D2L Corporation
2017-01-14T17:55:54-05:00
2017-01-14T17:55:54-05:00
D2L Corporation
Algebra II
The Arizona Mathematics Standards are a connected body of mathematical understandings and competencies that provide a foundation for all students. These standards are coherent, focused on important mathematical concepts, rigorous, and well-articulated across the grades. Concepts and skills that are critical to the understanding of important processes and relationships are emphasized. Algebra 2 students build on their foundational probability skills from middle school extending to conditional probability. Students determine independence of events and are able to apply conditional probability to everyday situations.
2016-12-22
2016
Arizona Department of Education
Conceptual Category
Number and Quantity
Domain
The Real Number System
A2.N-RN.A
Cluster
Extend the properties of exponents to rational exponents.
A2.N-RN.A.1
Standard
Explain how the definition of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
A2.N-RN.A.2
Standard
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Domain
Quantities
A2-N-Q.A
Cluster
Reason quantitatively and use units to solve problems.
A2-N-Q.A.1
Standard
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.
A2.N-Q.A.2
Standard
Define appropriate quantities for the purpose of descriptive modeling. Include problem-solving opportunities utilizing real-world context.
A2.N-Q.A.3
Standard
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities utilizing real-world context.
Domain
The Complex Number System
A2.N-CN.A
Cluster
Perform arithmetic operations with complex numbers.
A2.N-CN.A.1
Standard
Apply the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Write complex numbers in the form ( a+bi ) with a and b real.
A2.N-CN.C
Cluster
Use complex numbers in polynomial identities and equations.
A2.N-CN.C.7
Standard
Solve quadratic equations with real coefficients that have complex solutions.
Conceptual Category
Algebra
Domain
Seeing Structure in Expressions
A2.A-SSE.A
Cluster
Interpret the structure of expressions.
A2.A-SSE.A.2
Standard
Use structure to identify ways to rewrite polynomial and rational expressions. Focus on polynomial operations and factoring patterns.
A2-A-SSE.B
Cluster
Write expressions in equivalent forms to solve problems.
A2.A-SSE.B.3
Standard
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Include problem-solving opportunities utilizing real-world context and focus on expressions with rational exponents.
A2.A-SSE.B.3.c
Standard
Use the properties of exponents to transform expressions for exponential functions.
A2.A-SSE.B.4
Standard
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Domain
Arithmetic with Polynomials and Rational Expressions
A2.A-APR.B
Cluster
Understand the relationship between zeros and factors of polynomials.
A2.A-APR.B.2
Standard
Know and apply the Remainder and Factor Theorem: For a polynomial p(x) and a number a, the remainder on division by (x – a) is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
A2.A-APR.B.3
Standard
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, cubic, and quartic polynomials including polynomials for which factors are not provided
A2.A-APR.C
Cluster
Use polynomial identities to solve problems.
A2.A-APR.C.4
Standard
Prove polynomial identities and use them to describe numerical relationships.
A2.A-APR.D
Cluster
Rewrite rational expressions.
A2.A-APR.D.6
Standard
Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or for the more complicated examples, a computer algebra system.
Domain
Creating Equations
A2.A-CED.A
Cluster
Create equations that describe numbers or relationships.
A2.A-CED.A.1
Standard
Create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context. Focus on equations and inequalities arising from linear, quadratic, rational, and exponential functions.
Domain
Reasoning with Equations and Inequalities
A2.A-REI.A
Cluster
Understand solving equations as a process of reasoning and explain the reasoning.
A2.A-REI.A.1
Standard
Explain each step in solving an 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. Extend from quadratic equations to rational and radical equations.
A2.A-REI.A.2
Standard
Solve rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
A2-A-REI.B
Cluster
Solve equations and inequalities in one variable.
A2.A-REI.B.4
Standard
Fluently solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
A2-A-REI.C
Cluster
Solve systems of equations.
A2.A-REI.C.7
Standard
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
A2-A-REI.D
Cluster
Represent and solve equations and inequalities graphically.
A2.A-REI.D.11
Standard
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). Include problems in real-world context. Extend from linear, quadratic, and exponential functions to cases where f(x) and/or g(x) are polynomial, rational, exponential, and logarithmic functions.
Conceptual Category
Functions
Domain
Interpreting Functions
A2.F-IF.B
Cluster
Interpret functions that arise in applications in terms of the context.
A2.F-IF.B.4
Standard
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 a real-world context. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Extend from linear, quadratic and exponential to include polynomial, radical, logarithmic, rational, sine, cosine, tangent, exponential, and piecewise-defined functions.
A2.F-IF.B.6
Standard
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. Extend from linear, quadratic and exponential functions to include polynomial, radical, logarithmic, rational, sine, cosine, tangent, exponential, and piecewise-defined functions.
A2.F-IF.C
Cluster
Analyze functions using different representations.
A2.F-IF.C.7
Standard
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend from linear, quadratic and exponential functions to include square root, cube root, polynomial, exponential, logarithmic, sine, cosine, tangent and piecewise-defined functions.
A2.F-IF.C.8
Standard
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
A2.F-IF.C.8.b
Component
Use the properties of exponents to interpret expressions for exponential functions and classify those functions as exponential growth or decay.
A2.F-IF.C.9
Standard
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions.). Extend from linear, quadratic and exponential functions to include polynomial, radical, logarithmic, rational, trigonometric, exponential, and piecewise-defined functions
Domain
Building Functions
A2.F-BF.A
Cluster
Build a function that models a relationship between two quantities.
