Algebra II

In this course, students will expand their understanding of quadratic functions to cubic and higher-order polynomials. They will gain detailed experience in dealing with fundamental concepts associated with these polynomials, including least common factors and multiples, polynomial factorization, division, solving polynomial equations, and applying key polynomial theorems in various contexts.

Building on the solid foundations laid out in Algebra I, this course enables students to deepen their understanding of functions. They will explore global and local extrema, periodicity, even and odd functions, and invertible functions. They will be carefully guided through the process of performing graph transformations of functions and will learn to compute inverse functions seamlessly.

As the course progresses, students will enrich their knowledge of exponential functions. This includes a deep dive into logarithms, examining their graphs and properties. Students will learn to solve both exponential and logarithmic equations and further develop their aptitude for modeling scenarios with exponential functions, such as calculating compound interest.

Building upon the knowledge acquired in Geometry, this course facilitates deep explorations of trigonometric functions. Students will dive into the intricacies of the unit circle and discover how it elegantly extends the trigonometric ratios. Students will learn to apply the Law of Sines and Cosines effectively, graph trigonometric functions with precision, describe their distinct properties and master the techniques for transforming the graphs of trigonometric functions.

• Understand the hierarchy and properties of the real number system, including classifying natural, integer, rational, and irrational numbers.
• Convert repeating decimals to fractions and describe general properties of operations with rational and irrational numbers.
• Understand the fundamentals of complex numbers and perform arithmetic operations with them.
• Solve quadratic equations with imaginary and complex solutions, and understand the cyclic property of the imaginary unit.
• Identify and find the least common factors and multiples of monomials and polynomials.
• Factor polynomials using various techniques, including using the greatest common factor, difference of squares, grouping, sum/difference of cubes, and factoring biquadratic expressions.
• Divide polynomials using synthetic division, long division, and manipulation of rational expressions.
• Determine the roots of polynomial equations using the factor, remainder, and rational roots theorems.
• Graph polynomial functions, describing key features such as end behavior and roots.
• Identify one-to-one and invertible functions, restricting the range of a function to make it invertible, and the relationship between the domain and range of a function and that of its inverse.
• Analyze local extrema of functions, periodic functions, even and odd functions, and unbounded behavior of functions.
• Calculate the average rate of change of a function.
• Apply graph transformations, including translations, stretches, reflections, and combinations of these. Apply absolute value graph transformations.
• Determine the domain and range of transformed functions and locate points on the transformed graphs.
• Convert between exponential and logarithmic forms of expressions, evaluate logarithms, and use the properties of logarithms to simplify expressions.
• Solve exponential and logarithmic equations, including those with different bases.
• Graph exponential and logarithmic functions and understand the properties of these graphs.
• Model real-world scenarios with exponential functions, including financial applications such as compound and continuously compounded interest.
• Simplify, add, subtract, multiply, and divide rational expressions.
• Graph and analyze reciprocal and rational functions, including identifying asymptotes, roots, intercepts, and end behavior.
• Combine transformations of reciprocal functions and analyze their domains, ranges, and inverses.
• Simplify radical expressions, and solve radical equations, including those with extraneous solutions.
• Graph and analyze radical functions, including identifying key features of the graph such as domain, range, and intercepts.
• Write equations of circles, and calculate the center and radius of a circle from its equation, including completing the square.
• Calculate intercepts of circles and parabolas, and find intersections of these conics with lines.
• Understand and apply the focus-directrix property of a parabola.
• Develop a strong foundation in trigonometry, including understanding and applying trigonometric ratios, working with radians, and utilizing the unit circle.
• Master graphing and analyzing trigonometric functions, including applying graph transformations and describing their resulting properties. Use transformed trigonometric functions to model real-world scenarios.
• Develop and apply the Law of Sines and the Law of Cosines, using them to model and solve problems in real-world situations.