Cherokee County Schools

Mathematics Course of Study

Algebra II with Trigonometry

Algebra II with Trigonometry focuses on problem-solving skills that use a variety of methods to encourage the development of improved communication skills and foster a deeper understanding of the content area. In order to provide students with an appreciation of the power of algebra, applications involving real-life situations are incorporated throughout the course. The use of appropriate technology is also encouraged.

Algebra II with Trigonometry is required for all students seeking the Alabama High School Diploma with Advanced Academic Endorsement. Although this course is valuable for all students, it is strongly recommended for students who intend to pursue postsecondary studies. Prerequisites for the course are Algebra I and Geometry. Credit cannot be awarded for both Algebra II with Trigonometry and Algebra II.

Please use this document to plan mathematics lessons. The content standards define what students should know and be able to do at the conclusion of the course or grade. The order in which standards are listed within a course or grade is not intended to convey a sequence for instruction. Each standard is correlated with textbooks adopted by Cherokee County Schools. Bullets denote content that is related to the standards and required for instruction. Examples clarify certain components of content standards or bullets and are not exhaustive. Technology is integrated throughout the document. Statewide student assessments are not addressed since standards for Algebra II with Trigonometry are above the requirements for the Alabama High School Graduation Exam.

*ALABAMA COURSE OF STUDY*	*SAXON ALGEBRA 2*	*PRENTICE HALL* *ALGEBRA 2*
Review and Refresh	Lessons 2,3,4,5,6,7,8,9,10,11,12,13,14 19,24,25,26,27,33,47,53,79,80 82,83,87,88,91,96,97,98,123 124,125	Sections 1.1,1.2,1.3,2.2,2.3,3.1,5.4 9.1,12.3
1. Determine the relationships of subsets of complex numbers. Example: using Venn diagrams or tree diagrams to show how subsets of complex numbers are related	Lessons 117,122	Section 5.6
2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value. Examples: simplifying, (4-2i)², and	Lessons A,20,28,32,46,48,51,62,64 67,73,77,81,104,117	Section 5.6
*ALABAMA COURSE OF STUDY*	*SAXON ALGEBRA 2*	*PRENTICE HALL* *ALGEBRA 2*
3. Analyze families of functions, including shifts, reflections, and dilations of y = (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer), y = x² (quadratic), y = a^x (exponential), and y = log_ax (logarithmic). Example: comparing the graphs of y = 2^x, y = 2^x + 1, y = 2^x ^{+ 1}, and y = -2^x · Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains Example: finding the domain of y = or y = Identifying real-world situations corresponding to families of functions.	Lessons 43,68,85,94,94,100,102,113 115,118	Sections 2.1,2.5,2.6,5.1-3,7.8 8.1-3,9.2-3
4. Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions. · Using the zero product property, completing the square, and the quadratic formula · Deriving the quadratic formula	Lessons 4,5,23,38,39,40,45,48,50,55 58,63,70,71,77,85,86,93,95 96,100,105	Sections 5.5,5.7-8,6.2-6 9.3,9.6
5. Identify the characteristics of quadratic functions from their roots, graphs, or equations. · Generating an equation when given its roots or graph · Graphing a function when given its equation Examples: graphing equations of the form y = a(x-h)² + k; graphing equations of the form y = ax² + bx + c · Determining the maximum or minimum values of quadratic functions both graphically and algebraically Applying functions to real-world problems	Lessons 38,39,45,50,58,63,71,85,86 93,95,96,100,105,120	Sections 5.1-3 7.8
*ALABAMA COURSE OF STUDY*	*SAXON ALGEBRA 2*	*PRENTICE HALL* *ALGEBRA 2*
6. Perform operations on functions, including addition, subtraction, multiplication, division, and composition. · Determining the inverse of a function or a relation · Performing operations on polynomial and rational expressions containing variables Example: simplifying+ · Constructing graphs by analyzing their functions as sums, differences, or products	Lessons A,2,3,8,11,16,25,26,27,28 30,33,36,39,43,75,84,94 102,103,108,115	Sections 2.6 7.6-7 8.2-3 9.2,4-5
7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions. Example: solving x²- 8x > -12, 3^x = 81, 2 sin²x + sin x = 0, or log_x 2 = 5 · Solving equations using laws of exponents, including rational and irrational exponents · Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation	Lessons 6,7,38,39,40,45,48,50,55,58 63,70,71,77,86,93,95,96,100 105,115	Sections 1.4-5 2.6, 5.6-8 7.1-5 8.4-6 9.6, 14.2
*ALABAMA COURSE OF STUDY*	*SAXON ALGEBRA 2*	*PRENTICE HALL* *ALGEBRA 2*
8. Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices. Example: solving a system of linear equations using augmented matrices and row operations, matrix operations of a graphing calculator, or substitution · Evaluating the determinant of a 2x2 or 3x3 matrix Solving word problems involving real-life situations.	Lessons 13,15,17,21,23,29,34,52,59 61,65,74,76,84,85,86,90,92 95,97,100,101,111,115,120	Sections 3.2-3 4.1-3,5-8
9. Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx). · Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations Example: solving problems involving harmonic motion · Determining specific unit circle coordinates associated with special angles	Lessons 43 defines Must be supplemented	Sections 2.6 4.4 13.1-7
10. Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines. · Deriving formulas for Law of Sines and Law of Cosines · Determining area of oblique triangles	Lessons 43,44,49 Must be supplemented	Sections 14.3-5
*ALABAMA COURSE OF STUDY*	*SAXON ALGEBRA 2*	*PRENTICE HALL* *ALGEBRA 2*
11. Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.	Lessons 43,44 Add reciprocal trig functions	Sections 2.4, 6.1 13.2, 13.8, 14.3
12. Verify simple trigonometric identities using Pythagorean and/or reciprocal identities. Example: verifying cos²+ tan²cos² = 1	Identity verification in Advanced Math Book	Sections 1.6, 6.7-8, 9.7 12.1, 14.1, 14.6-7
13. Use different forms of representation to compare characteristics of data gathered from two populations. · Evaluating the appropriateness of the design of an experimental study Describing how sample statistics reflect values of population parameters.	Lesson 129	Section 12.5
*ALABAMA COURSE OF STUDY*	*SAXON ALGEBRA 2*	*PRENTICE HALL* *ALGEBRA 2*
14. Determine an equation of linear regression from a set of data. · Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes	Lesson 59	None Must supplement
15. Calculate probabilities of events using the laws of probability. · Using permutations and combinations to calculate probabilities · Calculating conditional probability · Calculating probabilities of mutually exclusive events, independent events, and dependent events	Lesson 116	Section 12.2
Enrichment Lessons	Lessons 24,30,35,37,49,54,56,89,91 99,110,112,114,119,121 122,126,127,128	Sections 3.4-6 10.1-6 11.1-6 12.4, 12.6-7

