Standardized Test Preparation

Arizona State Standards

Language Arts - Grade 10

Assessment Exam - AZM2 Math Grade 10

Reading Standards for Literature	eTAP Lesson
Craft and Structure
Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone. AZ.M2.ELA.9-10.RL.4	Figurative Language Figurative, Connotative, and Technical Meanings

Math - Grade 10

The Real Number System	eTAP Lesson
Use properties of rational and irrational numbers.
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. AZ.M2.Math.10.A1.N-RN.B3	Integers and the Number Line Adding and Subtracting Integers Dividing Rational Numbers
Quantities	eTAP Lesson
Reason quantitatively and use units to solve problems.
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays, include utilizing real-world context. AZ.M2.Math.10.A1.N-Q.A.1	Graphing Data
Define appropriate quantities for the purpose of descriptive modeling. Include problem-solving opportunities utilizing real-world context. AZ.M2.Math.10.A1.N-Q.A.2	Mathematical Modeling
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities utilizing real-world context. AZ.M2.Math.10.A1.N-Q.A.3	Analysis of Pollutants
Seeing Structure in Expressions	eTAP Lesson
Interpret the structure of expressions.
Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret expressions by viewing one or more of their parts as a single entity. AZ.M2.Math.10.A1.A-SSE.A.1	Factors and Greatest Common Factors (GCF) Factoring with the Distributive Property Factoring by Grouping
Use structure to identify ways to rewrite numerical and polynomial expressions. Focus on polynomial multiplication and factoring patterns. AZ.M2.Math.10.A1.A-SSE.A.2	Polynomials
Write expressions in equivalent forms to solve problems.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. AZ.M2.Math.10.A1.A-SSE.B.3	Factoring Trinomials Factoring Differences of Squares Perfect Square Factoring Graphing Quadratic Functions
Arithmetic with Polynomials and Rational Expressions	eTAP Lesson
Perform arithmetic operations on polynomials.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. AZ.M2.Math.10.A1.A-APR.A.1	Adding and Subtracting Polynomials Multiplying and Dividing Monomials
Understand the relationship between zeros and factors of polynomials.
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Focus on quadratic and cubic polynomials in which linear and quadratic factors are available AZ.M2.Math.10.A1.A-APR.B.3	Quadratic Formula Solving Quadratic Equations by Graphing
Creating Equations	eTAP Lesson
Create equations that describe numbers or relationships.
Create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context.Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.A-CED.A.1	Variables and Expressions Open Sentences
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. AZ.M2.Math.10.A1.A-CED.A.2	Graphing Systems of Equations Substitution
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. AZ.M2.Math.10.A1.A-CED.A.3	Graphing Systems of Inequalities
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. AZ.M2.Math.10.A1.A-CED.A.4	Solving Equations Using Several Operations
Reasoning with Equations and Inequalities	eTAP Lesson
Understand solving equations as a process of reasoning and explain the reasoning.
Explain each step in solving linear and quadratic equations 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. AZ.M2.Math.10.A1.A-REI.A.1	Solving Equations by Multiplication and Division
Solve linear equations and inequalitiesin one variable, including equations with coefficients represented by letters. AZ.M2.Math.10.A1.A-REI.B.3	Slope of a Line Slope Intercept Form of Equations
Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – k)2 = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Focus on solutions for quadratic equations that have real roots. Include cases that recognize when a quadratic equation has no real solutions. AZ.M2.Math.10.A1.A-REI.B.4	Completing the Square Sum and Product of Roots Discriminant Solving Inequalities by Addition and Subtraction
Solve systems of equations.
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. AZ.M2.Math.10.A1.A-REI.C.5	Why Do We Need Two Equations? Simultaneous Equations
Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Include problem solving opportunities utilizing real-world context. AZ.M2.Math.10.A1.A-REI.C.6	Simultaneous Equations With Strange Solutions The Addition - Subtraction Method
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, often forming a curve, which could be a line. AZ.M2.Math.10.A1.A-REI.D.10	How to Use Graphs
Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x) =g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations).Focus on cases where f(x) and/or g(x) are linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.A-REI.D.11	Solving Quadratic Equations by Graphing
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. AZ.M2.Math.10.A1.A-REI.D.12	Midpoint of a Line Segment
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). AZ.M2.Math.10.A1.F-IF.A.1	Function Notation Direct Variation Linear Parametric equations
Evaluate a function for inputs in the domain, and interpret statements that use function notation in terms of a context. AZ.M2.Math.10.A1.F-IF.A.2	Other Commonly Used Functions – Cosine and Tangent
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. AZ.M2.Math.10.A1.F-IF.A.3	What is a Function?
Interpret functions that arise in applications in terms of the context.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Include problem-solving opportunities utilizing real-world context.Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums.Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.F-IF.B.4	The Application of Equation Rules to Formulas
