# Standardized Test Preparation

## New York Regents

Assessment Exam - NY Regents 8th Grade Math
The Number System eTAP Lesson
Know that there are numbers that are not rational, and approximate them by rational numbers.
Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion eventually repeats. Know that other numbers that are not rational are called irrational.
NY.MATH.8.NS.1
Operations with Decimals

Rational & Irrational Numbers
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.
NY.MATH.8.NS.2
Integers and the Number Line
Expressions, Equations, and Inequalities eTAP Lesson
Work with radicals and integer exponents.
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
NY.MATH.8.EE.1
Raising Numbers to Various Powers

Rules of Exponents
Use square root and cube root symbols to represent solutions to equations of the form x2= pand x3 = p, where p is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.
NY.MATH.8.EE.2

Completing the Square

Squares and Square Roots

Perfect Square Trinomial
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
NY.MATH.8.EE.3
Base Ten Exponents
Perform multiplication and division with numbers expressed in scientific notation, including problems where both standard decimal form and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.
NY.MATH.8.EE.4

Understand the connections between proportional relationships, lines, and linear equations.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
NY.MATH.8.EE.5
Ratios and Proportions

Setting Up and Solving Equations
Use similar triangles to explain why the slope mis the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
NY.MATH.8.EE.6
Slope Intercept Form of Equations

Slope of a Line
Analyze and solve linear equations and pairs of simultaneous linear equations.
Solve linear equations in one variable. Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibilities is the case by successively transforming the given equation into simpler forms.
NY.MATH.8.EE.7a
Basic Operations

Simultaneous Equations With Strange Solutions

Changing Words into Math
Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.
NY.MATH.8.EE.7b
Factoring with the Distributive Property

The Substitution Method
Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Recognize when the system has one solution, no solution, or infinitely many solutions.
NY.MATH.8.EE.8a
Why Do We Need Two Equations?

Graphing Systems of Inequalities

When to do What

Summary
Analyze and solve pairs of simultaneous linear equations. Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.
NY.MATH.8.EE.8b
Solving Equations When Several Terms and Procedures are Involved
Analyze and solve pairs of simultaneous linear equations. Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.simultaneous linear equations.
NY.MATH.8.EE.8c
Simultaneous Equations

Summary
Functions eTAP Lesson
Define, evaluate, and compare functions.
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
NY.MATH.8.F.1
Summary

What is a Function?
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
NY.MATH.8.F.2
Visually Representing Numerical Data
Interpret the equation y= mx+ bas defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.
NY.MATH.8.F.3
Slope of a Line

Slope Intercept Form of Equations
Use functions to model relationships between quantities.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
NY.MATH.8.F.4
Functions as Graphs in the Coordinate System

Seeking Trends with Line Graphs
Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described in a real-world context.
NY.MATH.8.F.5
Graphing Data

Splitting up the Whole with Pie Graphs

Comparing Categories with Bar Graphs
Geometry eTAP Lesson
Understand congruence and similarity using physical models, transparencies, or geometry software.
Verify experimentally the properties of rotations, reflections, and translations.
1. Verify experimentally lines are mapped to lines, and line segments to line segments of the same length.
2. Verify experimentally angles are mapped to angles of the same measure.
3. Verify experimentally parallel lines are mapped to parallel lines.

NY.MATH.8.G.1
Tessellations Using Translations, Rotations, and Glide Reflections
Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.
NY.MATH.8.G.2
SSS and SAS Congruencies

ASA Congruencies

AAS and HL Congruencies
Describe the effect of dilations, translations, rotations,and reflections on two-dimensional figures using coordinates.
NY.MATH.8.G.3
Transformations
Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.
NY.MATH.8.G.4
Similar Triangles

Symmetry

Expressing Relationships Between Figures
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
NY.MATH.8.G.5
Corresponding Parts

Lines and Angles
Understand and apply the Pythagorean Theorem.
Understand a proof of the Pythagorean Theorem and its converse.
NY.MATH.8.G.6
Historical Beginnings

Other Commonly Used Functions – Cosine and Tangent
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
NY.MATH.8.G.7
The Application of Equation Rules to Formulas

Indirect Measurement with Similar Triangles
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
NY.MATH.8.G.8
The Theorem of Pythagoras

Distance Calculations

Other Functions in a Right Triangle – Secant, Cosecant, and Cotangent
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems.
NY.MATH.8.G.9
Cones

Cylinders

Solids with Curved Surfaces
Statistics and Probability eTAP Lesson
Investigate patterns of association in bivariate data.
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
NY.MATH.8.SP.1
Paired Data Sets and Scatterplots
Understandthat straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
NY.MATH.8.SP.2
Correlations