Topics in Algebra 2 Syllabus

Core Connections Algebra 2 is the third course in a five-year sequence of rigorous college preparatory mathematics courses that starts with Algebra I and continues through Calculus. It aims to apply and extend what students have learned in previous courses by focusing on finding connections between multiple representations of functions, transformations of different function families, finding zeros of polynomials and connecting them to graphs and equations of polynomials, modeling periodic phenomena with trigonometry, and understanding the role of randomness and the normal distribution in making statistical conclusions.

On a daily basis, students in Core Connections Algebra 2 use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Under teacher guidance, students learn in collaboration with others while sharing information, expertise, and ideas.

The course is well balanced between procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and transference). The lessons in the course meet all of the content standards, including the “plus” standards, of Appendix A of the Common Core State Standards for Mathematics. The course embeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.

Key concepts addressed in this course are:

• Visualize, express, interpret and describe, and graph functions (and their inverses, in many cases). Given a graph, students will be able to represent the function with an equation, and vice-versa, and transform the graph, including the following function families:

  • absolute value

  • exponential

  • linear

  • logarithmic

  • piecewise-defined

  • polynomial

  • quadratic

  • square root

  • trigonometric

• Use of variables and functions to represent relationships given in tables, graphs, situations, and geometric diagrams, and recognize the connections among these multiple representations.

• Application of multiple algebraic representations to model and solve problems presented as real world situations or simulations.

• Solving linear or quadratic equations in one variable, systems of equations in two variables, and linear systems of equations in three or more variables, including solving with graphical methods.

• Use of algebra to rewrite complicated algebraic expressions and equations in more useful forms.

• Rewriting rational expressions and arithmetic operations on polynomials.

• The relationship between zeros and factors of polynomials.

• Operations with complex numbers, and solving quadratic equations with complex solutions.

• Modeling periodic phenomena with trigonometric functions.

• Solving trigonometric equations and proving trigonometric identities.

• Calculating the sums of arithmetic and geometric series, including infinite geometric series.

• Concepts of randomness and bias in survey design and interpretation of the results.

• Use of a normal distribution to model outcomes and to make inferences as appropriate.

• Use of computers to simulate and determine complex probabilities.

• Use of margin of error and sample-to-sample variability to evaluate statistical decisions.

• Understand logarithms and their inverse relationship with exponentials.

• Use logarithms to solve exponential equations.