Algebra 2

Other Washington Mathematics sets

• Kindergarten
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Algebra 1
• Geometry
• High School Credits 1 & 2
• HS Math Credit 3
• Integrated HS Math 2
• Integrated Math 1
• Integrated Math 3

Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.N.CN.A.1

Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.N.CN.A.2

Solve quadratic equations with real coefficients that have complex solutions.N.CN.A.7

Interpret expressions that represent a quantity in terms of its context.A.SSE.A.1a, b

Use the structure of an expression to identify ways to rewrite it.A.SSE.A.2

Flexibly, efficiently, and accurately create an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression including factoring quadratic expressions, completing the square in a quadratic expression to reveal maximums or minimums, and using properties of exponents to create equivalent forms of exponential expressions to reveal properties of interest in the function.A.SSE.B.3a, b, c

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. A.SSE.B.4

Flexibly, efficiently, and accurately demonstrate that polynomials form a system similar to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.A.APR.A.1

Know and apply the Remainder 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).A.APR.B.2

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.A.APR.B.3

Prove polynomial identities and use them to describe numerical relationships.A.APR.C.4

Rewrite simple 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.A.APR.D.6

Flexibly, efficiently, and accurately create equations and inequalities in one variable and use them to solve problems.A.CED.A.1

Flexibly, efficiently, and accurately create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A.CED.A.2

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.A.CED.A.3

Flexibly, efficiently, and accurately rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A.CED.A.4

Solve rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.A.REI.A.2

Solve quadratic equations in one variable by inspection, factoring, completing the square and derive the quadratic formula from this form. Recognize when the quadratic formula give complex solutions and write them as a ± bi for real numbers a and b.A.REI.B.4a, b

Using a variety of strategies explain why the x-coordinates of the points where the graphs of the equations 𝑦𝑦 = 𝑓𝑓(𝑥𝑥) and 𝑦𝑦 = 𝑔𝑔(𝑥𝑥) intersect are the solutions of the equation 𝑓𝑓(𝑥𝑥) = 𝑔𝑔(𝑥𝑥) find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓𝑓(𝑥𝑥) and/or 𝑔𝑔(𝑥𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.A.REI.D.11

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. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries. Functions can include: polynomial, radical, rational, logarithms, absolute value, piecewise, and trigonometric. Linear, exponential, and quadratic relationships in increased complexity.F.IF.B.4

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions can include: polynomial, radical, rational, logarithms, absolute value, piecewise, and trigonometric. Linear, exponential, and quadratic relationships in increased complexity.F.IF.B.5

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.F.IF.B.6

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases including square root, cube root, and piecewise-defined functions, including step functions and absolute value functions, polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior, and exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.F.IF.C.7b, c, e

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function, including factoring and completing the square to reveal zeros, symmetry, and extreme values of a quadratic functions and non-integer constants for time with exponential growth and decay in context.F.IF.C.8

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions can include: polynomial, radical, rational, logarithms, absolute value, piecewise, and trigonometric. Linear, exponential, and quadratic relationships in increased complexity.F.IF.C.9

Write a function that describes a relationship between two quantities including determining an explicit expression, recursive process, or steps for calculation from a context, and combining standard function types using arithmetic operations.F.BF.A.1a, b

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. F.BF.A.2

Identify the effect on the graph of replacing 𝑓𝑓(𝑥𝑥) 𝑏𝑏𝑏𝑏 𝑓𝑓(𝑥𝑥) + 𝑘𝑘, 𝑘𝑘 𝑓𝑓(𝑥𝑥), 𝑓𝑓(𝑘𝑘𝑘𝑘), 𝑎𝑎𝑎𝑎𝑎𝑎 𝑓𝑓(𝑥𝑥 + 𝑘𝑘) for specific values of 𝑘𝑘 (both positive and negative); find the value of 𝑘𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.F.BF.B.3

Find inverse functions through focus on relationships between inputs and outputs.F.BF.B.4a

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.F.LE.A.4

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.F.TF.A.2

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.F.TF.B.5

Prove 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.F.TF.C.8

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.S.ID.A.4

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.S.IC.A.1

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. S.IC.A.2

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.S.IC.B.3

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.S.IC.B.4

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.S.IC.B.5

Evaluate reports based on data.S.IC.B.6

Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.HS.DS.1

Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.HS.DS.2

Create and analyze data sets and data displays, including but not limited to scatter plots, regressions, histograms and boxplots using technology to sort or filter data, summarize, and describe relationships between quantitative variables.HS.DS.3

Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.HS.DS.4