ALGEBRA 2

COURSE OVERVIEW

COURSE GOAL: To understand and apply the concepts and procedures from algebraic sense.

COURSE OBJECTIVES: (Math Essential Academic Learning Requirements are in parentheses following each objective.)

During this course the student will:

• Review the language and properties of basic algebra, and find sums, differences, products and quotients of real numbers. (1.1, 1.5)
• Solve equations and inequalities in one variable (including combined inequalities). (1.1, 1.2, 1.5, 2.1, 2.2, 2.3, 3.1, 3.3, 4.2, 4.3)
• Solve problems using equations, inequalities and absolute value equations and inequalities. (1.1, 1.2, 1.5, 2.1, 2.2, 2.3, 3.3, 4.2, 4.3)
• Use deductive reasoning to complete proofs. (1.3, 1.5)
• Work with linear equations in two variables and their graphs, find the slope of a line, and find equations for lines. (1.2, 1.3, 1.5, 3.1, 3.2, 3.3, 4.3)
• Solve systems of linear equations and inequalities in two variables and use them to solve problems. (1.2, 1.3, 1.5, 2.1, 2.2, 2.3, 3.1, 3.3, 4.2, 4.3)
• Use functional notation, graph functions, and find equations defining linear functions. (1.3, 1.5)
• Use the Laws of Exponents and scientific notation to simplify expressions, solve equations, and solve problems. (1.1, 1.5, 2.1, 2.2, 2.3)
• Multiply and factor polynomials, including quadratic polynomials. (1.5)
• Solve polynomial equations and use polynomial equations to solve problems. (1.5, 2.1, 2.2, 2.3, 5.1, 5.2, 5.3)
• Simplify rational expressions and complex fractions. (1.1, 1.5)
• Solve fractional (rational) equations. (1.1, 1.5, 2.1, 2.2, 2.3)
• Find roots of real numbers, simplify radical expressions and solve equations containing radicals. 1.1, 1.5, 2.1, 2.2, 2.3)
• Use the imaginary number ?i? and work with complex numbers. (1.5)
• Solve quadratic equations by completing the square and using the quadratic formula. (1.5, 2.1, 2.2, 2.3)
• Graph quadratic functions. (1.3, 1.5)
• Work with direct, inverse and joint variation and solve problems.(1.1)
• Use synthetic division to find rational roots of polynomial equations. (1.5)
• Use the distance and midpoint formulas.(1.5)
• Find equations for and graph circles and parabolas. (1.3, 1.5)
• Solve quadratic systems.(1.3, 1.5)
• Solve systems of linear equations in three variables.(1.5, 5.1, 5.2, 5.3)
• Work with exponential functions having rational and real number exponents. (1.5)
• Define and solve logarithmic functions using the laws of logarithms. (1.5, 2.3, 3.3, 4.3)
• Apply logarithms to solve exponential growth and decay problems. (1.5, 2.2, 2.3, 3.1, 3.3, 4.3, 5.2, 5.3)

MATERIALS: Commercial textbook, Algebra And Trigonometry, Structure and Method, Houghton Mifflin Co. and teacher-made handouts. Adapted equipment and materials for visually impaired students.

GRADING:

Attendance and daily assignments: 50%

Class participation:  20%

Tests: 30%    

TIME LINE: The text consists of ten chapters, each requiring 3-4 weeks to complete.

Chapter 1: Basic concepts of algebra, including the language of algebra, graphs of real numbers, operations on real numbers, solving equations and using equations to solve problems.

Chapter 2: Inequalities and proofs including solving inequalities in one variable, solving combined inequalities, solving problems using inequalities, working with absolute value, proving theorems.

Chapter 3: Linear equations and functions, including linear equations in two variables and their graphs, slope of linear equations, methods of finding equations of lines, solving systems of linear equations in two variables, using systems to solve problems, working with functions and linear functions, and relations.

Chapter 4: Products and factors of polynomials including using the laws of exponents, using prime factorization, solving polynomial equations and using polynomial equations to solve problems.

Chapter 5: Working with rational expressions including quotients of rational expressions, zero and negative exponents, scientific notation and significant digits, performing the mathematical operations on rational algebraic expressions, simplifying complex fractions, and solving fractional equations.

Chapter 6: Irrational and complex numbers to include properties of radicals, operations on radical expressions, equations containing radicals, the imaginary number i, and working with the complex number system.

Chapter 7: Solving quadratic equations and functions by completing the square and using the quadratic formula, the discriminant, relationships between roots and coefficients, equations in quadratic form, and graphing quadratic equations and functions.

Chapter 8: Variation and polynomial equations including direct variation and proportion, inverse and joint variation, dividing polynomials, synthetic division finding rational roots of polynomial equations and approximating irrational roots.

Chapter 9: Analytic geometry using the distance and midpoint formulas, graphs of circles and parabolas, solving quadratic systems graphically and algebraically, solving systems of three equations in three variables and using systems to solve problems.

Chapter 10: Exponential and logarithmic functions including working with rational and irrational exponents, composition and inverses of functions, definition and laws of logarithms, applications of logarithms, solving problems involving exponential growth and decay, and working with the natural logarithm.

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