Advanced Algebra is a full year high school mathematics course intended for the student who has successfully completed Analytic Geometry. This course is designed to prepare students for college‐level and real‐world mathematical reasoning. The concepts covered in this course integrate the topics of Statistics, Algebra II, and Trigonometry. Throughout the course, students will perform operations with rational, radical, and exponential expressions, explore higher order strategies necessary for analyzing multi‐level logarithmic, exponential, linear, quadratic and polynomial functions and equations. Students are exposed to several branches of mathematics and will explore ways in which each one can be used as a mathematical model in understanding the world.
The course seeks to help students expand their knowledge and skills so that they may achieve the following goals:
- Gain an increased awareness of math as a life skill.
- Understand how math is like a language, with a set of conventions.
- Realize that while mathematical models are useful in studying the world, they have limits.
In attaining these goals, students will begin to see the “big picture” of mathematics and understand how numeric, algebraic, and geometric concepts are woven together to build a foundation for higher mathematical thinking.
Upon successfully completing the course, the student should have mastered the following concepts:
- Solve exponential, logarithmic, and polynomial equations and inequalities.
- Perform basic and complex operations with polynomials.
- Solve single and multi‐variable equations and inequality statements.
- Solve systems of equations with graphing and substitution.
- Evaluate, graph and solve exponential equations.
- Be able to construct a formula or equation necessary to solve algebraic word problems involving area, perimeter, and linear systems of equations, basic probability and statistical reasoning, distance, and compounding interest.
- Evaluate functions and their inverses using sum, difference, product, quotient and composition of functions.
- Construct and analyze the graphs of the trigonometric functions.
- Verify equivalence statements and solve trigonometric equations and inequalities involving trigonometric identities, inverse trigonometric functions (sine, cosine and tangent only) and the unit circle.
- Apply fundamentals of solving triangles using right triangle trigonometry and special right triangles.
- Calculate measures of central tendency and interpret statistical data.