May 24th
May 24th
ADVANCED ALGEBRA AND TRIGONOMETRY
RECOMMENDED PREREQUISITE:
A grade of “B” or better in 352 Algebra II, or
Course 320 Honors Algebra II
BASIC TEXT: Advanced Algebra:
Tools for a Changing World, Prentice
Hall, 1998
SUPPLEMENTARY TEXTS: Algebra II with Trigonometry, Prentice Hall , 1993
REQUIRED MATERIALS: writing utensil, notebook, and scientific calculator
COURSE DESCRIPTION:
This course is intended to prepare students for the study of calculus at the
college level. It is a
study of algebraic techniques with an emphasis on coordinate geometry,
trigonometry and
quadratic systems . It is expected that students will have a sound knowledge of
Algebra II.
MISSION RELATED GOALS:
This class will provide the student with a variety of opportunities to
demonstrate academic
excellence and intellectual curiosity by communicating effectively, solving
complex problems,
and working with others toward a common goal .
STUDENT EXPECTATIONS FOR LEARNING ADDRESSED:
Students will be afforded opportunities to apply mathematical concepts to
real-world
applications. A variety of teaching methods will be used to foster an
environment that promotes
self-confidence and respect for others throughout the school and global
community.
GENERAL PERFORMANCE OBJECTIVES:
The student will be able to:
1. Graph polynomial and rational algebraic functions
2. Find the real LINE -help/quadratic-formula/zero-of-a-system-maple.html">zeros of a polynomial function.
3. Identify and write the equation of a conic from its graph.
4. Find the solutions of quadratic systems.
5. Perform operations and graph expressions involving real and rational
exponents.
6. Identify and apply the logarithm properties to simplify expressions and solve
equations.
7. Solve standard probability problems using a variety of counting techniques.
8. Solve basic statistical formulas to experimental data.
9. Identify and graph the trigonometric and inverse trigonometric functions.
10. Solve trigonometric equations and apply these to real-life situations.
UNITS AND THEMES:
I. Polynomial Functions (13 days)
|
12.P.6,12.P.7,12.P.8,12.P.11,
12.P.13, PC.P.2 |
II. Radical Functions & Exponents (12
days)
|
10.P.4,10.P.7,12.N.2,
12.P.5,12.P.8,12.P.11, 12.P.13 |
III. Exp onential Functions (11 days)
|
12.N.2,12.P.4,12.P.5,12.P.6,12.P.8,
12.P.11,12.P.13 |
IV. Graphing Unit (5 days)
|
12.P.6,12.P.7,12.P.8,12.P.11,
12.P.13 |
| V. Conic Sections (15 days) |
12.P.10,12.G.4, PC.P.8 |
VI. Periodic Functions & Trigonometry
(15 days)
|
12.P.4,12.P.6,12.P.8, 12.P.11,
12.P.13, 12.G.1, 12.G.2, 12.M.1,
PC.P.3, PC.P.4, PC.P.5 |
VII. Trigonometric Identities &
Equations (15 days)
|
12.P.4,12.P.6,12.P.8, 12.P.11,
12.P.13, 12.G.1, 12.G.2, 12.M.1,
PC.P.3, PC.P.4, PC.P.5 |
| VII. Review, Midterm, Final Exam (4
days) |
|
COURSE OUTLINE:
I. Polynomial Functions (13
days)
|
12.P.6,12.P.7,12.P.8,12.P.11,
12.P.13, PC.P.2 |
A. Solving Polynomials by Factoring
B. Synthetic Division
C. Remainder and factor theorem
D. Fundamental Theorem of Algebra
E. Rational Zeros Theorem
F. Solving polynomial equations
G. Applications |
|
II. Radical Functions & Rational
Exponents (12 days)
|
10.P.4, 10.P.7, 12.N.2, 12.P.5,
12.P.8, 12.P.11, 12.P.13 |
A. Roots and Radical Expressions
B. Multiplying and Dividing Radical Expressions
C. Binomial Radical Expressions
D. Rational Exponents
E. Solving Radical Equations
F. Graphing Radical Functions |
|
III. Exponential and Logarithmic
Functions (11 days)
|
12.N.2,12.P.4,12.P.5,12.P.6,12.P.8,
12.P.11,12.P.13 |
A. Exploring Exponential Models
B. Logarithmic Functions as Inverses
C. Properties of Logarithms
D. Exponential & Logarithmic Equations |
|
IV. Graphing Unit (5 days)
|
12.P.6, 12.P.7, 12.P.8, 12.P.11,
12.P.13 |
A. Quadratics
B. Quadratic Inequalities
C. Piecewise Functions |
|
| V. Quadratic Relations (15
days) |
12.P.10,12.G.4, PC.P.8 |
A. Circles
B. Parabolas
C. Ellipses
D. Hyperbolas |
|
VI. Periodic Functions and
Trigonometry (15 days)
|
12.P.4,12.P.6,12.P.8,12.P.11, ,
12.P.13,12.G.1,12.G.2,12.M.1,
PC.P.3, PC.P.4, PC.P.5 |
A. Exploring Periodic Data
B. Angles and the Unit Circle
C. Radian Measure
D. The Sine Function
E. The Cosine Function
F. The Tangent Function
G. Translating Sine and Cosine Functions
H. Reciprocal Trigonometric Functions |
|
VII. Trigonometric Identities and
Equations (15 days)
|
12.P.4,12.P.6,12.P.8,12.P.11, ,
12.P.13,12.G.1,12.G.2,12.M.1,
PC.P.3, PC.P.4, PC.P.5 |
A. Trigonometric Identities
B. Solving Trigonometric Equations Using Inverses
C. Right Triangles and Trigonometric Ratios
D. Area and the Law of Sines
E. The Law of Cosines
F. Angle Identities
G. Double-Angle and Half-Angle Identities |
|
VII. Review, Midterm, Final Exam (4 days)
SUGGESTED INSTRUCTIONAL STRATEGIES
1. Lecture
2. Written Exercises
3. Group Work
4. Projects
5. Use of Manipulatives
6. Use of a Variety of Questioning Techniques
7. Board work
8. Calculator Activities
9. Games (Math Jeopardy, etc.)
10. Student Presentations
11. A variety of assessment tools (partner quizzes, etc.)
SUGGESTED INTEGRATED ACTIVITIES:
1. Students will research the astronomer Hipparchus. They will use his
techniques
to calculate the heights of three buildings without measuring them directly.
Students will
prepare a report of their findings.
2. Students will construct a scale model of the catenary between the towers of
the
Golden Gate bridge and suspend weights to approximate the parabola formed. They
will
present a report comparing their model to the original.
USE OF TOOLS/TECHNOLOGY:
1. Use a classroom computer and an integrated software package (Graph Wiz, 3D
Images, Algebra (4.0), Math CAD).
2. Use the TI-83 Graphics Calculator.
3. Use an overhead projector with transparencies.
4. View video selections
5. Use computer laboratory
ASSESSMENT TECHNIQUES:
1. Students will take free-response performance tests.
2. Students will participate in classroom discussions and will demonstrate
problems
solving on the blackboard and/or overhead projector.
3. Students will work in cooperative situations and report out their results.
4. Students will prepare integration projects.
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