Keystone Exams Assessment Anchors and Eligible Content

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).

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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).

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Roots of a Quadratic

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).

Operations with Radical Expressions

Radical Functions

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).

Compound Interest

Dilations

Direct and Inverse Variation

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?).

Translating and Scaling Functions

Zap It! Game

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

Area of Triangles

Solving Formulas for any Variable

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).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

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).

Addition and Subtraction of Functions

Exponential Functions

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Translating and Scaling Functions

Zap It! Game

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).

Addition and Subtraction of Functions

Exponential Functions

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Translating and Scaling Functions

Zap It! Game

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).

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

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.

Graphs of Polynomial Functions

Quadratics in Factored Form

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).

Introduction to Exponential Functions

Points, Lines, and Equations

Translating and Scaling Functions

Zap It! Game

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.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

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

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

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.

Independent and Dependent Events

Correlation last revised: 5/20/2019

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