ALABAMA COURSE OF STUDY

SAXON ALGEBRA 2

PRENTICE HALL

ALGEBRA 2

Review and Refresh

Lessons

2,3,4,5,6,7,8,9,10,11,12,13,14

19,24,25,26,27,33,47,53,79,80

82,83,87,88,91,96,97,98,123

124,125

Sections

1.1,1.2,1.3,2.2,2.3,3.1,5.4

9.1,12.3

1. Determine the relationships of subsets of complex numbers.

Example: using Venn diagrams or tree diagrams to show how subsets of complex numbers are related

Lessons

117,122

Section

5.6

2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.

Examples: simplifying, (4-2i)², and

Lessons

A,20,28,32,46,48,51,62,64

67,73,77,81,104,117

Section

5.6

ALABAMA COURSE OF STUDY

SAXON ALGEBRA 2

PRENTICE HALL

ALGEBRA 2

3. Analyze families of functions, including shifts, reflections, and dilations of y = (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer), y = x² (quadratic), y = a^x

(exponential), and y = log_ax (logarithmic).

Example: comparing the graphs of y = 2^x, y = 2^x + 1, y = 2^x ^{+ 1}, and y = -2^x

· Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

Example: finding the domain of y = or y =

Identifying real-world situations corresponding to

families of functions.

