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ALGEBRA II
COURSE DESCRIPTION
Algebra II has historically been the third course in the college preparatory mathematics program. However, some schools allow many of their students to either take both Algebra II and geometry the same year or take Algebra U before they take geometry. Algebra II is an extension of Algebra I. Topics are added in the area of functions that expand the algebras to include conic sections and trigonometry, thus relating algebra to geometric concepts. Algebra II is generally preliminary to a course in analysis, analytical geometry and ideas of limits and the calculus. This course also ties together many of the ideas from arithmetic and geometry.
Critical Components
In order to satisfy the state graduation requirement, Algebra II should deal significantly with:
I. Problem Solving and Mathematical Reasoning
A. Goal:
Students will understand and show proficiency in problem solving.
Objectives:
Students will1. Read and properly interpret problem statements.
2. Select appropriate problem solving strategies.
3. Apply strategies to solve "real world" problems.
4. Use calculators and/or computers as problem solving tools.
5. Use estimation skills to check reasonableness of solutions.
B. Goal:
Students will apply an organized problem solving procedure.
Objectives:
Students will
1. Identify and analyze the problem.
2. Formulate a plan to solve the problem.
3. Solve the problem.
4. look back for patterns that can be useful for solving other problems.
II. Real Numbers and Properties
A. Goal:
Students will understand real numbers as a mathematical system.
Objective:
Students will1. Review basic computational operations in the real number system and solve problems in this system.
III. Equations and Inequalities
A. Goal:
Students will understand the use of equations and inequalities.
Objectives:
Students will1. Solve and graph equations and inequalities with applications.
2. Use absolute value functions.
IV. Functions
A. Goal:
Students will understand polynomial use and factoring.
Objectives:
Students will1. Factor a monomial, binomial, polynomial, quadratic polynomial.
2. Solve polynomial equations by factoring.
3. Use synthetic division and binomial expansion.
V. Powers, Roots and Complex Numbers
A. Goal:
Students will understand the use of powers and roots and their relationship.
Objectives:
Students will
1. Multiply, divide and simplify radical expressions.
2. Operate with powers and exponents.
B. Goal:
Students will use and understand complex numbers.
Objective:
Students will1. Solve equations and simplify expressions involving imaginary and complex numbers.
VI. Quadratic Equations, Graphs and Functions
A. Goal:
Students will understand the application of quadratic functions and equations.
Objective:
Students will1. Graph quadratic functions and relate them to the conic sections (ellipses, hyperbolas, parabolas).
2. Solve Systems of equations both linear and quadratic.
3. Derive the quadratic formula.
VII. Exponents and Logarithmic Functions
A. Goal:
Students will understand the relationship between logarithmic and exponential functions.
Objectives:
Students will1. Define and use logarithms and exponents as a inverse relation.
2. Solve exponential and logarithmic equations.
VIII. Sequence and Series
A. Goal:
Students will understand and use series and sequences.
Objectives:
Students will1. Define sequences and series.
2. Distinguish between arithmetic, geometric and other sequences and series.
3. Use the binomial theorem.
IX. Probability and Statistics
A. Goal:
Students will understand the basic principles of probability and statistics.
Objectives:
Students will1. Define and use permutations and combinations.
2. Apply the binomial theorem to probability.
3. Solve for median, mode, mean, and range.
4. use frequency distributions and histograms.
X. Trigonometric Functions
A. Goal:
Students will understand trigonometric functions and identities. Students will
1. Define and use trigonometric functions as circular functions as well as triangular functions.
2. Graph trigonometry functions.
3. Solve simple identities.
XI. Matrices
A. Goal:
Students will understand the use of matrices.
Objectives:
Students will1. Add, subtract and multiply matrices.
[../../../../../../../footer.htm]2. Solve systems of linear equations by the use of matrix methods.
