Cherokee County Schools

Mathematics Course of Study

Pre-Calculus

Alabama Course of Study: Mathematics	Saxon Advanced Math	Prentice Hall
1. Perform the vector operations of addition, scalar multiplication, and absolute value. · Determining coincidence, parallelism, collinearity, or perpendicularity of vectors · Using vectors to model real-life and mathematical situations	Lessons 14,29,30	Chapter 6 Sections 1,2,4
2. Define e using the limit forms of , , and .	Lessons 29,34,51,67	Chapter 9 Section 4 Chapter 10 Sections 1 & 3
3. Graph conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conic sections from their determining characteristics. Example: graphing x² – 6x + y² – 12y + 41 = 0 or y² – 4x + 2y + 5 = 0 Example: Writing the equation of an ellipse with center (5, -3), a horizontal major axis of length 10 and a minor axis of length 4.	Lessons 11,19,42,54,58,63,68 71,78,89,106,123,125	Chapter 8 Sections 1,2,3,4, & 5
4. Analyze the graphs of rational, logarithmic, exponential, trigonometric, and piecewise-defined functions by determining the domain and range; identifying any vertical, horizontal, or oblique asymptotes; and classifying the function as increasing or decreasing, continuous or discontinuous, and noting the type of discontinuity if one exists. Approximating rates of change using the difference quotient	Lessons 21,23,26,32,40,41,43 47,49,57,65,66,76,84 88,94,110,113,114,115 116,117,118,119,121 122,125	Chapter 1 Sections 1, 2, 3, & 5 Chapter 2 Sections 1, 2, 3, 4, & 7
5. Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions. Example: explaining the relationship of the graph of y = e^{x -2} to the graph of y = e^x · Determining the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses	Lessons 23,24,26,32,42,43,47 52,57,65,66,84	Chapter 3 Sections 1, 2, 3, & 4 Chapter 4 Sections 3, 4, 5, 6, & 7
6. Apply the laws of logarithms to simplify expressions and to solve equations using common logarithms, natural logarithms, and logarithms with other bases.	Lessons 26,40,49,51,59,67 82,88,98,103,111	Chapter 3 Sections 1, 2, 3, 4, 5, & 6
7. Solve trigonometric equations and inequalities using sum, difference, and half- and double-angle identities. · Verifying trigonometric identities	Lessons 27,36,48,50,52,60 65,72,76,80,81,85 87,90,93,96,97,100	Chapter 4 Sections 2, 3, & 8 Chapter 5 Sections 1, 2, 3, 4, 5, & 6
8. Use parametric equations to represent real-life and mathematical situations.	Lessons 18,25,28,36 44,53,85	Chapter 1 Sections 4, 5, & 6 Chapter 6 Section 3
9. Solve applied problems involving sequences with recurrence relations. · Determining characteristics of arithmetic and geometric sequences and series, including those defined with recurrence relations, first terms, common differences or ratios, n^th terms, limits, or statements of convergence or divergence · Expanding binomials raised to a whole number power using the Binomial Theorem	Lessons 38,77,86,91,99,102 104,107,112	Chapter 9 Sections 1, 2, 3, & 4
10. Find limits of functions at specific values and at infinity numerically, algebraically, and graphically. · Applying limits in problems involving convergence and divergence	Lessons 107,117,118,119	Chapter 1 Section 2 Chapter 2 Sections 4, 7, & 9 Chapter 10 Sections 1, 2, & 3
11. Convert coordinates, equations, and complex numbers in Cartesian form to polar form and from polar form to Cartesian form. · Graphing simple polar equations in the polar coordinate plane Example: graphing r = 2+2cosf or r = 2 + sin3f · Graphing polar coordinates and complex numbers	Lessons 14,29,35,46,47 57,64,66,79,95	Chapter 2 Sections 5 & 6 Chapter 4 Sections 3, 4, 5, 6, & 7 Chapter 6 Sections 2, 4, 5, & 6 Chapter 8 Sections 5 & 6
12. Determine the equation of a curve of best fit from a set of data by using exponential, quadratic, or logarithmic functions.	Lessons 34,38,45,55 61,75,83,92	Chapter 1 Section 1 Chapter 3 Sections 1, 2, 5, & 6 Chapter 6 Section 3 Chapter 9 Section 6

Alabama Course of Study: Mathematics

Saxon Advanced Math

Prentice Hall

1. Perform the vector operations of addition, scalar multiplication, and absolute value.

· Determining coincidence, parallelism, collinearity, or perpendicularity of vectors

· Using vectors to model real-life and mathematical situations

Lessons

14,29,30

Chapter 6

Sections 1,2,4

2. Define e using the limit forms of ,

, and .

