2nd Year Algebra
(Advanced Algebra)

Third Draft - Updated 6/20/00

Prerequisite: 1st year Algebra

This course utilizes and expands the skills taught in 1st Year Algebra. Properties of real numbers are applied to linear and quadratic functions and the solving of equations and systems of equations. Included topics are conic sections, complex numbers, exponents, logarithms, exponential, logarithmic and polynomial functions, sequences and series, and probability and statistics.

1. The student understands and applies the concepts and procedures of mathematics.

• 1. simplifies and evaluates complex algebraic expressions
• 2. solves and graphs equations, systems of equations, and formulas
• 3. evaluates linear, nonlinear, inverse, and absolute value functions
• 4. solves complex polynomial equations using a variety of methods
• 5. uses complex rational expressions and equations
• 6. solves systems of equations using matrix operations
• 7. solves and graphs conic sections
• 8. simplifies and solves complex radical expressions/equations

2. The student uses mathematics to define and solve problems.

• 1. identifies what information is missing or extraneous and compensates for it
• 2. develops complex algebraic expressions
• 3. applies appropriate methods, operations, and processes to construct a solution
• 4. shows all steps in problem solving

3. The student uses mathematical reasoning

• 1. makes and tests predictions and inferences to either support or contradict them
• 2. checks for reasonableness of results
• 3. supports arguments and justifies results using inductive and deductive reasoning
• 4. reflects on and evaluates procedures and results and makes necessary revisions

4. The student communicates knowledge and understanding in both everyday and mathematical language.

• 1. expresses ideas and situations using mathematical language and notations in appropriate and efficient form
• 2. collects, organizes, clarifies, and refines mathematical information by reflecting, verbalizing, discussing, or writing.

5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

• 1. applies algebraic formulas to solve problems from work and life situations
• 2. integrates the use of a variety of available technologies
• 3. investigates the mathematical knowledge and training requirements for occupational or career areas of interest
• 4. applies mathematical thinking and modeling in other disciplines