Integrated Math II

In this comprehensive course, students will fully master quadratic equations and functions, achieving fluency in the various methods for solving problems that involve quadratics. They will also explore how quadratic functions can be adeptly used in modeling real-world situations. Students will also explore fundamental concepts related to complex numbers.

Building on foundations laid out in Integrated Math I, students will extend their understanding of functions to encompass function arithmetic, composition, 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.

This course aims to broaden students’ knowledge to include crucial geometric concepts such as similarity, fundamental circle theorems, conic sections, and solid geometry. Concurrently, students will lay a robust foundation in trigonometry, delving into the unit circle and its pivotal role in extending trigonometric ratios and graphing trigonometric functions.

Finally, students lay solid foundations in probability and combinatorics and build on previous understandings of correlation and regression, further solidifying their skills in these areas.

• Develop a comprehensive understanding of the hierarchical nature of the number system and the role of complex numbers within it.
• Solve quadratic equations using various methods, including applying the zero product rule and completing the square and the quadratic formula.
• Graph and analyze quadratic functions, calculate the axis of symmetry using various methods and find intersections of lines and quadratic functions.
• Model real-world situations using quadratic functions, including vertical motion, revenue, cost, and profit functions.
• Further develop their understanding of more general polynomials, including finding the least common factor and least common multiple of two polynomials and describing numerical relationships using polynomial identities.
• Explore and develop a basic comprehension of complex numbers, including addition, subtraction, and multiplication. They will solve quadratic equations with complex roots and understand the cyclic property of the imaginary unit.
• Extend their knowledge of functions to incorporate function composition, describe one-to-one and many-to-one functions, local extrema, periodicity, even and odd functions, and vertical asymptotes of functions.
• Understand the concept of an invertible function, including how graphs of functions and their inverses are related, their domains and ranges, and compute inverses of linear, quadratic, exponential, and logarithmic functions.
• Strengthen their understanding of transformations in the plane to include graph transformations of functions, including vertical and horizontal translations, stretches, and reflections, composite transformations with multiple operations, and absolute value transformations.
• Work with absolute value functions and their associated graphs, describe their properties and further develop their understanding of absolute value equations to more complex cases involving extraneous solutions.
• Further explore exponentials and logarithms, including evaluating logarithms, applying the laws of logarithms, graphing exponential and logarithmic functions, and solving exponential and logarithmic equations.
• Model real-world situations using exponential functions, such as those involving compound interest, including continuously compounded interest.
• Understand geometric sequences, including finding a given geometric sequence's nth term and common ratio, and work with recursive formulas for geometric sequences.
• Utilize sigma notation, calculate the sum of arithmetic series, apply the binomial theorem, and explain how it relates to Pascal's Triangle.
• Solve radical equations, including cases with no real solutions.
• Understand and apply the concept of similarity, including utilizing similarity criteria for triangles, working with areas of similar polygons, and similarity transformations.
• Explore properties of circles, such as inscribed angles, Thales' theorem, and tangent lines.
• Investigate circles and parabolas as conic sections.
• Learn to identify and work with three-dimensional shapes, calculate surface areas and volumes of polyhedra and non-polyhedra, and explore Euler's formula and Platonic solids.
• 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.
• Learn the basics of probability and combinatorics, including Venn diagrams, compound events, factorials, permutations, and combinations.
• Analyze data using statistical methods, such as computing a data set's mean, variance, standard deviation, z-scores, and covariance.
• Further explore correlation and regression, including calculating linear correlation coefficients, carrying out linear regression, and analyzing residuals.