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.
- Inferences and Conclusions from Data: Student will understand random and non-random sampling and the biases they may cause and determine normal distributions and calculate variance and standard deviations from a data set.
- Polynomial Functions: Student will simplify algebraic expressions using several properties and operations, understand the graphic solutions to linear systems, and begin to understand complex numbers.
- Rational and Radical Relationships: Student will solve multi-step equations, write equations of a line given various information, use conjugates to rationalize the denominator of an algebraic expression, and solve different types of problems using rational equations.
- Exponents and Logarithms: Student will understand common and natural logarithms, exponential equations, and graphs of logarithms, square and cube roots, and exponential functions.
- Trigonometric Functions: Student will evaluate trigonometric and reciprocal trigonometric functions in degrees and radians and identify their graphs and specific parts of their graphs, and solve trigonometric equations using Pythagorean identities and substitution.
- Mathematical Modeling: Student will calculate the common difference of an arithmetic sequence, the common ratio of a geometric sequence, and extend them to the nth term, graph quadratics and analyze them as they are changed using different methods and use ratios or proportions to be able to calculate unit scales and solve problems.