# Standardized Test Preparation

## New York Regents

Note: Algebra standards are split between Algebra I and Algebra II, so may not appear in numerical order. (For example Real Numbers parts 1 and 2 may appear in Algebra II, and part 3 in Algebra 1.)<br /><br /><br />

## Algebra I - Grade 9

Assessment Exam - NY Regents Algebra I
Number and Quantity - The Real Number System eTAP Lesson
Use properties of rational and irrational numbers
Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.
NY.AI-N.RN.3a
Distributive and Additive Identity, Multiplicative Identity Property and Properties of Equality

Commutative and Associative Property

Basic Operations

Squares and Square Roots

Setting Up and Solving Equations
Categorize the sum or product of rational or irrational numbers.
1. The sum and product of two rational numbers is rational.
2. The sum of a rational number and an irrational number is irrational.
3. The product of a nonzero rational number and an irrational number is irrational.
4. The sum and product of two irrational numbers could be either rational or irrational.

NY.AI-N.RN.3b
Rational & Irrational Numbers
Number and Quantity - Quantities eTAP Lesson
Reason quantitatively and use units to solve problems.
Select quantities and use units as a way to:
1. interpret and guide the solution of multi-step problems
2. choose and interpret units consistently in formulas
3. choose and interpret the scale and the origin in graphs and data displays.

NY.AI-N.Q.1
Functions as Graphs in the Coordinate System
Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities
NY.AI-N.Q.3

Seeing Structure in Expressions eTAP Lesson
Interpret the structure of expressions.
Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
NY.AI-A.SSE.1a
Polynomials
Interpret expressions by viewing one or more of their parts as a single entity.
NY.AI-A.SSE.1b
Variables and Expressions

Open Sentences
Recognize and use the structure of an expression to identify ways to rewrite it.
NY.AI-A.SSE.2
Variables and Expressions

Open Sentences
Write expressions in equivalent forms to reveal their characteristics.
Use the properties of exponents to rewrite exponential expressions.
NY.AI-A.SSE.3c
Rules of Exponents
Arithmetic with Polynomials and Rational Expressions eTAP Lesson
Perform arithmetic operations on polynomials.
Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
NY.AI-A.APR.1
Polynomials
Understand the relationship between zeros and factors of polynomials.
Identify zeros of polynomial functions when suitable factorizations are available.
NY.AI-A.APR.3
Zeros of Polynomial Functions
Creating Equations eTAP Lesson
Create equations that describe numbers or relationships.
Create equations and inequalities in one variable to represent a real-world context.
NY.AI-A.CED.1
Inequalities and the Number Line

Solving Equations by Addition and Subtraction

Changing Words into Math

When to do What
Create equations that describe numbers or relationships.
Create equations and linear inequalities in two variables to represent a real-world context.
NY.AI-A.CED.2
Changing Words into Math

When to do What
Create equations that describe numbers or relationships.
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
NY.AI-A.CED.3

Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
NY.AI-A.CED.4
The Application of Equation Rules to Formulas
Reasoning with Equations and Inequalities eTAP Lesson
Understand solving equations as a process of reasoning and explain the reasoning.
Explain each step when solving a linear or quadratic equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
NY.AI-A.REI.1a
When to do What
Solve equations and inequalities in one variable. eTAP Lesson
Solve equations and inequalities in one variable.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
NY.AI-A.REI.3
When to do What
Reasoning with Equations and Inequalities eTAP Lesson
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Understand that the quadratic formula is a derivative of this process.
NY.AI-A.REI.4a
Completing the Square
1. inspection
2. taking square roots
3. factoring
4. completing the square
6. graphing
Recognize when the process yields no real solutions.
NY.AI-A.REI.4b
Completing the Square

Perfect Square Trinomial

Joe's Method

Solve systems of equations.
Solve systems of linear equations in two variables both algebraically and graphically.
NY.AI-A.REI.6a
Why Do We Need Two Equations?

