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Algebra II: 05
Recent ActivityInstructor: Mr. George
Course Overview:
- Algebra II teaches advanced algebraic concepts through the study of functions, “families of functions,” equations, inequalities, systems of equations and inequalities, polynomials, rational expressions, complex numbers, matrices, sequences, and series.
- Emphasis will be placed on the algebraic processes and their use in problem solving.
- Students will enhance their oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results throughout the course.
- All students must take the Virginia SOL test for Algebra II at the end of this course.
Required Materials:
- Textbook (needs to be covered, no Book Socks),
- Dedicated math 3-ring binder, divided into three sections: notes, homework, tests/quizzes
- Sharpened pencils
Class Announcements Week 6-14-2010Final Eams Week All Subjects
Week 6-7-2010Cumulative Review Algebra 2
Students will complete a cumulative review packet with questions as a final project. This review will include a test question bank for the final examination. All students that passed the End of Course test are exempt from the final exam but must still complete the cumulative review packet. Week 6-1-2010Cumulative Review Algebra 2
Students will complete a cumulative review packet with questions as a final project. This review will include a test question bank for the final examination. All students that passed the End of Course test are exempt from the final exam but must still complete the cumulative review packet. Week 5-17-2010SOL Review All domains.
Week 5-14-2010Linear Functions and Special Functions
Quadratic Equations and Functions
Equations and Rational Functions
Exponential and Logarithmic Functions
SOL Reporting Category
Relations and Functions
Virginia SOL AII.9
The student will find the domain, range, zeros and inverse of a function; the value of a function for a given element in its domain, and the composition of multiple functions. Functions will include exponential, logarithmic and those that have domains and ranges that are limited and/or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions.
Essential Question
· What is the difference between direct and inverse variation?
· What is joint variation?
· What is combination variation?
Week 5-1-2010Conics
Virginia SOL AII.18
The student will identify conic sections (circle, ellipse, parabola, and hyperbola) from his/her equations. Given the equations in (h, k) form, the student will sketch graphs of conic sections, using transformations.
Essential Question
· What are the different conics?
· How is each conic formed?
· How is a conic recognized in its standard algebraic form?
· How do transformations affect the graph of a conic? Week Ending: 4-1-2010Rational Expressions
AII.7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and for confirming the algebraic solutions.
Essential Questions
· What is a rational expression?
· How is a rational expression simplified and algebraically manipulated? Week 3-22-2010Polynomials and Exponential Functions
SOL AII.15
The student will recognize the general shape of polynomial, exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of these functions.
Essential Question
· What is the relationship between the degree of an equation and the graph of an equation?
· What is the relationship between exponential and logarithmic functions?
· How can the calculator be used to investigate the shape and behavior of polynomial, exponential, and logarithmic functions. Week Ending 3-5-10Great Week! We will test Monday on Arithmetic Sequences and move right into Arithmetic Series. Good Luck! Monday and Tuesday we will drill and practice on the Arithmetic Series in preparation for testing Wednesday.
Week Ending 2-26-10This week we will review Arithmetic Sequences, Arithmetic Series, Geometric Sequences, and Geometric Series.
It seems that we are still have a little cabin fever, therefore we will continue to drill and practice on these four concepts in attempt to catch-up. Week of 2-15-2010Sequence and Series
Virginia SOL AII.16
The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, finding the term, and evaluating summation formulas. Notation will include å and .
Essential Question
· What is the difference between series and sequences?
· What is the difference between arithmetic and geometric sequences and series?
· What is Sigma notation (Σ)?
· Where in real life are series and sequences applied?
Critical Attributes
A sequence is a mathematical pattern of numbers. A series is an indicated sum of a sequence of terms. Both sequences and series may be finite or infinite.
Two types of sequences and series are arithmetic and geometric. An arithmetic sequence is a sequence in which each term, after the first term, is found by adding a constant, called the common difference to the previous term. A geometric sequence is a sequence in which each term, after the first term, can be found by multiplying the preceding term by a nonzero constant, called the common ratio. The terms between any two nonconsecutive terms of a geometric/arithmetic sequence are called the geometric/ arithmetic means.
There are formulas that assist in determining elements of the sequence or sum of a series. The sigma notation (Σ) is one-way of writing a series. A recursive formula for a sequence describes how to find the term from the terms before it.
Real-world applications such as fractals, growth, tax, and interest are solved using sequences and series.
The student will use problem solving, mathematical communication, mathematical reasoning, connections and representations to:
· Distinguish between a sequence and a series.
· Recognize patterns in a sequence.
· Distinguish between arithmetic and geometric sequences.
· Use and interpret the notation: Σ, n, term, and .
· Write the first n terms in an arithmetic or geometric sequence.
· Find (the term) for an arithmetic or a geometric sequence given the formula.
· Find the sum, , of the first n terms of an arithmetic or geometric series including infinite series. Formulas will be given.
· Use arithmetic and geometric sequences and series to model real-life problems.
· Find a rule that fits a situation modeled by an arithmetic or geometric sequence.
Essential Understandings
· Sequences and series arise from practical situations.
· The study of sequences and series is an application of investigation of patterns.
Discussion Topics Class Files
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