Lessons

29,34,51,67

Chapter 9 Section 4

Chapter 10 Sections

1 & 3

3. Graph conic sections, including parabolas,

hyperbolas, ellipses, circles, and degenerate conic sections from their determining characteristics.

Example: graphing

x² – 6x + y² – 12y + 41 = 0

y² – 4x + 2y + 5 = 0

Example:

Writing the equation of an ellipse with center (5, -3),

a horizontal major axis of length 10 and a minor axis

of length 4.

Lessons

11,19,42,54,58,63,68

71,78,89,106,123,125

Chapter 8 Sections

1,2,3,4, & 5

4. Analyze the graphs of rational, logarithmic, exponential, trigonometric, and piecewise-defined functions by determining the domain and range; identifying any vertical, horizontal, or oblique asymptotes; and classifying the function as increasing or decreasing, continuous or discontinuous, and noting the type of discontinuity if one exists.

Approximating rates of change using the difference quotient

Lessons

21,23,26,32,40,41,43

47,49,57,65,66,76,84

88,94,110,113,114,115

116,117,118,119,121

122,125

Chapter 1 Sections

1, 2, 3, & 5

Chapter 2 Sections

1, 2, 3, 4, & 7

5. Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions.

Example: explaining the relationship of the graph of y

= e^{x -2} to the graph of

y = e^x

· Determining the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses

Lessons

23,24,26,32,42,43,47

52,57,65,66,84

Chapter 3 Sections

1, 2, 3, & 4

Chapter 4 Sections

3, 4, 5, 6, & 7

6. Apply the laws of logarithms to simplify expressions and to solve equations using common logarithms, natural logarithms, and logarithms with other bases.

Lessons

26,40,49,51,59,67

82,88,98,103,111

Chapter 3 Sections

1, 2, 3, 4, 5, & 6

7. Solve trigonometric equations and inequalities using sum, difference, and half- and double-angle identities.

· Verifying trigonometric identities

Lessons

27,36,48,50,52,60

65,72,76,80,81,85

87,90,93,96,97,100

Chapter 4 Sections

2, 3, & 8

Chapter 5 Sections

1, 2, 3, 4, 5, & 6

8. Use parametric equations to represent real-life and mathematical situations.

Lessons

18,25,28,36

44,53,85

Chapter 1 Sections

4, 5, & 6

Chapter 6 Section 3

9. Solve applied problems involving sequences with recurrence relations.

· Determining characteristics of arithmetic and geometric sequences and series, including those defined with recurrence relations, first terms, common differences or ratios, n^th terms, limits, or statements of convergence or divergence

· Expanding binomials raised to a whole number power using the Binomial Theorem

Lessons

38,77,86,91,99,102

104,107,112

Chapter 9 Sections

1, 2, 3, & 4

10. Find limits of functions at specific values and at infinity numerically, algebraically, and graphically.

· Applying limits in problems involving convergence and divergence

Lessons

107,117,118,119

Chapter 1 Section 2

Chapter 2 Sections

4, 7, & 9

Chapter 10 Sections

1, 2, & 3

11. Convert coordinates, equations, and complex numbers in Cartesian form to polar form and from polar form to Cartesian form.

· Graphing simple polar equations in the polar coordinate plane

Example: graphing r = 2+2cosf or r = 2 + sin3f

· Graphing polar coordinates and complex numbers

Lessons

14,29,35,46,47

57,64,66,79,95

Chapter 2 Sections

5 & 6

Chapter 4 Sections

3, 4, 5, 6, & 7

Chapter 6 Sections

2, 4, 5, & 6

Chapter 8 Sections

5 & 6

12. Determine the equation of a curve of best fit from a set of data by using exponential, quadratic, or logarithmic functions.

Lessons

34,38,45,55

61,75,83,92

Chapter 1 Section 1

Chapter 3 Sections

1, 2, 5, & 6

Chapter 6 Section 3

Chapter 9 Section 6

All material in this course is beyond the requirements of the AHSGE objectives.

A student in this course has already mastered all stated objectives and is preparing for college mathematics.

Technology can be integrated for each textbook at the publishers website.

For Saxon, go to: saxonpublishers.com

For Prentice Hall, go to: PHSchool.com

Math Curriculum Page