A2.1: Number Systems and Non-Linear Expressions & Equations

A2.1.1: Operations with Complex Numbers

A2.1.1.1: Represent and/or use imaginary numbers in equivalent forms (e.g., square roots and exponents).

A2.1.1.1.2: Simplify/evaluate expressions involving powers of i (e.g., i to the 6th power + iÂ³ = -1 Â?i).

A2.1.1.2: Apply the order of operations in computation and in problem-solving situations.

A2.1.1.2.1: Add and subtract complex numbers (e.g., (7Â?3i)Â?(2 + i) = 5Â?4i).

A2.1.1.2.2: Multiply and divide complex numbers (e.g., (7Â?3i)(2 + i) = 17+i).

A2.1.2: Non-Linear Expressions

A2.1.2.1: Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems.

A2.1.2.1.2: Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers-exponents should not exceed power of 10).

A2.1.3: Non-Linear Equations

A2.1.3.1: Write and/or solve non-linear equations using various methods.

A2.1.3.1.1: Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).

A2.1.3.1.2: Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x Â? 2) = 1 or the square root of (xÂ² + 21x) = 14).

A2.1.3.1.3: Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).

A2.1.3.1.4: Write, solve, and/or apply linear or exponential growth or decay (including problem situations).

A2.1.3.2: Describe and/or determine change.

A2.1.3.2.1: Determine how a change in one variable relates to a change in a second variable (e.g., y = 4/x; if x doubles, what happens to y?).

A2.1.3.2.2: Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).

A2.2: Functions and Data Analysis

A2.2.1: Patterns, Relations, and Functions

A2.2.1.1: Analyze and/or use patterns or relations.

A2.2.1.1.2: Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).

A2.2.1.1.3: Determine the domain, range, or inverse of a relation.

A2.2.1.1.4: Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes).

A2.2.2: Applications of Functions

A2.2.2.1: Create, interpret, and/or use polynomial, exponential, and/or logarithmic functions and their equations, graphs, or tables.

A2.2.2.1.1: Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics).

A2.2.2.1.2: Create, interpret, and/or use the equation, graph, or table of an exponential or logarithmic function (including common and natural logarithms).

A2.2.2.1.3: Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential, or logarithmic function.

A2.2.2.2: Describe and/or determine families of functions.

A2.2.2.2.1: Identify or describe the effect of changing parameters within a family of functions (e.g., y = xÂ² and y = xÂ² + 3, or y = xÂ² and y = 3xÂ²).

A2.2.3: Data Analysis

A2.2.3.1: Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.

A2.2.3.1.1: Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.

A2.2.3.1.2: Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.

A2.2.3.2: Apply probability to practical situations.

A2.2.3.2.1: Use combinations, permutations, and the fundamental counting principle to solve problems involving probability.

A2.2.3.2.3: Use probability for independent, dependent, or compound events to predict outcomes.

Correlation last revised: 9/16/2020

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