A2.F-BF.A.1
Standard
Write a function that describes a relationship between two quantities. Extend from linear, quadratic and exponential functions to include polynomial, radical, logarithmic, rational, sine, cosine, exponential, and piecewise-defined functions. Include problem-solving opportunities utilizing real-world context.
A2.F-BF.A.1.a
Component
Determine an explicit expression, a recursive process, or steps for calculation from a context.
A2.F-BF.A.1.b
Component
Combine function types using arithmetic operations and function composition.
A2.F-BF.A.2
Standard
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
A2.F-BF.B
Cluster
Build new functions from existing functions.
A2.F-BF.B.3
Standard
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), 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 using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Extend from linear, quadratic and exponential functions to include polynomial, radical, logarithmic, rational, sine, cosine, and exponential functions, and piecewise-defined functions.
A2.F-BF.B.4
Standard
Find inverse functions.
A2.F-BF.B.4.a
Component
Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, recognizing that functions f and g are inverse functions if and only if f(x) = y and g(y) = x for all values of x in the domain of f and all values of y in the domain of g.
A2.F-BF.B.4.b
Component
Understand that if a function contains a point (a,b), then the graph of the inverse relation of the function contains the point (b,a).
A2.F-BF.B.4.c
Component
Interpret the meaning of and relationship between a function and its inverse utilizing real-world context.
Domain
Linear, Quadratic, and Exponential Models
A2.F-LE.A
Cluster
Construct and compare linear, quadratic, and exponential models and solve problems.
A2.F-LE.A.4
Standard
For exponential models, express as a logarithm the solution to ab<sup>ct</sup> = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithms that are not readily found by hand or observation using technology.
A2.F-LE.B
Cluster
Interpret expressions for functions in terms of the situation they model.
A2.F-LE.B.5
Standard
Interpret the parameters in an exponential function with rational exponents utilizing real-world context.
Domain
Trigonometric Functions
A2.F-TF.A
Cluster
Extend the domain of trigonometric functions using the unit circle.
A2.F-TF.A.1
Standard
Understand radian measure of an angle as the length of the arc on any circle subtended by the angle, measured in units of the circle's radius.
A2.F-TF.A.2
Standard
Explain how the unit circle in the coordinate plane enables the extension of sine and cosine functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
A2.F-TF.B
Cluster
Model periodic phenomena with trigonometric functions.
A2.F-TF.B.5
Standard
Create and interpret trigonometric functions that model periodic phenomena with specified amplitude, frequency, and midline.
A2.F-TF.C
Cluster
Apply trigonometric identities.
A2.F-TF.C.8
Standard
Use the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
Conceptual Category
Statistics and Probability
Domain
Interpreting Categorical and Quantitative Data
A2.S-ID.A
Cluster
Summarize, represent, and interpret data on a single count or measurement variable.
A2.S-ID.A.4
Standard
Use the mean and standard deviation of a data set to fit it to a normal curve, and use properties of the normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, or tables to estimate areas under the normal curve.
A2.S-ID.B
Cluster
Summarize, represent, and interpret data on two categorical and quantitative variables.
A2.S-ID.B.6
Standard
Represent data of two quantitative variables on a scatter plot, and describe how the quantities are related. Extend to polynomial and exponential models.
A2.S-ID.B.6.a
Component
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context.
A2.S-ID.C
Cluster
Interpret models.
A2.S-ID.C.10
Standard
Interpret parameters of exponential models.
Domain
Making Inferences and Justifying Conclusions
A2.S-IC.A
Cluster
Understand and evaluate random processes underlying statistical experiments.
A2.S-IC.A.1
Standard
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
A2.S-IC.A.2
Standard
Explain whether a specified model is consistent with results from a given data-generating process
A2.S-IC.B
Cluster
Make inferences and justify conclusions from experiments, and observational studies.
A2.S-IC.B.3
Standard
Recognize the purposes of and differences between designed experiments, sample surveys and observational studies.
A2.S-IC.B.4
Standard
Use data from a sample survey to estimate a population mean or proportion; recognize that estimates are unlikely to be correct and the estimates will be more precise with larger sample sizes.
Domain
Conditional Probability and the Rules of Probability
A2.S-CP.A
Cluster
Understand independence and conditional probability and use them to interpret data.
A2.S-CP.A.3
Standard
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
A2.S-CP.A.4
Standard
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
A2.S-CP.A.5
Standard
Recognize and explain the concepts of conditional probability and independence utilizing real-world context.
A2.S-CP.B
Cluster
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
A2.S-CP.B.6
Standard
Use Bayes Rule to find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
A2.S-CP.B.7
Standard
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
A2.S-CP.B.8
Standard
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Standards for Mathematical Practice
A2.MP.1
Standard
Make sense of problems and persevere in solving them.
A2.MP.2
Standard
Reason abstractly and quantitatively.
A2.MP.3
Standard
Construct viable arguments and critique the reasoning of others.
A2.MP.4
Standard
Model with mathematics.
A2.MP.5
Standard
Use appropriate tools strategically.
A2.MP.6
Standard
Attend to precision.
A2.MP.7
Standard
Look for and make use of structure.
A2.MP.8
Standard
Look for and express regularity in repeated reasoning.