Simultaneous Equations

The Substitution Method

Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.
NY.AI-A.REI.7a

Graphing Systems of Equations
Represent and solve equations and inequalities graphically.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
NY.AI-A.REI.10

Given the equations y=f(x)and y=g(x):
1. recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x)
2. find the solutions approximately using technology to graph the functions or make tables of values
3. interpret the solution in context

NY.AI-A.REI.11
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
NY.AI-A.REI.12
Graphing Systems of Inequalities
Interpreting Functions eTAP Lesson
Understand the concept of a function and use function notation.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
NY.AI-F.IF.1
Functions
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NY.AI-F.IF.2
Functions
Recognize that a sequence is a function whose domain is a subset of the integers.
NY.AI-F.IF.3
Functions
Interpret functions that arise in applications in terms of the context.
For a function that models a relationship between two quantities:
1. interpret key features of graphs and tables in terms of the quantities
2. sketch graphs showing key features given a verbal description of the relationship.
i>
NY.AI-F.IF.4
Equations as Relations
Interpret functions that arise in applications in terms of the context.
Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
NY.AI-F.IF.5
Ordered Pairs

Equations as Relations
Interpret functions that arise in applications in terms of the context.
Calculate and interpret the average rate of change of a function over a specified interval.
NY.AI-F.IF.6
Slope of a Line
Analyze functions using different representations.
Graph linear, quadratic,and exponential functions and show key features
NY.AI-F.IF.7a

Graph square root, and piecewise-defined functions, including step functions and absolute value functions and show key features.
NY.AI-F.IF.7b

For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.
NY.AI-F.IF.8a
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
NY.AI-F.IF.9

Building Functions eTAP Lesson
Build a function that models a relationship between two quantities.
Determine a function from context.Define a sequence explicitly or steps for calculation from a context.
NY.AI-F.BF.1a
Functions
Build new functions from existing functions.
Using f(x)+ k, k f(x), andf(x+ k):
1. identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), andf(x + k) for specific values of k (both positive and negative)
2. find the value of k given the graphs
3. write a new function using the value of k
4. use technology to experiment with cases and explore the effects on the graph

NY.AI-F.BF.3a
Graphing Systems of Equations
Linear, Quadratic, and Exponential Models eTAP Lesson
Construct and compare linear, quadratic, and exponential models and solve problems.
Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.
NY.AI-F.LE.1a
Function Notation

Direct Variation
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
NY.AI-F.LE.1b
Direct Variation
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.
NY.AI-F.LE.1c
Direct Variation

Exponential Functions and Data
Construct a linear or exponential function symbolically given:
• a graph
• a description of the relationship
• two input-output pairs (include reading these from a table).

NY.AI-F.LE.2
Exponential Functions and Data
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
NY.AI-F.LE.3
Exponential Functions and Data
Interpret expressions for functions in terms of the situation they model.
Interpret the parameters in a linear or exponential function in terms of a context.
NY.AI-F.LE.5
Exponential Functions and Data
Interpreting Categorical and Quantitative Data eTAP Lesson
Summarize, represent, and interpret data on a single count or measurement variable.
Represent data with plots on the real number line (dot plots, histograms, and box plots).
NY.AI-S.ID.1
Showing Orderly Data with Histograms
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (inter-quartile range, sample standard deviation) of two or more different data sets.
NY.AI-S.ID.2
Data Calculations
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
NY.AI-S.ID.3
Methods of Collecting, Representing, & Displaying Data
Summarize, represent, and interpret data on two categorical and quantitative variables.
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
NY.AI-S.ID.5
Methods of Collecting, Representing, & Displaying Data
Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
NY.AI-S.ID.6a
Exponential Functions and Data
Interpret linear models.
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
NY.AI-S.ID.7
Slope of a Line
Calculate (using technology) and interpret the correlation coefficient of a linear fit.
NY.AI-S.ID.8
Correlations
Distinguish between correlation and causation.
NY.AI-S.ID.9
Correlations