Advanced Algebra 2
The general goal of this course is to develop algebraic skills and to apply these skills in the solution of problems. The topics to be covered include operations and properties of real and complex numbers, solutions of linear and quadratic equations, inequalities and systems, linear programming, operations on polynomials and rational expressions, the binomial theorem, analysis of relations and functions, analysis of conics, logarithmic and exponential functions, sequences and series, operations with matrices, data collection, probability and statistics, measure of central tendency and problem solving.
The book that is used for this course is a college level book, Intermediate Algebra, 5th edition, written by Mark Dugopolski.
Upon completion of this course, the student will be able to:
- Simplify, add, subtract, multiply and divide integers, rational numbers, irrational numbers, complex numbers, and polynomials.
- Solve linear and quadratic equations and inequalities in one variable, including ones involving absolute values. Students will be able to use these equations to solve application problems.
- Solve elementary linear programming problems.
- Find function values, inverse functions, and determine domain, range, and graphs of the inverse function.
- Find the vertex and the axis of symmetry of a quadratic function, graph it, and determine the minimum or maximum of the function.
- Solve systems of three linear equations by using substitution, linear combination, Cramer’s Rule, or inverses of the coefficient matrices.
- Factor polynomials and find the solution to polynomial equations with rational zeros.
- Evaluate and operate on expressions containing rational and real exponents and to rewrite them as a logarithmic statements.
- Solve and graph logarithmic and exponential equations and check for extraneous solutions.
- Analyze data, then draw and justify conclusions based on this analysis. They will then be able to use this information to answer questions about real-life situations.
- Simplify expressions with roots and/or rational exponents and solve radical equations.
- Determine the type of conic, rewrite in standard form for that conic, and locate the various parts of that conic, given the equation of the conic.
- Evaluate factorials and Pascal numbers and will be able to recognize patterns among them.
- Solve logarithmic equations and to check for extraneous solutions.
- Use the binomial theorem to expand a binomial that is raised to a power and will be able to find a specified term of this expansion.
- Find the probability of an event by using the fundamental counting principle, combinations, union, intersections, and complements.