 Barnegat High School
 Honors Algebra 2
Math: Maxwell, K
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Honors Algebra 2
This course is designed with intense academic rigor, strong critical thinking skills, and requires responsible study skills both in and out of the classroom to prepare students that will be pursuing a fouryear college degree and/or more advanced degrees.
Students will be able to:

Use the mean and standard deviation of a data set to fit it to a normal distribution, estimate population percentages, and 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.4

Understand that statistics is a process for making inferences about population parameters based on a random sample from that population. SIC.1

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

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

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

Evaluate reports based on data. S.IC.6
Students will be able to:

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. 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. Emphasize linear and exponential models. S.ID.6a

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.REI.6
Students will be able to:

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. F.BF.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. F.IF.B.4

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. F.IF.C.9

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

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
Students will be able to:

Use the structure of an expression to identify ways to rewrite it. For example, see

x4y4as (x2)2(y2)2, thus recognizing it as a difference of squares that can be factored as (x2y2)(x2+y2). A.SSE.A.2

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

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 in one variable. b. Solve quadratic equations by inspection (e.g., for x 2 = 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. A.REI.4b

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2+y2 =3 . A.REI.7
Students will be able to:

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. F.IF.7.c

Prove Polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 – y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. A.APR.4

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.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.3 I
Students will be able to:

Explain how the definition of the meaning 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. N.RN.1

Rewrite expressions involving radicals and rational exponents using the properties of exponents. N.RN.2

Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. F.BF.3

Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. F.IF.7.b

Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. A.REI.2

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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.4

Write a function that describes a relationship between two quantities.* b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. F.BF.1

Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1. F.BF.4a
Student will be able to:

Use the properties of exponents to interpret expressions for exponential functions. F.IF.8b

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

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Use the properties of exponents to transform expressions for exponential functions. A.SSE.3

Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. F.LE.4

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

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

Explain why the xcoordinates 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 cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A.REI.11
Students will be able to:

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. A.REI.1

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. F.IF.B.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.6

Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. A.REI.2
Students will be able to:

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. ASSE.4.

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.2
Students will be able to:

Understand the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. FTF1

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. FTF2

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. FTF5

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. FTF8
Students will be able to:

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”). S.CP.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. S.CP.2

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. S.CP.3

Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. S.CP.4

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

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. S.CP.6

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. S.CP.7