Lessons

43,68,85,94,94,100,102,113

115,118

Sections

2.1,2.5,2.6,5.1-3,7.8

8.1-3,9.2-3

4. Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

· Using the zero product property, completing the square, and the quadratic formula

· Deriving the quadratic formula

Lessons

4,5,23,38,39,40,45,48,50,55

58,63,70,71,77,85,86,93,95

96,100,105

Sections

5.5,5.7-8,6.2-6

9.3,9.6

5. Identify the characteristics of quadratic functions from their roots, graphs, or equations.

· Generating an equation when given its roots or graph

· Graphing a function when given its equation

Examples: graphing equations of the form y = a(x-h)² + k; graphing equations of the form y = ax² + bx + c

· Determining the maximum or minimum values of quadratic functions both graphically and algebraically

Applying functions to real-world problems

Lessons

38,39,45,50,58,63,71,85,86

93,95,96,100,105,120

Sections

5.1-3

7.8

ALABAMA COURSE OF STUDY

SAXON ALGEBRA 2

PRENTICE HALL

ALGEBRA 2

6. Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

· Determining the inverse of a function or a relation

· Performing operations on polynomial and rational expressions containing variables

Example: simplifying+

· Constructing graphs by analyzing their functions as sums, differences, or products

Lessons

A,2,3,8,11,16,25,26,27,28

30,33,36,39,43,75,84,94

102,103,108,115

Sections

2.6

7.6-7

8.2-3

9.2,4-5

7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as

well as simple trigonometric, exponential, and logarithmic functions.

Example: solving x²- 8x > -12, 3^x = 81, 2 sin²x + sin x = 0, or log_x 2 = 5

· Solving equations using laws of exponents, including rational and irrational exponents

· Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

Lessons

6,7,38,39,40,45,48,50,55,58

63,70,71,77,86,93,95,96,100

105,115

Sections

1.4-5

2.6, 5.6-8

7.1-5

8.4-6

9.6, 14.2

ALABAMA COURSE OF STUDY

SAXON ALGEBRA 2

PRENTICE HALL

ALGEBRA 2

8. Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices.

Example: solving a system of linear equations using augmented matrices and row operations, matrix operations of a graphing calculator, or substitution

· Evaluating the determinant of a 2x2 or 3x3 matrix

Solving word problems involving real-life

situations.

Lessons

13,15,17,21,23,29,34,52,59

61,65,74,76,84,85,86,90,92

95,97,100,101,111,115,120

Sections

3.2-3

4.1-3,5-8

9. Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx).

· Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations

Example: solving problems involving harmonic motion

· Determining specific unit circle coordinates associated with special angles

Lessons

43 defines

Must be supplemented

Sections

2.6

4.4

13.1-7

10. Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

· Deriving formulas for Law of Sines and Law of Cosines

· Determining area of oblique triangles

Lessons

43,44,49

Must be supplemented

Sections

14.3-5

ALABAMA COURSE OF STUDY

SAXON ALGEBRA 2

PRENTICE HALL

ALGEBRA 2

11. Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

Lessons

43,44

Add reciprocal trig functions

Sections

2.4, 6.1

13.2, 13.8, 14.3

12. Verify simple trigonometric identities using Pythagorean and/or reciprocal identities.

Example: verifying cos²+ tan²cos² = 1

Identity verification in

Advanced Math Book

Sections

1.6, 6.7-8, 9.7

12.1, 14.1, 14.6-7

13. Use different forms of representation to compare characteristics of data gathered from two populations.

· Evaluating the appropriateness of the design of an experimental study

Describing how sample statistics reflect values of

population parameters.

Lesson

129

Section

12.5

ALABAMA COURSE OF STUDY

SAXON ALGEBRA 2

PRENTICE HALL

ALGEBRA 2

14. Determine an equation of linear regression

from a set of data.

· Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes

Lesson

None

Must supplement

15. Calculate probabilities of events using the laws of probability.

· Using permutations and combinations to calculate probabilities

· Calculating conditional probability

· Calculating probabilities of mutually exclusive events, independent events, and dependent events

Lesson

116

Section

12.2

Enrichment Lessons

Lessons

24,30,35,37,49,54,56,89,91

99,110,112,114,119,121

122,126,127,128

Sections

3.4-6

10.1-6

11.1-6

12.4, 12.6-7

After much review and study, both textbooks need to be supplemented to cover the entire course of study. The course of study is very broad and covers a lot of material that both textbooks cover in detail in the next book in their respective series. Both are weak in the area of statistics and probability and must be supplemented. Both series address these areas in the next book, which will cover the Algebra 3/Statistics course.

Technology can be incorporated for each book at the following websites:

Saxon at saxonpublishers.com

Prentice Hall at PHSchool.com

Math Curriculum Page