Keystone Exams Assessment Anchors and Eligible Content
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 + i³ = -1 – 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., (7 – 3i) – (2 + i) = 5 – 4i).
A2.1.1.2.2: Multiply and divide complex numbers (e.g., (7 – 3i)(2 + i) = 17 + i).
A2.1.2.1: Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems.
A2.1.2.1.1: Use exponential expressions to represent rational numbers.
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
Operations with Radical Expressions
Simplifying Radical Expressions
A2.1.2.1.3: Simplify/evaluate expressions involving multiplying with exponents (e.g., (x to the 6th power) times (x to the 7th power) = x to the 13th power), powers of powers (e.g., (x to the 6th power) to the 7th power = x to the 42nd power) and powers of products (e.g., (2x²)³ = 8x to the 6th power).
Exponents and Power Rules
Multiplying Exponential Expressions
A2.1.2.2: Simplify expressions involving polynomials.
A2.1.2.2.1: Factor algebraic expressions, including difference of squares and trinomials.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
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).
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 – 2) = 1 or the square root of (x² + 21x) = 14).
A2.1.3.1.4: Write, solve, and/or apply linear or exponential growth or decay (including problem situations).
Compound Interest
Exponential Growth and Decay
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).
Solving Formulas for any Variable
A2.2.1.1: Analyze and/or use patterns or relations.
A2.2.1.1.1: Analyze a set of data for the existence of a pattern, and represent the pattern with a rule algebraically and/or graphically.
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
Geometric Sequences
A2.2.1.1.3: Determine the domain, range, or inverse of a relation.
Introduction to Functions
Logarithmic Functions
Radical Functions
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).
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
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).
Graphs of Polynomial Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
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
Quadratics in Polynomial Form
Quadratics in Vertex Form
A2.2.2.1.4: Translate a polynomial, exponential, or logarithmic function from one representation of a function to another (graph, table, and equation).
Exponential Functions
Graphs of Polynomial Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex 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 = x² and y = x² + 3, or y = x² and y = 3x²).
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic 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
A2.2.3.1: 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
Trends in 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.
Independent and Dependent Events
Correlation last revised: 7/13/2022