Alabama Course of Study

TEAM-Math

AHSGE

Glencoe

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

N1. Distinguish between various number sets: Complex (Course of Study #1)

VVII-8

5-9  p. 270-275

5-9 p. 280

6-5 p. 315

7-5 p. 374-375

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

 Examples:  simplifying,

 (4-2i)², and

N2. Understand and apply concepts and properties of complex numbers (Course of Study #2)

VII-8

5-9 p. 270-275

6-5 p. 315-316

7-5 p. 372,374-375

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

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

a.  Performing operations on polynomial and rational expressions containing variables

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

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

N3. Perform operations involving:

a.  Real numbers with radicals

b.  Complex numbers (Course of Study #2)

c.  Common logarithms

d.  Rational expressions (Course of Study #6)

e.  Calculate a determinate for a 2x2 and 3x3 matrix (Course of Study #8)

I-1, I-2, I-3, II-3, III-1, III-2

VII-8

VII-4, VII-8

VII-1, VII-8

5-9 p. 270-275

6-5 p. 315-316

7-5 p. 372,374-375

5-2,5-3,5-4

7-7,7-8 p.390-394

7-9 p.399

For more…p.404-405

Getting started p.521

9-1-9-2,9-6

10-2 p.531

Practice quiz p.617

Getting started p.699

13-7 p.749

extra practice p.844,859

3-1 – 3-4

4-5,4-6,4-8,4-8F p.182-191

review p. 212

extra practice p.835

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).

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

b.   Identifying real-world situations corresponding to families of functions

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

a.  Constructing graphs by analyzing their functions as sums or differences

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

a.  Using the zero product property, completing the square, and the quadratic formula

b.  Deriving the quadratic formula

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

a.  Generating an equation when given its roots or graph

b.  Graphing a function when given its equation

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

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.

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

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

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

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

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

b.  Determining specific unit circle coordinates associated with special angles

A1. a. Identify and graphically represent: (Course of Study #3)

y=kx

y=a^x

y=k/x

y = x²

y=x³

y=log_ax

y=[x]

y=sin x

y=cos x

y=tan x

Constructing graphs by analyzing their functions as sums, differences, or products (Course of Study #6 c)

b. Translate, rotate, dilate, and reflect linear, quadratic, cubic, rational, exponential, logarithmic, trigonometric, absolute value, and radical      functions. (Course of Study #3)

c. Analyze families of functions including:

·Domain (Course of Study #3)

·Range

·Restricted domains

·Roots (Course of Study #4)

·Maximum and minimum values (Course of Study #5)

Given a graph, table of values, or its equation.

d. Determine period and amplitude of sine, cosine, and tangent functions from graphs or basic equations. (Course of Study #9)

e. Solve equations and inequalities including:

·Quadratics

·Absolute value

·Radical

·Exponential

·Common logarithmic

·Linear systems in 2 and 3 variables, including matrices.  (Course of Study # 8)

·Develop quadratic formula

·Trigonometric

·Rational

III-1,III-2,VII-8

III-1,VII-8

III-1,VII-8

V-3,VI-1,VII-8

VI-1,VII-4,VII-8

IV-2,VII-4,VII-8

III-1,V-1,VI-1,

    VII-8

III-1, VII-8

II-2,VII-8

I-4,VII-8

II-3,V-1,V-4,

     VI-1,VII-8

VI-1,VII-8

VI-1, VII-8

III-1,VII-8

V-1,V-4,VI-1,

    VII-8

IV-1,VII-8

VI-1,VII-8

VI-1,VII-8

VI-1,VII-8

VII-1,VII-8

2-1 p.56-61

2-2, 2-3,2-4

2-6 p. 93-95

2-7 p.99-101

For more… p.104

4-4 p. 181

6-1

6-6P

6-6

7-9 p.397-398

8-1 p.416

9-4

9-5

10-1 p.523,527-528

10-2

extra practice p. 830-831

7-7 p.383,387

6-2 – 6-5

Getting started p.345

7-1 - 7-3

7-4 p. 370

7-5 – 7-6

8-7 p.460

extra practice p.841

Chapter 6

6-3 p.303,

7-5 374-376

3-1 p.110-115

3-3 p. 123-127

6-1 – 6-2  p.286-299

6-7 p.335 – 337

7-1 p.348-349

7-2 p.353-358

7-9 p.395-399

8-2 p.420-423

8-3 p.428-429

8-4 p.435-437

10-1 523-524

14-1 762-768

extra practice p. 846-847

6-5 p. 313-319

6-6 p. 326-329

review p. 339

3-1 – 3-4

4-5 p.182-188

4-6 p.189-191

4-8

4-8F

review p.212

extra practice p.835

CH 4 matrices

4-8 p 203-207

14-1 p762-768

14-2 p 769-776

14-6 p 791-797

c.  Solving word problems involving real-life situations

A2. Solving word problems involving real life situations. (Course of Study #8)

VI-1, VII-8

This objective is addressed throughout.

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

a.  Determining the inverse of a function or a relation

b.  Performing operations on polynomial and rational expressions containing variables

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

A3. Perform operations on functions:

a. +

b. -

c. x

d. /

e. Composition

f. Inverse

g. Factor polynomials including sum and difference of cubes

I-4,VII-8

VII-8

VII-8

VII-8

VI-1,VII-8

VII-8

VII-8

VII-1, VII-8

5-2,5-3,5-4

7-7 p. 383,387

7-8 p.390-394

7-9 p.399

review and practice test p.404-405

getting started p.521

9-1-9-2,9-6

10-2 p.531

11-7 p.617

getting started p.699

13-7 p.749

extra practice p.844,859

Alabama Course of Study

TEAM-Math

AHSGE

Glencoe

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

Example:  verifying cos² + tan²cos² = 1

G5. Verify simple trigonometric identities using Pythagorean and/or reciprocal identities. (Course of Study #12)

VII-1,VII-8

14-3 p 777-781

14-4 p 782-785

14-5 p 786-790

14-6 p 791-797

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

a. Deriving formulas for Law of Sines and Law of Cosines

b. Determining area of oblique triangles

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.

G6. Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

a. Deriving formulas for Law of Sines and Law of Cosines

b.Determining area of oblique triangles (Course of Study #10)

G7. 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. (Course of Study #11)

VII-1,VII-4,

    VII-8

VII-1,VII-4

VII-1,VII-4

VII-1,VII-2

VII-1

13-4 p 725-732

13-5 p 733-738

13-1 p 700-708

13-2 p 709-715

13-3 p 717-724

13-6 p 739-745

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

a. Evaluating the appropriateness of   the design of an experimental study

b. Describing how sample statistics reflect values of population parameters

D2. Use different forms of representation to compare characteristics of data gathered from two populations.

a.Evaluating the appropriateness of the design of an experimental study

b.Describing how sample statistics reflect values of population parameters (Course of Study #13)

VII-8

12-9 p 682-685

14.  Determine an equation of linear regression from a set of data.

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

D3. Determine an equation of linear regression from a set of data.

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

(Course of Study #14)

VII-8

2-5 p 81-88

6-2 F p300

7-2F p 359

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

a.Using permutations and combinations to calculate probabilities

b.Calculating conditional probability

c.Calculating probabilities of mutually exclusive events, independent events, and dependent events

D5. Calculate probabilities of events using the laws of probability.

a. Using permutations and combinations to calculate probabilities

b. Calculating conditional probability

c. Calculating probabilities of mutually exclusive events, independent events, and dependent events

(Course of Study #15)

VII-6,VII-8

VII-6

VII-6

12-2 p 638-643

12-3 p 644-650

12-4 p 651-657

12-5 p 658-663