Algebra II

Other Maryland Mathematics sets

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Define appropriate quantities for the purpose of descriptive modeling.HSN.Q.A.2

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

Use the relation <em>i² = -1</em> and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.HSN.CN.A.2

Solve quadratic equations with real coefficients that have complex solutions.HSN.CN.C.7

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

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.HSA.SSE.B.3

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.HSA.SSE.B.4

Know and apply the Remainder Theorem: For a polynomial <em>p(x)</em> and a number <em>a</em>, the remainder on division by <em>x - a</em> is <em>p(a)</em>, so <em>p(a) = 0</em> if and only if <em>(x - a)</em> is a factor of <em>p(x)</em>.HSA.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.HSA.APR.B.3

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

Rewrite simple rational expressions in different forms; write <em>a(x)/b(x)</em> in the form <em>q(x) + r(x)/b(x)</em>, where <em>a(x), b(x), q(x)</em>, and <em>r(x)</em> are polynomials with the degree of <em>r(x)</em> less than the degree of <em>b(x)</em>, using inspection, long division, or, for the more complicated examples, a computer algebra system.HSA.APR.D.6

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.HSA.CED.A.1

Explain each step in solving a simple 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.HSA.REI.A.1

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

Solve quadratic equations in one variable.HSA.REI.B.4

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.HSA.REI.C.6

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.HSA.REI.C.7

Explain why the x-coordinates of the points where the graphs of the equations <em>y = f(x)</em> and <em>y = g(x)</em> intersect are the solutions of the equation <em>f(x) = g(x)</em>; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where <em>f(x)</em> and/or <em>g(x)</em> are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.HSA.REI.D.11

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.HSF.IF.A.3

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; end behavior; and periodicity.HSF.IF.B.4

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.HSF.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.HSF.IF.C.7

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.HSF.IF.C.8

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).HSF.IF.C.9

Write a function that describes a relationship between two quantities.HSF.BF.A.1

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

Identify the effect on the graph of replacing <em>f(x) by f(x) + k, kf(x), f(kx)</em>, and <em>f(x + k)</em> for specific values of <em>k</em> (both positive and negative); find the value of <em>k</em> 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.HSF.BF.B.3

Find inverse functions.HSF.BF.B.4

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).HSF.LE.A.2

For exponential models, express as a logarithm the solution to <em>ab^ct = d</em> where <em>a, c,</em> and <em>d</em> are numbers and the base <em>b</em> is 2, 10, or <em>e</em>; evaluate the logarithm using technology.HSF.LE.A.4

Interpret the parameters in a linear or exponential function in terms of a context.HSF.LE.B.5

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.HSF.TF.A.1

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.HSF.TF.A.2

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.HSF.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.HSF.TF.C.8

Derive the equation of a parabola given a focus and directrix.HSG.GPE.A.2

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.HSS.ID.A.4

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.HSS.ID.B.6

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

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

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.HSS.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.HSS.IC.B.4

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

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

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").HSS.CP.A.1

Understand that two events A and B are 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.HSS.CP.A.2

Understand the conditional probability of <em>A</em> given <em>B</em> as <em>P(A</em> and <em>B)/P(B)</em>, and interpret independence of <em>A</em> and <em>B</em> as saying that the conditional probability of <em>A</em> given <em>B</em> is the same as the probability of <em>A</em>, and the conditional probability of <em>B</em> given <em>A</em> is the same as the probability of <em>B</em>.HSS.CP.A.3

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.HSS.CP.A.4

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.HSS.CP.A.5

Find the conditional probability of <em>A</em> given <em>B</em> as the fraction of <em>B</em>'s outcomes that also belong to <em>A</em>, and interpret the answer in terms of the model.HSS.CP.B.6

Apply the Addition Rule, <em>P(A</em> or <em>B) = P(A) + P(B) - P(A</em> and <em>B</em>), and interpret the answer in terms of the model.HSS.CP.B.7