Relate the domain of a function to its graph and, where applicable, to the quantitativerelationship it describes. AZ.M2.Math.10.A1.F-IF.B.5	Interpolating to Find the Function When You Know the Angle
Calculate and interpret the average rate of change of a continuous function (presented symbolically or as a table) on a closed interval. Estimate the rate of change from a graph. Include problem-solving opportunities utilizing real-world context. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.F-IF.B.6	Graphs of Polynomial Functions
Analyze functions using different representations.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.F-IF.C.7	Simple Quadratic Functions
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square of a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. AZ.M2.Math.10.A1.F-IF.C.8	Zeros of Polynomial Functions
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Focus on linear, quadratic,exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.F-IF.C.9	Quadratic Functions in Intercept Form
Building Functions	eTAP Lesson
Build a function that models a relationship between two quantities.
Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from real-world context.Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.F-BF.A.1	Negative and Rational Exponents
Build new functions from existing functions.
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph. Focus on linear, quadratic, exponential and piecewise-defined functions (limited to absolute value and step). AZ.M2.Math.10.A1.F-BF.B.3	Factoring Quadratics
Linear, Quadratic, and Exponential Models	eTAP Lesson
Construct and compare linear, quadratic, and exponential models and solve problems.
Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. AZ.M2.Math.10.A1.F-LE.A.1	The number e Exponential Functions and Data Graphs of Exponential Functions Square Root Functions
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or input/output pairs. AZ.M2.Math.10.A1.F-LE.A.2	Radical Functions
Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. AZ.M2.Math.10.A1.F-LE.A.3	Graphs and Dipgrahs
Interpret expressions for functions in terms of the situation they model.
Interpret the parameters in a linear or exponential function with integer exponents utilizing real world context. AZ.M2.Math.10.A1.F-LE.B.5
Summarize, represent, and interpret data on a single count or measurement variable.	eTAP Lesson
Summarize, represent, and interpret data on a single count or measurement variable.
Represent real-value data with plots for the purpose of comparing two or more data sets. AZ.M2.Math.10.A1.S-ID.A.1	Visually Representing Numerical Data
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. AZ.M2.Math.10.A1.S-ID.A.2	What are Statistics? Probability
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers if present. AZ.M2.Math.10.A1.S-ID.A.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. AZ.M2.Math.10.A1.S-ID.B.5	Data Calculations
Represent data on two quantitative variables on a scatter plot and describe how the quantities are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Focus on linear models. Informally assess the fit of a function by plotting and analyzing residuals. AZ.M2.Math.10.A1.S-ID.B.6	Paired Data Sets and Scatterplots Correlations Functions as Graphs in the Coordinate System
Interpret linear models.
Interpret the slope as a rate of change and the constant term of a linear model in the context of the data. AZ.M2.Math.10.A1.S-ID.C.7	Seeking Trends with Line Graphs
Compute and interpret the correlation coefficient of a linear relationship. AZ.M2.Math.10.A1.S-ID.C.8	Regression Models and Least Square Methods
Distinguish between correlation and causation. AZ.M2.Math.10.A1.S-ID.C.9
Conditional Probability and the rules of Probability	eTAP Lesson
Understand independence and conditional probability and use them to interpret data.
Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events. AZ.M2.Math.10.A1.S-CP.A.1	Multiple Events Conditional Probability
Use the Multiplication Rule for independent events to understand that two events A and Bare independent if the probability of A and B occurring together is the product of their probabilities and use this characterization to determine if they are independent. AZ.M2.Math.10.A1.S-CP.A.2	Binomial Distributions Normal Distributions Dependent & Independent Variables
Quantities	eTAP Lesson
Reason quantitatively and use units to solve problems.
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays, include utilizing real-world context. AZ.M2.Math.10.G.N-Q.A.1
Define appropriate quantities for the purpose of descriptive modeling. Include problem-solving opportunities utilizing real-world context. AZ.M2.Math.10.G.N-Q.A.2
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities utilizing real-world context. AZ.M2.Math.10.G.N-Q.A.3
Congruence	eTAP Lesson
Experiment with transformations in the plane.
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc AZ.M2.Math.10.G.G-CO.A.1	Definition - Circles Definitions - Geometry Line and Angle Relationships
Represent and describe transformations in the plane as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not AZ.M2.Math.10.G.G-CO.A.2	Transformations Properties of Isometrics
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself AZ.M2.Math.10.G.G-CO.A.3	Tessellations Using Translations, Rotations, and Glide Reflections
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. AZ.M2.Math.10.G.G-CO.A.4	Constructing Perpendicular Bisectors Constructing Parallel Lines
Given a geometric figure and a rotation, reflection, or translation draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another. AZ.M2.Math.10.G.G-CO.A.5	Definitions of Figures Constructing Points of Concurrency
Understand congruence in terms of rigid motions.
