2 | Study Types |

107 | 7.3 | Randomness in Groups |

108 | 7.4 | Describing Distributions |

109 | 7.5 | Normal Distributions |

110 | 7.6 | Areas in Histograms |

111 | 7.7 | Areas under a Normal Curve |

112 | 7.8 | Not Always Ideal |

113 | 7.9 | Variability in Samples |

114 | 7.10 | Estimating Proportions from Samples |

115 | 7.11 | Reducing Margin of Error |

116 | 7.12 | Estimating a Population Mean |

117 | 7.13 | Experimenting |

118 | 7.14 | Using Normal Distributions for Experiment Analysis |

119 | 7.15 | Questioning Experimenting |

120 | 7.16 | Heart Rates |