This course builds upon the body of knowledge and skill set learned from Algebra 1 and moves beyond. The course is the first semester of Algebra 2 and includes the topics: Linear Equations, Inequalities, and Systems; Advanced Systems and Matrices; Functions; Quadratic Functions; Polynomial Functions. Algebra 2 is approved by the University of California A-G as mathematics (category C).
Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course at an accelerated rate.
In this module, students gain a comprehension of the following:
• How to solve multi-step linear equations and inequalities, including those involving absolute value.
• How to graph linear equations and inequalities using slope, intercepts, and standard form.
• How to write linear equations given points, slopes, or real-world context, and identify parallel and perpendicular lines.
• How to solve systems of equations and inequalities using graphing, substitution, and elimination methods.
• How to apply systems of inequalities and linear programming to solve optimization problems.
• How to solve systems of equations in three variables using substitution and elimination.
• How to perform matrix operations, including addition, subtraction, scalar multiplication, and matrix multiplication.
• How to calculate determinants and use Cramer’s Rule to solve systems of equations.
• How to find inverses of 2×2 matrices and use them to solve systems of equations.
• How to solve systems using augmented matrices and Gaussian/Gauss-Jordan elimination.
• How to identify functions, use function notation, and determine domain, range, and continuity.
• How to analyze function graphs and identify intercepts, extrema, and intervals of increase or decrease.
• How to sketch graphs of parent and piecewise functions and apply transformations.
• How to perform operations on functions, including composition, and classify them as even, odd, or neither.
• How to find and verify inverse functions both algebraically and graphically.
• How to analyze the features of quadratic functions, such as vertex and axis of symmetry.
• How to solve quadratic equations by graphing, factoring, completing the square, and using the quadratic formula.
• How to simplify and perform operations with complex numbers.
• How to model real-world problems with quadratic functions and interpret graphs and solutions.
• How to graph and solve quadratic inequalities and linear-quadratic systems.
• How to perform operations with polynomials and simplify using exponent rules.
• How to graph polynomial functions and analyze end behavior and turning points.
• How to factor polynomials completely using special products and grouping techniques.
• How to solve polynomial equations algebraically and graphically, and interpret the solutions.
• How to expand binomial expressions using Pascal’s Triangle and the Binomial Theorem.