Use geometric definitions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent AZ.M2.Math.10.G.G-CO.B.6	SSS and SAS Congruencies
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. AZ.M2.Math.10.106 G.G-CO.B.7	Triangle Inequalities
Explain how the criteria for triangle congruence (ASA, AAS, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. AZ.M2.Math.10.G.G-CO.B.8	ASA Congruencies AAS and HL Congruencies
Prove geometric theorems.
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. AZ.M2.Math.10.G.G-CO.C.9	Postulates of Geometry Geometric Proofs
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangle are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. AZ.M2.Math.10.G.G-CO.C.10	Proving Angle Conjectures Indirect Measurement with Similar Triangles Special Right Triangles
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and rectangles are parallelograms with congruent diagonals. AZ.M2.Math.10.G.G-CO.C.11	Parallelograms and Parallel Lines Related Proofs Corresponding Parts
Make geometric constructions.
Make formal geometric constructions with a variety of tools and methods. Constructions include: copying segments; copying angles; bisecting segments; bisecting angles; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. AZ.M2.Math.10.G.G-CO.D.12	Duplicating Segments and Angles Constructing Perpendiculars Constructing Angle Bisectors
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle; with a variety of tools and methods. AZ.M2.Math.10.G.G-CO.D.13	The Centroid
Similarity, Right Triangles, and Trigonometry	eTAP Lesson
Understand similarity in terms of similarity transformations.
Verify experimentally the properties of dilations given by a center and a scale factor: Dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. AZ.M2.Math.10.G.G-SRT.A.1	Symmetry Tessellations with Polygons
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for 107 triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. AZ.M2.Math.10.G.G-SRT.A.2	Similar Triangles
Use the properties of similarity transformations to establish the AA, SAS, and SSS criterion for two triangles to be similar. AZ.M2.Math.10.G.G-SRT.A.3	SSS and SAS Congruencies
Prove theorems involving similarity.
Prove theorems about triangles. Theorems include: an interior line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. AZ.M2.Math.10.G.G-SRT.B.4	Properties of Isosceles Triangles
Use congruence and similarity criteria to prove relationships in geometric figures and solve problems utilizing real-world context. AZ.M2.Math.10.G.G-SRT.B.5	Proportions with Area and Volume
Understand and apply theorems about circles.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. AZ.M2.Math.10.G.G-SRT.C.6	Sine and Cosine and the Unit Circle
Define trigonometric ratios and solve problems involving right triangles.
Explain and use the relationship between the sine and cosine of complementary angles. AZ.M2.Math.10.G.G-SRT.C.7	Definitions - Sine and Cosine
Use trigonometric ratios (including inverse trigonometric ratios) and the Pythagorean Theorem to find unknown measurements in right triangles utilizing real-world context. AZ.M2.Math.10.G.G-SRT.C.8	The Theorem of Pythagoras
Circles	eTAP Lesson
Understand and apply theorems about circles.
Prove that all circles are similar. AZ.M2.Math.10.G.G-C.A.1	Definition - Circles
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. AZ.M2.Math.10.G.G-C.A.2	Chord Properties Tangent Properties Arcs and Angles
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. AZ.M2.Math.10.G.G-C.A.3	Circumference/Diameter Ratio
Find arc lengths and areas of sectors of circles.
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. AZ.M2.Math.10.G.G-C.B.5	Arc Length Areas of Circles
Expressing Geometric Properties with Equations	eTAP Lesson
Translate between the geometric description and the equation for a conic section.
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. AZ.M2.Math.10.G.G-GPE.A.1	Completing the Square
Use coordinates to prove geometric theorems algebraically.
Use coordinates to algebraically prove or disprove geometric relationships. Relationships include: proving or disproving geometric figures given specific points in the coordinate plane; and proving or disproving if a specific point lies on a given circle. AZ.M2.Math.10.G.G-GPE.B.4
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems, including finding the equation of a line parallel or perpendicular to a given line that passes through a given point. AZ.M2.Math.10.G.G-GPE.B.5	Parallelograms and Parallel Lines Related Proofs
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. AZ.M2.Math.10.G.G-GPE.B.6	Midsegments
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. AZ.M2.Math.10.G.G-GPE.B.7	Areas of Rectangles and Parallelograms
Geometric Measurement and Dimension	eTAP Lesson
Explain volume formulas and use them to solve problems
Analyze and verify the formulas for the volume of a cylinder, pyramid, and cone. AZ.M2.Math.10.G.G-GMD.A.1	Solids with Curved Surfaces
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems utilizing real-world context. AZ.M2.Math.10.G.G-GMD.A.3	Cylinders Cones
Visualize relationships between two-dimensional and three-dimensional objects.
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. AZ.M2.Math.10.G.G-GMD.B.4
Modeling with Geometry	eTAP Lesson
Apply geometric concepts in modeling situations.
Use geometric shapes, their measures, and their properties to describe objects utilizing real-world context. AZ.M2.Math.10.G.G-MG.A.1	Definition Number and Picture Patterns
Apply concepts of density based on area and volume in modeling situations utilizing real-world context. AZ.M2.Math.10.G.G-MG.A.2	What is Density?
Apply geometric methods to solve design problems utilizing real-world context. AZ.M2.Math.10.G.G-MG.A.3	Mathematical Modeling